







Interest compounded daily 
20031008 

From Terie: If I owe $2000.00 @ 6.25% compounded daily for 54 days. How much do I owe in interest? Answered by Penny Nom. 





Standard Deviation 
20031007 

From Rebecca:
I have a task to complete, which is to calculate the mean and standard deviation of something. I have done this but am then asked to write a short explanation of my findings.
I know what the mean is about, and I thought I knew what the standard deviation meant too  shows the variation from the mean. However, on a task I completed earlier the feedback I got said 'you need to tell us that it is talking about the middle 66% of the data'  that has thrown me, I don't understand that. Can anyone help me get my head round this??? Answered by Penny Nom. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





Arrangements around a circular table 
20031007 

From Lori: How many arrangements can 6 people be seated round a circular table? Answered by Penny Nom. 





Indeterminate forms 
20031006 

From A teacher: Is it possible for me to find any geometrical interpretation without using calculus to explain indeterminate forms? Answered by Chris Fisher. 





Functions, graphs and derivatives 
20031005 

From Jathiyah: I wanted to know how would you tell (on a graph diplaying two funtions), which funtion is the derivative of the other? Answered by Walter Whiteley. 





The slope of a tangent 
20031001 

From A student:
find the slope of the tangent to each curve at the given point f(x)=square root 16x, where y=5 Answered by Penny Nom. 





A rectangle in a circle 
20030927 

From Abdu: A rectangle ABCD is inscribed in a circle. If the length of AB is 5 and length of BC is 12, what is the area of circle outside the rectanlge ABCD? Answered by Penny Nom. 





Relatively prime 
20030927 

From James: what is the definition a relative prime numbers? Answered by Penny Nom. 





0/0 
20030925 

From Thomas: How is 0/0 ever defined. Answered by Penny Nom. 





Absolute value 
20030923 

From Crystal: I am trying very hard to understand Absolute Value, and I cannot seem to grasp the idea. I do not know why we use it, what the point of it is. I do not know how to use it. I know that it is always positive or zero, and I assume it relates to distance, but how can you use it in equations. Please explain it to me as simply as possible, thank you. Answered by Walter Whiteley. 





The golden ratio 
20030923 

From Phillip: The Golden Section can be made from an equilatereral triangle inscribed within a circle. The Golden Section is achieved by joining the mid points of two arms of the triangle to the circumference. I can prove this by erecting a perpendicular to the line outside the circle, but am interested to see how it can be proved from within the circle. Answered by Chris Fisher. 





Primes 
20030923 

From Julie:
#1. Suppose you are given a number (n) and told that 1 and the number (n) divide into (n). Does that mean (n) is prime? #2. Suppose that p is a prime number greater than or equal to 3. Show that p+1 cannot be a prime number. Answered by Penny Nom. 





The Sieve of Eratosthenes 
20030918 

From Lynn: My daughter has been asked to find all the prime numbers by using the Sieve of Eratosthenes. I have no understanding what this means. Answered by Penny Nom and Claude Tardif. 





1 + 1 = 10 
20030917 

From David: could you please explain to me how 1+1=10 thanks Answered by Penny Nom. 





Applications of logarithms 
20030916 

From A student: I have a project due in my algebra two class dealing with logs and where they are used in life, but I am having trouble finding websites that relate. So I would really appreciate it if you couldhelp me. Answered by Penny Nom. 





Notation 
20030915 

From Kim:
Question: i have a couple of questions 1. write in standard form a)4x2x8 b) 5 to the power of 4 . . . Answered by Penny Nom. 





Substitution method 
20030914 

From John:
Hello, my name is john and while I was finishing up my work I stumbled into these problems. a/4b=1 a+b=11 and 6ab=5 4a3b=8 Thanks a lot. I really need some help :) John Answered by Penny Nom. 





The volume of an earthen pit 
20030912 

From Bruce: This shape would occur at the four corners of a rectangular shaped earthen pit with sloping sides (1:1.5). Depth is 14'. Top dimensions are 170' by 158'. After calculating the easy volume components of this shape, we are left with the end corner pieces. 21' base, 14' height, side hypotenuse 25.24' and corner diagonal 32.83'. We're confused. Thank you for any help you may provide. Answered by Penny Nom. 





The digits in 349 
20030912 

From Franik: in the number 349, which number has the least value, and why? Answered by Penny Nom. 





Two line segments and a plane 
20030911 

From Laura: Do all figures made up of two segments lie in a plane? Answered by Penny Nom. 





Area of a rectangular room 
20030911 

From Kelly: The area of a rectangular room is 238 square feet. The width is 3 feet less than the length. What are the dimensions? Answered by Penny Nom. 





The general equation for a sphere 
20030911 

From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom. 





The mean house price 
20030910 

From Carol:
Question: I have to find the mean from the following example: Price Range £000  No of Houses  55 and under 60  3  60 and under 65  6  65 and under 70  13  70 and under 80  21  80 and under 100  15  100 and under 130  7  130 upwards  1  I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom. 





Converting from base 10 to base 5 
20030910 

From Susy:
My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5. His first question of: 24(10) he has calculated to be 4x5 + 4x1 = 44 (5) The next question however is the tricky one.İ We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it. 25 (10) = _________________ 100 (5) Can you help us figure out how we reach the answer. Answered by Claude Tardif and Penny Nom. 





How high does the sequence of numbers go 
20030907 

From Shayna: My quetion is "How high to the sequence of numbers go"? e.g. one, ten, hundred, thousand, million, billion, trillion, and from there is my queston. Answered by Penny Nom. 





Making a square 
20030907 

From A student: if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80İ*İnİ=İsquareİnumber, what is the least value of n which will yield a square. Answered by Penny Nom. 





Consecutive integers 
20030907 

From Amy: I was wondering if there was a proper way to write the solution to a problem requiring consecutive integers? Is it okay to write the solution as 5,4,3,2,1 or must it be written as 1,2,3,4,5? Answered by Penny Nom. 





Order of operations 
20030907 

From Brian:
It has to do with the 4 rules of operations, Parentheses first before operations outside/evaluate all exponential expressions/all multiplication and divisions/then all additions and subtractions. Who made these rules and when did they make them,,, I know its somewhat of an unorthadox question but I must know. I would really appreciate it. Answered by Penny Nom. 





7,473,000,000 divided by 52000 
20030906 

From A student: I am having trouble with a question. 7,473,000,000 divided by 52000. Our calculater gets 147311.5385. I come up with 143711.53846, and then the number starts to repeat itself Answered by Penny Nom. 





Can 2 vertical planes intersect? 
20030906 

From Erin: My question is can 2 vertical planes intersect? Answered by Penny Nom. 





One million seconds 
20030904 

From Vince: If you can write a number each second for one million seconds, how many hours would it take? Answered by Penny Nom. 





Four digit combinations 
20030904 

From Emma: I seriously need to find out all the four digit combinations from 0 to 9!!! My name Is Emma Dibitt and I'm going into 8th grade and I'm a student!!! Answered by Penny Nom. 





Grooming the king's horses 
20030904 

From Janelle: the stable boy had 90% of the kings horses groomed.the next day the king acquired 25% more horses. Now there was 105 horses not prepared for the kings men. How many horses did the king originally have? Answered by Penny Nom. 





A 16 foot ladder 
20030904 

From Kelly: Two buildings are separated by a threefoot alleyway. Fatima wants to use a 16 foot ladder to reach a window in the wall of one of these buildings. If she places the foot of the ladder against the base of the other building, how far up the wall will the top of the ladder reach?? Answered by Penny Nom. 





One percent of a billion 
20030904 

From Charles: What is one percent of one billion? Answered by Penny Nom. 





Positive, negative and zero 
20030904 

From Brian: Can the Value of zero be positive or can it be negative or can it be both. Answered by Penny Nom. 





The game of 24 
20030903 

From A student: We have a game where four numbers must equal 24 using addition, subtraction, multiplication and/or division.İ I am stuck on the following four numbers  12, 24, 9 and 17. Answered by Penny Nom. 





A boat travels 12 km upstream... 
20030903 

From Sohaib: A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3km/hr throughout, find the speed of the boat in still water, giving your answerİcorrect to 3 decimal places. Answered by Penny Nom. 





Why percentage? 
20030903 

From Vicky: My cousin aske me a question about the use of percentages and I'm not sure how to answer it. He wants to know why when there is a sale in a shop we use percentages and not fractions or decimals. Answered by Penny Nom. 





Percentage markup 
20030903 

From Virginia:
I am confused and hope you can help. I have looked high and low for a "chart" persay to go by when I am having to calculate markup percentages. Example if I have a List price of $1838.00 and my cost is $955.76 and I want to mark it up 30%. My colleage says it should be divided by .7 I don't understand how he arrives at .7 from 30 percent. Answered by Claude Tardif. 





Profit margin 
20030903 

From Chet:
My salesman calculates a customers profit margin by dividing what the customer paid by what he sells for, then subtracting that answer from 1. For example a customer sells a product for $15. He bought it for $10. 15/10=.66 Subtract that from 1 and get a profit % of 33% Here's my question: If I want to figure what a reseller will sell a product for if he wants 40% margin(by the technique above), what formula do I use? Let's say I want to sell a product for 8.50, and I want the reseller to make 40% Answered by Penny Nom. 





Two row arrays 
20030903 

From Madalyn: My question is, what are #'s that can not be arranged in two row arrays called? Answered by Penny Nom. 





A helicopter rises vertically 
20030902 

From Kate: A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)^{2} How far above the ground will the helicopter be after 3 seconds? Answered by Penny Nom. 





Water in a tank 
20030902 

From A parent: if a tank is 48 inches long 14 inches wide and 18 inches deep if a yardstick was inserted into the tank and measured 2 inches of water in the tank how many gallons of water would be in the tank. Answered by Penny Nom. 





A theorem in geometry 
20030902 

From Diego: Please refer to figure in attached file. P is a point on the chord AB of a circle such that the tangent PT which touches the circle at T is equal to AB. How do we prove that PT^{2} = AP x BP. Answered by Dieter Ruoff and Penny Nom. 





The units digit of 57 to the 28th power 
20030901 

From Maria:
If 57 is raised to the 28th power, what must be the units digit in the result? If you raise 7 to the 500th power, what is the numeral that will appear in the units digit position? Answered by Penny Nom. 





A 6 team schedule 
20030831 

From A scheduler: I saw that someone put on your web site a team schedule and you helped them figure it out.İ I have 6 teams that want to play each other once, and believe it or not, I cannot figure it out. Answered by Penny Nom. 





20% of 40% of 500 
20030831 

From A student: What is 20% of 40% of 500? Answered by Penny Nom. 





Terminology 
20030831 

From Maria: My daughter Veronica is a rising 6th grader and has to complete some Summer Math assignments and would like to ask you three questions:  ___________ are number pairs that have a product of 1.
 You can name any point on a plane with two numbers. These two numbers are called _____________.
 A _______________ is the size of a cube that is exactly 1 inch on each edge.
Thanks, Answered by Penny Nom. 





The quadratic formula 
20030831 

From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a yvariable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston. 





Newton's binomial theorem 
20030830 

From William: According to page 126 of Murtha & Willard's "Statistics and Calculus" (PrenticeHall, 1973), Newton's binomial theorem can proved inductively. I suppose that was his method, which I would like to see. Answered by Penny Nom. 





I can Guess your birthday 
20030829 

From Michelle: Hi I am trying to explain to my children how this problem works. It was sent to me on the internet and I can not figure it out. They keep asking me how it works and I can not tell them. The problem is: "I can Guess your birthday:: Answered by Penny Nom. 





How many cubic yards must I purchase? 
20030829 

From Walt:
I am trying to determine how much top soil I must purchase (by the yard). The area is 80' x 15' and I want it 3" thick. How many cubic yards must I purchase? Answered by Penny Nom. 





Converting to base 10 
20030828 

From Karen: My son is in 5th grade.İ He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.İ Can you explain it to me in the simplest terms? Answered by Penny Nom. 





Graphing a piecewise function 
20030824 

From Amber: How do i begin to graph a piecewise function, absolute function or step function? Answered by Penny Nom. 





Simplify 
20030824 

From Jessica: I have been asked to simplify the expression (5a2)(2b2)(3b)+(7a2)(2b2)+(3a)(5a)(4b) and the answer is apparently 44(a2)(b2). For the life of me I can't figure out how they derive this. Answered by Penny Nom. 





Why is 5 to the 0 power always 1? 
20030824 

From Crystal: Why is 5 to the 0 power always 1? Answered by Penny Nom. 





A rule with a variable 
20030824 

From Crystal: what is a rule with a variable Answered by Penny Nom. 





X.9999... and X+1 
20030823 

From David: I have read your answers to the questions on rational numbers, esp. 6.9999... = ? and still have a question: The simple algebraic stunt of converting repeating decimals to rational numbers seems to work for all numbers except X.999999.... where X is any integer. The fact that the method yields the integer X+1 in each case seems to violate the completeness axiom of the real numbers, namely that there is no space on the number line which does not have an number and conversely that every geometric point on the number line is associated with a unique real number. In the case of 3.999... for example, it seems that both the number 4 and the number 3.9999.... occupy the same point on the number line. How is this possible??? Answered by Penny Nom. 





A golf tournament 
20030823 

From Dale: I am running a golf tournament with twelve golfers. We will be playing four rounds of golf. I don't want to schedule the same two players together more than twice (if possible). How would I make a schedule that each player would play at least once with every other player? I would appreciate any help that you can give me. Answered by Denis Hanson. 





A worm on a hill 
20030821 

From Lisa and Samantha: A WORM IS AT THE BOTTOM OF A 10 FOOT HILL. HE CRAWLS UP THE HILL 4 1/2 FEET A DAY. AT NIGHT WHEN HE REST HE SLIDES DOWN 2 1/2. HOW LONG DOES IT TAKE THE WORM TO CRAWL UP THE HILL. Answered by Penny Nom. 





Two equations 
20030821 

From Jennifer:
The following problems have me stuck and any help would be greatly appreciated seeing my text book is doing me no favours:
3^{2a+1}  283^{a} + 9=0 and 5^{2m}  5^{m}=20 Answered by Penny Nom. 





39 consecutive natural numbers 
20030819 

From A student: Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Answered by Penny Nom. 





The volume of a fuel tank 
20030816 

From Phil: I hope you can help me out with a small problem. My boat has a fuel tank measuring 1680mm long x 630mm wide x 130mm high. Can you tell me how much fuel it will hold in both litres and imperial gallons. Answered by Penny Nom. 





The number of three digit combinations 
20030816 

From Fred: There are four close friends having a heated discussion concerning the the number of three digit combinations using the numbers 0 through 9. The discussionİinvolves the daily lottery.İ Any assistance you can lend would be greatly appreciated. Answered by Penny Nom. 





Acres 
20030813 

From A landowner: Can you please tell me how many total acres the following measurements would equal? 280 feet by 80 feet 220 feet by 70 feet 200 feet by 75 feet Answered by Penny Nom. 





Making a blanket 
20030813 

From Liz: Please help me figure this out. I am making a blanket the directions call for a piece of material measuring 72"X45". Instead of one piece I'd like to make a patchwork quilt but the squares need to equal 72"X45". Centered on the bottom of the longest edge is an 18" square. Answered by Harley Weston. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.ğ The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ğ (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





Yards and cubic feet 
20030811 

From Sonya: How many cubic feet are in a yard? Answered by Penny Nom. 





A sphere inscribed in a cone 
20030810 

From A student: A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone (b)volume of the shaded space( to 3 sig fig) Answered by Penny Nom. 





The side length of a regular octagon 
20030809 

From Rich: If I know the distance between the parallel lines of an octagon and want to find the length of the sides, can I just divide that distance by 2.414 to reveal the length of the sides? I work construction and just curious if I am figuring it right. Answered by Penny Nom. 





Liters in a pool 
20030805 

From A parent: I need to know how many litres in a 12 foot diameter, 3 foot deep pool? Any help much appreciated as I need to add the correct amount of chemicals Answered by Penny Nom. 





Diagonals in an octagon 
20030804 

From Amanda: How many diagonals are in an octagon??? What would be a drawing of those diagonals??? Answered by Penny Nom. 





Two precalculus problems 
20030804 

From Kate:
Please help me verify the identity: cos2x(sec2x1)=sin2x Also I am having trouble withdetermining whether f(x) is odd, even, or neither f(x)=x3x Answered by Penny Nom. 





The incline of a road 
20030803 

From A driver: incline % grade as to degree. ie 6% hwy grade= what degree of incline? Answered by Penny Nom. 





Percentage decrease in sales 
20030731 

From Linda: If I had sales in January of 2002 that were $42,493.73 and sales that were $37,281.59.İ The difference is $5374.50.İ What is the percentage of decrease in sales? Answered by Penny Nom. 





Inserting a comma ever three digits 
20030725 

From Linda: when writing a large number, why do we insert a comma every three numbers instead of every two or four numbers? Answered by Penny Nom. 





Cutting some wood 
20030725 

From Betty: My husband is building a six sided wood circle and would like to know the angle to cut the pieces. Answered by Penny Nom. 





The area of an odd shaped piece of property 
20030724 

From Barry: What is the formula for figuring the square footage of an odd shaped piece of property? Answered by Penny Nom. 





Surface area of a sphere 
20030723 

From Rob: I have a shere with a circumference of 12 feet. What is the total surface area of the shere in square feet and how did you find it? Answered by Penny Nom. 





nine digit numbers 
20030723 

From John: With a nine digit number, with each of the nine digits having a possibility of 10 different numbers then what is the total number of possible mathematical variations in the nine digit number. i.e. Social Security numbers have nine digits and if each of the nine digits have a possibility of being any one of ten numbers, i.e. 0,1,2,3,4,5,6,7,8,9. Then what is the formula to calculate the maximum possible number of variations in this nine digit number and what is the mathematical maximum possible number of variations of this nine digit number? Answered by Penny Nom. 





Natural logarithms 
20030722 

From Amanda: I'm going into my senior year of high school. I will be taking AP calculus, and my teacher gave us some homework over the summer. However, there are two things that I do not understand how to do. The first is, she wants us to be able to generate a unit circle by hand using 30, 60 and 90 degree triangles. I have used the unit circle in trigonometry, however I was never taught how to draw it. Secondly, I need to know how to do natural logarithms without a calculator. I was not taught how to do this, and the worksheet I was given only showed me how to complete them using a calculator. Answered by Claude Tardif. 





A pyramid with its top cut off 
20030721 

From David: What is the name given to a 3D shape that looks like a pyramid with its top cut off? Answered by Penny Nom. 





Slope 
20030720 

From Brian:
You are placing a pipe 60 feet long at a slope of 1.5%. How would you figure the amount of drop from the inlet of the pipe tot he outlet of the pipe? and what is the answer . If you are trying to keep a shoulder slope of a road between 3/4'' per foot and 11/2'' per foot . If the shoulder is 10 feet wide, how would you figure how much lower should the outside of the shoulder be than the edge of pavement and what is the answer ? Answered by Penny Nom. 





x+3 = 15x 
20030719 

From Nathan: Without the use of trial and error, is there a way of solving for x where x + 3 = 15x? I know that x = 0.1875, but how do I find whether x + 3 is positive or not if I did not have this information (In other words, how would I solve whether the xvalue was 3 or less, or if it was more than 3)? Answered by Claude Tardif and Penny Nom. 





"cubic feet" of a refrigerator 
20030716 

From Ron:
Is the volume of a home appliance (e.g. fridge or freezer) calculated in a different way? I am planning to replace both my fridge and my freezer but I'm unable to determine what size replacement to get. For example, one company descibes their fridge as being 32"(L) x 30"(W) x 66" (H). I converted those measurements to feet (2.67 x 2.5 x 5.5) and I calculate the fridge to be 36.7 cubic feet. However, the company says the fridge is 18 cf. Answered by Chris Fisher. 





Cathy's Clothing 
20030715 

From Cathy: I am supposed to write a practical and useful word problem that would use the following algebriac inequality to solve it: 12x + 25 > 15x + 10. State the quanity that represents x and solve the inequality. Answered by Penny Nom. 





Preparing 100ml of a 30% alcohol solution 
20030713 

From Justin: My question is how do you prepare a 100ml of a 30% alcohol solution using 95% alcohol? Answered by Penny Nom. 





Sunshine? 
20030711 

From lori: It is noon, your lunch hour, but you cannot go out because there is a terrific hailstorm. Turning on your radio you hear the weathercaster predict that the hail will change to rain and that it will pour all day today. How can you determine whether the sun will be shining in 36 hours? Answered by Claude Tardif. 





A problem with lugs 
20030711 

From Lori: A young man's car developed a flat tire as he was driving along a deserted street. He pulled over to the curb and did all the usual things: removed the hub cap, unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them fell down a nearby grate. Peering through the bars of the grate the man thought that he could see the lugs about 6 feet below in a shallow water puddle. He had a problem. How do you think he solved it? Answered by Penny Nom. 





A mixture problem 
20030710 

From A student: Having a problem with word problems. example A chemist mixes a 10% acid solution with a 50% acid solution to form 400mL of a 40% solution. How much of each solution should be used. Answered by Penny Nom. 





A triangle in the complex plane 
20030710 

From Scott: The vertices O and A of an EQUILATERAL triangle OAB in the complex plane are located at the origin and 3 + 3i. Find all possible values for the complex number representing the vertex B. Give the location of B in both polar and cartesian form (to 2.d.p) Answered by Penny Nom. 





E(X + Y) and V(X + Y) 
20030710 

From Reuben:
I'm a teacher trying to find a way to make some stats work from first principles. The topic is expectation algebra and it is for the top age level in high school. By using a set of data I can show how the mean is the same as the expected value ie 2,2,3,4,4 is 15 / 5 = 3 also, 2x0.4+3x0.2+4x0.4=3. I can also show this to work for the variance in the same style but using Sum(xmean)^{2}/n and the Var(X) version of squaring x then multiplying by the probability ( all this for random independant samples). Now comes the tricky bit.....when I try to show E(X+Y) = E(X) + E(Y) from setting up two data sets I get it to work only if I add each item from X to each item from Y. However, I can't get it to work for V(X+Y)=V(X) + V(Y) from two sets of data. There must be something missing in my knowledge of how the sets are required to add together or my knowledge of expectation algebra. I am familiar with proofs but still want to show my students that the basic formulae work from groups of data whether done the long way or by use of formulae. Can you help please? Answered by Penny Nom. 





An onsale DVD player 
20030709 

From Kim: I have a DVD player with a regular selling price of $175 and percentage of discount is 10 percent. How to solve for discount amount and sale price? Also, when you figure out the sale price how to figure out commission amount when percentage of commission is 5 percent? Answered by Penny Nom. 





A wooden deck around a pool 
20030709 

From Dat: A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.  If the pond is square, what are its dimensions?
 If the pond is rectangular and the length of the is three times its width, what are the dimensions of the pond?
 If the pond is circular, what is the diameter of the pond?
 Which pond has the most area?
Answered by Penny Nom. 





Two cars 
20030709 

From Nicole: Two cars start off at the same point on a striaght highway facing opposite directions. Each car drives 6 miles, talkes a left turn, and drives for 8 miles. How far apart are the two cars. Answered by Penny Nom. 





Is 3/5 CLOSEST to 0, 1/2 or 1? 
20030709 

From A student: I would like to know is 3/5 CLOSEST to 0, 1/2 or 1. And can 3/10 go either way as to be closest to 0 or 1/2. Answered by Penny Nom. 





A geometry problem 
20030708 

From Chris: My name is Chris, I work for a custom fabricator company. I am needing a formula for the Height (H) shown in the attached picture. The picture shows dimensions for my current application. If you could please, assign variables to the dimensions. Answered by Harley Weston. 





Volume of water in a pool 
20030706 

From An other: How many litres of water are in a pool that is 16 feet in diameter and 35 inches deep? Answered by Penny Nom. 





The length of fabric in a roll 
20030703 

From Paul: We receive rolled fabric as part of our process and I would like to know is there a formula that could be used to estimate the overall length of the roll with out rolling the fabric out and measuring its length. Answered by Harley Weston. 





Contradiction in the Procedural Precedence and the Distributive property 
20030703 

From Arthur: When complicated expressions exist on both sides of a fraction, and both these expressions contain like and unlike terms with "literal" coefficients, the procedural precedence suddenly gets extremely confusing and seems impossible to simplify. This seems confusing and impossible to simplify because there is a HUGE contradiction in the way Procedural Precedence and the Distributive property deal with Parentheses. The Procedure says you MUST deal with what's INSIDE the parenthesis FIRST, BEFORE dealing with ANYTHING on the outside where as the Distributive property contradicts that by saying to go ahead and ignore the Precedence and use a factor on the outside of the Parenthesis. Answered by Claude Tardif. 





C is 10 more then the square of... 
20030703 

From Carolina:
C is 10 more then the square of the quotient of the sum of x and y , and the product of x and y. Which equation expresses this relationship?
A. C=(x+y +10)^2 ___ xy
B. C=(x+y)^2 + 10 ___ xy
C. C=(xy)^2+10 ___ x+y
D. C=(x+y)^2 + 10 ___ xy
Answered by Penny Nom. 





The domain of 1/g(x)  5 
20030703 

From Barbara: If the range of g(x) is ( neg. infinity,4] and the domain of g(x) is ( neg. infinity, infinity), how do I find the domain of 1/g(x)  5? Answered by Penny Nom. 





How much soil will be removed? 
20030702 

From Amy: My site is 1230' (eastwest) by 1300' (northsouth) and we need to remove 2 feet of soil from the entire site, how much soil will be removed? Answered by Penny Nom. 





Setting up a word problem 
20030630 

From Christie: A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral. Answered by Penny Nom. 





A ruler and compass construction 
20030629 

From Mandy: I have been searching for instructions on how to do this using a compass. Can you please send instructions step by step on how to bisect a segment into any given number of segments. (example, a way that it will work for bisecting segment into 3, 4, or even 5 congruent parts) Answered by Penny Nom. 





Solve x = y^z for z 
20030628 

From Nathan: If x = y^z is there a way to solve for z, if x and y are given, without guessing or already knowing the answer?
ie: 64 = 2^z 6 is the obvious value for z. Is there a way I could solve for this variable using a formula, which would also apply when more complex values were substituted for x and y? Answered by Penny Nom. 





Polynomials degree 4 and bigger 
20030626 

From Stephen:
How do I show kids how to find all the zeros for polynomials degree 4 and bigger.
For examples: r(x) = x^{5}11x^{3}7x^{2}+77 = (x^{2}11)(x^{3}7) and s(x) = x^{4}121 = (x^{2}11)(x^{2}+11) Also am I correct when I say that the following are irreducible? f(x) = x^{2}11 g(x) = x^{3}7 h(x) = x^{4}5 Answered by Harley Weston. 





Odd powers of sine and cosine 
20030625 

From Antonio: Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the powerreducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Answered by Harley Weston. 





Sesame Street on Stage 
20030625 

From Christie: Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid $15 to gain entrance, while Jamie and John Jacobs and their 2year old daughter got in for $19.50. What is the ticket price for adults? Answered by Penny Nom. 





43(m+1)=(38) 
20030625 

From Jamie:
I have a problem, like most of your mailers, I do remember BEDMAS but maybe I'm missing the finer points! It's been a while, he goes 43(m+1)=(38) Answered by Penny Nom. 





Interest compounded daily 
20030624 

From Jeff: What would be the amount of interest charged or accrued and how is it calculated on principal balance of $209.12 @ 6% interest rate compounded daily for 70 days? Answered by Penny Nom. 





pst and gst 
20030624 

From Robin: I need to find an easy solution to remembering how to calculated the gst and pst once I have the total amount. ex: my total is $154.40, I have to find the gst and then the pst. I live in bc so the taxes are 7% for gst and 7.5% for pst. Answered by Penny Nom. 





Flim 
20030624 

From Dan: I have a 4th grader and the word (Flims) came up in her summer text, Answered by Penny Nom. 





An inch and a millimeter 
20030621 

From Greg: The conversion factor for inches to millimeters 25.4 It strikes me as very odd that it's not some infinite decimal. I could understand this if one system was derived from the other but as I understand it they were derived independently. Is the conversion 25.4 or 25.4000XXXXXXX? If it's just 25.4 then how did that happen? Answered by Harley Weston. 





Numbers John likes 
20030620 

From Steve: John likes 400 but not 300; he likes 100 but not 99; he likes 2500 but not 2400.
Which does he like? 900 1000 1100 1200 Answered by Penny Nom. 





The sum of two numbers is 5 and their difference is 
20030616 

From Akhil: The sum of two numbers is 5 and their difference is 11. What is the product of the two numbers? Answered by Penny Nom. 





A 40% markup 
20030612 

From Nick: I am attempting to determine the Retail price of an item that costs me 11.00. Our company wants to sell it at a markup of 40%. I calculated this two ways, first the way I thought it should be done. Second, the way the calculator does it (and my accountant).
 Cost + Cost*(percentmarkup/100)= retail price 11.00 + 11.00*.40 = retail price 11.00 + 4.40 = 15.40 retail price
 Using the calculators Mark Up key the answer is 18.33. Or 7.33 more than the cost or 67%.
I am confused by this Mark Up key and how it calculates. I used a cost of $10.00 and marked it up 50%. I thought it should equal $15.00 but the calculator says $20.00? This seems to be 100% markup, yes? Can you explain the difference between the way I did it and the way a Business calculator does it? Answered by Penny Nom. 





A project about crosses 
20030610 

From Joel:
I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)? Cross Number  Area sq cm  1  5  2  13  3  25  4  41  5  61  I also need to know what the formula is for it? Answered by Penny Nom. 





Teaching second grade 
20030610 

From A teacher: I am going to be teaching second grade next year. How can I differentiate instruction in mathematics to meet the needs of all of my students, from those who need intervention to those who need challenges? What are some techniques I can try for this grade level? Answered by Diane Hanson. 





Two trig problems 
20030610 

From Bett:
I have this ongoing trouble with trig and solving triangles with laws of cosines and sines!! For example if it asks to solve triangle FGH, given angle G=102.7 , side f=14.2, and h=18.6. Now do I use law of cosines because I don't have the measure of an angle and length of the opposite side??I don't know where to go from here,I am totally confused!!! I also have a problem with this word problem I have been doing. It asks: An airplane flies 847.5 km at a bearing of 237.3 degrees. How far south and west fo its original position is it? Huh? Please help! Answered by Penny Nom. 





How many gallons are in 83 liters? 
20030609 

From Anita: How many gallons are in 83 liters? Answered by Penny Nom. 





Definitions and descriptions 
20030608 

From Tammy: MY DAUGHTERS TEACHER ASKED HER TO GIVE BOTH A DESCRIPTION AND A DEFINITION OF THE FOLLOWING ... CIRCLE, SQUARE, TRIANGLE,HEXAGON...... THE LIST GOES ON. WHAT IS THE DIFFERENCE BETWEEN DEFINITION AND DESCRIPTION ? DO A CIRCLE FOR AN EXAMPLE PLEASE. Answered by Penny Nom. 





The metric and Imperial systems 
20030608 

From Ashlee: i am a year 8 student, and i am doing my Maths talent quest on the Metric and Imperial number system.
i was wondering, where did the 2 systems orginate and if possible, a little bit or information.
I also need to know the conversions of ounce, foot, mile..etc..from imperial to metric. Answered by Penny Nom. 





A radio controled car 
20030608 

From Robert: I have a radio controled car (scale size 1/43). This car can travel 490 ft. per minute. I would like to know how fast that is at that scale size in miles per hour (and Kilometers per hour)? Answered by Penny Nom. 





Spacing the spindles for a railing 
20030606 

From Jennifer:
Scott is a homebuilder. He builds railings in which he places spindles. Spindles ar evertical posts taht are equally spaced beneath a horizontal bar. Scott would like a mathematical model to help him determine the amount of space to put between each spindle. The railing must follow the following criteria: The spaces between each spindle must be equal except for the ones at either end. Theses spaces are smaller. They are half the width of a spindle less than the other spaces. The number of spindles needs to be minimized since spindles are costly. Help Scott determine what width of space to use between the spindles. Create a mathematical model to determine the width of space between each spindle in termso f the number of spindles. Use an 8' (96") railing that has 2 1/2" wide spindles. Explain your thinking. For safety reasons the maximum width of a space is 4" Generalize you model to determine the width of spaces for total railing of length L and spindle width s Answered by Penny Nom. 





The square footage of a section of land 
20030604 

From Diane: We are trying to calculate the square footage of a section of land with the following dimensions:
One end is 100 feet. The other end is 105 feet.. One side is 350 feet and the other side is 372 feet. I calculated the area as 35,875 sq. feet, however, the brochure for the land says the area is 36,200 + sq. feet. Answered by Leeanne Boehm. 





$22,534.56 is what percent of $27,820.00? 
20030604 

From Minnie: $22,534.56 is what percent of $27,820.00? Answered by Penny Nom. 





BEDMAS 
20030531 

From Kristie: (3x50)+20/5=?
I know bedmas but i forget how to do it. Answered by Penny Nom. 





$1/week for week 1 and then double each week 
20030528 

From A student: I AM DOING A PROJECT FOR MATH I AM TRYING TO CREATE A SEQUENCE BASED ON: MAKING A SALARY OF $1/WK FOR THE FIRST WEEK WITH IT DOUBLING EVERY WEEK FOR 52 WEEKS, SO MY SEQUENCE LOOKS LIKE THIS: 1,2,4,8,16,32,64,128,256,512,1024 ETC. THERE WOULD BE 52#'s TOTAL IN MY SEQUENCE.I BELIEVE IT IS CALLED A FINITE SEQUENCE. MY QUESTION IS HOW DO I CREATE A FORMULA/RULE FOR THIS PARTICULAR SEQUENCE? MY GOAL BEING TO FIND THE 52nd TERM IN THE SEQUENCE. Answered by Penny Nom. 





5 to the power n 
20030528 

From Sam: What is the integer n for which
5 to the n power + 5 to the n power + 5 to the n power + 5 to the n power + 5 to the n power = 5 to the 25th power? Answered by Penny Nom. 





Millimeters to inches 
20030528 

From Brian: I am a music instructor just trying to get a horn repaired. I have been trying to get replacement pearls for a keyboard of a horn. The mechanic needs the measurement in inches. The calibers say that the size is .115 mm can you tell me what that is in inches, I tried your formula of 2.54 mm per inch but this is a smaller size and I cannot seem to figure it out. Answered by Penny Nom. 





George and his goat herd 
20030527 

From A student:
George the bulgarian goatherd drives his father's goats into a valley each morning and lets them browse there all day before driving them home in the evening. he notices that each morning the goats immediately separate into groups and begin to feed the number and sizes of the initial groups vary some days there are nine and so days there are three or fewer. there can be groups of one or the whole group. about every five minites one goat breaks away from each feeding group and these breakaway goats form into a new group. George has noticed that by the afternoon, even though the goats continue their regrouping the sizes of the groups have stabilised, and there is always seven feeding groups. How many goats are there in the herd? What are the sizes of the feeding groups once they have stabilised? Answered by Penny Nom. 





Two sequences that agree in the first 4 terms 
20030526 

From A student: Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest? Answered by Penny Nom. 





The crosssection of a football field 
20030525 

From Francis: Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly. height from base to highest point 45.75 centimetres distance of the field 50 metres a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the crosssection is a parabola, find the algebraic model that describes this shape. b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line. Answered by Harley Weston. 





Two piles of cards 
20030524 

From Sam: A standard deck of 52 cards (26 red, 26 black) is separated into two piles, not necessarily equal in size. The first pile contains seven times as many black cards as red cards. The second pile contains a number of red cards that is a multiple of the number of black cards in that pile. How many red cards are in the first pile? Answered by Penny Nom. 





An array of pennies 
20030523 

From Saundra: If you have 100 pennies and you are suppose to make an array do you arrange the pennies by date? Answered by Penny Nom. 





The weight of a fish tank 
20030520 

From A ponderer: I had a question pertaining conversion units..I have a fish tank at home and the dimensions are 24, 44, and 48 inches, I want to find out how much it weighs in pounds when filled up with water...knowing water is 62.4 pounds per cubic feet...do I just divide the 62.4 pounds to 12 because I"m trying to find out through cubic inches. Answered by Penny Nom. 





The HCF and LCM of polynomials 
20030520 

From Charanpal:
Question: Find the HCF and LCM of the polynomials given below. Verify that he productof these HCF and LCM differs from the product of the polynomials, if at all, by a factor of 1  1x^{2} and x^{3} 1
 1  x^{2} and x^{4}  1
Answered by Penny Nom. 





A trig identity 
20030520 

From Patty: Please help with the following
1/ tanx + cotx = sinxcosx Answered by Penny Nom. 





R= 5.3lnx + x. 
20030511 

From A student: Reaction R to a dose x is given by: R= 5.3lnx + x. For a certain drug, R must not exceed 21. Show that a dose between 8 and 12 units satisfies this requirement & find, correct to 5 decimal places, the greates value of x which satisfies this condition? Answered by Harley Weston. 





Subtracting rational expressions 
20030510 

From Simone: hi, i'm totally lost. i understand that you need to find a lowest common denominator to subtract two fractions (rational expressions) with different denominators. but what if the denominators are "x1" and "x". is x the common denominator? if so what happens to the "1"? do you know of any live online help i can get with the following: 3/(x1)  (12x)/x i've looked through my notes and have no examples that quite match that i can follow to get through it. please help! Answered by Penny Nom. 





x6square root of x +8=0 
20030510 

From Elizabeth: x6square root of x +8=0 Answered by Penny Nom. 





Circumference 
20030509 

From A parent: Find the circumference use 3 1/7 for pi
1. r= 28 ft. 2. D=98 cm Answered by Penny Nom. 





Real numbers 
20030509 

From Sirena: what is a "real" number Answered by Penny Nom. 





sin theta = 7/8 
20030507 

From Patty: If sin0 = 7/8 and 0 is in quadrant 2, find the other five trigonometric functions of 0. (report your answers in radical form) Answered by Penny Nom. 





ABCD*4 = DCBA 
20030507 

From Dee:
In the following problem, if the letters A, B, C and D represent some number, what numbers would they represent so that: ABCD*4 = DCBA Answered by Penny Nom. 





2/sqrt(2) 
20030507 

From Mike: I was looking at an example of csc 45 deg where csc = hyp / opp = 1 / (sqrt(2) / 2) = 2 / sqrt(2) = sqrt(2) I just don't get this. If sqrt(2) = 1.4142145..... How can 2 / sqrt(2) = sqrt(2) as the example shows? Answered by Penny Nom. 





Rules of exponents 
20030505 

From Carl: Hi, I am a student who would like to recall how to multiply exponents. Here is such an equation: 6.02569 X 10^{25} X 5.25^{4} =?
Also, adding exponents. Don't I just add subtract the exponents separately? Such as 5^{23} +15^{12} =?? Answered by Penny Nom. 





Write sin(3x) in terms of sin(x) 
20030505 

From A student: Write sin 2x in terms of sin x Answered by Penny Nom. 





Four digit palindromes 
20030505 

From Heather: How many palindromes were in between the numbers 1000 and 9999? Answered by Penny Nom. 





Integrating e^x sin(x) 
20030503 

From Lech: I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Answered by Penny Nom and Claude Tardif. 





The volume of air flowing in windpipes 
20030502 

From James: The volume of air flowing in windpipes is given by V=kpR^{4}, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: R_{o}  R = cp, where R_{o} is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*R_{o} < R < R_{o}, find the factor by which the radius of the windpipe contracts to give maximum flow? Answered by Penny Nom. 





positive multiples of 10 that are the sum of four consecutive integers 
20030501 

From Taurus: How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers? Answered by Penny Nom. 





A circle, tangent to two circles and a line 
20030430 

From Keith: I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Answered by Chris Fisher and Harley Weston. 





A binomial probability 
20030430 

From Erica: In a biathlon, athletes shot at 20 targets. A particular athlete had a probability of 0.18 of missing a target. Assuming a binomial distribution, what is the probability, to the nearest thousandth, that the athlete hit exactly 16 targets? Answered by Andrei Volodin. 





Some shapes 
20030429 

From Suzanne:
 What shape has 12 edges all the same length?
 What shape has 3 surfaces and 1 is curved?
Answered by Penny Nom. 





Profit for a dance studio 
20030428 

From Craig: A dance studio charges $80 per student for a series of 2 hour lessons. The studio's costs are $30 per hour for the instructor, $15 per lesson for the room rental, and $3 per student for miscellaneous expenses. If x is the number of students enrolled in the class, express the studio's profit P(x) in terms of x. Find the profit if 10 students are enrolled in the class. Answered by Penny Nom. 





A skill testing question 
20030427 

From Allan: it is a contest Labatt Blue can you please give me the answer some people are saying 154 and some 34 Answered by Leeanne Boehm and Harley Weston. 





20% of 40% of 500 
20030427 

From A student: What is 20% of 40% of 500 Answered by Penny Nom. 





The product of four consecutive integers is 3024. 
20030425 

From pillar: The product of four consecutive integers is 3024. What are those numbers. Answered by Penny Nom. 





Gallons of rain 
20030425 

From Jocelyn: If you have a surface of 6500 square feet and 1 inch of rain falls on the surface, how many gallons of water does this equal? Answered by Penny Nom. 





38 minus 10 plus 12 divided by 4 times 16 
20030423 

From James: please help me work this math problem 38 minus 10 plus 12 divided by 4 times 16 Answered by Harley Weston. 





Hidden by the curvature of the Earth 
20030423 

From Shirley: There are 2 six foot men. What would the distance be between them before one could not be seen because of the curvature of the earth? Answered by Penny Nom. 





Two intersecting graphs 
20030423 

From Patty:
a) graph the equation x^{2}  y  4 = 0
x^{2} + y^{2} = 9 on the same set of coordinate axes. I did not have a problem with this. The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places. Answered by Penny Nom. 





8 faces, 12 vertices, and 18 edges 
20030422 

From Thomas: I would like to know the proper name for this geometrical solid. It has 8 faces, 12 vertices, and 18 edges? Answered by Penny Nom. 





One one 
20030422 

From Brad: find the next two rows of numbers?
1
1 1
2 1
1 1 1 2
3 1 1 2
1 1 1 2 1 3
Answered by Leeanne Boehm. 





The effectiveness of a drug 
20030422 

From A student: A certain drug is found to be effective 80% of the time. Find the probability of successful treatment in two out of four cases. Answered by Andrei Volodin. 





Manipulating exponents 
20030421 

From Denita: Rewrite using only positive exponents:
(4a^4b^2)^4 * (4a^ 3 bc^2)^ 3 Answered by Harley Weston. 





Chopping trees 
20030419 

From Tamara:
The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him. He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work. Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down? Answered by Penny Nom. 





A tangent to a circle 
20030418 

From Lech: The line with equation y=mx is a tangent to the circle with equation x2+y26x6y+17=0. Find the possible values of m. Answered by Harley Weston. 





Interest compounded daily 
20030418 

From Bruce: I recently received $7,987.68. This amount consisted of $7,543.61 invested at 6% per annum, compounded daily. I am trying to find out how many days this investment accrued interest. Answered by Penny Nom. 





The substitution method 
20030414 

From Patty:
I need help with the following: 5x  4y = 13 2y + 3x = 1 Answered by Penny Nom. 





The square of my age was the same as the year 
20030414 

From Pat: Augustus de Morgan wrote in 1864, "At some point in my life, the square of my age was the same as the year." When was he born? Answered by Penny Nom. 





Area of a trapezoid 
20030413 

From A road builder: My husband works with asphalt building roads. There are times when one end of the road will be (for example) 100ft wide the other end would be( for example) 200ft wide and he must figure the area in square feet. So far it has been a guessing game because he dosen't have the formula to figure the square feet. Answered by Penny Nom. 





Incremental standard deviation 
20030412 

From Carlos: I need to calculate the standard deviation for a group of data, but I don't know in advance what is the mean. Is there a way to adjust the STDV for each datum without keeping all of the previous values? This is needed basicaly for performance, so I won't need to read twice the same data (spend processing time) nor save the previous values (spend memory). Answered by Andrei Volodin and Penny Nom. 





A fractional inequality 
20030408 

From Jessica: Solve for x. Write in interval notation.
[(x^{2})9]/[x5] >= 0 Answered by Penny Nom. 





The surface area of a cube 
20030407 

From Sarah: if the volume of a cube is 64 cm, then what's the total surface area? I also want to know how to show my work. Answered by Penny Nom. 





Jo's books 
20030407 

From Miguel: Jo announces, "I have more than 999 books." Jean says: "No Jo! You have fewer than 1,000 books." Mary says: "Jo has at least 1 book." Only one of these statements is true. How many books does Jo own? Answered by Penny Nom. 





The area of a parallelogram 
20030406 

From A student: Find the area of the parallelogram with vertices (0,0),(7,2),(10,7),(3,5) Answered by Penny Nom. 





The height of an equilateral triangle 
20030406 

From Rosa: If Each side of an equilateral triangle is 10 m. What is the height? Answered by Penny Nom. 





How many hits? 
20030406 

From Jack:
My name is Jack. I'm a uncle. Student is in the 5th grade email is above. If a baseball player at sping training had a good season with the following: one seventh of his hits were doubles. 12.5% of his hits were home runs. But didn't have any triples. How many hits did he have? Can you give me an explanation of you solved the problem. Answered by Penny Nom. 





Divide a circle in 8 equal pieces 
20030404 

From Naomi: I have to divide a circle in 8 equal pieces but can only cut 3 times can you please help me Answered by Penny Nom. 





Uses of conic sections 
20030401 

From William: My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful. Answered by Leeanne Boehm. 





Doubling the size of an object 
20030401 

From Dave: If I have a known surface area and volume of an unknown object and I want to double the size of the object, how do I find the new area and volume? Answered by Walter Whiteley. 





A handshake problem 
20030331 

From Jaylan: Suppose you and your partner attend a party with n other couples. Several handshakes took place. No one shook hands with himself (or herself) or with their partner, and no one shook hands with the same person more than once. After all the handshaking was completed, suppose you asked each person, including your partner, how many hands they had shaken. Each person gave a different answer.
Determine how many hands did you shake and how many hands did your partner shake when n=5 Answered by Penny Nom. 





Quadratic word problems 
20030330 

From A student: Question: i think i know the basics of how to solve direct quadratic equations,but how do i go about solving those word problems? i have tried them times and again, but nothing seems to work at all!they are driving me crazy! pls help!:):):):):)  bob & nick earned $1260 each. bob's hourly wage is $3 more than nick's hourly wage. he worked 2h less compared to nick. find the number of hours nick worked.
 there are 2 tanks in henry's house. in tank A, the fish are all goldfish. they are bought at a total cost of $259. in tank B, there are only guppies. the guppies were bought at a cost of $1.20 each. a day later,henry bought 3 more goldfish and put them into tank A. the number of guppies in tank B is now twice the number of goldfish in tank A.the total cost of all the fish that henry has presently,i.e. goldfish & guppies, is $355.30. given that the cost of each goldfish is the same,
a)find the initial number of goldfish in tank A b)find the total cost of all the guppies.  a particular disc can be made to rotate at 2 different speeds. if it is made to rotate slower by 135 revolutions per hour, it wld require an additional 2.7 hour to make 315 revolutions. find the higher speed at which it can operate.
Answered by Penny Nom. 





12*nC2 = n! 
20030330 

From A tutor: Solve for "N"
12*nC2=N! Answered by Walter Whiteley. 





The vertex of a cone 
20030327 

From Holly: I read your response to Callie about whether a cone has a vertex or not. Is it ONLY a vertex if both halves of the cone are together or can one half of the illustration have a vertex? Answered by Walter Whiteley. 





Can twice a square be a square? 
20030325 

From Mike: The other day it occurred to some students that they could think of no square number which is an integer, which can be divided into two equal square numbers which are intergers, Or put another way, no squared integer when doubled can equal another square integer. For example 5 squared plus 5 squared is 50, but 50 is not a square number. Answered by Walter Whiteley and Claude Tardif. 





A royal flush 
20030324 

From Vikki:
A poker hand consists of 5 cards selected randomly from an ordinary deck of cards: find the probability of a ROYAL FLUSH : the 10 , jack, queen,king and ace of the same suit. I was thinking somewhere along the lines of: *the number of ways to get the suit is 4C1 *the number of ways to get a 10 out of the 13 cards etc.... ...but Im not sure I am going about this the right way, could you help? Answered by Andrei Volodin. 





Friends and enemies 
20030324 

From Becky:
Consider a room that contains six people. Any two people are either friends of each other, or they are enemies. A. Argue why there are three people, all who are friends, or there are at least three people, all who are enemies
B. Rephrase the situation using graph terminology, using all of these terms correctly: vertex, edge, graph, complement, clique, independent set, and bipartite. Answered by Penny Nom. 





A triangle and a circle 
20030321 

From Jynks: We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle. Answered by Penny Nom. 





Scientific notation 
20030320 

From A student: what is one millionth times one thousand in scientific notation. Answered by Penny Nom. 





Gallons in a tank 
20030320 

From Leslie: I am trying to figure the liquid gallons in a water tank that is 19" wide by 29.25" long and is 12.25" high. Could you tell me the formula to figure this out. Answered by Penny Nom. 





Harmonic numbers 
20030319 

From Becky: Harmonic numbers are Hn = 1 + ? + 1/3 + . . . + 1/n
Use induction to prove the following theorem: For all natural numbers n, H1 + H2 + . . . + Hn = (1+n)Hn  n Answered by Penny Nom. 





A recurrence relation 
20030319 

From Becky: Solve this recurrence relation, with the initial conditions.
A1 = 10 A2 = 100 An = 10a n1 + 29a n2 Answered by Penny Nom. 





The origin of integers 
20030319 

From Travis: What are the real life usages of integers? Also what is the origin of integers? Answered by Harley Weston. 





1 followed by a million zeros 
20030319 

From David: What do you call the number represented by the numeral '1' followed by one million zeros? Answered by Penny Nom. 





Two algebra problems 
20030318 

From Kayla: 1st question If a+b divided by a equals 6 and b+c divided by c equals 9, compute the numerical value of a divided by c. ( Your answer will be mumbers only, no variables.)
2nd question Three adjacent faces of a box (a rectangular prism) have areas of 7, 14, and 18 square inches. Find the volume of the box. (Hint: Choose variables to represent the three sides of the box and then figure out the problem.) Answered by Peny Nom. 





Three proffs of a trig identity 
20030318 

From Nadene: Prove the identity. cos [x + (ypi/2)] = sin (x+y)
A hint was also provided which is: "Apply cos (alpha + beta) first then within that apply cose (alphabeta)" Answered by Penny Nom. 





An equilateral triangle 
20030317 

From Shirley: An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible? Answered by Penny Nom. 





A sequence that converges to e 
20030316 

From Dane: Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.1^{11} = 2.8531167... 1.01^{101} = 2.731861... 1.001^{1001} = 2.71964085... 1.0001^{10001} = 2.71841774... 1.00001^{100001} = 2.7182954... 1.000001^{1000001}1 = 2.178231875... 1.0000001^{10000001} = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'1^{1'infinite number of zeros'1} = e. Answered by Penny Nom. 





Runs 
20030316 

From Diana: How many arrangements are there with n 0's and m 1's, with k runs of 0's? (A run is a consecutive set [1 or more] of the same digit; eg. 000 111 0 11 00 has three runs.) Answered by Penny Nom. 





Distributing r identical balls into n distinct boxes 
20030316 

From Diana: How many ways to distribute r identical balls into n distinct boxes with exactly m boxes empty? Answered by Penny Nom. 





Working backwards 
20030314 

From Melody: Triva went to the ardcade at the state fair to win some goldfish. She already had some goldfish at home, but wanted more. She won enough goldfish to double her stock. Her mom made her give four away. She put her new ones in the tank with the others, by the morning half of the goldfish had died. Triva's friend gave her six more. The next morning twothirds of her goldfish died. She was left with two goldfish after giving one to a friend. How many goldfish did she start with? Answered by Penny Nom. 





1575 
20030313 

From Sharyn: find 6 integers that when multiplied with each other equal +1575 and when the same integers are added together equal zero. there are more positives than negatives and one of the numbers is a double digit between 10 and 20 Answered by Penny Nom. 





An arc of a circle 
20030312 

From Melissa: A strip of wood is 16 ft. long and is bent in the arc of a circle. Two radii, from the center of the circle to the ends of the arc, form a right angle. What is the approximate distance from one end of the wooden arc to the other? Answered by Penny Nom. 





Harmonic numbers 
20030312 

From Becky: What can you tell me about the limit of harmonic numbers as it reaches infinity? Answered by Penny Nom. 





Monomials 
20030311 

From Roxy: Explain why (x+y)z is not equal to xz+yz? P.S. Z is an exponent Answered by Penny Nom. 





Surface area of a sphere 
20030311 

From Kim: a sphere has a surface area of 128 pi sq. units. What is its exact radius? formula is 4 pi r^{2} I believe but how do I get radius Answered by Penny Nom. 





Division names 
20030310 

From A parent: what is the answer to a division problem called Answered by Penny Nom. 





Three digit number 
20030310 

From Grace: What three digit positive integer is exactly 32 times the sum of its digits? Answered by Claude Tardif. 





A question on combinations 
20030306 

From Jose:
I'm an architect student and have a question on combinations. I have a grid of 3 x 3, hence a total of 9 spaces. I have 3 elements to place in this grid. How many possible ways are there of arranging this elements on this grid ? (order, orientation not important) First putting the elements each in its own space and secondly allowing the elements at a given moment to "share" one space. Since I got kind of obsessed with this I went ahead and graphically did all the combinations allowing "sharing", a grand total of 729. How could I have known this before hand ? Answered by Penny Nom and Claude Tardif. 





Mary typed a six digit number 
20030306 

From Pillar: Mary typed a six digit number, but the two 1's did not show. What appeared instead was 2002. How many different sixdigit numbers could she have typed? Answered by Penny Nom. 





(n+17)(n+7) = 0 
20030305 

From Janea:
What is the answer to 1. (n+17)(n+7)=0 What is the answer to:2. (y15)(y100)=0 Answered by Penny Nom. 





Can a square be a rhombus? 
20030304 

From Beth: Can a square be a rhombus? Some sources say yes, some say no. Some sources define a rhombus as a quadrilateral and parallelogram with equal sides, but without right angles. Some sources say a square is a special case of a rhombus. Clarity, please! Answered by Walter Whiteley. 





y < 2x + 1 
20030301 

From Erika: how can I solve and graph y<2x+1 and which side in the graph should i shade after i finish solving my inequality? Answered by Penny Nom. 





Finding the area when the perimeter is known 
20030228 

From Yvette: What is the size of an area in sqare feet when the perimeter totals 842 feet. Sides are 190ft+180ft+200ft+54ft+118ft+100ft. Answered by Penny Nom. 





______cm=0.048km 
20030227 

From Antonette: ______cm=0.048km Answered by Penny Nom. 





Can a square be considered a rectangle? 
20030227 

From Carla:
Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? Answered by Penny Nom. 





A number line 
20030227 

From Shery:
My seventh grader problem of the month 0__________1______________5____> This is a arrow, the number should be below A.Mrs Decker created an arrow representing a number line shown above. She wanted to find points and label them with a heart (G) for Valentine's Day so that the fraction 5/g is less than 1. (be sure to mark the G and not the fraction 5/g). She pondered, "Are there any other locations for G?" Is so help her description the location of all these points. If not why not? Answered by Penny Nom. 





A regular polygon 
20030226 

From Melissa: The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? Answered by Penny Nom. 





X times Y equals ten million 
20030226 

From Baneen: Would you be able to tell me which two numbers would compute ten million without any number having zeros in it? Answered by Penny Nom. 





(x^{y})^{z} = 64 
20030226 

From Melissa: How many ordered triples of positive intergers (xyz) satisfy (x[raised to the y])raised to the z = 64? Answered by Penny Nom. 





A section of land 
20030225 

From Bev: How many acres in a section of land? How many square miles is in a secion of land? Answered by Penny Nom. 





The length of an arc 
20030224 

From Gavin: does anyone have a formula for calculating the length of an arc if I have the circle radius and the cord length of the arc?? Answered by Penny Nom. 





Excluded values 
20030222 

From Josh: Why do you think it is necessary to include the "excluded values" when you write your answers to rational expressions? Answered by Penny Nom. 





A trig identity 
20030222 

From Ron: We have spent hours trying to solve the following identity without success. Can you give us some hints as to how it is done?
1 + tan(x) tan(2x) = tan(2x) cot(x) 1 Answered by Penny Nom. 





The number of possible outcomes with 8 games 
20030221 

From Gianni: If 8 basketball games being played(no ties), which means a total of 16 teams, what are the total number of possible outcomes that can occur. Answered by Penny Nom. 





Percentage change in completion rate 
20030221 

From Remo: In the year 2000 300 out of a possible 600 completed a phone survey for a total of 50% completion rate. In the year 2001 20 out of 100 possible people completed the survey when it was redone. This is a completion rate of 20% To figure out the percentage change between the years can just use the difference between the percentage figures I already have? Or can I calculate it the same as you would for nonpercentage numbers. For example you gave an example here of a salary increase from $20 to $95 being an increase of 375%. Would I solve my problem the same way expect substituting my percentages (.5 and .2) in place of $20 and $95? Answered by Penny Nom. 





Deduct 60% from $150.00 
20030221 

From Mike: How do you get this answer? deduct 60% from $150.00 Answered by Penny Nom. 





Percentage decrease 
20030220 

From Hope: What number decreased by 33^{1}/_{3}% is 30? Answered by Penny Nom. 





Density 
20030219 

From Rob: What is the formula for converting cubic feet to pounds? (with any substance) Answered by Penny Nom. 





Hundreds, thousands, millions,... 
20030219 

From Karissa and Jasmeen: hundreds, thousands, millions,  can you help us with the rest of this sequence  we are trying to find the largest number Answered by Penny Nom. 





Sasha's candies 
20030218 

From Pat: Ticktactoe
Sasha and Trudy are playing ticktactoe. Sasha agrees to give trudy two pieces of candy for each game Sasha loses, and Trudy agrees to give Sasha three pieces of candy for each game that Trudy loses. After playing thirty games, Sasha has the amount of candy that he started with. If no ties occurred, how many games did Sasha win? Answered by Paul Betts. 





Order of operations 
20030216 

From A student: How is the order of operation used in everyday life other than in a math class or at school? Also .... Can you give me a list of all the mathematician that are still living that uses the order of operation? Answered by Claude Tardif. 





Numbers in base 5 
20030216 

From Lori: I'm trying to help my 6th grader with converting numbers like 82 to base 5 and 182 to base 12. We saw your examples on 613, but still are confused. Answered by Penny Nom. 





Order of operations 
20030215 

From Debbie: Question: 20(9+4)x7=? Possible answer 71 or 49? Answered by Penny Nom. 





A determinant 
20030213 

From A student:
I have to find the determinant of the following matrix 2  3  1  2  4  3  0  2  5  1  4  2  1  3  5  2  3  4  1  2  6  0  3  2  4  Answered by Penny Nom. 





Wrap a rope around the equator 
20030212 

From Ali: If you take a rope and wrap it around the equator and then overlap it 6ft. and cut off the extra then you loosen it up so the ends meet how far would it stand off the ground? Answered by Penny Nom. 





Multiples of all four of the numbers 2, 3, 4, and 5 
20030211 

From Stephanie: How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5? Answered by Penny Nom. 





Storyteller figurines 
20030210 

From A student: It takes 3/4 of an hour to bake a storyteller figurine. If only one figurine can be baked at a time, how many can be baked in 6 hours? Answered by Penny Nom. 





Splitting weight 
20030210 

From Jin Ho: A balance scale has only two weights, 1 ounce and 4 ounces. In only three weighings split 180 ounces of seed in two bags of 40 and 140 ounces. Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





Three consecutive positive intergers 
20030209 

From Yew: Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.
ex. (7)(8)(9) = 504 = 6 (84) Answered by Penny Nom. 





AABBBCCCCAABBBCCCC... 
20030209 

From Patty: The pattern AABBBCCCCAABBBCCCC continuously repeats. What is the 2003rd letter in the pattern? Please help, I am trying to figure out. Answered by Penny Nom. 





Millilitres and millimeters 
20030209 

From Iwan: I was just wondering whether a millilitre was equal to a millimetre, if not, what is there difference. Answered by Penny Nom. 





BEDMAS 
20030209 

From Stefanie: I do remember the rules of BEDMAS, but for some reason this question puzzles me. 6 X 9  3 + 44 I started with the Multiplication 54  3 + 44 But then I got stuck, do I proceed with adding the 44 and subtracting the 3 or figure out what 3 + 44 is, but then how would that work with 54?
Answered by Penny Nom. 





Two investments 
20030207 

From A student: you have $7200 in principal and invest different sums @ 10% and 14%. You receive 920 at end of term. (one year)What amounts are invested at what rate? Answered by Penny Nom. 





The area of an isoceles triangle 
20030207 

From A student: I have to find the area of an isoceles triangle with one angle side of 30 degrees, and length of base 5. Could you please help me solve this problem? Answered by Penny Nom. 





A 15% markup 
20030207 

From Holly: what is 15% markup of 58.89? please show equation and why? which is correct? 58.89 divided by .85 or 58.89 times 1.15 Answered by Penny Nom. 





Two equations in two unknowns 
20030206 

From Patrick: What are all ordered pairs of real numbers (x, y) for which: y^{x2  7x + 12} = 1 and x + y = 6? Answered by Penny Nom. 





Transformations of pattern blocks 
20030206 

From Cheryl: I am trying to help my 8th grade son with Transformations  use of patttern blocks. He has to trace a figure and reflect it across the xaxis, which I can do, but then it indicates include ordered pairs  that confuses me. Answered by Penny Nom. 





Two airplanes leave Dallas 
20030206 

From A student: TWO AIRPLANES LEAVE DALLAS AT THE SAME TIME AND FLY IN OPPOSITE DIRECTIONS. ONE AIRPLANE TRAVELS 80 MILES PER HOUR FASTER THAN THE OTHER. AFTER THREE HOURS, THEY ARE 2940 MILES APART. WHAT IS THE RATE OF EACH AIRPLANE? Answered by Penny Nom. 





The sum of the first 1000 even integers 
20030206 

From Jill: What is the sum of the first 1000 even integers? Answered by Paul Betts. 





Milliliters 
20030204 

From James: What is a milliliter? Answered by Penny Nom. 





Factoring 
20030204 

From Marcin: I am having a really hard time with the factor theorem. Can you please help me with the following? (a'3 means a to the exponent 3)
a)8a'3+64b'3c'6 b)8x'412x'344x'2+24x c)x'421x'2100
Answered by Penny Nom. 





Filling in the back yard with dirt 
20030204 

From Joe:
We just bought a house and need to start filling in the back yard with dirt to level it out. I measure 37'x 56' by 2' deep on an angle. I will be building a retaining wall at the 2' deep portion. The slop will go from the 2' to nothing at the top or near the house. I can't remember how to get the Sq. foot or cubic yards. Answered by Penny Nom. 





A train with 2 cars 
20030204 

From Michael: A train with 2 cars is traveling at a speed of 80 km/hr from town X to town y, located 800 km from each other. At the same moment that the train departed, a passenger started to walk back and forth from one end of car B to the other at a speed of 100cm/sec. Arriving in town Y, the passenger had already gone and returned 720 times. The length of car A is that of car B plus one fourth of the length of the locomotive, and the length of the locomotive equals the length of Car A plus one fifth of the length of car B. What is the total length of the train? Answered by Penny Nom. 





Problem solving 
20030203 

From Brigitte: My daughter is having lot's of problem with problem solving she is in grade 6. she is using mathematics in action from macmillan/ mcgraw hill. Do you know of any way she can get help, and if there is any tests on line Answered by Diane Hanson. 





Arithmitic sequence 
20030201 

From A student: I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why. Answered by Claude Tardif. 





Combinations of 1,2,3,4,5 and 6 
20030201 

From Kyle: Today I was aked a question by my geometry teacher. It was, what is the sum of all the possible combinations of the numbers 1, 2, 3, 4, 5, and 6. He said all the possible combinations were 720. I would like to know how u could do this, and what the answer is. Answered by Penny Nom. 





1+2+3+...+500 
20030131 

From Brian: What is the sum of the numbers from 1 to 500 inclusive? Answered by Paul Betts. 





Triangle perimeter 
20030130 

From An Aunt:
Hi I'm the aunt of a middle school child. He need help with two problems and I don't understand how to show he how to do them. Can you help me.  How do you find the perimeter for X=4, X=0.7, and X=5/6?
 And an acute triangle that bottom is (3X+1) cm, left side is (X+4) cm and the right is (2X+5)cm.
Can you show me not only the answer but also the steps that you used. Answered by Penny Nom. 





I have three circles... 
20030130 

From Tony: I HAVE THREE CIRCLE THAT IS CIRCLE TOGETHER: IN CIRCLE A, THE NUMBERS ARE: 11 I KNOW IS IN CIRCLE A, BUT I HAVE THE: 5 THAT IN A AND C, I HAVE THE 2 IN THE CIRCLE C AND B AND AND A, THE CIRCLE C I KNOW THAT 10 IS IN THE CIRCLE THE 4 IN CIRCLE A: AND B: IN CIRCLE B, I KNOW NUMBER 13 IS IN CIRCLE B; BUT I HAVE THE 3 IN CIRCLE B AND C AND I HAVE THE 2 IN CIRCLE B AND C AND A ,THE 4 IN CIRCLE B AND A. HOW DO I FIND THE SUM IN CIRCLE C AND IN B IN BOTH CIRCLE A AND B AND B AND C NOT IN CIRCLE B, AND NOT CIRCLE C. Answered by Penny Nom. 





Fibonacci exam 
20030128 

From Mike:
My son will be participating in the national math contest. He is a grade 4 student but will be writing the Fibonacci exam for grade 5. He has been given last years exam for practice. Parents have been ask to assist for this part. I was therfore hoping for a little "inside" help on several questions with answers & short explanations. This with a would be greatly appreciated.(from last years exam)  With 3 weights, Mathusalem can weigh any object that has a weight which is smaller or equal to 13 kg, but that weighs a whole number of kilograms. He wants to weigh an object of 7 kilograms. To do so, he must place two of the weights on the left side of the scale, and the third one on the right side. Which one will he have to place on the right side
a)4 b)3 c)6 d)2 e)5  Mathilda uses a rectangular prisms to build stairs. The cross section of each prism is a square which has a side of 1 dm. Mathilda has already put in place 4 steps of a staircase that must have a height of 10 dm. When finished, the staircase will have a volume of 550 dm3. What will the width of the staicase in dm be?
a)10 b)55 c)11 d)1 e)100  The year 1991 was the last palindrome year of the second millennium. The year 2002 is the first palindrome year of the third millennium. Including 2002, how many palindrome years will there be, altogether, in the third millennium ?
a)8 b)2 c)10 d)182 e) 9 Greatly appreciated, Mike
Answered by Penny Nom. 





Factoring a trinomial 
20030126 

From A student: how do you factor: Xsquared + 8x + 12 Answered by Penny Nom. 





Extraneous solutions 
20030124 

From Paul:
What is an extraneous solution and in what cases do you get one? How do you know it is extraneous? Answered by Penny Nom. 





Some 5th grade problems 
20030124 

From Sabrina:
[What is the greatest common factor of 20,28, and 36?] next problem is [5k+7(k+8)= ] next problem [Curtis simplified 0.8 divided by 0.2 x 0.04 and got 10. Latoya Simplified and got 1.6. is either correct? Can you explaine how you got the answer please.] Answered by Penny Nom. 





Dorothy and the wizard 
20030124 

From Ken:
dorothy was going to see the wizard of oz...she stopped at the bakery and bought a box of cookies. she met the scarecrow and gave him half the cookies. she ate half of the remaining cookies and threw one half cookie away. she met the tin man and gave him half the cookies. she ate half the remaining cookies and threw one half cookie away. she met the lion. she gave him half of her cookies. she ate half the remaining cookies and threw the LAST half cookie away. how many cookies did dorothy leave the bakery with? Answered by Penny Nom. 





6 digit numbers from 0,0,2,2,4,4 
20030123 

From Amanda: How many 6 digit numbers can you make from the numbers 0,0,2,2,4,4, giving that 0 cannot come first. The number has to contain 2 twos, 2 fours, and 2 zeros. Answered by Penny Nom and Claude Tardif. 





The cousin of Sally's sister's boyfriend 
20030123 

From Michael: Sally went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Sally cannot carry more than 2.5kg, and that the eggs were raw, calculate how many eggs the cousin of Sally's sister's boyfriend received. Answered by Penny Nom. 





The area of a regular ngon 
20030122 

From Sophie:
We have been given a piece of maths coursework. A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. she does not mind what the shape is but it must have a perimeter of 1000m. She wants to fence off the plot of land which contains the maximum area. Investigate the shape, or shapes that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. I have investigated many shapes, and I feel that a circle will have the biggest area. However we have also been asked to investigate shapes with 20 and 30 sides. My dad said that there is a formula for finding out any area of land. Do you know of this formula, if so I would be very grateful if you were to email it to me. Answered by Penny Nom. 





Rational expressions 
20030122 

From A student:
// = the main fraction line 1.) a+1/a1 + a1/a+1 // a+1/a1  a1/a+1 2.) 2/a(squared)3a+2 + 2/a(squared)a2 // 2/a(squared)1 + 2/ a(squared)+4a+3 Answered by Penny Nom. 





The least common denominator 
20030121 

From Brittan: Hi there I need help! My name is Brittany and i am in the 6th grade. I need help finding the least common denominator(LCD), and the book says Find the LCM of the denominators and i've done that and then it says write equivalent fractions,using the LCM as the least commonn denominator.The directions say Use the LCD to write each pair as like fractions. and the problem is 1/8 and 5/40. Could u explain how in the word u do this? Thanks a lot Brittany Answered by Penny Nom. 





A penny, a nickel, a dime, a quarter, and a loonie 
20030121 

From Blaine: I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? Answered by Penny Nom. 





Jo's books 
20030121 

From debra: Jo announces: I have no more than 999 books. Jean says: No Jo, You have fewer than 1,000 books. Mary says: Jo has at least 1 book.
Only one of these statements is true, How many books does Jo own?
I do not know HOW to approach this problem and solve it. Answered by Penny Nom. 





Why quadratic? 
20030121 

From Dan: Why are equations of the form aX^{2} + bX + c =0 call quadratic? The quad indicates 4 but the power is 2. Answered by Penny Nom. 





Cutting a board 
20030120 

From George: A person has a sheet of board which he saws into two (2) pieces. The length of the first piece is two thirds the length of the original board, while the length of the second piece is four feet longer than the first piece. How long was the original board? (the length is defined as the longer of the two sides of the board) Answered by Penny Nom. 





Division by zero 
20030119 

From David: I've been to your site and am interested on the subject of division by 0. It's easy enough to give answers, but it's very hard, especially in this case, to make someone understand a mathematical problem. It's been about a year since my Calc class, and we never went over division by 0, only infinite numbers and such. My question is: How would you work a problem of (real number) / 0 ? As ignorant as it may sound to you, I am having trouble grasping this since I've only begun to understand some of it. Perhaps you could help. Answered by Harley Weston. 





25% more 
20030116 

From Charlie: If I buy something for $10 and want to sell for 25% more, do I multiply by 1.25 or divide by .75? Or another way  why do I get $13.33 when dividing by .75 ? Answered by Penny Nom. 





Radians 
20030116 

From Erikson: I am a student in the 10th grade and attending advanced math at my high school. I was assign to do a report about the unit circle and the radian. But there seems to be no information available about the history of the radian; who first found out about them, which civilizations used it if any. Well, hopefully you'll assist me in this troubling question. Thank you for your kind consideration. Answered by Penny Nom. 





0.027 acres 
20030116 

From Cory Lee: How many square feet are in How many square feet are in .027 acres?? Answered by Penny Nom. 





NO REDHATTED DWARVES ALLOWED 
20030114 

From Dulce:
There are 1000 dwarves in Dwarfland. Now as you know, dwarves are born with either red or white hats on. The dwarves in Dwarfland love to party. Every night, they all flock to the same club to dance the night away. One day, a sign is posted at the club: "NO REDHATTED DWARVES ALLOWED". A certain number of days pass, after which all of the whitehatted dwarves are in attendance,and none of the reds. How did the red hats know not to come? Assumptions:  The number of red and whitehatted dwarves need not be equal. There are at least 1 of each color.
 There are no reflections or mirrors in Dwarfland (i.e. the dwarves can't see the color of their own hat), and no dwarf can reveal through direct or indirect means the color of another dwarf's hat.
 There is NO COMMUNICATION among dwarves
 No whitehatted dwarf ever misses a night of partying
Answered by Claude Tardif. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





Would it be worth paying $20K for 4 chances... 
20030113 

From Steve:
If I've got 4 chances to to achieve X goal, and in each chance that I have I've got a 65% chance of achieving this goal, what is my overall probablity of achieving this goal? Also, what would it be after each of my 4 chances (i.e., for my 2nd chance, would it be (.65 * (.65*.65)? I've forgotten some basic probablity theories, and would appreciate any help on this. With the probablities above, would it be worth paying $20K for 4 chances to achieve the goal or $8.5K for only 1 chance to acheive the goal? (at 65% probability) Answered by Andrei Volodin. 





5x(2)32/8 
20030113 

From A student: I'm having problems solving this question: 5x(2)32/8 Answered by Penny Nom. 





What is larger than infinity? 
20030112 

From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston. 





Cubic yards in a gravel pile 
20030110 

From Ron: I am looking to find a way to measure gravel piles to get yards. They are generaly not square.it would be like pouring sand out of a bag into a pile. they generaly are concave in dimension. can you help. I have attached a picture to show a small scale what I am working on is in much larger volume. Answered by Harley Weston. 





A rectangular prism 
20030109 

From Julie: How many faces on a rectangular prism and how many bases? Can the base also be a face and can a face also be a base? Answered by Diane Hanson. 





Intercepts 
20030108 

From Nay: my name is nay 8th grade student how do i figure out an intercep and does it always have to have (0, ) or ( ,0)? Answered by Penny Nom. 





Repeating decimals 
20030108 

From A student: If k=.9repeating, and 10k=9.9repeating then 10kk=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify? Answered by Penny Nom. 





The area of my lot 
20030107 

From Linda: I have a lot that is 210 feet in the front, 240 feet in the back and the sides each measure 150 feet. How many square feet is this all together and how close to an acre is it? Answered by Penny Nom. 





Integration of 1/(2+cos(x)) 
20030107 

From A student: integral from pi to 0 of dx/(2+cos x) i used the substitution t=tan(x/2) and i ended up with integral from +infinity to 0 of 2dt/(t^{2}+3) which looks like an inverse tan function , and i ended up with sqr(27)/2 pi , which is not the same as my calculator's answer , so i suspct i am doing some thing wrong. can some one tell me where i am going wrong please. Answered by Penny Nom. 





Mean and median 
20030104 

From Jan:
I have a question re: mean and median. I know what the difference is but just need some clarification on when you would use the mean and when you would use the median. Isn't it the case that with a skewed distribution the average (mean) would be higher or lower than the median, but with a normal distribution they would be very similar values? If you have any examples to help explain this that would be greatly appreciated. I am a teacher (of sorts!) and the person who is asking me the question is actually my boss! Answered by Penny Nom. 





Constructions of polygons 
20030103 

From Garrett: Our teacher just finished the constructions unit, and he mentioned briefly about odd sided figures such as pentagons and septagons, only that they're very hard. My question is, how do you draw, with a compass and a straight edge, a pentagon and septagon? Answered by Chris Fisher. 





Two numbers have a ratio of 5:3 
20030101 

From Patricia: Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers? Answered by Penny Nom. 





Augmented matrix 
20021231 

From Michelle: I am trying to augment a matrix so that i can find the values of the variables a, b, and c. For the life of me i can't find a solution to the matrix: 3 5 2 ' 22 2 3 1 ' 9 4 3 3 ' 1 I thank you for your help, Michelle Answered by Penny Nom. 





Successive coefficients in Pascal's Triangle 
20021227 

From Quincy: There is a formula connecting any (k+1) successive coefficients in the nth row of the Pascal Triangle with a coefficient in the (n+k)th row. Find this formula Answered by Penny Nom and Walter Whiteley. 





Averages of Averages 
20021221 

From Amy: If in the month of October the % of Payments Received was 80.74% and in November it decreased to 69.36%. Can you take the 80.7469.36/69.36 to get the % of difference. In otherwords can you take the % of difference when the numbers you are comparing are %'s???? Can you also take an average of an average? For example, average number of payments received in October was 25.00%, average number of payments received November was 50.00%, and the average number of payments received in December was 15.00%. Do you average (25.00%, 50.00% and 15.00%) or do you have to go back to the numbers that calculated the averages. For example, October 25.00% was based on 25 payments being received out of a possible 100. So instead of taking the average of the averages, do you take the average payments and the average customers over the 3 months and calculate the average??? Answered by Harley Weston. 





20% of 40% of 500 
20021219 

From Richard: What is 20% of 40% of 500? Answered by Penny Nom. 





The intersection of conics 
20021219 

From Glenda: We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Answered by Chris Fisher and Harley Weston. 





The units digit of 2 to the power of 31921 
20021218 

From A student: If 2 to the power of 31921 is multiplied out, what will be the units digit? Answered by Penny Nom. 





Odd and even 
20021217 

From Martin: I am a graduate engineer trying to teach single digit addition to my 8 year old granddaughter. My questions follow. Assume a child does not know what multiplication and division are. Assume the child knows how to count from 0 to 10 How do you explain that 2, 4, 6, 8 and 10 are even numbers And 1, 3, 5, 7 and 9 are odd numbers And these three facts?  when you add two even numbers, the answer is even
 when you add two odd numbers, the answer is even
 when you add an even number and an odd number, the answer is odd?
Can all of these be reasoned out, without using the concepts of multiplication or division? Answered by Diane Hanson. 





Calculations 
20021215 

From Mahdi: This problem is rather general, but it usually makes a lot of problems. I almost have no difficulty in math and physics questions, but unfortunately I'm not at all accurate in simple one or two digit calculation. I even sometimes make silly mistakes in simple sums like 7+4=12 or 4+5=11! Is there any effective way to reduce these mistakes? Answered by Walter Whiteley. 





A bouncing ball 
20021214 

From Eman:
Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.  Find the maximum height to which the ball rises after two bounces.
 Find the total distance that the ball has traveled when it hits the floor for the tenth time.
 Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.
Answered by Penny Nom. 





Two modes 
20021212 

From ali: I have a math assignment to pick the mode in a set of data. 12 and 21 both appear twice in the data set. What is the mode? Answered by Penny Nom. 





Units 
20021212 

From Debbie: The general equation for a parabola is y = ax^{ 2} + bx + c, where a, b, c are constants. What are the units of each constant if y and x are in meters? Answered by Penny Nom. 





Construct a pentagon 
20021212 

From Mary: We were wondering what the instructions/formula, stepbystep, is to make a pentagon. Answered by Chris Fisher and Penny Nom. 





A sphere with a hole  cylindrical shells 
20021211 

From Kathy: Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters.) You discover that both napkin rings have the same height, h.  Guess which ring has more wood in it and why.
 Check you guess: Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h.
Answered by Penny Nom. 





Factoring 
20021211 

From Larry: Question:
how do u factor trinonmials
EX: X^{ 3} + Y^{ 3}
X^{ 3}  8Y^{ 3}
8X^{ 2}  72
64A^{ 3}  125B^{ 6} Answered by Penny Nom. 





Find a, b and c 
20021210 

From Sameer: Question:
a+b+c=180 b=a+(120/25) c=b(13010)/6 a=? b=? c=? Answered by Penny Nom. 





Fractions 
20021210 

From Jean: What are some activities to use with advanced students in grade 7 to apply their knowledge of fractions and decimals. I'm looking for a project type of activity. Answered by Diane Hanson. 





Quadratic equations 
20021210 

From Katie: just bugging the hell outta me and I cannot figure it out for the life of me.
1)x2x1 =0 Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is
2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it! Answered by Penny Nom. 





y = 1  sin(x + 60) 
20021210 

From Eman: Sketch the graph of y = 1  sin(x+60). for 0 <= x<= 360, giving the coordinates of the maximum and minimum points and the pints where the curves crosses the y axis. Answered by Penny Nom. 





ALL of the possible 3 digit combinations of 0  9 
20021209 

From Melissa: I need to find out ALL of the possible 3 digit combinations of 0  9. Eg: 000,001,002,003. This is going to take me VERY LONG time. Any suggestions. Answered by Penny Nom. 





How many billions equal one trillion? 
20021207 

From Ryan and Aylah: How many billions equal one trillion? We believe that the answer is one thousand times one billion equals one trillion. Please help us with the answer to this question. Answered by Penny Nom. 





A function that is onto but not onetoone where f:N>N 
20021206 

From Lisa: A function that is onto but not onetoone where f:N>N Answered by Penny Nom. 





Integer arithmetic 
20021205 

From A student: Would you please help me with a question?
I am just learning about integers. Can you show me in a way I might understand....My teacher can tell me what is required to do the math, but it just doesn't make sence to me.
(+4)  (3) =+7
Why is the answer not +1 Answered by Diane Hanson. 





A rope trick 
20021205 

From Jerry: My name is Jerry and I am a math teacher at the secondary school level in the greater Toronto area. I posed the following problem to my enriched grade 10 math class that I found in the book called "Mathematics and the Imagination" by William Kastner. According to the author, it is posible for two people linked to each other with two ropes around their hands, to separate themselves without letting go of the rope. The students had lots of fun trying to accomplish this problem using skipping ropes from the Phys Ed department, but with no success. Answered by Penny Nom. 





Factoring a cubic 
20021205 

From Dorota: I got a problem with factorise the expression 2x^{3}+11x^{2}5x50. Answered by Penny Nom. 





Which is the better buy? 
20021204 

From Lynda: my question is the big can held 18 ouces and cost $2.52.The small can held only 12 ounces and cost $1.08. Find both unit prices. which can was better buy? Answered by Penny Nom. 





65,125 
20021204 

From Brittany: I am a threedigit number.When you reverse my digits,a larger number is formed.the product of me and the new number is 65,125.What number am I. Answered by Chris Fisher and Claude Tardif. 





The dimensions of a box 
20021203 

From Paula: My son, who is in secondary school, needs to make a box with the inside dimensions of 1.25 cubic feet. It's supposed to be more in the shape of a rectangle than a square. I would like to know the equation to use to find the inside dimensions of a box if I know how many cubic feet (or inches) I need the inside to be. Answered by Penny Nom. 





A Normal probability problem 
20021203 

From A student: The height of married men is approximately normal with mean 70 and standard deviation 3. The height of married women is approximately normal with mean 65 and standard deviation 2.5. What is the probability that a random married woman is taller than a random married man? Answered by Andrei Volodin. 





A geometric sequence 
20021202 

From Wanda: the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence. Answered by Penny Nom. 





Tiffany plays first board for her middle school chess team 
20021202 

From Patty: Tiffany plays first board for her middle school chess team. Since she joined the team last year, she has won 27 of 51 tournament games. That's a winning percentage of about 53%. If Tiffany went on a winning streak, how many games would she need to win in a row to raise her winning percentage to 60% Use variables and equations to communicate the method you've used to solve the problem. Answered by Penny Nom. 





How do you estimate the equation of a parabola? 
20021201 

From Audrey: How do you estimate the equation of a parabola? I have a project where a must find parabolas in magazines and then estimate their equation. Answered by Penny Nom. 





Trigonometry 
20021201 

From Lance: My question is:
FIND ALL SOLUTIONS cosx=1sin(x/2) if x[0,2pi)
ALSO:
Given cscx=5/4 and cot>0, find csc(x/2) and cot(x/2) Answered by Penny Nom. 





Trigonometry problems 
20021201 

From Chiara:
 Find tan 35pi/4
 Graph y = cos^{2}x  2sinx
Answered by Penny Nom. 





The height of a triangle 
20021129 

From Dean: Could you please tell me the formular for me to calculate the height of a triangle. I have the angles and side lengths. I am trying to calculate the height of an isosceles triangle, does this make a difference from a normal triangle or is the formular the same. Answered by Penny Nom. 





Constructing a tangent to two circles 
20021128 

From Tom: I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Answered by Chris Fisher and Penny Nom. 





x + y=80 and x + z=100 
20021128 

From PJ: x + y=80 x + z=100 can you solve for x, y or z? Answered by Penny Nom. 





Miles per hour 
20021128 

From Liz: If a car has traveled 16 miles in 30 minutes, how many miles per hour did they go? Answered by Penny Nom. 





The length of an arc 
20021127 

From Nancy: If all I have is the length between 2 ends of an arc (72"), how do I find the length of the arc at its apex and the radius? Answered by Penny Nom. 





Combinations of 1,2,3,...,10 
20021127 

From Gord: If I had the numbers from 110 how many different combinations would i have.....would it be 100....since that is 10 squared. Answered by Penny Nom. 





[x*(x+2)] + 1 = (x+1)(x+1) 
20021127 

From Melissa: While teaching the multiplication table to my daughter I noticed an interesting pattern. It goes something like ...Take a whole number ...add two to it ...multiply the two numbers together ...add one to the resulting number ...it will now be equal to the original number plus one, squared. Answered by Claude Tardif. 





Making 7 
20021126 

From Bill: At one time I had the answer to this math equation but I have lost it and can't seem to regain it. I may be going at it wrong but as I recall there were the numbers 1 through 4, and the std operators, +, , /, *, and parentheses. The object was to make the four numbers with the operators equal to 7. Each number and operator may be used only once. My 9 year old loves these quizzes but I can't give it to her if I can't provide the correct answer. Answered by Claude Tardif. 





A two stage rocket 
20021126 

From Hoda: a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex). Answered by Claude Tardif. 





A lampshade from a cone 
20021126 

From Ellsie: I need to make a pattern to cover an old lampshade. This is actually the bottom portion of a cone. Please help me figure out how to draw this pattern, so that we can complete our project. Answered by Penny Nom. 





Decimals in everyday life 
20021124 

From Fritz: How do you use decimals in your every day life? Answered by Penny Nom. 





Factor completely 
20021121 

From Shelley: these two questions are to be factored completely but i have no idea how to factor them  (x4y)^{ 2}  3(x4y)  4
 x^{ 6} + y^{ 6}
Answered by Penny Nom. 





Filling A swimming pool 
20021121 

From Sarah: A swimming pool is being filled by three pumps. Alone pump A would take 6 hours, pump B would take 3 hours, and pump C would take 3 hours. If all three pumps are used to fill the pool, what fraction of the process is pump A. Answered by Penny Nom. 





The volume of a juice jug 
20021121 

From Edward: I try to find the measurement for a juice jug. I have the height of the jug and need the jug to hold 2.5 Liter of juice. Can you help me out with the formula. Answered by Penny Nom. 





Performance reviews 
20021121 

From Lara: Perhaps you can help. He's doing performance reviews at work. The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year. The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year. How do I solve for the other performance review numbers. Answered by Penny Nom. 





What percent is the same as three eighths? 
20021121 

From Katelin: What is the percent of three eight's? Answered by Penny Nom. 





Composites, primes, factors and common factors 
20021120 

From Connie: My son can't remember what a composite number is, what a prime number is and the explaination of factors and common factors. Help! Answered by Penny Nom. 





Differentiating inverses 
20021120 

From Amy: f(x)= x^{3}+x+1, a=1 find g'(a) (g = f^{ 1}). I am having trouble finding g(a). Answered by Penny Nom. 





4 x abcd = dcba 
20021120 

From A student: Say you have a four digit number (e.g. abcd) and you multiply the number by 4. The answer you get will be the reverse order of the number you started with (dcba). What is the number? The four digits (a,b,c,d) cannot be the same number or cannot be repeated. Answered by Penny Nom and Claude Tardif. 





abc,abc 
20021120 

From Pam: Prove or disprove that "every number of the form abc,abc (where a, b, and c represent digits) is divisible by 7,11, and 13" Answered by Penny Nom. 





Round to hundredths 
20021119 

From Brittany: Can u tell me how to do a problem like this:
35 divded by 4.8= Round to hundreths. Answered by Penny Nom. 





Why is 5 divided by 1/7 greater than 5 divided by 2/3? 
20021119 

From Elizabeth:
 Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
 Is the least common multiple of two prime numbers always their product? Why or why not?
Answered by Diane Hanson and Penny Nom. 





The horse race 
20021119 

From Pat: The Horse Race Three horses run a race. In how many different ways can the three horses finish the race if ties are allowed? Answered by Penny Nom. 





A cubic 
20021118 

From Jessica: "For what values of the constant p does f have 3 distinct real roots?" The function is f(x)= x^{3}  6x^{2} + p, where p is an arbitrary constant. Answered by Claude Tardif and Penny Nom. 





Gears and ratios 
20021117 

From Matt: if gear A has 12teeth and Gear B has 16teeth and gear C has 10teeth and gear A turns 40 times how many times will gear C turn Answered by Penny Nom. 





The 24 game 
20021116 

From Michael: Hello, my name is Michael and I am in elementary school .. We have a game we play in math class called 24 game. In it each card has 4 numbers on it. Each number can only be used once, in any order, using multiplication, subtraction, division, or addition. We are stuck on one and wondered if you could help. The four numbers are 109164. And they must equal 24. Any clues? Answered by Penny Nom. 





A 40% markup? 
20021115 

From Amy: Please help? I own a basket and bouquet company, I have two retail stores with a markup of 40% on the price of the items I sale to them. I do not understand their conversion chart and I hope you can help me. A bouquet that I sale for $12.50 wholesale to the retail is marked up at a rate of 1.675 or (40%). I do not understand how the calculation of 1.675 is arrived at ... how is this 40%. I was told to multiply my wholesale price of $12.50 X 1.675 and I would arrive at the markup price of 40% the retailer would sale the item for. Answered by Penny Nom. 





The product of two consecutive numbers is 41 more than their sum 
20021115 

From A mother: THE PRODUCT OF TWO CONSECUTIVE NUMBERS IS 41 MORE THAN THE SUM OF THE NUMBERS. WHAT ARE THE NUMBERS? Answered by Penny Nom. 





The substitution method 
20021115 

From A student: Solve by using the substitution method. x = 3y  1 x + 2y = 9 Answered by Penny Nom. 





A pattern in a table 
20021114 

From Thamar: how do you solve for pattern in a table like
the top row is  2  6  12  17  z  the bottom row is  9  13  19  24  blank  question ask in each blank space write a rule to find the next number in the table Answered by Penny Nom. 





Algebra 
20021113 

From Carol: I am a confused parent trying to help my dau hgter solve some math problems and I need help. 3[x4]=27 Answered by Penny Nom. 





For what divisors can you get a remainder of 8? 
20021113 

From David: When dividing a 3digit number by a 1digit number, for what divisors can you get a remainder of 8? Answered by Penny Nom. 





The volume of water in a hose 
20021113 

From David: I trying to find out how much water 500 ft of 3/4 inch hose will hold. I'd also like to know how you figured the answer. Answered by Penny Nom. 





Subdividing a circle 
20021111 

From David: Say you have a cirlcle. Then you draw 2 dots on the circle. Then you connect the dots with lines. The circle is divided into 2 parts. If you do the same with 3 dots and connect each dot to each dot with a line then you get a circle with 4 parts. 4 dots with lines connecting all (6 lines) = 8 parts.... Answered by Claude Tardif. 





Fuel consumption 
20021111 

From Guy: When a car is driven 'normally' the feul consumption is 7.5 per litres per 100km. On a particular journey the car was driven in 'hard' and the consumption changed to 9.1 litres per 100km. Fuel cost 80p per litre. Calculate:
a) The extra feul consumed. b) The extra cost of feul, in pounds, for the journey when the car was driven in 'hard'. Answered by Penny Nom. 





Radicals with fractional radicands 
20021111 

From A student: how do I simplify radicals with fractional radicands? ex. 7sqrt(2) + sqrt(50)  2sqrt(18) 10sqrt(3/5)  24sqrt(5/3) 3sqrt(2/9) + 1/2sqrt(32) + sqrt(9/8) Answered by Penny Nom. 





x intercepts 
20021110 

From Laura: Find the x intercepts for the graph of the equation. x^{ 2}  x  12 = 0 Answered by Penny Nom. 





(93+n)+158=93+(28+158) 
20021110 

From Parents: (93+n)+158=93+(28+158) Answered by Penny Nom. 





A bus is 60% occupied 
20021109 

From Joe: A bus with a seating capacity of 60 people is 60% occupied. At the next stop onethird of the people get off the bus and 3 people get on the bus. The bus is now ___% occupied. Answered by Penny Nom. 





Three bags of marbles 
20021108 

From A student: I have 3 bags of marbles 1 bag is labeled blue; 2nd bag is labeled red; 3rd bag is labeled blue & red all the bags are mismarked your job is to take one marble from 1 bag look at it and correctly label all the bags Answered by Penny Nom. 





Prime numbers 
20021108 

From Lonna: Is 2 a prime number or not?? Why is 1 not considered a prime number? Answered by Penny Nom. 





Two tanks of water 
20021108 

From A student: A 2000 L tank containing 550 L of water is being filled with water at the rate of 75 L per minute from a full 1600 L tank. How long will it be before the two tanks have the same amount of water? Answered by Penny Nom. 





Cubic centimeters 
20021107 

From Rita: Was in emergency room yesterdayMD aspirated 40cc of fluid from my kneewhat does a "cc" equate to? Answered by Penny Nom. 





G = 3H  5 
20021107 

From Kash: G=3H5, for H solve for the given variable Answered by Penny Nom. 





The identity property 
20021107 

From Stephanie: I am a student teacher this semester in the third grade. I was looking at our math competencies and saw that we needed to teach the identity property. Is this the same as the distributive property? If not, what is it? Answered by Penny Nom. 





Chisanbop 
20021107 

From Paul: I'm trying to find the book/books that explain this system? I have one small book that explains the very beginning of the system, but covers only about 10 to 20%. I'v tried several book sellers and have had no luck. Answered by Diane Hanson. 





Substitution 
20021106 

From John Paul: I took a math test last week, and there was a problem which the teacher checked as incorrect. It was:
Solve: (a)RcTc=360;(b)RmTm=480;(c)Rm=2Rc; (d)Tm+Tc=15 I solved the problem and I got the following values for each variable.
For Rc=40 For Tc=9 For Rm=96 For Tm=5 I don't see nothing wrong, but the teacher checked it as wrong. Could it be a checking mistake? Answered by Claude Tardif. 





Determining a parabola 
20021106 

From Shelley: let (0,3) and (1,9)and (1,1) be given points in a parablola. Determine a b and c Answered by Penny Nom. 





What is nth term? 
20021106 

From Joga: What is nth term: First sequence: 2, 4,7,11, 16, nth term Second sequence: 4,10, 28, 82, nth term Answered by Penny Nom. 





18m11+ 7 
20021106 

From Sophia: what is 18m11+ 7 (m = to 12)? Answered by Penny Nom. 





A house's selling price 
20021105 

From Tanisha: a CERTAIN REALESTATE AGENT RECEIVES $6 FOR EVERY $100 OF A HOUSE'S SELLING PRICE. HOW MUCH WAS A HOUSE SOLD FOR IF THE AGENT $10,725._ Answered by Penny Nom. 





Compass points 
20021105 

From Mhairi: I was asked this in maths but I am not sure if it is geography. Name all the compass points? We have been given 8 but he told us there is more and we have to name them. Answered by Chris Fisher. 





The percentage grade of that hill 
20021105 

From Cathy: If there is an 80ft climb over a kilometer(about 3280ft) what is the percentage grade of that hill? Answered by Penny Nom. 





An octagon of perimeter 1,000 meters 
20021105 

From Stephen: my son has to work out the area of a octagon with a outside perimeter of 1,000 metres, Answered by Penny Nom. 





Clown has eight steps to climb 
20021105 

From A mom: I'm a parent of a grade two student. What is the best way to help my son figure out a math comprehension problem? Clown has eight steps to climb, is shown in a picture with front foot on third step and behind foot on first step. Each time he climbs three steps, he falls back two. How many times did he have to climb up to reach the top. Should I get him to do a line graph or math equations. On his own he came up with the answer seven. I think the answer is six. I did 0+3=3, 32=1, 1+3=4 and so on, In think my why is alittle confusing to him. Is there a simplier why to explain it to him. Answered by Diane Hanson. 





A twelvevolume set of encyclopedias 
20021104 

From Ron: A novice librarian shelved a twelvevolume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go? Answered by Penny Nom. 





Rounding 27.27 
20021103 

From A parent: If you have a problem 27.27 and you need to round to the first 7 the answer would be 27 Would 27.0 be acceptable as well or is it completely wrong. Answered by Penny Nom. 





Mathematics and Music 
20021101 

From Hannah: I am looking for a science fair project to compare math and music and how they relate. If you have any project ideas for me, they would be greatly appreciated. Answered by Walter Whiteley. 





How would you find the length of the chord? 
20021031 

From A draftsperson: If given the length of an arc and the distance from the midpoint of the arc to the midpoint of a chord, how would you find the length of the chord and the radius of the arc. The chords endpoints are the same as the the arcs endpoints. Answered by Penny Nom. 





A coin is tossed 11 times 
20021031 

From A student: There are 2 people that are playing a game in which a coin is tossed 11 times. The first player gets a point for a toss of heads. The 2nd player gets a point for a toss of tails. whoever gets 6 points wins. Suppose that so far the first player has 2 points and the second player has 4 points. What is the probability that the first player wins the game? Answered by Andrei Volodin and Penny Nom. 





Mrs. Klein has been losing 1 pound a week for the last year 
20021030 

From Brett: On her diet, Mrs. Klein has been losing 1 pound a week for the last year. Her husband weighs 110 pounds more than she does now. If his weight is twice what her weight was 6 weeks ago, how much does mrs. Klein weigh now? Answered by Penny Nom. 





An isosceles triangle 
20021030 

From Stan: What two different base lengths can an isosceles triangle have with sides on both remaining at 13 inches? How do I show this? Answered by Paul Betts and Peny Nom. 





A triangular prism 
20021030 

From Daniel: I was wondering what a triangular prism was. Answered by Diane Hanson. 





How many empty seats are there? 
20021029 

From Ronnie: Three new students arrived in class. Teacher says there are 210 ways you can set. How many empty seats are there in the classroom? After new student are assigned seats, how many empty seats will remain? Answered by Penny Nom. 





Variance 
20021029 

From Ade: I am trying to solve a standard deviation question, I have 30 data points to use, should I group the data before solving for variance or should I just use the raw data. Answered by Andrei Volodin. 





Simplifying Variable Expressions 
20021028 

From Erika: i would like to ask you a mathematical question on Simplifying Variable Expressions. The question is 2(n4)+3. Answered by Penny Nom. 





Jimmy's hits 
20021027 

From Patty: One seventh of Jimmy's hits were doubles 12.5% of his hits were homeruns Jimmy had 82 singles He did not have any triples
How many hits did Jimmy have? (Be sure to include the equation that represents the number of hits) Answered by Penny Nom. 





10 hours before 7:15 
20021027 

From Jessica: It is evening 7:15. What time would it be 10 hours earlier? Answered by Penny Nom. 





An identity? 
20021027 

From Jenna: I can't prove
1sinQ 1  = tanQ +  1+sinQ cosQ
Answered by Penny Nom. 





The four colour theorem 
20021027 

From Rhonda: is there an actual equation for the four colour map theorem??? i cannot find it anywhere!! if so can you give a breif description on how it works!! Answered by Penny Nom. 





x^{ 4} + x^{ 5} = 100 
20021027 

From Bill: One of my students has stumped me. He asked how to solve the equation 4^{ x} + 5^{ x} = 100 All I can think of are graphing methods to get an approximate solution. What am I missing? Answered by Harley Weston. 





What are the digits? 
20021024 

From Ebenezer: There are three digits. The middle digit is zero and the sum of the first and last digits are is 13. When the number is reversed it is increased by 297. What are the digits? Answered by Penny Nom. 





Averaging grades 
20021024 

From Richard: I'm using a grading program for the first time this year. (ok, that's not a question) I require my students to record their grades in a Scorekeeper when they get them back. I'd like to know if my students can keep up with averaging their grades just as the grading programs automatically averages them when I put them in the spreadsheet. Answered by Penny Nom and Claude Tardif. 





How many trees were planted in March? 
20021020 

From Allison: The number of trees planted by the Alpine Nursery in April was 3 more than twice the number of trees planted in March. If 71 trees were planted in april, write and solve an equation to find how many trees were planted in March. Answered by Penny Nom. 





Is a square a rectangle? 
20021020 

From Nona: Are squares rectangles? Third grade math teacher told a student this was true. Grandmother needs confirmation on this! Answered by Claude Tardif and Harley Weston. 





At the zoo 
20021020 

From A student: The number of adults at the zoo was 2/9 the number of children. there are 700 more children than adults. The number of men was four times the number of women. The number of girls was four times the number of boys. Find the total nymber of men and boys at the zoo. Answered by Penny Nom. 





Simplify 
20021019 

From A student: well i need to simplify this problems out and i cant do it so here is one 3x^2+6x45  = 3x^2+21x+30 Answered by Penny Nom. 





Exponential notation 
20021019 

From Ivy: I understand how to figure out for example 4 to the power of 3,what I don't understand is how to figure it out using both negative numbers and negative exponents,as an exaple 4 to the power of 6 and what makes this different that (5) to the power of 7,please help me if you can.I am an adult taking correspondence and finding it quite frustrating. Answered by Penny Nom. 





Is it a prime? 
20021019 

From JV: 6x to the third power plus 5x plus 15, is that prime or not prime, and whichever it is, how can you prove it? ya dig? Answered by Claude Tardif. 





Use each digit 19 only one time each,... 
20021019 

From Megan: Use each digit 19 only one time each, divide the numbers into 3 groups, make one 2 digit number, one 3 digit number, and one 4 digit number. There are 6 combinations of these numbers in which you can multiply the 2 digit and 3 digit number together to get the 4 digit number (using each digit 19 one time each). What are they!!!!!!!!!???????????? Answered by Claude Tardif. 





An identity in trigonometry 
20021017 

From Alex: I really need help with proving this identity. (1+cosx+sinx)/(1+cosxsinx) = secx + tanx Answered by Penny Nom. 





The orthocentre 
20021017 

From Elsie:
 Find the orthocentre of the triangle with vertices at A(3,4), B(10, 3) and C(3,2).
 Find the distance of point X(3,8) from the line that passes through Y(2, 2) and Z (3, 2).
Answered by Chris Fisher. 





The repetition of doing many straight forward problems 
20021016 

From Dan: I am the father of a very bright 9 year old girl. She is very interested in math and she grasps concepts very quickly. I am concerned that she may become bored with the repetition of doing many straight forward problems. Her current math teacher has her working in a challenging math book and she is doing 3+ digit multiplication. She misses 2 or 3 out of ten of these problems due to simple addition errors. Should she continue to practice these problems until she can get them all correct? Or, should she move on? Answered by Kathy Nolan and Claude Tardif. 





Integers in real life 
20021015 

From Rica: What are the real life usages of integers? Answered by Peny Nom. 





A sale price 
20021015 

From Chester: A jacket is on sale for 32% off. Find the original if the sale price is $89.00 Answered by Penny Nom. 





6% grade 
20021015 

From Micheal: When I am driving down the road and see a sign that says for example steep grade ahead 6% grade etc etc what does this mean? Answered by Penny Nom. 





Two problems 
20021014 

From Seçkin: i am from turkey i am a teacher in a collage i have two difficult question which i havent solve yet these are very important for me.... Answered by Claude Tardif. 





A functional equation 
20021014 

From Rob: Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n)
b) f(f(n))=3(n) Answered by Claude Tardif. 





Two problems 
20021014 

From Eva:
a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Answered by Leeanne Boehm and Penny Nom. 





Pythagoras in three dimensions 
20021014 

From Miki: A room is 6m long, 5m wide and 3 m high. Find the distance from the corner of the floor to the opposite corner of the celing. Answered by Peny Nom. 





Three algebra problems 
20021013 

From Veronica: Solve the following inequality: 5(xsqured4)/(xto the 5th(2x5)to the 3rd) < or equal 0 Solve the following equations for all roots square root of x+2=1+square root of 2x+3 what's ZERO FACTOR PROPERTY??? The hypotenuse of an isosceles right triangle is 7cm. long. Determine the lenghts of the other sides. Answered by Leeanne Boehm. 





Tree diagrams 
20021012 

From Denean:
 For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?
 In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?
Answered by Penny Nom. 





Statistics 
20021011 

From Ed: Suppose 25 percent of all U.S. workers belong to a labor union. What is the probability that in a random sample of 100 U.S. workers, at least 20 percent will belong to a labor union? Answered by Claude Tardif. 





Kilometers to miles 
20021009 

From A student: how many miles are in 16 kilometers? Answered by Leeanne Boehm. 





Nixon, Jefferson, and Madison 
20021008 

From Lisa: The longestlived US presidents are John Adams(age90), Herbert Hoover (also90), and Harry Truman (88). Behind them are James Madison, Thomas Jefferson, and Richard Nixon. The lattter three men lived a total of 249 years, and their ages at the time of death form consecutive odd integers. For how long did Nixon, Jefferson, and Madison live? Answered by Penny Nom. 





8 squares from 12 sticks 
20021008 

From A student: If you have 12 sticks the same size, how do you make them into 8 squares? Answered by Claude Tardif. 





Baseball, basketball and football 
20021008 

From Debbie: The school newspaper is interviewing 6th grade students to see what sports they follow regularly on TV. Of the 70 students interviewed; 40 enjoyed basketball; 40 enjoyed baseball; 40 enjoyed football; 20 enjoyed basketball and football; 22 enjoyed baseball and basketball; 27 enjoyed football and baseball; and 12 enjoyed all three sports. How many students out of the 70 interviewed didn't follow any one of the three sports? Answered by Leeanne Boehm, Penny Nom and Walter Whiteley. 





A complex quadratic 
20021006 

From Michael: I would like to know, how to solve this Complex number: quadratic equation. ix^{ 2} + x i = 0 Answered by Harley Weston. 





Relatively prime 
20021004 

From Natasha: I really need help with this middle level math question. My little brother is asking me and I have no clue what the answer is. Explain what it means when two numbers are negatively prime. (?) Answered by Kathy Nolan and Penny Nom. 





$100 is split between four guys. 
20021003 

From Stephan: $100 is split between four guys. A,B, C, and D. How much money does if person get if B has four more dollars than A, C has 8 more dollars than B, and D has twice as much money as C? Answered by Penny Nom. 





Rational expressions 
20021003 

From Ashley: 1/x(squared) + 5/xy Answered by Penny Nom. 





Exponent 0 
20021002 

From Debbi: can you please tell me what the exponent 0 is (i.e. 7^{0}) Answered by Penny Nom. 





The interrelations of the propositions in Euclid I 
20021001 

From Rob: I'm a student at St. John's College in Santa Fe New Mexico, are school is devoted to the great books and we're now reading Euclid's Elements in english and Attic Greek. We have an assignment to show a frequency or flow chart of how all the propositions of book one are interrelated. Answered by Chris Fisher. 





Two rate problems 
20020930 

From Rebecca:
 There are two small holes in the bottom of a tub filled with water. If opened, one hole will empty the tub in three hours; the other will empty it in six hours. If both holes are opened at the same time, how long will it take to empty the tub?
 An airplane flies 400 miles per hour in calm air. It can cover 900 miles flying with the wind in the same time that it can cover 700 miles against the wind. What is the speed of the wind?
Answered by Penny Nom. 





A geometry problem 
20020929 

From Sonia: Given ABCD; m a. Find the measures of b. Is there enough information for you to conclude that Answered by Penny Nom. 





0.99999... 
20020926 

From Erica: Yesterday in my 8th grade math class we were being taught how to convert a Repeating Decimal into a fraction. Since I, for some odd reason, seem to understand math better than the rest of my classmates, i began to drown out my teachers explaination for the rule. While she was about half way through with explaining mixed decimals i came up with an unsolvable question. Like I said before, I understand how to turn a repeating decimal into a fraction, but how would I turn a repeating .9 into a fraction? We all know it would equal 9/9, but doesn't 9 over 9 also equal 1? Even though it comes very close to one, it never really equals one. I'm very confused about this and i would love it if you could clear this up for me. Answered by Penny Nom. 





Proof by induction 
20020926 

From Pooh: Use induction to show that
1^{ 2} + 2^{ 2} + .....+n^{ 2} = (n^{ 3})/3 + (n^{ 2})/2 + n/6 Answered by Paul Betts. 





Painting a car 
20020924 

From A student: Dan can paint a car in 4 hours. Luke can pain the same car in 6 hours. Working together, how long would it take them to pain the same car? Answered by Penny Nom. 





Number play 
20020924 

From Julie: Organize these numbers and the operations so that each equation is correct. Use each coice only once per equation.
36 18 12 6  + ( ) /
_________________________ = 22
_________________________ = 41 Answered by Claude Tardif. 





Dividing fractions 
20020923 

From Angie: When I was taught to divide a fraction, I was told to multiply the reciprocal. Many times I find I can just divide the fraction, and it saves all the simplifying after. For example, 4/6 x 9/14 divided by 2/4 I would say 4x9divided by 2=18 over 6x14divided by 4 =21, so the answer is 18/21 but if I multiply the reciprocal, I would end up with 4x9x4 over 6x14x2 which equals 144/168. So, why are we taught to do it this way? Is it necessary? Answered by Chris Fisher. 





A cone that is cut off at the top 
20020923 

From Stuart: I have to work out the dimensions and arcs of a cone that is cut off at the top. I.e Top diameter is 33mm to bottom diameter is 43mm and the depth is 80mm Are you able to work what the flat of this cone would be as I need to design within the flat area and then have it cut out. I really need to know what the flat of it is before it is cut and curled to form the above cone. Answered by Walter Whiteley. 





Solving an equation 
20020922 

From Emanuel: how do u solve these problems?:
30/x=7+ 18/2x
3m+1/4 = 2 32m/3 Answered by Penny Nom. 





Ceiling 
20020922 

From Joe: Does the ceiling of a number mean the ceiling of 1.3 is 2 and the ceiling of 1.5 is 2 and the ceiling of 1.8 is 2. Or the ceiling of 1.3 is 1.5? Answered by Penny Nom. 





A max/min problem 
20020921 

From Evelina: A window is the shape of a rectangle with an equilateral triangle on top. The perimeter of the window is 300 cm. Find the width that will let the maximum light to enter. Answered by Penny Nom. 





Fractional exponents 
20020920 

From Jill: The problem is with fractional exponants: 10 1/3 mult. by 10,000 The 1/3 is an exponant of 10. Answered by Penny Nom. 





The entire earths' population would fit in the state of Texas 
20020918 

From Roz: I have been told that the entire earths' population would fit in the state of Texas and each person would have 1/2 acre. Is this true. Answered by Chris Fisher. 





How long will it be before you reach your friend? 
20020916 

From Margaret: Your friend runs at 8 miles per hour and you drive at 40 miles per hour, hence the diatance between you is decreasing at 32 miles per hour. You firend left 2 hours before you so how far has he gone in that 2 hours? How long will it take for the distance between you to decrease to 0 miles if the distance is decreasing at 32 miles per hour? Answered by Penny Nom. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





A million sheets of 30 cm long paper 
20020915 

From Jennifer: if you put a million sheets of 30 cm long paper end to end, how many kilometer long would the paper be from begining to end? Answered by Penny Nom. 





Formulating equtions 
20020914 

From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions  Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have?
 The Tigers played 48 games. They won twice as many as they lost. How many did they win?
 There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there?
 A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece.
Answered by Penny Nom. 





Sums of evens 
20020914 

From Rosa: How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + .... Answered by Leeanne Boehm and Harley Weston. 





Mixing solutions 
20020913 

From Margaret: In a chemistry laboratory the concentration of one solution is 10% hydrocholoric acid (HCl) and that of a second soulution is 60% HCl. How many mL of each should be mixed to obtain 50 mL of a 30% HCl solution?? Answered by Penny Nom. 





Base 5 numbers 
20020913 

From Vera: ? how do you change a base 10 number to base 5 Answered by Penny Nom. 





How many dominoes? 
20020913 

From A student: Dominoes are split into two halves. If you were allowed up to 6 dots on each half, how many options of dominoes could you get? Answered by Penny Nom. 





The number of decimal places in 1 over a power of 2 
20020912 

From Allan: Does anyone notice that the maximum number of decimal place of the number 2 dividing 1 and its increment (4, 8, 16...etc) is the same as the power of number 2? eg. 2^{2}=4, thus the max number of decimal of ^{1}/_{4}=0.25 which is 2 decimal place and 2 is the number of power of 2 take 64 as example: 2^{6}=64, and take ^{1}/_{64}=0.015625 which has 6 decimal place (and is the power 6) Is there such a law in math? If yes, can you tell me what it is? Or is this my discovery? Answered by Paul Betts. 





Use a 4 four times 
20020912 

From Amanda: The question is what is if you can only use a 4 four times and get the answer 12, 10, and 6 Answered by Claude tardif. 





7+8+9+...+1000 
20020911 

From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom. 





The quadratic formula 
20020911 

From Kathleen: im having a problem trying to understand quadratic formulas can u please help me i have problems like 3x^{2}  4x  11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me. Answered by Penny Nom. 





The sum of the first one hundred even numbers 
20020910 

From Arthur: What is the sum of the first one hundred even numbers? Answered by Penny Nom. 





A fish weighs 10 pounds more than half its weight. 
20020910 

From Rebecca: A fish weighs 10 pounds more than half its weight. How much does it weigh? Answered by Penny Nom. 





The factor theorem 
20020910 

From Yael: Prove (x  a  b) is a factor of x^{3}  a^{3}  b^{3}  3ab (a + b) Answered by Penny Nom. 





How do start from 2700 and get 35% back out? 
20020909 

From Dennis: 2000 x 0.35 = 700 + 2000 = 2700 How do start from 2700 and get 35% back out? If I have 2700, how do I figure out that 35% of 2000 is 700 and adding the two them together will get me 2700? Answered by Penny Nom. 





A linear function 
20020909 

From Chad: If y = 9x  13 does it represent a linear function? And if it does what is its slope and is it a direct variation? Answered by Peny Nom. 





The community garden 
20020908 

From Michele: Bryce, Duanne, Juliana and Sonya share a 40ft by 48 ft rectangular portion of the community garden in the neighborhood. With this space each has their own rectangular garden plot. Bryce is the only one with a square plot. its are is 1/2 the area of Duanne's The area of Bryce's plot is 2/3 the area of Julianna's plot. Their plots have one side in common. Sonya's garden has an area twice that of Julianna's garden. What are the dimensions of each person's garden plot? Answered by Leeanne Boehm. 





Algebra 
20020908 

From Heather: This question is from an 8th grade Algebra classs. I am a parent asking for help to explain to my child. Q: d=25t^{2}. Answered by Leeanne Boehm. 





Mean, median and mode 
20020908 

From Ramona:
 How do you calculate the mean, median, and mode?
 what are each of their definitions?
Answered by Leeanne Boehm. 





Weighing pumpkins 
20020908 

From Jennifer: Suppose five pumpkins are weighed two at a time in all possible ways. The weights in pounds are recorded as 16, 18, 19, 20, 21, 22, 23, 24, 26, and 27. How much does each individual pumpkin weigh. NO FRACTIONS! Answered by Penny Nom. 





The area of a triangle 
20020907 

From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom. 





Sanding a wooden block 
20020907 

From Wanda: If a wooden block, 2in height, 3in width, and 6in length is sanded and 1/8 of an inch is removed from the top and from the bottom, how much is the volume of the block decreased? Answered by Penny Nom. 





Subsets of the Real Number System 
20020907 

From Christine: In looking for a French equivalent of the word "integer", I found that the word seems not to actually exist in French, and that Canadian schools use the term "natural number" to describe what we have been trained to call "whole numbers," while using the term "whole number" to describe what we have been trained to call "integers." Answered by Claude Tardif. 





Social security numbers 
20020906 

From Chris: How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 09 in multiple different spots. Answered by Penny Nom. 





I am a 3 digit number. 
20020906 

From Jasmine: I am a 3 digit number. My last digit is 3 times my first digit. My firat digit is twice my middle digit. What numbers am I? There are at least 2 correct answers? Answered by Paul Betts. 





8,27,64 . . . 
20020905 

From Mike: We have been trying with no luck all night to complete the following math pattern (next 3 entries) 8,27,64 . . . Any ideas?? Answered by Penny Nom. 





What really is pi? 
20020905 

From Rachel: what really is pi? 3.1444 Answered by Penny Nom. 





Dan is 4 inches taller than Mike. 
20020904 

From A parent: Dan is 4 inches taller than Mike. Together they are 8 feet 8 inches tall. How tall is each boy in feet and inches. Answered by Penny Nom. 





1/8 in decimal form 
20020904 

From A student: explain how you put 1/8 in a decimal form Answered by Penny Nom. 





Intercepts 
20020904 

From Tamara: Why is it that the x intercept the value of y is 0 and at the y intercept the value of x is 0? Answered by Leeanne Boehm. 





1, 2, 4, 8, 16, 32, etc. 
20020904 

From Ginger: I've been working with finding the nth term for a few weeks, and i can't seem to figure this one out! 1, 2, 4, 8, 16, 32, etc. Answered by Leeanne Boehm. 





Monthly rent 
20020904 

From Al: How do you figure monthly rent if the charge is 11.00 per sq. ft. and there are 1,000 sq. feet? Answered by Leeanne Boehm. 





A limit 
20020903 

From Circe:
Lim 3x^{ 3}+ax+a+3 /(x^{ 2}+x2), X>2 Answered by Penny Nom. 





Addends can be grouped differently but the sum does not change 
20020903 

From Jodia: I have been searching the web for over an hour & a half now for the answer to the following question: The _____ states that addends can be grouped differently but the sum does not change. Answered by Penny Nom. 





A schedule for a fantasy football league 
20020901 

From Steve: i am in a ten(10) team league, split evenly into two five team divisions. we play a thirteen(13) game schedule and would like to play each team in your own division twice, and each team in the other division once. according to my rudimentary mathematics that equals 13 games. a good schedule should look somthing like this: team 15 = division 1 team 610 = division 2 team 1 should play teams 25 twice and teams 610 once. Answered by Claude Tardif. 





A group of 9 
20020831 

From William: what is the mathmatical name for a group of nine like a group of 3 is called 'triplets' Answered by Penny Nom. 





Proof by induction 
20020831 

From Tabius: Use mathematical induction to prove that the following formulae are true for all positive integers: a) 1 + 3 + 5+...+(2n  1) = n^{ 2} b) 2^{ n} > n. Answered by Penny Nom. 





How many cubic feet are in a cubic mile? 
20020830 

From William: How many cubic feet are in a cubic mile? Answered by Penny Nom. 





A square of tiles 
20020830 

From Rosa: How do I go about finding a formula for the number of tiles I would need to add to an arbitrary square to get to the next sized square? Answered by Penny Nom. 





3810+12divided by4multiplied by 16 
20020830 

From Brenda: my math question is as follows: 3810+12divided by4multiplied by 16=? Answered by Penny Nom. 





< and > 
20020830 

From Kelsey: What is the origin of the greater (>) than and less (<) than signs? Answered by Harley Weston. 





A solution to an equation 
20020828 

From A student: How do you determine whether a pair of numbers is a solution for an equation? If you could identify the specifics steps I need to take to determine whether it is a solution or not would be appreciated! Thanks i.e. x4=0 Pairs of numbers as possible solutions (4,7) (3,4) (0,4). Answered by Penny Nom. 





Student to teacher ratio 
20020828 

From A student: central middle school has 2470 students and the ratio of students to teachers is 26:1 how many new teachers are needed to reduce this to 19:1? Answered by Penny Nom. 





Mixing gas and oil 
20020827 

From Sherry: how do I calculate the correct fuel ratio for a boat motor? 50:1 the oil containers only say how many ounces to add to 5 gallons of fuel to make a 50:1 ratio.(13 ounces to 5 gallons of fuel) I have a 20 gallon tank so what if I add 11.6 gallons of fuel, what formula would I apply to get the correct measurement of oil to add? Answered by Penny Nom. 





Common Denominator 
20020826 

From Slobodanka: What is a Common Denominator? Answered by Penny Nom. 





The tangent to a curve and the tangent of an angle 
20020826 

From A teacher: Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)? Answered by Chris Fisher. 





Divisibility of 5^{ 2002} 
20020825 

From Simon: I need to ask you a question if 5^{ 2002} and 3^{ 2002} are divisible by 26. Answered by Penny Nom. 





Express 5120 as a sum of consecutive numbers 
20020825 

From Todd: Express 5120 as a sum of more than 1 consecutive number. Answered by Leeanne Boehm. 





When does an inequality represent the area above the line? 
20020825 

From Tamara: How do you determine that an inequality represents the area above the line and when do you include the line in the solution? Answered by Penny Nom. 





Cubic yards of concrete 
20020824 

From Michael: if you have a 10" dia pipe 8' long how many cubic yards would it take to fill with concrete. how how would you go about figuring it out. and also if you would how many cubic feet, cubic inches in a cubic yard. i know you don't need to answer, seeing i am not in school, but would appreaciate it. Answered by Penny Nom. 





Sets and elements 
20020822 

From Dianne: I want to know why its okay to say that, for example, 6 is an element of the set of integers, but you get counted off for saying that the set of 6 is an element of the set of integers. How come? Answered by Judi McDonald. 





Gallons in a cylindrical tube 
20020821 

From Heidi: IF I HAVE A 12" DIA TUBE WITH 1/4" WALL AND 72" IN LENGTH HOW MANY GALLONS OF WATER WILL THIS HOLD Answered by Penny Nom. 





Parallelograms 
20020821 

From Moorthy: 11 parallel lines are intersected by another 9 parallel lines.Then how many parallelograms are formed? Answered by Walter Whiteley. 





The 20 kilometer walk 
20020820 

From A student: THE 1996 OLYMPIC GOLD METAL WINNER FOR THE 20 KILOMETER WALK WAS JEFERSON. HIS TIME WAS 1HOUR, 20 MIN,AND 7SECONDS. HIS TIME WAS NOT GOOD ENOUGH TO BEAT THE WINNER IN 1988 BY JOSEF. HIS TIME WAS 1 HOUR,19 MIN, 57 SECONDS. WHAT WAS THE WALKING RATE OF EACH PERSON? Answered by Penny Nom. 





Sole Mates Shoes 
20020819 

From Robert: Sole Mates Shoes has expenses of $9,592 per month. What must the store's total income be if it is to make a profit of 12%? Answered by Penny Nom. 





When is 1! + 2! + 3! + ... + x! a square? 
20020819 

From Sarathy: Solve : 1! + 2! + 3! + ... + x! = y^{ 2} How do i find the solutions ? Answered by Claude tardif. 





Combination locks 
20020817 

From John: How many combinations of three number codes can occur with a standard combination lock? The range of possible numbers is 039 which allows 40 different possible choices each turn of the dial. Each combination requires exactly three numbers (i.e. three turns of the dial). E.g. 35405. Allow for reuse of the same number three times e.g.101010. I don't think there is any preference shown for certain number combinations. Can you explain how the total is derived? Someone at the YMCA this week put this question to me and I gave an answer but I am not sure I am rightso I have come to you. Answered by Penny Nom. 





Volume of a sphere 
20020816 

From Rahul: How do i find the volume of a sphere without the knowledge of calculus? Answered by Walter Whiteley. 





Distance in 3space 
20020816 

From David: The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = 8.213, and z = 11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. Answered by Penny Nom. 





Probability 
20020816 

From Chris:
There are two possible outcomes for a random event, A and B. The probability of A being the outcome is 63%, and B 37%. What is the likelihood that B will be chosen twice, consecutively? Three times, ten? Answered by Andrei Volodin. 





Variable expressions 
20020815 

From Brittany: I am just learning variable expressions. My homework is to write a variable expression for each word phrase;
example :
the number of minutes in s seconds the cost of x cartons of juice at $.75 each And etc.
I don't understand it Answered by Penny Nom. 





A paper model of a cone 
20020814 

From Bruce: I have made a paper model of a cone, cut a sloping section, and removed the top. I have drawn the major and minor axis on the paper surface of the section. The major axis is not symmetrical about the minor axis. To me, this is not an ellipse. To me, an ellipse is a tubular section, because this gives a symmetrical major axis. What is your opinion? Answered by Walter Whiteley and Chris Fisher. 





The circumference of a 72 
20020814 

From Linda: What is the circumference of a 72" diameter circle? Answered by Penny Nom. 





Two equations 
20020726 

From Derek: 1. 3x + 2y = 4 2. 7x + 2y = 24 finding x and y. Answered by Penny Nom. 





Some inequalities 
20020725 

From A student:
1)5 <= 3X+1 < 1 2)4X2 < 6 OR X+2 > 9 Answered by Penny Nom. 





Musical Scales 
20020724 

From Terence: Given that there are 12 notes in a musical octave, what is the maximum number of musical scales possible within that octave, if each scale has a minimum of 5 notes and a maximum of 9 and we start all the scales from the same note? In case you don't know anything about music, a scale is a progression of notes where you start on a specific note and end on that same note an octave higher. There are twelve different notes between these two similar notes. Which notes you choose to play determine the sound of the scale. Anything less than five notes would not make for a very interesting scale. Anything more than nine and you would be playing almost 'every' note in the scale, not leaving much room for distinction in how you organize these notes. I assume you first have to figure out the maximum number of variations possible in a 5note scale (with 12 notes at your disposal). Then do the same for a 6note scale, then a 7note, then an 8note, and so on. Then add up the results. How to find this maximum number of variations for each scale size though is what I don't know. Answered by Leeanne Boehm. 





20 men dig 40 holes in 60 days 
20020724 

From Lindsey: 20 men dig 40 holes in 60 days. So, 10 men can dig 10 holes in how many days? Answered by Penny Nom. 





x + 5 + x, if x = 4 
20020723 

From Elisa: x + 5 + x, if x = 4 Answered by Leeanne Boehm. 





7th grade math lesson plans 
20020723 

From Peter: Where can I get samples of 7th grade math lesson plans and curriculum for the whole year? Answered by Leeanne Boehm. 





As much greater than 47 as it is less than 105 
20020723 

From Joe: To find the number in question you need to find the number exactly halfway between 47 and 105. Another way of thinking about the number that is halfway between two other numbers is as the average of the two numbers given. Answered by Leenaan Boehm. 





Domain of a function 
20020720 

From Andy: I'm having difficulty in finding the domain of 1/(x^{2} 2x + 4) one over x squared minus 2 x plus 4. Answered by Penny Nom. 





Percentage 
20020720 

From Sally: If 20% of 100 is 80, then why is the percentage difference between 80 and 100 25%. Answered by Penny Nom. 





Place six numbers around a triangle 
20020719 

From Monika: I need to place six numbers around a triangle, as such that one number is on each corner, and one number on each side making three numbers in one line, adding up to two hundred exactly. The number I have to use are, 40, 50, 60, 70, 80, 90. I have to use each one once, there for, each number cannot be repeated. Answered by Claude Tardif and Chris Fisher. 





Can you make up a word that adds up to 1000000? 
20020719 

From Adrie: My question is elementary and I am a student Please help me with the following conundrum, as it is driving me crazy.
'When the letters in the alphabet are given values from 1 to 26 for A to Z, can you make up a word that adds up to 1000000 ( one million )used as a multiplication?'
Like 'cat' would be 3*1*20 = 60 Answered by Claude Tardif. 





Order of operations 
20020718 

From Danna: I would like to know how to solve this type of problem; I already have the answer. Problem: 2 [5 (4 + 6)  2] = 96 Also, what do you call this type of problem? Thanks a lot. Answered by Penny Nom. 





Division by zero 
20020718 

From James: Why is division by zero undifined (i have to proof that division by zero is undifined) Answered by Chris Fisher. 





A rope around a post 
20020715 

From Nic: My daughter who is in the 10th grade asked me this ?, you have a pole 45 inches high, 22inches around. You have a rope 1/2 thick, how many feet of rope would you use to go from top bottom of pole to top. Answered by Penny Nom. 





A probability problem 
20020712 

From Yvonne: What is the probability of 38 people choosing the same five options, given a choice of 15? Perhaps you could just give me the formula with an explanation. I am an English teacher doing educctional research, but am stuck because I don't have the math experience to help me. Answered by Andrei Volodin. 





Two cubes 
20020712 

From Vanessa: The edges of a cube are 50% as long as the edges of another cube. What percent of the volume of the larger cube is the volume of the smaller cube? Answered by Peny Nom. 





Pigs in pens 
20020710 

From Shannon: A farmer has 21 pigs and 4 pens, he must put an odd number of pigs in each pen, how does he do it? Answered by Penny Nom and Chris Fisher. 





The Praxis II test 
20020709 

From A student: I am taking the Praxis II test and I can't seem to answer certain styles of questions. Please help!!!!!!  In a class of 29 children, each of 20 children has a dog and each of 15 has a cat. How many of the children have both a dog and a cat?
 If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the number of people at the show? a. 102 b. 80 c. 36 d. 30
 In order to estimate the population of snails in a certain woodland, a biologist captured and marked 84 snails there were then released back into the woodland. Fifteen days later the biologist captured 90 snails from the woodland, 12 of which bore the markings of the previously captured snails. If all of the marked snails were still active in the woodland when the second group of snails were captured, what should the biologist estimate the snail population to be based on the probabilities suggested by this experiment? a. 630 b. 1,010 c. 1040 d. 1080.
Answered by Paul Betts. 





A polygon inscribed within an ellipse  Part 2 
20020708 

From Steven: I recently sought your advice about a problem that I have been working on for eight years or so concerning a polygon inscribed within an ellipse. I think that I may have confused matters by the way in which I put the question and hope that the enclosed diagram will clear matters up. In the ellipse below I have drawn three chords inscribed within one quadrant ( this would pertain to a twelve sided figure within the whole ellipse). These chords are exactly the same length as each other, for example if the major axis of the ellipse was 360 and the minor axis 240 I have worked out that a twelve sided figure would have sides of 78.2487. However I worked this out empirically with a method that could only be described as gruelling I would be most grateful if you could tell me of a method that would work for any ellipse and any number of sides. Answered by Chris Fisher. 





The base 10 multipliction table 
20020707 

From A student: These are two questions from Math for Elementary Teachers and they have me stumped. You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins? The product of the diagonals of any 2x2 matrix in the base 10 multiplication table are equal. Why? Answered by Penny Nom. 





A box that holds 22.4 liters 
20020707 

From Jon: How do I find the measurements required to make a box that holds 22.4 liters of something? Answered by Penny Nom. 





Equivalence relations on a set of cardinality n 
20020706 

From Siddhartha: what is the no. of equivalence and transitive relations on a set of cardinality n? Answered by Penny Nom. 





An equalateral polygon inscribed within an ellipse 
20020630 

From Steven: How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse? I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero? Answered by Chris Fisher. 





Math test 
20020628 

From Dustin: I have a really important placement test to take in 2 weeks. I need to have a strong comprehension of algebra and I have't taken a math class in about for years. I'm 24 and am going back to school. I want to get ahead and into math 96, and must pass this test to do that. Do you know of a book or a wab site that can teach me a few formulas that will give me the edge I need. If I have the right text for the job i'll study day and night to pass. Answered by Leeanne Boehm. 





Future value 
20020627 

From Susan: If one were to invest $115 a month for 20 years and expect a 4% annual return, what is the value of this money in 20 years? Answered by Leeanne Boehm. 





What is the next term? 
20020621 

From A student: What is the next term in the sequence: 1, 5, 14, 30..... Answered by Penny Nom. 





Counting 
20020621 

From Rachel: How many different numbers of 2 different digits each can be formed using the digits (1,3,5,7,9)?
How many triangles are formed by the vertical of a regular hexagon? Answered by Penny Nom. 





Jack and Jill wrote letters 
20020619 

From Angel: jack and jill each bought a stationary # of sheets of paper in each box were the same # of envelopes were the same jill wrote letters consisting of 3 pages jack wrote letters consisting of 1 page
when they wrote all letters jill had 50 envelopes left and jack had 50 sheets of paper left how many pieces of paper and how many envelopes? Answered by Leeanne Boehm. 





Integrating x^x 
20020618 

From Jeremy: I am a student at the University of Kansas and I am wondering if there is a general antiderivative for x^{ x} (i.e. the integral of x^{ x} dx)? I've looked in a bunch of Table of Integrals and have found nothing (can you guys find it?), so I'm sort of wondering if this may be a research type question. Answered by Claude Tardif. 





A good rule of thumb when driving 
20020613 

From Lisa: A good rule of thumb when driving is that you should be about one car length away from the car in front of you for every 10 miles per hour that you are travelling. Suppose you follow this rule perfectly (so you are exactly the correct distance away). You are waiting at a stop light with your front bumper just touching the car in front of you. The light turns green and the car in front accelerates at a constant rate "r". Calculate how you should accelerate in order to follow the rule. Answered by Penny Nom. 





The cross country team 
20020612 

From Denae: In cross country, a team's score is the sum of the first five finishers on the team. The captain of the team finished 2nd in the meet. The next four finishers on the team placed in consecutive order. The team score was 40. in what places did the other members finish? Answered by Penny Nom. 





An equilateral triangle 
20020611 

From Sarah: Hi. My name is Sarah. I'm a secondary student taking a Math 30C course by correspondence. The question has two parts.
The first part is: Draw an equilateral triangle XYZ. Draw the altitude from X to YZ. Choose any point P inside the triangle or on the triangle. Draw perpendiculars from P to the sides of the triangle. The Second part is:
Measure the altitude h and the 3 perpendiculars s, t, and u to the nearest mm. Repeat as many time as is necessary until you can state a generalization concerning h, s, t, and u. If you could help me, it would be greatly appreciated. Answered by Penny Nom. 





Drawing cards 
20020611 

From Ed: What is the probability of drawing without replacement from a standard deck of 52 cards the following 5 card hand ...... the ace of spades, 2 tens and 2 face cards Solution 1: ^{1}/_{52} x ^{4}/_{51} x ^{3}/_{50} x ^{12}/_{49} x ^{11}/_{48} Solution 2: Using Combination theory ..... (1C1 x 4C2 x 12C2) divided by (52C5) Can you help us understand which answer is correct and why the other is not? Answered by Penny Nom. 





Successive coefficients in the nth row of Pascal's Triangle 
20020610 

From Tim: There is a formula connecting any (k+1) successive coefficients in the nth row of Pascal's Triangle with a coefficient in the (n+k)th row. find this formula. Answered by Penny Nom. 





0.63 of an acre 
20020608 

From Sherry: how many square feet are in 0.63 of an acre Answered by Penny Nom. 





Regular polyhedra 
20020607 

From Sandra: The other day a colleague and I were talking about polyhedra. Is regular a term applied to polyhedra or just polygons? If so, then what would define a regular polyhedron? Would it mean all faces are regular or would it mean that all faces are identical and regular? That is, could a pyramid with equilateral triangles for lateral faces and a square base be considered regular or must the base also be an equilateral triangle? Answered by Chris Fisher. 





The mean distance travelled 
20020607 

From A student: If Rosalia travels 1000 km Sheree travels 280 km Daniel travels 50 km Mica travels 200 km Connor travels 500 km Eric travels 250 km Hillary travels 300 km What was the mean distance travelled? How do you arrive at the answer? Answered by Penny Nom. 





Constructing the square root of 3 
20020607 

From Allan: I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge. Answered by Penny Nom. 





Perimeter 
20020605 

From Tava: I'm a grade four student from St. Mary school. In class we've been dicussing perimeters. So this is what we did; First we each got a piece of paper in the shape of the geoboards and our teacher told us to find as many different shapes of area of 12 square units. During this time we were given to find perimeters of shapes that had twelve square units one of our classmates discovered the biggest perimeter possible with twelve square units of 26 units. Another classmate discovered the smallest perimeter of fourteen units. Here's a question: Why are all the shapes with fourteen units all the same shape? and why are all the shapes with twentysix units can be different? After we found the biggest and smallest shapes our teacher told us we each had to find at least one shape of the biggest and smallest. After we each foud a shape with a perimeter of twentysix and fourteen we had to find different shapes with different perimeters. During that time we discovered different perimeters. What we found was fourteen all the way up to twentysix, but they all went by two's. Why didn't they count up by 14, 15, 16, 17, 18 etc? I think it's because the area is an even number. See if you added one "block" or "square" to it you always add three because at least one of the sides is together with another side. Whyare all the perimeters all even numbers? Answered by Penny Nom. 





A polynomial 
20020605 

From Melissa: I'd like to know what is a polynomial( the definition and an explication)? And is 7x a polynomial? and why? Answered by Penny Nom. 





The area of a circle 
20020603 

From Jessica: I am doing a maths assigment for university, which is aimed towrds primary school students(k6). I was wondering if you could give me some information as to how I could describe to students the rule for finding the area of circle, using a circle cut up into equal sectors (like a pizza). I know it has something to do with the fact that you can make these shapes into a parallelogram, but I am a bit uncertain as to how I can express this idea clearly and articulately to students. Answered by Penny Nom. 





Ratios and weights on Neptune 
20020603 

From Janice: The ratio of an object's weight on earth to it's weight on Neptune is 5:7. How much would a person who weighs 150 pounds on earth weigh on Neptune. Answered by Penny Nom. 





Ounces and cubic centimeters 
20020530 

From Martin: How many ounces are in 600cc of liquid? Answered by Penny Nom. 





11........1 
20020529 

From Un eleve: Démontrer que tout nombre impair non multiple de 5 admet un multiple de la forme:11........1 Answered by Claude Tardif. 





Conics 
20020529 

From Brooke: Which conic cannot be generated by an intersection of a plane and a double napped cone? Answered by Chris Fisher. 





Overlapping circles 
20020529 

From Naman: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Answered by Harley Weston. 





The sum of the areas of two regular decagons 
20020527 

From A parent: The sum of the areas of two regular decagons is 39 square inches, and their radii are in the ratio of 2:3. Find the area of the larger decagon. Answered by Paul Betts. 





Linear programming 
20020527 

From Jes: A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of $8 on each Part I and $5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit? Answered by Claude Tardif. 





Cubic feet and cubic yards 
20020527 

From John: how do you find the cubic feet/cubic yard of area 10 feet wide by 15 ft long by 2 inches high Answered by Penny Nom. 





Onefourth of a number is added to onethird of the same number 
20020526 

From A student: When onefourth of a number is added to onethird of the same number, the result is 28. What is the number? Answered by Penny Nom. 





A spotlight shines on a wall 
20020525 

From Barb: A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight toward the bldg at a speed of 1.6 m/s, how fast is his shadow on the bldg decreasing when he is 4m from the bldg? Answered by Penny Nom. 





A schedule for 24 golfers 
20020525 

From John: I am working on a schedule for 24 golfers. 6 groups of 4. I have 8 golf days (twice per week for a month). Ideally, I would like to schedule all 24 golfers in 6 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible? Answered by Chris Fisher. 





 n + 4  +  3  2n  = 16 
20020524 

From Randall: I don't seem to be able to solve this:  n + 4  +  3  2n  = 16 Answered by Penny Nom. 





Blood donations 
20020523 

From Fiza: One particular high school encourages students to donate blood. the high school gym is set up for purpose. the distribution of blood type in north america is as follows.
Type O:44% Type B:10% Type A:42% Type AB:4% (a) what is the probability that the first two people in the line up have the same type of blood? ANSWER: I donn't know how many people are in the line. so how can I answer this question. (b) what us the probability thar none of the first five people in the line up have type AB blood? Answered by Andrei Volodin. 





3 radians subtends an arc of 27 meters 
20020522 

From Kyle: In circle O, a central angle of 3 radians intercepts an arc of 27 meters. Find the number of meters in the length of the radius. Answered by Penny Nom. 





Bob swam across a river 
20020522 

From Torri: Bob swam across a river 420 ft wide. A strong current carried him 580ft downstream as he swam. Find x, the distance bob actually swam. Answered by Penny Nom. 





Telephone banking 
20020522 

From Fiza: To use telephone banking to pay bills, the customer has to enter the last three digits of each bill. the numbers 0 to 9 can be used. if the number happened to be the same on more tan one bill, the customer has to enter the first three digits as well. (a) what is the probability that a person has 2 bills to register with the same last three digits? ANSWER:P(2 bills to register)=1/10P3 1/(10!/7!), 1/(10*9*8)=.001389 (b) what is the probability that a person with 10 bills to register has at least 2 bills with the same last three digits? ANSWER:P=1/(10*10*10) =0.001 Answered by Andrei Volodin. 





The average of two averages 
20020522 

From RJ: in a class with 22 students, the average garde on an exam was 68%, in another class with 32 students, the average grade on the same exam was 78%, what was the overall for the two classes? round your answers to the nearest whole number. Answered by Leeanne Boehm. 





Un octogone 
20020521 

From Yves: Si j'ai un octogone ayant 8 pieds de diamètre,comment fais t'on pour trouver la mesure de un de ces cotés et quel est cette grandeur. Answered by Claude Tardif. 





A popular television game show 
20020519 

From Amrita: On a popular television game show, contestant must first answer a question by placing 4 given events in ascending or desending order in the quickest time. (a) if a contestant does not know how any of the events should be arranged, how many different ways could the question be answered?
Answer: 4!= 24 (b)a contestant has to arrange the events that correspond to A, B, C, and D. one contestant is positive that event D follows directly after avent B, but does not know about the other s. how many different ways could this contestant arrange the letters A, B, C, and D, list the possibility
Answer: which I didn't get Answered by Penny Nom. 





Probability and investment 
20020519 

From Bally: Investors do not invest all their money in the investment predicted to be the best beuause it is too risky. an investor holds shares in three independent cmpanies. company A, Company B, compnay C. an analyst predicts the probability of profit increases for each company as follows. Company A:0.70 Compamy B:0.50 Compnay C:0.65 (a) If the analyst's predictions are true, what is the probability that all three comapanies show a profit incresse?
ANSWER: I try using vin diagram but it did'nt work, I dont know any other ways to solve this question (b) if the analyst's predictions are true, what is the probability that at least one comany shows a profit increase? Answered by Andrei Volodin. 





Conditional probability 
20020519 

From Manny: In a certain school, it is known that 80% of the students use the internet for school projects, 60% use email on a regular basis, and 90% use the internet for school projects or for email on a regular basis. a student from this school is selected at random Determine thge probability that the student used email, given that the student used the internet for school projects. ANS: how can i solve this question by useing the vin diaagram Answered by Andrei Volodin. 





Flying with the wind 
20020519 

From SaraJean: It takes 6 hours for a plane to travel 720 km with a tail wind and 8 hours to make the return trip with a head wind. Find the air speed of the plane and the speed of the wind current. Answered by Penny Nom. 





How far apart are the transmitters? 
20020518 

From Jeff: A ship at sea is 70 miles from one transmitter and 130 miles from another. The measurement of the angle between the signals is 130 degrees. How far apart are the transmitters? Answered by Penny Nom. 





Find the angle measures 
20020518 

From Amanda: In triangle ABC; the measure of angle A is 20 degrees more than twice the angle B. The measure of angle C Is five times angle B. Find the angle measures. Answered by Penny Nom. 





Chord length 
20020517 

From Ashlie: How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! Answered by Penny Nom. 





On which assignment did I do better 
20020517 

From Denise: I have 2 writing assignments in class. The first assignment, which had a mean of 10 and a standard deviation of 2, I got a score of 12. The second assignment had a mean of 18 and an s.d. of 3, I got a 21. I need to know which assignment did I do better, relative to my classmates? Answered by Andrei Volodin. 





Sequences that agree on their first four terms 
20020516 

From Mike: Are there two formulas that define sequences that agree on their first four terms, but differ on the fifth term and all succeeding terms? Answered by Chris Fisher. 





Thank you gifts 
20020515 

From Navi: Children usually attend birthday parties where a thank you gift is given to the children who attent the party. a family likes to hand out books at thankyou gifts. (a) One child invited to the party is given 2 books as gift. if there was 15 different books to choose from, how many diffrent gifts were possible? Answeer: I did this way 15C2=105
(b) if the 15 books consisted of 8 nonfiction and 7 fiction, how many diffrent gifts were possible if at least 1 of 2 books were fiction? Answered by Penny Nom. 





Day care 
20020513 

From Sonam: In many familes, both parents work. as a result, there is increasing need for day care. data was collected; and in one year in Canada, approximately 32% of children aged 0 to 11 years were in day care for at least 20h per week. (a) what is the probability, in a random poll of 60 children form the age of 0 to 11, that more than 15 children are in day care at least 20 h per week? nearest tenth of one %
ANSWER: P(children are in daycare at least 20h)= 60/60C14 = to the answer (b) what is the probability, in a random pool of 60 children that fewer than 20 are in day care at least 20 h per week?
ANSWER: P= 20/60= 33.3% stay in day care for 20h per week, I dont know if these answers are right please help me out. Answered by Andrei Volodin. 





What is Calculus About? 
20020513 

From A student: I am a high school senior and have to write an essay answering the question "What is Calculus?" I need some ideas. Thanks Answered by Walter Whiteley. 





A game of dice 
20020513 

From Mika: To play a game a dice is rolled to see who plays first. four players are going to play the game. what is the probability that at least two people roll the same number? ANSWER: P(least 2 people roll the same #)=number of player/total outcome P = 4!/4C2 = 24/4C2 = 4 the answer is 40% Answered by Andrei Volodin. 





An award ceremony 
20020513 

From Mika: Five students are equally qualifide their school at an award ceremony. two students will be randomly chosen to go to the ceremony.
(a) if Tony is one of the five student, what is the probability that he will be chosen? Ans: 2/5C2=0.2 which is 20% (b)Tony's friend, Allecia, who was also eligible to go, has been chosen. what is the Tony's probability of being chosen after he learns that allecica is going: Ans: 1/5C1=0.2 I think the answes are wrong please help me with these questions Answered by Andrei Volodin. 





Some algebra 
20020511 

From A student:
/x  2 ^4/x = 8
/ = square root sign ^ = 4th root of x
also, dividing 2x3 3 6x __________ 4 + 2x
the 2x3 is 2x to the third Answered by Penny Nom. 





A ski trip 
20020510 

From Navi: A ski trip at the school has been arranged. there are 30 students that have paid for the trip and 6 parents that have volunteered to chaperone. to transport the students and parents easily, they are to be divided into two group. one group has 10 students and 2 parents, and the other group has 20 students and 4 parents. (a) How many different group of 10 students can be formed? ANSWER:
(b) How many different groups consistinmg of 10 students and 2 parents are possible? ANSWER:
(c) kelly is one of the students going on the ski trip, and kelly's mother volunteered to be one of the chaperones. kelly's mother would prefer to be in the smaller group and not in the same group as kelly. if this wish is honoured, how many ways can the smaller group and its chaperones be chosen? ANSWER: Answered by Harley Weston. 





The law of cosines and obtuse angles 
20020509 

From Bryant: The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle. Answered by Penny Nom. 





A rectangular marquee 
20020507 

From Alyaa: a marquee with rectangular sides on a square base with a flat roof is to be constructed from 250 meters square of canvas. find the maximum volume of the marquee. i find this topic so hard Answered by Harley Weston. 





Forming a committee 
20020506 

From Navi: A committee is to be formed to investigate what activites teenagers have available in small communities. the committee is to have 7 members, chosen randomly form interested community members. there are 10 parents, 5 teenagers, and 4 adult without children who have all expressed an interest in serving on the committee. what is the probability that the adults without children are all on the committee? Answered by Andrei Volodin and Penny Nom. 





Oven lights 
20020506 

From Manny: Q.A manufacturer of stoves has to buy oven lights from from two diffrent companies because one company alone cannot meet its demand. the manufacturer purchases 60% of the oven lighs from comany A and the rest form Company B. Past experiecnce shown that 1% of Company A's oven are defective oven and 2.5% of Company B's oven light are defective. Determine the probability that a defective oven light is supplied by company A. Answered by Andrei Volodin. 





How will I use calculus in my career? 
20020506 

From Meridith: How will I, hopefully a future secondary mathematics teacher, use calculus in my career if I'm not teaching calculus? Answered by Walter Whiteley. 





3 = 2x 
20020505 

From Timothy: My question is 3 = 2x How do I isolate the variable here? Answered by Penny Nom. 





A probability tree 
20020504 

From A student: Karl and Naomi roll three dice. Karl gives $10 to Naomi if the number 5 turns up once, twice or three times. Naomi gives Karl $3 in all other cases. A) construct the probability tree for this situation.
B) Does Karl have an advantage in this game? Justify your answer. My problem is I am unfamiliar on how to draw this probability tree and seem to be having a lot of difficulties, when you have a chance please answer this math problem and get back to me with the results. Answered by Penny Nom. 





An identity(?) 
20020502 

From A student: prove identity sin^{ 2}x/1sinx= secx+1/secx
Answered by Paul Betts. 





8/13*26/27 
20020501 

From Arias: 8/13*26/27= Answered by Penny Nom. 





Square numbers 
20020501 

From Sally: Is one considered a square number? Answered by Penny Nom. 





oneths 
20020430 

From Logan: why are there tenstenths hundredshudreths, but not oneths if that made no sense then how about this why does everything have two ways of saying things like tens and tenths but not a oneths Answered by Claude Tardif. 





Factor 12x^2  20x  8 
20020430 

From Crystal: Factor Completely: 12x^{2}  20x  8 Answered by Penny Nom. 





The Dugout, Don's Basement, Cd Corner,... 
20020430 

From A student: The Dugout, Don's Basement, Cd Corner, Harry's Deli, Bill's Software, Anne's Footwear, and Joanne's House cleaning. The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and mode are both $70. The certificate from The Dugout is worth the most and the one from Joanne House cleaning is worth the least. The total value of the gift certificates from CD Corner, Harry's Deli, and Anne's Footwear is $270, but Anne's Footwear certificate is worth $50 more than the one from Harry's Deli. The Cd Corner gift certificate is equivalent to the mean for this group of three. What is the value of the gift certificates from each store? Answered by Penny Nom. 





What's the next term? 
20020429 

From A student: Find the nth term for the following: 1) 12, 30, 56, 90, 132 2) 6, 30, 84, 180, 330 3) 8, 15, 24, 35, 48 4) 10, 17, 26, 37, 50 5) 24, 40, 60, 84, 112 6) 24, 60, 120, 336, 504
Please show the FULL working out. Answered by Penny Nom. 





Trains and cracker boxes 
20020429 

From Lindsay: 1)Two trains are 250 miles apart on the same track heading towards eaxh other at 7AM The first train travels at 55mph, the second at 75mph. At what time would they crash? 2)A cracker box measures 12 by 2 by 18 inches. The company wants to double the amount of crackers, but keep the shapes the same[similar] Find the new length[nearest tenth of an inch] Answered by Penny Nom. 





Conversion of units 
20020429 

From Matt: I am having trouble finding a workable equation for the following problem, particularly the conversion of two systems of measurement. The question states that there are 27 grams of salt in a kilogram of seawater. And it asks how many tonnes (1 tonne = 1000 kilograms) of salt are there in one cubic kilometer of ocean. It also says that the density of seawater is 1.1 g/cm3. What is the equation and how do I figure out how many kilograms there are in a cubic kilometre? Answered by Harley Weston. 





A 6,000 gallon tank 
20020428 

From Someone with a big tank: I was wondering if you can find out information about how much liquid fuel can fit in a 6,000 GAL. tank. Right now I do not have the exact dimensions of this tank but I will have it the 29th of April. Could you please Email me and let me know if you can answer this question after I have the correct specifications. Answered by Penny Nom. 





0/4 = ? 
20020428 

From Danielle: I am embarrased to be asking this question, but... is it possible to have a fraction with a zero? For example, 0/4. This does not make sense to me and I do not know what it would be representing, other than nothing! Is it proper to express such a fraction? Answered by Peny Nom. 





A triangular prism 
20020428 

From A student: Need the formula for the surface area of a triangular prisim? Answered by Penny Nom. 





a+b=10 and ab=40 
20020427 

From April: What two numbers add to ten and multiply to forty? (a+b=10, a*b=40) I think the answer includes radicals and/or imaginary numbers. Answered by Penny Nom. 





Designing a ballot 
20020426 

From Kelley: I want to design a ballot for four elections. Actually all the candidate races are on 1 ballot. I need to know how many different ballot styles would be needed for all of the candidates to be in each rotation an equal number of times. For example:  A,B,C & D are running for mayor
 E,F,G & H are running for congress
 I,J & K are running for senate
 L,M & N are running for governor
They are all on the same ballot. But in each race their name (for instance A) has to be in the #1 rotation, #2 rotation, #3 rotation, and #4 rotation for his race on this ballot an equal number of times as B,C and D. The same goes for the other candidates for their perspective races. How many total ballot styles will there be? Answered by Penny Nom. 





Triangular numbers 
20020426 

From Anika: Can you please tell me what a triangular number is? Answered by Penny Nom. 





Functions and relations 
20020425 

From Erin: Here's a few math problems that might drive a person insane ;)  If 2f(x)  3f(1/x) = x^2 what is f(2)?
 What are the domain and range of the following relations?
 x^2  4y^2 = 25
 4x^2 + 9y^2 = 36
 The port of Swan Harbor is 200km away from Merry Town Inlet on a bearing of N50E from Merry Town. A ship leaves Merry Town at 8am and sails N15W at 15 km/h. At the same time, a second ship leaves Swan Harbour on a course of S80W at 20km/hour. How close, to the nearest km, are the two ships at 13:00?
 Prove the identity. 1+sinx + cosx/ 1sinx + cosx = 1+sinx / cosx
Answered by Penny Nom. 





How much of that total is G.S.T? 
20020424 

From Darlene: If I have $1700.00 how much of that total is G.S.T? not 1700.00 + gst ____ + _____ gst = 1700.00 Answered by Patrick Maidorn. 





Arithmetic progressions 
20020424 

From David: I have been searching everywhere for the formula to mathamatical progression. Answered by Penny Nom. 





An Olympiad problem 
20020423 

From Aurora: I wrote a mathematical Olympiad the other day and there was one question that I could not work out. The question was If ab = 1, bc =2, cd =3, de =4 and ea = 6, what does a + b + c + d +e = It was a multiple choice and the answers were : 43/6; 47/6; 49/6; 53/6; 61/6 The correct answer was 61/6, but how can do you get to that answer? Answered by Anrei Volodin. 





A test drive 
20020423 

From Jennie: At 9 A.M. a test car driving at a constant speed passes a marker 50 miles from it's starting point. At noon the car is about 130 miles from the marker. If the test drive ends at 1:30 P.M., how far will the car be from its starting point? Answered by Penny Nom. 





25m = 100 
20020422 

From Megan: If 25m = 100, Then m equals what number? Answered by Penny Nom. 





Lines of symmetry 
20020422 

From Cindie: How many lines of symmetry do the following figures contain? trapezoid: rhombus: hexagon: pentagon: Answered by Walter Whiteley. 





Problem solving 
20020420 

From Kathy:
 Zachary wanted to run the shoreto shore marathon next month, a 26 mile race from one side of the island where he lived to the other. He decided to work up to 26 miles by running five days a week for the next five weeks. Each day he'd run one mile longer than he did the day before, except for the first day of the week, when he'd run the same number of miles he ran on the last day of the previous week. He wanted his last two practice runs to be 26 and 27 miles long.
How many miles would he have to run on his first practice run?
 A school just bought a new set of encyclopedias. The front and back covers are 1/8 inch thick, and the pages are 1/100 inch thick (in other words, there are 100 pages per inch). the 26 volume set has a total of 5,250 pages. If you assume there is no extra space left between books, then .........
What length of bookshelf will the encyclopedias take up? Answered by Penny Nom. 





Solve for x 
20020420 

From A student: solve for x. cx 2x+b  =  a c Answered by Peny Nom. 





Cubic yards 
20020420 

From Pat: I HAVE AN AREA 10'x6'I WOULD LIKE TO PUT LOAM ON IT 5" DEEP HOW MANY CUBIC YARDS OF LOAM DO I NEED? Answered by Harley Weston. 





An augmented matrix 
20020420 

From A student: Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is a+2b+c=0 2a+5b+4c=1 ab9c=5 Answered by Penny Nom. 





Solving for x 
20020419 

From Susan: I'm having a little trouble solving these equations for x. I can't seem to separate x fully from the other numbers. Please help! Here are the problems: (2x1)/(x2)(x^{ 2}+3) = 0 and y/(x+1)=z/x Answered by Penny Nom. 





Moving a triangle 
20020418 

From A student: find the verticles of a triangle after it is translated 2 units to the left and then is reflected across the graph of y=x+2. The original verticles of the triangle are (2,0), (3,2), and (6,2). Answered by Peny Nom. 





How many different account numbers are possible? 
20020418 

From Andrene: how many different account numbers are possible if the account numbers consist of a letter of the alphabet, followed by five numerical digits, and followed by another letter. Answered by Penny Nom. 





Arc length 
20020417 

From Vix: Find the point on the curve r(t)=(12sint)i(12cost)j+5tk at a distance 13pi units along the curve from the point (0,12,0) when t=0 in the direction opposite to the direction of increasing arc length. Answered by Harley Weston. 





Ratios 
20020417 

From A student:
 Medication is givin at 1cc. per 20 pounds of body weight. A dog weighs 16 pounds how many ccs. of medication does the dog get?
 Dr. Lee wants you to prepare 1000 ml. of a 10% dextrose solution in lactaed ringers for diuresis or a patient you have a 1 L bag of lactated ringers and 500 ml of 50% dextrose for injection. How would you prpare the solution?
Answered by Penny Nom. 





Related rates 
20020417 

From Molly: A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared? Answered by Penny Nom. 





Two algebra problems 
20020414 

From Ashley: Question 1: For all values of a, let < a > be defined as < a > = 4a  4 . Which of the following equals < 6 >  < 5 >? A: < 2 > B: < 3 > C: < 4 > D: < 5 > E: < 6 > Question 2: If 5n + p = 3 and 2m  10n = 2, what is the value of m + p? Answered by Penny Nom. 





A polynomial 
20020414 

From A student: A polynomial function is described by the following conditions: f(x) has two real zeros at x= 2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a yintercept at (0,2) Sketch a polynomial function that satisfies the above conditions. Write an equation for function f(x) Write another function g(x) that also satisfies the above parameters. Answered by Penny Nom. 





How many gallons of water in a cubic foot? 
20020414 

From Richard: I am tring to find out how many gallons of water in a cubic foot. Answered by Penny Nom. 





The vertex of a cone 
20020413 

From Callie: Does a cone have a vertex? Answered by Penny Nom. 





The square root of four 
20020413 

From Frank: In a recent quiz we where asked the square root of four. The quizmaster gave the answer as not only 2 but also 2. Being pedantic I queried this. Although 2 squared is 4, does it follow that the root of 4 is 2 Can you enlighten us? Answered by Claude Tardif and Penny Nom. 





The bleep test 
20020413 

From Lorraine: I am currently undergoing training and have asked about a fitness test called the bleep test. The bleep test involves running continuously between two points that are 20m apart. These runs are done in time to a prerecorded bleep sounds on a prerecorded audio cassette. The time between the recorded bleeps decrease after each minute. I would like to do my own personal version for training but I have to work out the following before doing this: I need to find out the time inbetween the beeps at least for the first level so I can work out the difference for the other levels: The information given to me for the first level is : A 20 meter run at 8.5km/hr (how long would it take?) Please let me know if there is any way in working out this query with the information given. Answered by Leeanne Boehm. 





Calculate profit 
20020413 

From Allison: If I sell something for $75; and my cost is $40, I make $35 profit. How do I calculate the profit percent I made on that transaction? Answered by Penny Nom. 





Diagonals in a polygon 
20020410 

From Murray: If you have a regular polygon with n sides and you draw all (n3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into. Answered by Caude Tardif and Chris Fisher. 





n +1, n+2, n+3, and n+4 are all composite 
20020409 

From Jonathan: Find the small integer n such that n +1, n+2, n+3, and n+4 are all composite Answered by Penny Nom. 





The Proof in the Pudding 
20020409 

From A student: The host at a party turned to a guest and said, "I have three daughters and I will tell you how old they are. The product of their ages is 72. The sum of their ages is my house number. How old is each?" The guest rushed to the door, looked at the house number, and informed the host that he needed more information. The host then added, "The oldest likes strawberry pudding." The guest then announced the ages of the three girls. What are the ages of the three daughters? Answered by Claude Tardif. 





Sodding the yard 
20020408 

From Craig: my parents want to lay sod in our back yard. the sod cost $2.00 per square foot. The size of our yard is 20x20 and 26x41 Answered by Penny Nom. 





Area of a triangle 
20020407 

From Puzzled: What is the surface area of a triangle 13 ft x 13 ft x 18 ft? Answered by Penny Nom. 





3/4n6=12 
20020407 

From Diane: I am in 6th grade advanced math and I just started Algebra. My teacher tries to explain it to me but I just can't get it. I am having difficulty understanding it. Please HELP!!! I will type a problem, if you could answer it and show your work so i can understand it that would be great. Please explain in simple terms. here is a couple problems I am having trouble with, PROBLEM #1 3/4n6=12 Answered by Penny Nom. 





Composition of functions 
20020406 

From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = x^{2}  4 and g(x) = sqrt(x) The range of f(x), x<=4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(x^{2}  4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? Answered by Claude Tardif. 





Pairs of equations 
20020404 

From A student:
high school level student is asking
y=4x x=4y
x+y=5 3x+2y=20
y=x1 3xy=4
x+y=3 2x3y=9
x+5y=4
3x+15y=1
. . .
Answered by Penny Nom. 





Two triangles 
20020403 

From Scott: Consider 2 triangles: Triangle PMB and Triangle PLA. Triangle PLA is contained within Triangle PMB. Side LA is parallel to Side MB. Point L is located on Side PM. Point A is located on Side PB. If the ratio PL:LM = 5, then what is PB:PA ?? Answered by harley Weston. 





Take It! 
20020403 

From Bryan: You are playing Take It! for $180,00 with a total stranger. There are 180 identical balls in a big vase. Each player in his turn, reaches into the vase and pulls out 1,5,or8 balls. These balls are discarded. The player who takes the last ball from the vase wins the $180,000. A flip of the coin determines that you will go first. Are you glad? How many will you take out on the first move, and how will you proceed to win the prize? Answered by Claude Tardif. 





Common fractions to decimal fractions 
20020402 

From Natalie: My questions are: "how can I change 23/60 into a decimal. and give my answer to 2dp."?????????? 2nd question:for each of these pairs, which is bigger?
4/7 or 36%____________ 3/11or 0.29____________ 14/24 or 0.57___________ Answered by Penny Nom. 





Pascal's Triangle 
20020402 

From Brian: It's about (a+b)^{x}. I remember there a triangle with numbers to remember for a faster solution. Can you please teach me? Answered by Penny Nom. 





If you conect all the vertices of a regular ngon... 
20020401 

From Murray: If you conect all the vertices of a regular ngon with lines you will have (n3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other. Answered by Claude Tardif. 





Area of an octagon 
20020401 

From Someone: What is the actual square footage of a 12' octagon? Answered by Penny Nom. 





All four eights in three consecutive hands 
20020401 

From Blair: What are the odds against the same person holding all four eights in three consecutive hands. Answered by Brian Alspach. 





Meg's biscuits 
20020329 

From Tami: Meg's biscuits recipe calls for 4 cups of flour for every 1.5 cups of milk. If Meg uses 6 cups of flour, how many cups of milk will she need? Answered by Penny Nom. 





The reciprocal of a decimal mixed number 
20020329 

From A student: How do I find the reciprocal of a decimal mixed number? Answered by Penny Nom. 





Some 5 card hands 
20020328 

From A student: From a standard deck of cards how many 5 card hands are possible consisting of a. exactly 4 hearts
b. two cards of one kind and three of another(like a full house). Answered by Penny Nom. 





100 from four 9's 
20020327 

From A student: My teacher gave us a math problem to try and figure out and I am stumped. The problem was this.... by only using four nines, how can you get an answer of 100? You can add, subtract, multiply or divide...anything you need to do ,but you can only use four nines. Answered by Leeanne Boehm. 





If the matrix A is inverible and AB =AC, then B = C 
20020327 

From Vikki: i hope you can help i am soooo stuck here goes: a)
A= 0 1 B= 1 1 c= 2 5 0 2 3 4 3 4
A,B and c are matrices Evaluate AB and Ac (which I can do) then
b) I need to prove that if the matrix A is inverible and AB =AC, then B = C. Why does this not contradict what happened in part a)? Answered by Leeanne Boehm. 





Cube roots 
20020326 

From Kathy: My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without? Answered by Penny Nom. 





A triangle in a circle of radius 6 
20020326 

From Marko: In a circle of radius 6, a triangle PQR is drawn having QR = 8 and PQ = 10. Determine the length of PR Answered by Chris Fisher. 





A lottery question 
20020325 

From Noel: I want to take all numbers in a Lotto game from 1 to 45 and ditribute them between 9 boxes each containing 5 numbers. Each number is used only once.  What is the probability that I derive the correct combination of 5 numbers in the draw?
 What is the probability if I take a systems game and now distribute 9 numbers into each of 5 boxes? Once again, the numbers are used only once.
 Can you explain what formulae are used and how the answer is derived? Is this a distribution or combination problem? Or is it a combination of both distribution and combination?
Answered by Andrei Volodin and Penny Nom. 





Unit fractions 
20020323 

From Laura: Write 1/2 as the sum of ten different unit fractions. Answered by Claude Tardif. 





A hamburger and a soft drink 
20020323 

From A student: A GROUP OF FRIENDS WENT OUT TO LUNCH. EACH BROUGHT A HAMBURGER AND A SOFT DRINK. TOGETHER A HAMBURGER AND A SOFT DRINK COST MORE THAN A DOLLAR. THE TOTAL COST FOR THE GROUP WAS $17.81. THERE WAS NO TAX OR TIP INCLUDED. IF A HAMBUGER COSTS 2 CENT MORE THAN TWICE A SODA, FIND THE COST OF THE HAMBURGER. Answered by Leeanne Boehm. 





A probability problem 
20020323 

From Kate: If I have a spinner and then spinner has the numbers 1,2,3,4 on it and it is spun 3 times, what is the probability that the spinner will stop on 4,3,and 1 ? In that order? Answered by Leeanne Boehm. 





A trigonometric identity 
20020322 

From Debby: I am stuck on a problem and wondering if you can help?? It is: Prove the following: sec^{2}(X)+csc^{2}(X) = sec^{2}(X)csc^{2}(X) Answered by Harley Weston. 





Mr. Byrd's drive to work 
20020322 

From Mr. Bollen: Mr. Byrd leaves his house at 7:00am to go to work. If he drives 40 mph he will arrive 3 minutes late and if he drives 60mph he arrives 3 minutes early. At what speed will Mr. Byrd have to drive in order arrive exactly on time. Please describe how you arrived at your answer. Answered by Claude Tardif and Penny Nom. 





Range of values for standard deviation 
20020322 

From Susan: What is the range of values for standard deviation? Is it between 0 and +3? Is it between +1 and +3? Answered by Andrei Volodin. 





What fraction of the world's motor vehicles are built in Canada? 
20020320 

From A student: About 1/4 of the world's motor vehicles is built in Canada or the United States. About 1/5 of the world's motor vehicles are built in the United States. What fraction of the world's motor vehicles are built in Canada? Answered by Claude Tardif. 





Adding algebraic fractions 
20020320 

From Dolores: I get totally confused with this problem. I get confused with the getting the lowest terms. 4/x5 + 2/x 10/x^25x Answered by Penny Nom. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley. 





F = 3 + 3 
20020319 

From Jessica: F= 3 + 3 WHAT IS F????? Answered by Penny Nom. 





A set of points in space 
20020318 

From Victoria: Describe the given set with a single equation or a pair of equations: The set of points in space that lie 2 units from the point(0,0,1) and at the same time 2 units from the point (0,0,1). Answered by Penny Nom. 





24x^4 + 3x 
20020318 

From gary: 24x^{ 4} + 3x Answered by Penny Nom. 





Interest owing 
20020317 

From Dean: I am an investor. If I lend to someone on January 1, 1999, $1000 to be paid back interest at 2% per year (simple interest, ie not compounded), and on July 15, 1999, I lend the same person $1,500 more (total loan is now $2,500) but at 18%, and once again on October 15, 1999, I lend to the same person another $1,500, and the person pays me back the principle($4,000) and interest on January 1,2001: What is the total (principle plus interest) due me? The tougher question is: what was my blended rate of return on my total outlay of money? Is there a formula you can give me so that I can perform my own calculations? Answered by Harley Weston. 





Combinations? 
20020316 

From Sara: A combination lock has three dials numbered 0  9. Give a mathematical reason why "combination" is a bad name for this type of lock. Answered by Penny Nom and Chris Fisher. 





How much olive oil? 
20020315 

From Annie: Joe used 1/3 cup of olive oil, which was 3/4 of the amount that he had. How much olive oil did he have! Answered by Penny Nom. 





Testing a hypothesis 
20020314 

From A student: A large distriutor of cosmetics has kept his outstanding accounts receivable to a mean age of 18 days over the past year. This average is considered a standard by which to measure the efficiency of the credit and collections department. Management wishes to check if receivables in the current month is over standard and will do this at a significance level of 0.50. A random sample of 100 accounts yields an average of 20 days with a standard deviation of 9 days. what should management conclude? Answered by Andrei Volodin. 





The square root of i 
20020314 

From Arlene: what is the square root of i, if i=x+yi? what is the square root of 1i? i'm getting problems like these in which I do not understand. Answered by Harley Weston. 





3 5/8 and 2 1/4 
20020313 

From Shirley: 3 5/8 and 2 1/4 what is the percentage of 2 1/4 to 3 5/8. Answered by Penny Nom. 





15 miles at 13 miles per hour 
20020312 

From Rich: If I were traveling 15 miles at 13 miles per hour how long will it take? Answered by Penny Nom. 





My 1978 Chevy has a 350 cubic inch engine 
20020311 

From Sharon: If my 1978 Chevy has a 350 cubic inch engine, about what size engine would that be in liter? Answered by Penny Nom. 





x and yintercepts 
20020310 

From A student: I have the problem f(x)= ^{X5}/_{X2+X6} and I have to find the vertical asymtope, horizontal asymtope, xintercept, and yintercept. And graph the problem. I am having problems finding the yintercept. Answered by Harley Weston. 





The best time to teach math 
20020310 

From West: My name is West. I teach 4th grade. I would like to know if there is any research which tells about the best time to teach math. Should it be taught in the a.m. or p.m. Answered by Walter Whiteley. 





Multiplying decimals 
20020310 

From Kaitlin: I just recently had a test on multiplying decimals and I did not do really well on it. Only 5 kids out of 19 got a passing grade. My teacher says that she will give us a different test and we can take it again, but I'm still not sure of it. My teacher has taught me a lot and she had done a wonderful job of it but I'm just confused with where to put the decimals and stuff like that. I have a math practice workbook that I do for fun and they have nothing on decimals in it. I have checked on websites to try to find worksheets but I really couldn't find a good one. Can you please help me either give me some tips or clues or send me a worksheet. Answered by Penny Nom. 





The isosceles triangle of smallest area 
20020308 

From Lettie: can you find the isosceles triangle of smallest area that circumscribes a circle of radius of one? Answered by Walter Whiteley. 





Percentage difference 
20020308 

From Tedd: Can you give me the formulas for calculating percentage differences between two numbers? For example: if the first number is 10 and the second number is 15, then the second number is 50% larger than the first number. However, the formula to calculate that percentage won't work if the first number is greater than the second number as in the following example: The first number is 15 and the second number is 10, with the second number being 33.3% less than the first number. Or maybe I'm mistaken and the same formula will work in both situations. Answered by Penny Nom. 





Factor completely 
20020307 

From Taylor: I'm supposed to completely factor this but I don't know what to do with all the variables. a^{3}b^{5}  a^{2}b^{5}  12ab^{5}. Does it have anything to do with b^{5} being a common factor or am I completely off? Answered by Penny Nom. 





A sequence 
20020307 

From Caroline: hi, here is the problem,
1 11 21 1211 111221 _ _ 2_ _ _ we can't get the sequence of the last line ,with the 3rd number being 2,thanks Answered by Walter Whiteley. 





The square root of 2 
20020305 

From Roger: Does two (2) have a square root or do the numbers just keep going? Are there any other numbers that behave like two when it comes to extracting the square root? Answered by Penny Nom. 





A circular wading pool 
20020304 

From Patrick: The community of melfort is planning to build a circular wading pool in the park. The pool will cover an area of 1000m^{2}. The building committee has decided to put a 5m cement pad around it. How much additional area will the cement pad take up? Answered by Harley Weston. 





The slope of a tangent line 
20020304 

From Ridley: Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Answered by Harley Weston. 





Percentage 
20020303 

From Nathan: I have two questions:  25% of what number is 195?
 42 is what percent of 112?
Answered by Penny Nom. 





Mixed numbers, whole numbers and improper fractions which are less than 2. 
20020303 

From Dawn: Change each mixed number to a whole number and an improper fraction which is less than 2. 3 1/2 = 2 / Answered by Penny Nom. 





What number am I? 
20020303 

From Samantha: I am an even number that has more ones than tens. My thousands digit is the quotient of 9 divided by 3 and my tens digit is the sum of 3 and 3. I have no hundreds. What number am I?......Please answer this for me...The answer I come up with is 3,060...Is this right?.. Answered by Penny Nom. 





The median with ties 
20020227 

From Marcel: What, exactly, is the proper way to determine the median of a set of numbers when doubles or triples of a number are part of that set? Do the doubles count as two and the triples three, or does each count only as one toward determining the median. Answered by Harley Wston. 





Two circles inscribed in a rectangle 
20020227 

From Amina: Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle. Answered by Penny Nom. 





Simplify this expression 
20020226 

From Francine: 2X power 5 Y power 3 times 18 X power 5 Y power 3 divided by X power 1/3 Y power 1/4.
I came up with 36  X 1/3 Y 1/4 The book says 36 x1/3 y1/4. I don't get it. Answered by Penny Nom. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





The substitution method 
20020224 

From Joe: whats the answer to this question? 3x+y=11 x+2y=3 its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you Answered by Penny Nom. 





A hat of a different color 
20020224 

From Kirstin: A teacher made a deal with 3 of his students. He said that if you can guess what color hat you have on your head without looking, I will pass you. There were 2 red hats and 3 blue hats. The deal worked like this: The three students would close there eyes, and the teacher would put a hat on each of their heads and then hide the other 2. Then one at a time, the students would open their eyes and try to figure out what color hat was on their head. The student could guess or pass. This is what happened when they put their deal to the test: A boy named Arturo was first and opened his eyes but wasn't sure so he passed so he didn't get it wrong. Belicia was next and she passed too because she wasn't sure. Also she thought about the fact that Arturo didn't know. Carletta was last and without even opening her eyes, she knew for sure what color hat she was wearing and her answer was right. So i have to figure out what color hat she's wearing for sure. Answered by Claude Tardif. 





350 students took the math A exam 
20020222 

From Jim: at a high school 350 students took the math A exam. 82% passed the test. 40 students that failed the exam in june, took the exam in August. 70% of this group passed the August test. How many of the original 350 students have passed the exam before september? Answered by Paul Betts and Penny Nom. 





1,4,27,____,_____46656 
20020221 

From Brenda: 1,4,27,____,_____46656..... please find the fourth and fifth numbers in this sequence. Answered by Penny Nom. 





Alfredos house number 
20020221 

From Aunt Patty: Alfredos house number is between 20 and 35. The sum of the digits is less than 5. If you subtract 1 from it you would get a multiple of 3. If you add three, you get a multiple of 5. What is Alfredos house number. Answered by Penny Nom. 





Proof by induction 
20020220 

From Tamaswati: How do I prove the assertion that "the determinant of an upper triangular matrix is the product of the diagonal entries" by mathematical induction? (Before I check this assertion for a few values of n how do I rephrase the assertion slightly so that n appears explicitly in the assertion?) Answered by Penny Nom. 





An octagonshaped deck 
20020220 

From An instructor: How can you solve for finding the side measurements of an octagonshaped deck that is 10 feet long and 10 feet wide. Answered by Penny Nom. 





When will the calendar be the same as 2002? 
20020220 

From John: When will the calendar be the same as 2002? I know the answer is 2013, but I don't know how to answer this mathematically, or if it is possible to do so. This is a ninth grade level algebra question my daughter received from her teacher. Any ideas? Answered by Chris Fisher, Patrick Maidorn and Penny Nom. 





Shipping charges 
20020219 

From Sohail: A mail order company charges a fixed fee for shipping merchandise that weighs 1 pound or less, plus an additional fee for each pound over 1 pound. If there shipping charge for 5 pounds is $4.80, and for 12 pounds is $6.20, find the fixed fee and the additional fee. Answered by Penny Nom. 





A farmer takes 100 animals to the market to sell. 
20020219 

From Ann: A farmer takes 100 animals to the market to sell. All are sold and $100 is earned. The prices were $5.00 per cow, $1.00 per sheep and $.05 per pig. At least one of each kind of animal was sold. How many of each kind of animal did the farmer take to market? Answered by Penny Nom. 





Sampling distributions 
20020218 

From A student:
 given: n = 40, standard deviation is not known, population of individual observations not normal. does the central limit theorem apply in this case? why or why not?
 for an estimation problem, list two ways of reducing the magnitude of sampling error?
 What will happen to the magnitude of sampling error if the confidence level is raised all other things remaining the same? justify your answer?
Answered by Harley Weston. 





Double square roots 
20020217 

From Ali: i have a question about how to do double square roots with variables and powers. example : v/"" v/"" 81y^{8} Answered by Harley Weston. 





A degree 5 polynomial 
20020217 

From Carla: Write an equation for a polynomial of degree 5 given the following zeros: 7+3i, 2+sqrt(13), 6 Answered by Penny Nom. 





Can the standard deviation ever = 0? 
20020216 

From Karen: If given a class of 30 people who take a test with a mean of 80. Can the standard deviation ever = 0? If so, why? Answered by Penny Nom. 





Diameter of a pipe 
20020216 

From Landry: I am trying to calculate the dia. of a pipe 60 inches long that will hold a gallon of water. What is the formula? Answered by Penny Nom. 





The perimeter of an ellipse 
20020214 

From Harry: I am planning to build a coffe table with an ellipse of 24x36 for the top. I wish to decorate the edge and need to know the lenght of the perimeter for lay out purposes. Is there an easy way to approximate this figure with out using intergal calculus? Answered by Penny Nom. 





Nets for pyramids 
20020214 

From Michelle: I want to have my students create nets for pyramids and I need to know how to find the correct range of degrees for the interior congruent angles of the isosceles triangular faces. For example, I know for a squarebased pyramid that 77 degrees will work; however, I know other angle measures will also work. I'm just not sure how to find the minimum degree measure to have the net actually "work". I'm assuming the maximum would be 89 degrees, although that would make for a very tall pyramid. Answered by Penny Nom. 





36 is 20% less than _____? 
20020213 

From Lori: 36 is 20% less than _____? Answered by Walter Whiteley. 





A man and his wife walk up a moving escalator 
20020213 

From Monty: A man and his wife walk up a moving escalator. The man walks twice as fast as his wife. When he arrives at the top, he has taken 28 steps. When she arrives at the top, she has taken 21 steps. How many steps are visible in the escalator at any one time. Answered by Peeny Nom and Claude Tardif. 





What is 20 to the thousandth power? 
20020212 

From Kristi: What is 20 to the thousandth power? Answered by Paul Betts. 





Three bugs on a line 
20020212 

From Murray:
 Three bugs are crawling on the coordinate plane. They move one at a time, and each bug will only crawl in a direction parallel to the line joining the other two.
 If the bugs start out at (0,0), (3,0), and (0,3), is it possible that after some time the first bug will end up back where it started, while the other two bugs switch places?
 Can the three bugs end up at (1,2), (2,5), and (2,3)?
AND
 A single peg is placed at the bottom lefthand corner of a grid that extends infinitely far up and to the right. You play a game in which you are allowed to make the following move: if the hole immediately above and the hole immediately to the right of a peg are both empty, you can remove the existing peg and place pegs in those two holes instead.
 Show that, no matter how you move, you can never remove all the pegs from the 3by3 square at the bottom lefthand corner of the grid. (b)
 Is it possible to remove all the pegs from the six holes closest to the bottom lefthand corner of the grid (the region indicated in the picture below)?
Answered by Claude Tardif. 





The slopes of the sides of the Great Pyramid 
20020209 

From Christina: The Great Pyramid is the largest of the Egyptian pryamids. When it was built, it was 481 feet tall and had a square base with 755foot sides. The pyramid has two different slopesone along its sides and the other along its edges. Which slope is steeper? Answered by Penny Nom. 





The number of hidden cubes 
20020205 

From Katie: This problem is about finding the number of cubes visible and hidden in a cube.
In a cube that is 3x3, 19 cubes can be seen. 8 are hidden. In a cube that is 4x4, 37 cubes can be seen. 27 are hidden. In a cube that is 5x5, 61 cubes can be seen. 64 are hidden. In a cube that is 6x6, 91 cubes can be seen. 125 are hidden. The question is: Explain how you could find the number of small cubes that are visible and hidden in a cube of any size. Answered by Paul Betts and Penny Nom. 





Parabolas 
20020203 

From Kuang: Who is credited for working with or studying the Parabola? What is a conic section? What does a parabola look like? How is a parabola formed? Where and how are parabolas used today in the real world? Answered by Harley Weston. 





Number conversions and averages 
20020203 

From A student: A table has the measurements of 1.6m by 2m, how much material is needed to cover table? I converted to cm then multiplied but got an answer of 32000cm ,so I divide by 100 to get to metres  the answer was 320 which I know is wrong  please explain!! Also I need to explain in my own words what an 'average' is and I am struggling. Answered by Penny Nom. 





Square arrangements of clovers 
20020203 

From Cassie: Clyde had a strange fascination with numbers. One day he decided to mount his 4 leaf clover collection in groups of square numbers.he took a long piece of butcher paper and glue and began this arduous task.There was 1 clover,4 clovers.and then 9 clovers in the third set. what would be in the seventh set of 4 leaf clovers? Answered by Penny Nom. 





Zeta[2]=(Pi^{2})/6 
20020202 

From alex: Can you please tell me a proof that Zeta[2]=(Pi^{2})/6 Answered by Chris Fisher. 





I am a fraction 
20020201 

From Anthony: I am a fraction that is greater than 1 but less than 2. The sum of my numerator and denominator is 11. My denominator subtracted from my numerator is 1. What fraction am I? Answered by Paul Betts. 





The Euclidean Algorithm 
20020131 

From Murray: Can you please explain to me why the euclidean algorithm works? Answered by Penny Nom. 





Baseball and sit ups 
20020131 

From A student: A baseball team won 8 more games than it lost. If it played 56 games, how many games did it win? On the first day of practice, Paul did 3 sit ups. On the second day he did 5, and on the the third day he did 8, and on the fourth day he did 12. If this pattern continued, how many situps did ihe do on the sixth day of practice? Answered by Penny Nom. 





The size of a lot 
20020126 

From Claudia: I own a piece of property that I need to know the square feet for assessment purposes. The figure they came up with is wrong. They measured from one point to another and halved the sums but that means I own the cul de sac and we don't. My lot is 55 feet wide and one side is 108.96 feet and the other side is 146.04 that extends all the way to a circle. The front of the lot on the cul de sac is stated on the survey like this. 78.21 feet where R=40 feet. This large arc is taken off the size of our land. How many square feet is our lot. Answered by Harley Weston. 





Logico mathematical knowledge 
20020123 

From A teacher: How does young children's logico mathematical knowledge develop? Answered by Walter Whitely. 





Adding algebraic fractions 
20020123 

From Francine:
Hello, I've come up with an answer for the following problem but it's not the same as the book's answer. However, the book has a lot of mistakes in it and I don't know if I'm doing it properly or not. Your help would be soooo appreciated. It's driving me crazy.The problem is:
2 + 3 + 4
 +  + 
(x1)^3 (x1)^2 (x1)
[(x1)^3 is (x1) to power of 3 etc.] Answered by Penny Nom. 





Some trig problems 
20020122 

From Grant:
Solve each problem for theta(there is no sign on my computer)for 0 is less than or equal to theta which is less less than 360  2cosx1=0
cosx=1/2 Anwser 60,300
 tanx2sinxtanx=0
tanx(2sin+1)=0 (factor ?) tanx=0 and sin= 1/2 (solve from there?)
 2sinxcscx=0
2sinx1/sinx=0 3sinx1=0 3sinx=1/3(?)
 4cos(2x)+2cosx= 1
8cosx+2cosx+1=0 10cosx+1=0 10cosx= 1/10 (?)
 cos(2x30)=1/2
cos2xcos30=1/2 cos2xcos301/2=0 i don`t know what to do know
 Sinx+cosx=0
Square both sides? Answered by Claude Tardif. 





Miles and kilometers 
20020122 

From Dennis: I'm in the middle of purchasng a vehicle and it was built in Canada. Therefore it is in kilometers and not in miles. I forgot how many kilometers are in a mile. It registers as 183,049 kilometers. Answered by Penny Nom and Judi McDonald. 





Normal distribution 
20020121 

From Danielle: A teacher gave a test on which the students' marks were normally distributed, but the results were pathetic. The mean was 52% and the standart deviation was 12%. The teacher decided that the top 10% of the students should get A's, the next 20% should get B's, the next 40% should get C's, the next 20% should get D's, and the bottom 10% should get F's. To the nearest percent, what are the cutoff marks that will result in an A, B, C, D, and F? Answered by Penny Nom. 





Successive differences 
20020120 

From Linsey: what is the rule for working out the formula for a sequence with three lines of difference? eg.
1, 3, 7, 15, 29
1st line differences: 2, 4, 8, 14
2nd line differences: 2, 4, 6
3rd line differences: 2, 2 Answered by Penny Nom. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





The distance across a circle 
20020118 

From Douglas: If you know how far around a circle is (say earth) 25000 miles how do you calculate the distance across? Answered by Penny Nom. 





Making 24 
20020117 

From Renee: My 4th grade daughter and I need to find a simple math sentence using 5, 5, 3, & 7 to equal 24. You can add, subtract, divide or multiple. Answered by Penny Nom. 





A sale on eggs 
20020117 

From A student: A store had a sale on eggs, selling 13 eggs for the usual price of a dozen eggs. As a result, the price of the eggs was reduced by 4 cents a dozen. What is the original price for a dozen eggs? Answered by Penny Nom. 





My salary is doubled everyday for 30 days 
20020117 

From Kanishk: I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Answered by Penny Nom. 





A sequence 
20020116 

From Chris: I have spent two days trying to determine the pattern to the following set of numbers: 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,____. I need the next four numbers to the sequence. Answered by Claude Tardif. 





Children and probability 
20020116 

From Bill: If a family has four children, what is the probability that all 4 are the same sex? Answered by Vanrei Volodin. 





Negative exponents 
20020116 

From Julie: If z to the power of 4= 1/z4 then how would you solve 1/t2? Answered by Penny Nom. 





Linear regression 
20020116 

From Murray: If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]m*x[m]b) is at its absolute minimum. Answered by Harley Weston. 





50% 
20020115 

From Lakarrieh: 4 is 50% of what number? Answered by Penny Nom. 





What is a group of three numbers called in a large number? 
20020115 

From Laurie: What is a group of three numbers called in a large number? My son has this question on his 4th grade worksheet. I've taught middle school math for 7 years and nver heard of it. Answered by Paul Betts. 





8% tax 
20020115 

From A student: total price including tax is $13359.60 8% tax was paid What is the dollar amount of tax paid? Answered by Penny Nom. 





Algebra review questions 
20020114 

From A student:
 A wildebeast was observed racing a distance of 86.4m in 4.8 seconds. Find the speed of the wildebeast in m/s.
 8x  7  5x = 23
 7 z  3 (z + 2) = 26
Answered by Penny Nom. 





Adding vectors 
20020112 

From Lena: how do you add vectors together? If you are given the length and angles of both vectors and are asked to add/subtract them, how do you do it? I know you are supposed to do the head to tail method, but whenever i try it i get the wrong answer. I need help setting it up. example: A is 2.7cm, and 60 degrees, B is 1.6cm and 135 degrees, find the magnitude and amplitude Answered by Penny Nom. 





The tangent function 
20020112 

From Justine: if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1? Answered by Penny Nom. 





The famous "train problem" 
20020112 

From Karen: How do you solve the famous "train problem"? For example, 2 trains leave different stations at the same time. One is traveling at 50 mph and the other at 40 mph. How long does it take them to meet? Answered by Penny Nom. 





Papy's Computer 
20020111 

From MaryAnne: My secondgrade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8. Answered by Harley Weston. 





Why do integers have the symbol of Z? 
20020111 

From Stephanie: Why do integers have the symbol of Z? Natural numbers have the symbol of N, whole numbers have the symbol of W. Our professor has asked us to find out why the letter Z is represented for integers. Answered by Penny Nom. 





A sequence of number pairs 
20020110 

From Terry: Three is the first number of a pair, and 8 is the second.
a. If 50 is the first number, what is the second number? b. If 200 is the first number, what is the second number? c. If 89 is the second number, what is the first number? d. If a number n is the first number, what is the second number?
38 411 514 617 ____ ____ ____ 1029 ____ ____ ____
Answered by Peny Nom. 





Glasses of wine 
20020110 

From A student:
6 glasses of regular wine (12% alcohol) would equal aprox.? glasses of wine (8% alcohol)
a)9.33 b)8.5 c)7.75 d)9.0 Answered by Peny Nom. 





A simplification problem 
20020110 

From A Parent: FIND (A / B) . (C / D) where A = Y squared + 3 . Y cubed B = Y squared + 4 C = 2 . Y + Y squared D = Y + 4 Y squared + 3 Y cubed Answered by Penny Nom. 





An octagon inscribed in a circle 
20020110 

From Kent: A circle of 30 in. diameter has an octagon (8 equal chords) inscribed in it. What is the length of each chord? Answered by Chris Fisher. 





Nickles, dimes, quarters and fifty cent pieces 
20020108 

From A parent: The total for all coins counted is $4,564.50 The last coin added to the pile is a 50 cent piece There are 8 times as many 50 cent pieces as there are quarters There are 6 times as many dimes as nickles How many of each are there? Answered by Penny Nom. 





All of the Christmas trees are fiftyfive percent off. 
20020108 

From A teacher: All of the Christmas trees are fiftyfive percent off. Madison bought a tree and paid $103.50. Assuming no tax, what was the original price of the tree? Answered by Penny Nom. 





Maple trees and pine trees 
20020106 

From A student: A team of scientists found that in a forest there was four maple trees for every nine pine trees.How many maple were there if they counted 45 more pine than maples? Answered by Penny Nom. 





Catenary 
20020102 

From Jason: I am a high school math teacher. I was asked by a friend who is in architectural design for a method for determining the volume of what he called a Catenary. The Catenary curve is modeled by the equation y=a cosh(x/a). I ran into a mess when I tried to compute the volume of the solid formed by revolving that curve around the yaxis. Any help you can provide would be greatly appreciated. Answered by Harley Weston. 





Isoperimetric quotients 
20020102 

From A student: I'm stuck on my GCSE Maths coursework, what do isoperimetric quotients measure? Answered by Penny Nom. 





2/3 vs 3/4 
20020102 

From Julia: So, here's my question. Some of the problems they've had to do starts off with two fractions, and they have to tell whether the two fractions are:  The first one is greater than the second one
 The first one is less than the second one, or
 They are equal.
One day my son had the problem of 2/3 vs 3/4. Without drawing out a pie chart, how in the world can a child "eyeball" a problem like this and tell what the correct answer is? I've also tried to teach about making common denominators, but that's going over his head at this point. Answered by Denis Hanson and Harley Weston. 





Fractions to decimals and percents 
20011231 

From A student: 2/5 , 4/8 , 4/10 , 3/5 , 6/8 , 7/7 (what is the decimal and percent for each)
1/5 , 1/10 , 1/8 , 1/1 (what is the decimal for each)
100 PERCENT, WHAT IS THE DECIMAL?
The ratio of boys to girls in a class is 1:4. What percent of the class are girls? Answered by Penny Nom. 





A hyperbola centered at (0,0) 
20011228 

From Carla:
 Find the equation of the hyperbola centered at (0,0) with vertices at (0,3) and (0,3) that is asymptotic to the lines y=+5x.
 Find the equation of a hyperbola in standard position foci (1,5) and (1,7) and eccentricity 2.
Answered by Peny Nom. 





Two algebra problems 
20011224 

From Cass: if the graph of a equation is 2x^{2}  y^{2} = 8 passes through point (6,k), find the positive value of k. if 5^{x2  2 x} = 1, find positive value of x Answered by Penny Nom. 





The probability that the area of a triangle is smaller that 1/8 
20011221 

From Hoda: Given unit square pick two points on adjacent sides of the square , what is the probability that the area of the resulting triangle is smaller that 1/8? I tried to tackle the problem by first sketching a square with the four vertices at (0,0), (1,1), (0,1) and (1,1). The answer seems to be the area under the curve y=0.25/x between 1 and 0, but how can you integrate such a function when ln0 is undefined? any help would be highly appreciated. Answered by Andrei Volodin. 





Feeding Jumbo 
20011221 

From Lupe: There are 2 dogs one named major and the other jumbo. major weighs 100 pounds and jumbo 150 pounds. they eat dry dog food which comes in a 40pound bag that cost $30. Together, major and jumbo eat a whole bag a week. major eats two fifths of the bag while jumbo eats the rest.How much would it cost to feed jumbo in february, which has 28 days? Answered by Penny Nom. 





450 students 
20011219 

From Jessie: My teacher told me that the number of ways of lining up the 450 students in our school is larger than the number of atoms in the universe. Is this right? This question came to Good Question, a regular feature on the CBC Morning Edition radio show in Saskatchewan. Answered by Denis Hanson and Harley Weston. 





Getting to B in the shortest time 
20011219 

From Nancy: A motorist in a desert 5 mi. from point A, which is the nearest point on a long, straight road, wishes to get to point B on the road. If the car can travel 15 mi/hr on the desert and 39 mi/hr on the road to get to B, in the shortest possible time if...... A.) B is 5 mi. from A B.) B is 10 mi. from A C.) B is 1 mi. from A Answered by Penny Nom. 





Simultaneous equations 
20011217 

From Matthew: 4x + y = 4 2x  3y = 5 what is x and y Answered by Penny Nom. 





Making toys 
20011217 

From Karen: Jonathan and Morgan are two of Santa's elves. Jonathan can make a toy in eleven hours. Morgan can make the same toy in nine hours. How long it take for both Jonathan and Morgan to make the toy if they were working together? Answered by Claude Tardif. 





Composition of functions 
20011216 

From Paula:
 if f(x)= 3x1 and g(x)= 1/2x + 3 find fog(2)
 find the values of x for which tanx=0
Answered by Penny Nom. 





A 1 m by 1 m square box in the xyplane 
20011215 

From Murray: Inside a 1 m by 1 m square box in the xyplane, there are finitely many line segments, whose lengths sum to exactly 10 m. Show that there exists a straight line in the plane which crosses at least six of these line segments. (Hint: first, show that there exists a straight line in the plane which crosses at least five of these line segments.) Answered by Claude Tardif. 





A rightangled triangle 
20011213 

From Pamela, Jeff, Kayleigh and Jacob: A rightangled triangle has one side that is 8 cm shorter that the hypotenuse. The other side is 1 cm shorter than the hypotenuse. Find the length of the sides. Answered by Penny nom. 





Algabra 
20011213 

From Stephanie: My name is Stephanie. My grade 7 class is doing some strange form of algebra which I've never done nor seen before. We are doing equations like these: 3y  6 + 7  4y = 6y  6. I don't really understand them and was wondering if you could help me do my homework and explain how to at the same time. It would be really great if you could!!!!! Thank you so much! Stephanie  9x  5  8 + x = ?
 5 + 6x  3y + x + 8y = ?
 x  3 + 5x + 6y + 8x  9= ?
Answered by Penny Nom. 





Reduce 79,537/3,623,420 
20011213 

From Eliana: How do you reduce 79,537/3,623,420. Answered by Claude Tardif. 





A 7% increase 
20011212 

From Lorraine: how do you calculate an old salary if the only information you have is current salary and the percentage increase received. For example if I make $15.86 an hour and I received a 7% increase, how much did I used to make? Answered by Penny Nom. 





For 7 the multiplicand is 143 
20011212 

From Cory: For 7 the multiplicand is 143 I am asked to solve this, if you could help me it would be greatly appreciated! Answered by Penny Nom. 





A quadrilateral with 0 sets of parallel sides 
20011212 

From Jess: Ok well for quadrilaterals a parallelogram is a 4 sided figure with 2 sets of parallel sides and a trapezoid is a 4 sided figure with 1 set of parallel sides. So is there a name for a quadrilateral with 0 sets of parallel side? Answered by Chris Fisher. 





Painting walls 
20011212 

From Rizwan: 3 sixth graders painted 4 walls in 3.5hrs. At that rate, how many walls would they paint in 7 hrs. Answered by Penny Nom. 





Recalling the basic facts 
20011212 

From A parent: My son is in 4th grade and is a very bright student. He is in the gifted program and makes straight A's on his report card and has through out school so far. My question is how can I teach him to memorize his basic math facts? He does well in math, but when he is placed in a times situation for completing math fact sheets he freezes up. He can not recall the basic facts when questioned at any other time either. He will calculate the answer in his head, like 6 + 3, but he can't just come out with the answer quickly. How can I help him? Answered by Claude Tardif. 





Division symbol 
20011212 

From Amanda: What is the name of the symbole used in a long divison problem that seperates the two factors? It looks like a little house. Answered by Penny Nom. 





Exponential form 
20011211 

From Crystal: Hi, I am asking a question on behalf of a homeschooling grade 11 student. She is having trouble with changing something like (3^{4})^{2} into a exponential form. First of all she needs to know what the term means "exponential form" and then the process of it. Answered by Penny Nom. 





y = zx  x  c 
20011211 

From Andrew: Could you please help me work out the value of x where: y = zx  x  c Answered by Penny Nom. 





Normal lines 
20011211 

From Kristie: Why are perpendicular lines called normal lines? Answered by Chris Fisher. 





Cinderella clothes 
20011211 

From A student: If cinderella clothes, inc. has determined that 0.5% of all incoming phone calls involve complaints, what is the probability that in 200 incoming calls there are more than one complaint? Answered by Andrei Volodin. 





y= (3x+2)/(4x5) 
20011205 

From Courtney: y= (3x+2)/(4x5) solve for x Answered by Penny Nom. 





Piles of coins 
20011205 

From A student: Sharon has less than 20 coins. When she puts them in piles of 5, she has 1 left over. When she put them in piles of 3, she also has 1 left over. How many coins does Sharon have? Answered by Penny Nom. 





QED 
20011205 

From Derek: What does Q.E.D. mean? Answered by Harley Weston. 





Fractions in lowest terms 
20011205 

From Thomas: how to change decimal to a fraction in the lowest terms .7 .65 .019 .0111 .225 .1225 .625 .25 .025 .26 .875 .5 .75 .750 .33 .09 .44 .15 .12 .90 .044 .2500 .95 .500 .02 .40 .125 .1276 .00009 .45 .125 .1276 .375 .975 .054 .0005 .20 .2 .0001 .85 .80 .9 .0007 9.8 10.17 25.75 48.4 80.35 19.64 276.20 31.042 18.1034 Answered by Penny Nom. 





Two equations in two unknowns 
20011204 

From Courtney: y = 3x + 2 y = 4x  5
solve for x Answered by Penny Nom. 





Permutations and combinations 
20011203 

From Linda: There are 12 people who can be chosen for a project. Q1. Suppose that 2 people refuse to work together. How many groups of 7 can be chosen to work on a project? Q2. Suppose that 2 people insist on working together or neither will work on the project. How many groups of 7 can be chosen to work on the project? Answered by Penny Nom. 





83.3% 
20011203 

From Ellie: Please explain how a percentage like 83.3% is changed into a fractions. The answer given is 5/6 and I changed 83.3% to a regular decimal of .833, which would be 833/1000. How do they get 5/6 from that? HELP Answered by Chris Fisher. 





Integers 
20011202 

From Alison: How do you use integers in your everday life? Answered by Harley Weston. 





Solving x^23x+5=0 
20011130 

From Katy: How do you find the solution to x^{2}3x+5=0? Answered by Penny Nom. 





Can a infinite set be smaller than another infinite set? 
20011129 

From Carlos: Can a infinite set be smaller than another infinite set? If so why? Answered by Chris Fisher and Penny Nom. 





3, 6, 10, 15, 21 
20011129 

From Patrick: we are trying to find the expression to solve for the nth term in the pattern 3, 6, 10, 15, 21 Answered by Denis Hanson. 





A lighthouse and related rates 
20011129 

From Melissa: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom. 





Multinomial theorem 
20011128 

From Murray: Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am) Answered by Harley Weston. 





Slope intercept form 
20011127 

From A student: what is slope intercept form? Answered by Penny Nom. 





Numerical problems 
20011127 

From Yossi: I am preparing a 45 minutes class for K12 students. The problem is to show that algebraic equivalent expressions are not always numerically equivalent. In particular I would like to show one of these dangers: cancellation that occurs during the subtraction of nearly equal quantities. Do you have a good reference I could use to prepare my class. In particular to be able to show some examples and how one can avoid this type of error. I also would like to show examples with practical use. I tried to look up in the web but did not find anyhting appropriate. Answered by Chris Fisher. 





Original value 
20011127 

From Lisa: We are trying to find the original value of a product marked up by 10%. What is the formula to determine the original value? Answered by Penny Nom. 





Dual spaces 
20011126 

From Hoda: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of L^{p} is equal to L^{q}. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of l^{p} is equal to l^{q}. Answered by Doug Farenick. 





Ratios and proportions 
20011126 

From Adam: I am doing a project where I come to this website and ask a math expert about a certain topic. My topic is ratios and proportions. Can you please tell me what your job is and how you use ratio's and proportions in your job. Can you also please explain what ratios and proportions are. Answered by Harley Weston. 





A health club 
20011125 

From Maria: A health club with a membership of 650 people operates a running track and an indoor swimming pool. A survey of the membership indicates that 68% use the running track, 44% use the swimming pool, and 8% use neither. If a member is chosen at random, what is the prbability that the member uses: a) Both the track and the pool? b) Only the track? Answered by Penny Nom. 





L'Hopital's Rule 
20011125 

From Mike: I'm a high school senior. I'm in ap calculus and was wondering if you know the proof of L'Hopital's Rule? Our teacher said he has never been able to find it in a math book and was unable to derive it himself. Answered by Claude Tardif. 





Undetermined coefficients 
20011122 

From Hoda: The equation is: y"  2y' + y = t e^{t} + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Ate^{t}+Be^{t}+C, but all I get is C=4 and I tried (At^{2}+Bt+C)e^{t}+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Answered by Harley Weston. 





Ratios 
20011121 

From Mike: Simplify these ratios. 7 1/4 inches to 2 feet. $0.02 per $1.75 Answered by Peny Nom. 





Matrix 
20011121 

From Hoda: I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix? Answered by Patrick Maidorn and Penny Nom. 





A tangent line 
20011121 

From A student: write an equation of the line tangent to the graph of
e^{y} + ln(xy) = 1 + e at (e,1) Answered by Harley Weston. 





A hypercube 
20011120 

From Ace: Can I get a picture of a hypercube Answered by Patrick Maidorn. 





Rewriting and evaluating formulas 
20011119 

From A conserned mother: Due to the wide range of temperatures experienced in Canada, engineers who construct roads must allow for expansion and contraction of the road surface. The following formula is used to calculate the amount of expansion E to allow for: E= kL(Tt), where k is the constant of expansion for the road surface. L is the length of the section of highway in metres. T is the temperature of the air in degrees Celsius. t is the temperature, in degress Celsius, at which the section of the highway was constructed. Answered by Walter Whiteley. 





Cardinality of sets 
20011119 

From Tania:
 Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}.
 Show that (the cardinality of the natural numbers set) N = NxNxN.
 Show that the cardinality of the set of prime numbers is the same as the cardinality of N+
Answered by Walter Whiteley. 





Gallons 
20011119 

From Shawn: Do we use British or American gallons in Canada? Answered by Chris Fisher. 





Translated by the vector (5,2) 
20011119 

From Jennifer: Give the image of (p,q) when translated by the vector (5,2). Answered by Penny Nom. 





The "pi" of a circle in hyperbolic space 
20011119 

From Alex: How can you find the "pi" of a circle in hyperbolic space (or is it the same). I would like to know because our environment is hyperbolic and if the "pi" of hyperbolic space is irrational, it would follow that space is non discrete. I would greatly appreciate any help in this question. Answered by Walter Whiteley. 





Box and Whisker plots 
20011119 

From Rod: In our Prealgebra course, we have been studying Box and Whisker plots. Recently, we learned how to decide whether a data point is an outlier or not. The book (Math Thematics, McDougall Littell) gave a process by which we find the interquartile range, then multiply by 1.5. We add this number to the upper quartile, and any points above this are considered to be outliers. We also subtract the number from the lower quartile for the same effect. My question: where does this 1.5 originate? Is this the standard for locating outliers, or can we choose any number (that seems reasonable, like 2 or 1.8 for example) to multiply with the Interquartile range? If it is a standard, were outliers simply defined via this process, or did statisticians use empirical evidence to suggest that 1.5 is somehow optimal for deciding whether data points are valid or not? Answered by Penny Nom. 





Renee, Paulo and Peter 
20011118 

From Sue: Renee is 5 years older than Paulo. she is also 7 years older than Peter. The sum of their ages is 21. How old is each person. Answered by Penny Nom. 





Number sequences 
20011117 

From Stephanie: My name is Stephanie. My grade 7 math class is studying number sequences and, to me, they make almost no sense at all. Here I wrote down 2 of the many problems I have for homework and was wondering if you could explain them to me (I have to find the next 3 numbers in each sequence.) It would be a big help! 10, 14, 18, 22, _, _, _. 12, 21, 39, 75, _, _, _. Answered by Penny Nom. 





A box of pants and shirts 
20011117 

From Debbie: I need to determine the volume of a box that is 4'HX4'WX4'L. The box contains uniform pants and uniform shirts. I need to know how many shirts and pants are in the box. When folded, the uniform shirt is .5 inches thick. The pants are also .5 inches thick. Answered by Penny Nom. 





How do you get to 100 by using 6 nines? 
20011117 

From A student: How do you get to 100 by using 6 nines? Answered by Claude Tardif. 





Magic squares 
20011117 

From A student: 7th grader wanting to find solution to magic square:
place the integers from 5 to +10 in the magic square so that the total of each row, column, and diagonal is 10. The magic square is 4 squares x 4 squares. Answered by Penny Nom. 





Some functions without numbers 
20011116 

From A student: I have a worksheet that is about functions. It doesn't only use numbers. I need help to figure out the function and the solution to how the answer is solved. Answered by Claude Tardif. 





Numbering pages 
20011115 

From Lucy: A printer uses 1008 digits to number the pages of a book. How many pages are there in the book? Answered by Penny Nom. 





Negative numbers 
20011115 

From Jewel: If zero means nothing or an empty set, then how can a number be less than zero, as in negative number? My understanding of negative numbers is distance from a set point in a given direction. Thus having a negative and positive side of a line is arbritary and is related to displacement rather than value. Am I in error? Answered by Penny Nom. 





A clap of thunder 
20011115 

From Frustrated Mom: While getting a recipe for the Thanksgiving feast. The teacher was talking on the phone with a friend who lives four miles north of her. She saw a flash of lightning through the window: fifteen seconds later, she heard a clap of thunder. Ten seconds after that she heard the thunder over the phone. Where did the lightning strike in relation to the teacher's house. (There are two possible answers. Sound travels about 1/5 mile per second. Some people say it's not good to be on the phone in a thunderstorm). Answered by Claude Tardif and Penny Nom. 





what number doubled plus 20 will give you 4/3 the original number 
20011115 

From Hank: what number doubled plus 20 will give you 4/3 the original number
2 x__ + 20 = 4/3 of the original number Answered by Penny Nom. 





(a+b) squared and a squared plus b squared 
20011114 

From Kristen:
(a+b)^{2} = a^{2} + b^{2} Is this true for all whole numbers, and why? Answered by Penny Nom. 





Subsets of a countably infinite set 
20011114 

From Tania: How could I show (and explain to my son) that any countably infinite set has uncontably many infinite subsets of which any two have only a finite number of elements in common? Answered by Claude Tardif. 





3x1/2(x4)+5= 3 
20011113 

From Tausa: 3x1/2(x4)+5= 3 Answered by Penny Nom. 





Inequalities 
20011113 

From Pat: When writing the solution to an inequality, why is the solution written in set notation? {x/ } Answered by Penny Nom. 





Prove that the medians of triangle PQR meet in a central point G. 
20011111 

From Jessica: Use a scalene triancle with one point (0,b) on the y axis, another point (2c, 0) on the xaxis and the last point, (2a,0) on the xaxis. Prove that the medians of triangle PQR meet in a central point G. Answered by Penny Nom. 





A cubic 
20011110 

From Louise: x^{3} + 9x^{2}  7x  63 Answered by Penny Nom. 





1 minus 5(y) equals negative 2 
20011110 

From Judy: 1 minus 5(y) equals negative 2 Answered by Penny Nom. 





A circle and triangle overlap 
20011109 

From Tara: A circle and triangle overlap as shown.the area of the circle is three times the area of the triangle.If the common region is removed,then the area of the rest of the circle would be 14 sq cm more than the area of the rest of the triangle.How many sq cm are in the area of the complete triangle. Answered by Penny Nom. 





A circle and a triangle 
20011109 

From Tasha: I have a circle that has an equalateral triangle inscribed in it. The tip of the triangle (B) is at the center of the circle with the other corners (A & C) extending to the sides of the circle. I need to know the equation to find the linear length of AC. I also need to find the cordial length of the circle from point C to A. Answered by Penny Nom. 





Third side of Acute Triangle 
20011109 

From Don: I gave this problem to my children, 9th and 12th grade and they are not(me too!) sure of the answer. I am trying to determine the length of the third side of an acute triangle. I know two of the lengths but I do not know the angles. Is there a proper formula to use to find the length of the third side? Thank you. Answered by Chris Fisher and Penny Nom. 





12 pairs playing bridge 
20011109 

From Diana: I have 12 pairs playing bridge against one another for 12 games. I need to have each pair partnered with another pair  but only once. I'm looking for a schedule for play for all 12 games. They should only be able to play against another team only once also. (ex: 1/2 v 3/4 then 4/2 v 3/1) Thank you for this opportunity to solve my dilemma. Answered by Claude Tardif. 





Asymptotes 
20011109 

From Frank:
given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Answered by Chris Fisher and Penny Nom. 





A 3 dimensional 5 pointed star 
20011108 

From Kent: I am looking for a formula that will give me a layout for a 3 dimensional 5 pointed star. I want to form it out of sheet metal, using 5 polygons and soldering them at the apex. Can you please help me with this? I would like to be able to give the formula the height of the star from the bottom two points to the top point and also how deep the star is. Thank you very much! Answered by Judi McDonald. 





Manufactures golf balls 
20011106 

From Kevin: A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eighthour shift. A. How many yellow golf balls are tested for defects during the day? Explain your reasoning. B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning. Answered by Penny Nom. 





Counting CD's 
20011106 

From Jason: An older brother said to his younger brother, "Give me 8 of your CDs, then I will have twice as many as you." The younger brother replied, "No, you give me 8 of yours instead, and then we'll have an equal number." How many CDs does each boy have? Answered by Chris Fisher. 





2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 
20011105 

From Cynthia: justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom. 





Squares of negative numbers 
20011103 

From Susana: I wanted to know if I can square a negative number..? Answered by Leeanne Boehm. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





A lighthouse problem 
20011102 

From A student: A lighthouse at apoint P is 3 miles offshore from the nearest point O of a straight beach. A store is located 5 miles down the beach from O. The lighthouse keeper can row at 4 mph and walk at 3.25 mph.
a)How far doen the beach from O should the lighthouse keeper land in order to minimize the time from the lighthouse to the store?
b)What is the minimum rowing speed the makes it faster to row all the way? Answered by Harley Weston. 





15 % of 24.95 
20011101 

From Puzzled: How do I take 15% of a number I have forgotten Answered by Penny Nom. 





8w15 = 3w10 
20011101 

From A student: 8w15=3w10, w =????? Answered by Paul Betts. 





Division by zero 
20011031 

From Stacy: I have a question about dividing with zero. When the numerator is zero, the answer is zero. But when the denominator is zero, the answer is undefined. Why? I don't understand Answered by Claude Tardif. 





(3)to the power 2, divided by 3 
20011031 

From Raz: what is (3)to the power 2, divided by 3= Answered by Penny Nom. 





m  8 
20011030 

From Danita: Can you please email me the answer to m 8 for m = 20 and how you got the answer Answered by Penny Nom. 





3pi/2  pi 
20011029 

From Karen: I need to simplify this a) 3pi/2  pi Answered by Penny Nom. 





A sample size problem 
20011028 

From Charles: The U.S Transportation Dept. will randomly sample traffic reports to estimate the proportion of accidents involving people over the age of 70. The Dept. has no advance estimate of this proportion. how many reports should the dept select to be atleast 97% confident that the estimate is within .01 of the true proportion? Answered by Harley Weston. 





Three problems 
20011028 

From Brenda:
 Joseph is planting bushes around the perimeter of his lawn. If the bushes must be planted 4 feet apart and Joseph's lawn is 64 feet wide and 124 feet long, how many bushes will Joseph need to purchase?
 The cost of a long distance phone call is $1.50 for the first two minutes and $0.60 for each additional minute. How much will Maria pay for a 24 minute phone call?
 Find the next three numbers in the pattern. 1,3,7,15,31,___,____,___.
Answered by Penny Nom. 





Is the tree a pine tree? 
20011027 

From Kate: Suppose Stock Brokers tell the truth 2/5 of the time, and 1/3 of the trees in a given forest are Pine. If 4 Stock Brokers say that a certain tree in that forest is Pine, what is the probability that the tree is indeed a Pine tree? Answered by Penny Nom. 





Negative times negative is positive 
20011026 

From Mary: I have a question about adding and multiplying positive and negative numbers. When we add two negative numbers the answer is negative BUT when we multiply two negative numbers the answer is positive. I don't understand. Why? Answered by Penny Nom. 





Why do you flip the inequality sign? 
20011026 

From Sean: I have a question about an inequality problem. Here it is: Solve and graph 5  3x => 17. (=> is greater than or equal). Please tell me why you flip the inequality sign when divinding by a negative number. Answered by Penny Nom. 





Concavity of f(g) 
20011025 

From Troy: Suppose f & g are both concave upward on (infinity,infinity). Under what condition on f will the composite function h(x)= f(g(x)) be concave upward? Answered by Walter Whiteley. 





An algebraic fraction 
20011025 

From brandi: 4x  5 _____ =4 37x Answered by Penny Nom. 





Metric units 
20011025 

From Kelly: i am helping my kids out with school work and don't remember meters,centimeters decimeters and all those. We have to change meters into cm.....and so on..........is there a place on the web to look for some kind of help in these questions Answered by Penny Nom. 





Where is the fourth point? 
20011024 

From Mike: Four points are placed at random on a piece of paper. Connect the three points of the triangle of the largest area. What is the possibility that the fourth point is in the triangle? Answered by Penny Nom. 





A geometric series 
20011024 

From Tashalee: The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms? Answered by Penny Nom. 





Free pamphlets 
20011024 

From Salman: a travel agency has limited number of six different free pamphlets about the beetle islands. the agent tells you to take any that you want, but not more than two of any kind. Assuming that you take at least one pamphlet, how many choices could you make Answered by Penny Nom. 





A right angled triangle 
20011023 

From Carissa: How do you : Triangle ABC is rightangled at A. Calculate the length of the third side if b = 3 and c = 6, express the answer as a surd in its simplest form. Answered by Harley Weston. 





The distributive law 
20011023 

From Carissa: How do you simplify the following using the distributive law :
5 squareroot 2+3 squareroot 2? Answered by Penny Nom. 





A $10,00 prize 
20011023 

From Michelle: The grand prize for winning a contest is $10,000. After 28 percent of the prize is deducted for taxes, the winner receives the balance of the prize in annual payouts of equal amounts over a 3year period. How many dollars will the prizewinner receive each year of the 3 years?(Disregard the $ sign when gridding your answer.) Answered by Penny Nom. 





Squaring the circle 
20011023 

From Margaret: I have the following question that I cannot answer on my own (I don't know where to begin): Is it possible construct a square whose area will equal the area of a given circle? Please Explain why or why not. Answered by Penny Nom. 





The average of two polygons 
20011023 

From Irene: How can I prove that the average of two polygons will give me another one? Answered by Walter Whiteley. 





Multiplying vectors 
20011022 

From Murray: Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b) Answered by Harley Weston. 





Lines in the plane 
20011021 

From Greg:
*If the line with equation 3x4ky= 16 has yintercept 2, find k. *Write the equation of the line passing through (2,5) and perpendicular to the line passing through (2,4) and (6,1) Answered by Penny Nom. 





Water in a conical tank 
20011020 

From Sarah: The problem: Water flows into a conical funnel at a continuous rate of one gallon per minute (One gallon = 231 Cu.In.). The height of the funnel is 5" and the diameter is 8". The 1st formula: I need to develop a formula that will give the volume, in cubic inches, of the water in the funnel at any time t (in seconds). V = f(t). The 2nd formula: I need to develop a formula that will give the height of the water in the funnel at any time t (in seconds). h = f(t). Answered by Penny Nom. 





Why quadratic for a second degree equation? 
20011020 

From Jana: Why do we use the word quadratic to describe second degree equations? Answered by Penny Nom. 





A goat in a square pen 
20011019 

From Brad: A goat is tied to one corner of a square pen 20 ft. on a side.  If the goat's tether is 10 ft. long, what percentage of the grass in the pen can the goat reach?
 What should the length of the tether be so that the goat can reach half of the grass?
Answered by Penny Nom. 





Symmetry of f(x) = ax^n 
20011018 

From Mohammed: a function of the form f(x)=ax^{n}, where a doesn't equal 0 and n is a positive integer is called a power function . how is the exponent in the equation of a power function related to the symmetry of its graph? Answered by Penny Nom. 





414 is what percent of 5,624? 
20011018 

From A student: 414 is what percent of 5,624? Answered by Penny Nom. 





A function or not a function? 
20011018 

From Christian: Which are the following are not functions?  y = x^{2}
 y = x^{3}
 x = y^{2}
 y = 3
Answered by Leeanne Boehm. 





Tenths, hundredths, and thousandths 
20011017 

From Cheri: I would like the French terms for the decimal place values of tenths, hundredths, and thousandths. (I would be interested in the Spanish terms also if you had them.) Answered by Maria Torres and Claude Tardif. 





Column doesn't add up to 100% 
20011017 

From A student: why don't some tables I'm studying in a column add up to 100%? Example: N=338, but responses to questions asked in survey I'm studying equal of 24.3, 9.8, 43.8, DON'T add up to 100%. I'm assuming that some people surveyed out of the 338 didn't bother responding, but is there another problem related to proportion or ratio being used, but improperly labeled on graph?. Note at bottom of table says: "number in parenthesis are numbers of cases" and 338 was in parentheses. I'm lost. Answered by Penny Nom. 





A line in 3 dimensions 
20011017 

From Murray: I'm working on a complicated proof and i need the equation for a line in 3 dimensions. Answered by Claude Tardif. 





Dividing a circle 
20011017 

From Ahmeen: I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Answered by Walter Whiteley. 





Dimensions of a frame 
20011016 

From Rachel: A rectangular picture frame has a perimiter of 44.2 cm.The width of the frame is seven tenths of its length what are the dimensions of the frame? Answered by Penny Nom. 





Proof by induction 
20011016 

From John: Can you help me with any of these?  For any natural number n > 1, prove that
(4^{n}) / (n + 1) < [(2n)!] / [(n!)^{2}].
 For any natural number n > 1, prove that
1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) > sqrt(n).
 For any natural number n and any x > 0, prove that
x^{n} + x^{n  2} + x^{n  4} + ... + x^{n} >= n + 1. Answered by Penny Nom. 





Some algebra 
20011015 

From James: I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.  (7x^{2} – 3yz)^{2} – (7x^{2} + 3yz)^{2}
 Use Pascal’s triangle to expand (2x – y)^{4}
 8x^{3} y  x^{3} y^{4}
 (m + 3n)^{2} – 144
 12x^{4} y – 16x^{3} y^{2} – 60x^{2} y^{3}
 p^{3} q^{2} – 9p^{3} + 27q^{2} – 243
Answered by Peny Nom. 





Squares of one digit numbers 
20011015 

From Needa: What two twodigit numbers are each equal to their rightmost digit squared? Answered by Penny Nom. 





Rules of exponents 
20011014 

From Carissa: how do you work this out? Investigate the relationship between a,b,c and d if 2^{a}*2^{b}=4^{c}/4^{d}? Answered by Leeanne Boehm. 





Absolute Value 
20011014 

From Susan: I am a homebound teacher, and my nineth grade algebra I student is having trouble understanding absolute value. Please send me an idea about how to best help her. She may be out of the classroom the entire year. Answered by Chris Fisher. 





Odd plus even is odd 
20011014 

From James: Why is the sum of an odd number and an even number always odd? Answered by Peny Nom. 





Area of a quilt 
20011014 

From Jack:
 how would you find the area of the quilt? which is a square
 how would you fined the area of each square?
Answered by Penny Nom. 





Theme day 
20011014 

From A teacher: I woulld like a math theme for a theme day in a high school, grades 912. Our last theme was fractal fest. Answered by Penny Nom and Claude Tardif. 





Maximize the area 
20011013 

From Mike:
I have no clue how to do this problem. Here is what the professor gave to us: A=LW
C=E(2L+2W) + I(PL) Where P = # of partitions E= cost of exterior of fence I = cost of interior of fence C = total cost of fence . . . Answered by Harley Weston. 





Mathematical & conventional meaning of a word 
20011012 

From A student: What is the mathematical & conventional meaning of a word? Like the word Rational or Median. Answered by Penny Nom. 





60 seconds in a minute 
20011011 

From Andy: I am a fourth grade teacher. Yesterday my students asked "Why are there 60 seconds in a minute?" Which also led to 60 minutes in an hour? I have had trouble determining why the number 60? Any help would be appreciated. Answered by Penny Nom. 





4 sinx cosy = 1 
20011010 

From A student: How would i differentiate the following example in terms of t (x and y are functions of t) 4 sinx cosy = 1 Answered by Claude Tardif. 





Acres 
20011010 

From Allison: how many feet are there in an acre? Answered by Chris Fisher. 





e^{ix} = cosx + isinx 
20011010 

From Peter: Given: e^{ix} = cosx + isinx  substitute x for x to find e^{ix}, simplifying your answer
 use the given and part a to find an identity for cosx making no reference to trig functions
 find an identity for sinx
 .
 .
Answered by Penny Nom. 





When will the ship disappear? 
20011010 

From Stacy: If the sail of a ship were a 100 ft. tall and you were a mouse at the edge of the shore looking out at it, how far out would the ship be when it disappears? ( your eye level is level with the water.) Answered by Harley Weston. 





Ratio and proportion 
20011010 

From Steve: Where would you use a proportion and/or a ratio in a real life job or problem. Answered by Leeanne Boehm and Walter Whiteley. 





Six nines 
20011009 

From A mom: My middle schooler (sixth) has to calculate the integers 020 using only 6 nines. We have done all but the integer 14. He can not use decimals or double the nine like 99 or 19. the fraction 9/9 is okay. Keep in mind of course the order of operations. Answered by Claude Tardif. 





Pythagoras & magic squares 
20011009 

From John: My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 345 triangle, and the fact that his teacher told him there was also a 51213 triangle, i.e. both rightangled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on. I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7order square would also generate a rightangled triangle for him. He found that 72425, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...  Is there a rightangled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and
 Is each triangle unique (or, as he put it, can you only have one wholenumbersided rightangled triangle for each triangle whose shortest side is an odd number)?
Answered by Chris Fisher. 





Lucas' theorem 
20011009 

From Tania: How could I demonstrate: nCp is congruent to floor(n/p) (modulo p)? where rCk is a binomial coefficient, rCk = r(r1)...(rk+1)/k(k1)...1, and p is a prime number Answered by Richard McIntosh. 





Binomial probabilities 
20011008 

From Amna: I had a few binomial probability questions which I can not use from the tables as instructed:  If 60 % of television viewers are watching a certain program, what is the probability tha tmore than half of those selected in a random sample of five will be watching the specified program?
 If it is known according to Mendel's Law, that we can expect in teh long run to have 3 white, 1 brown rabbits in every 4 rabbits of a certain type, what is the probability that 2 in a litter of 3 will be white?
 On the average, 2% of the items sold in a department store are returned for refunds. what is the probability that of its next five items sold, at most two will be returned for refunds?
Answered by Leeanne Boehm. 





Mystery mathematician 
20011008 

From A student: Theres a mathematician that was born on October 16 1879 in England and died on October 1 1921 in England. Suffered from severe disabilities. Did poorly in his degree and settled for a pass degree. Was awarded the Allen scholarship for research in 1904. He also applied logic to Physics in papers such as On Some Points in the Foundation of Mathematical Physics (1908). Who is it? Answered by Claude Tardif. 





15 mice in 4 cages 
20011008 

From Chelsea: How can you fit 15 mice into 4 cages with an odd number of mice in each cage? Answered by Claude Tardif and Harley Weston. 





Finite differences 
20011008 

From Murray: My name is Murray and I am a 10th grade student. Me and my friend have recently discovered and proved a theorem of a relitively advanced nature. It is that the the nth difference of an nth degree equation = n! times the coefficient of the highest power. One of my teachers said this theorem is part finite and that she thinks she has seen it before, but she does not remember what it is called, at what level it is taught, who discovered it or when it was invented. I would greatly appretiate answers to any of these questions. Answered by Chris Fisher. 





Locusts 
20011008 