







Standard deviation 
20050102 

From Urial: Find the standard deviation of the given data set
To get the best deal for CD dealer, Jessica called eight appliance stores and asked the cast of a specific model. The prices she quoted are listed below.
$300, $203, $272, $332, $440, $119, $129,$254
Answered by Penny Nom. 





A 4digit access code 
20050102 

From Missi: I need to find the 4 digit number to access my voice mail. These numbers will be 09 & numbers can be repeated. Could you provide me with a list of possibly combinations? If not, do you know anywhere that I could get a list of combinations so I don't have to write it all down? Answered by Harley Weston. 





A line from the center of the patch to the periphery 
20050101 

From Sandrine: I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use? Answered by Denis Hanson and Harley Weston. 





A geometry problem 
20050101 

From Alexandra: In triangle ABC, b=40, and angle A= 30 degres. What values of BC will give two solution for angle B? Answered by Penny Nom. 





The golden ratio 
20041231 

From Cristina: let x represent the longer segment. to find the golden ratio, write a proportion such that the longer of the two segments is the geometric mean between the shorter segment and the entire segment.Use the quadratic Formula to solve the proportion for X. Find the value in both radical and decimal form. Answered by Penny Nom. 





The area of a triangle 
20041230 

From Perry: What is the area of a triangle with dimensions 3"X5"X7"? Could you provide the formula? Answered by Penny Nom. 





Gallons in a cylinder 
20041229 

From Dean: I have 2 cylinders:
Cylinder A = 8'D x 12'H
Cylinder B = 10'D x 15'H
Each 1ft represents how many gallons of fluid?
Cylinder A=?
Cylinder B=? Answered by Penny Nom. 





Cubic yards of dirt 
20041228 

From Stephen: How many cubic feet or yards of dirt would be required to cover a 5 acre tract of land to a depth of 10 feet of compacted dirt? Answered by Penny Nom. 





Six digit numbers with at least one 7 
20041227 

From Behzad: How many sixdigit numbers contain at least one 7 in their decimal expansion? Answered by Penny Nom. 





2^9833 days from today 
20041226 

From Pauline: Today is Monday, 1 October 2001. What day of the week will be 29833 days from today? Answered by Penny Nom. 





Half of five 
20041226 

From Pauline: Why is four half of Five? Hint: It's the middle half? Answered by Penny Nom. 





Modelling monthly temperature with a cosine 
20041225 

From Regis: The average monthly temperature for a location in Ontario as a function of month number can be modelled using the equation y = a cos[k(t + b)] + d. Answered by Harley Weston. 





An arithmetic progression 
20041224 

From A student: the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50 Answered by Penny Nom. 





Irrigation and a sector of a circle 
20041223 

From Chuck: A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Answered by Harley Weston. 





252 x ? is a cube 
20041222 

From Andrea: What is the smallest positive interger by which 252 can be multipled so the result is a perfect cubed? Answered by Penny Nom. 





Making the number 99999 
20041222 

From Lisa: Make as many equations as possible to make the number 99999 using all of the numbers 09 but only once per equation. example 01234 + 98765 = 99999 she needs to make 150+ equations. Answered by Paul Betts. 





A Reuleaux triangle 
20041222 

From Bob: I am trying to remember the name given to the regular figure constructed from three arcs. The figure is like an equilateral triangle except with arcs for each side. Answered by Chri Fisher. 





Divisibility by 15 
20041219 

From Lisa: My son was asked to find divisiblity rules for 15. We have been unable to find the answer. Does it exist? Answered by Leeanne Boehm and Denis Hanson. 





The gradiant of a hill is 9% 
20041218 

From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom. 





Two intersecting lines 
20041218 

From James: Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes! Answered by Harley Weston. 





A two equation fact family 
20041217 

From Tony and Hailey: My Daughter Hailey had this question as part of her 4th grade math homework. Name 2 fact families that have only two equations. For the life of me I can't figure it out. Any ideas? Answered by Penny Nom. 





0.999..., asymptotes and infinity 
20041217 

From Mike: My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!! Answered by Claude Tardif and Harley Weston. 





2^10 = 1/2^x  1 
20041213 

From Randy: Could you explain to me how the following equation is solved please.
2^10 = 1/2^x  1 Answered by Harley Weston. 





ln(x)/x 
20041211 

From Tina: What is the derivative of (ln x)/x? The double derivative? Answered by Penny Nom. 





A geometric proof 
20041211 

From Hanna: Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram Answered by Penny Nom. 





A sequence 
20041211 

From Amanda: Find the nth term of the following sequence
4, 10, 28, 82 Answered by Penny Nom. 





Three calculus problems 
20041209 

From Ashley: Hi, I am having a lot of trouble with three calculus questions and was wondering if you could help Answered by Penny Nom. 





Strings of 4 digits from 1,2,...,7 
20041209 

From Tom: How many different combinations can be made of the numbers 17 in 4 string combinations in any order? EX:7235, 3517, etc...
And if you were to include the same 2 numbers in every combination, how many would that make? EX: Using 1 & 2: 1274, 5142, 2751, etc... Answered by Penny Nom. 





Combinations 
20041209 

From Keith: i have a bucket that can hold 12(or x) number of rocks. if i have 13(or y) rocks how many different combinations of rocks can i put in the bucket without having the exact same 12(or x) rocks in the bucket. is there a formula that can be used for this problem in all cases and if so how and why does it work. Answered by Penny Nom. 





A regular hexagon is inscribed in a circle. 
20041208 

From Abraham: A regular hexagon is inscribed in a circle. What is the ratio of the length of a side of the hexagon to the minor arc that it intercepts?
(1) pi/6
(2) 3/6
(3) 3/pi (This is the correct answer.)
(4) 6/pi
I found the length of the minor arc to be (pi)(r)/3 by doing a sixth of the circumference(2pi r).But I can't find the length of the radius to finish off the problem. If I knew the radius I would then plug it into the above and then use the radius again to be the length of the side because the triangle(one of the six of a hexagon) is equilateral. But can you show me how to get the radius to be 3? Thank you so much.
Answered by Walter Whiteley. 





A belt around two pulleys 
20041207 

From Ian: a belt is stretched around two pulleys whose centers are d units apart and whose radii are R and r respectively (obviously R+r<d). the challenge is to find the length of the belt, l as a formula in terms of R, r, and d only. Answered by Penny Nom. 





An arc of a circle 
20041205 

From Ruben: i have an arc 55 inches wide, 12 inches high at the centerline of the arc. how can i determine the diameter of the circle that would correspond to the arc. Answered by Penny Nom. 





Geometric sequence 
20041204 

From Lesa: Find a formula for the geometric sequence: (√3  √2), (4  √6), (6√3  2√2), … Answered by Penny Nom. 





Probability 
20041204 

From A parent: Consider a 30 sided polygon. If three diagonal are selected at random, what is the PROBABILITY that they share a common endpoint? Answered by Denis Hanson. 





"a" cubed minus "b" cubed 
20041202 

From Denise: "a"cubed minus "b"cubed equal (ab) times
("a"squared plus "ab" plus "b"squared)?
I know this is a formula, but why is it true? Answered by Penny. 





Select a card from the deck. 
20041202 

From Heidi: Select a card from the deck. What is the probability that this card will be red? Show the number of expected outcomes versus the number of total possible outcomes. What type of event does this represent? Answered by Penny. 





1/x + 1/y = 2/31 
20041201 

From matt: I have this problem which I think is a bit more tricky than usual.
x and y are positive integers.
1/x + 1/y = 2/31 Answered by Claude Tardif. 





e = ln(b/a) solve for a 
20041201 

From Daniel: I am trying to make "a" the subject of this equation "e = ln(b/a)" but am not sure if i'm doing it right. Any help would be appriciated, Answered by Claude Tardif. 





The volume of a sphere 
20041130 

From Lyndsay: twenty cubic metres of air are pumped into a spherical hot air balloon with each given diameter: 1.0m; 2.0m; 3.0m; 4.0m; 5.0m;6.0m
a)calculate the new diameter, new suface area, and new volume of each balloon. Answered by Penny Nom. 





The substitution method 
20041128 

From A student: I Was working and i ran into this problem can you help me solve it using the substitution method?
3x2y=10
x+5y=27 Answered by Penny Nom. 





The tangent line at an inflection point 
20041128 

From Louise: the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is... Answered by Penny Nom. 





Computing confidence intervals 
20041126 

From Christie: I was given a question with N=100, sample proportion is 0.1 compute the 95% confidence interval for P? I have tried this several ways but do not know how to do without means, standard deviations, standard error of the mean? I asked my teacher and she said I have all the info I need. Can you help???? Answered by Penny Nom. 





A right triangle 
20041124 

From Bruce: In triangle ABC.
Angle ABC is 90 degrees.
Side AB measures 34.
Side BC measures 31.
What does side AC measure? Answered by Penny Nom. 





Slicing cubes 
20041123 

From Anthony: You are working with a power saw and wish to cut a wooden cube 3inches on aside into 27 1inch cubes. You can do this by making six cuts through the cube keeping the pieces together in the cube shape. Can you reduce the number of necessary cuts by rearranging the pieces after each cut? Answered by Chris Fisher. 





Cost before the markup 
20041123 

From Norman: the sum of eg $130 includes the markup of 30%.
However I need to calculate the percentage to apply to the $130 to assess the cost ie $100. Answered by Penny Nom. 





A graph with certain properties 
20041122 

From A student: i was asked as a question in coursework to sketch the graph with the following characteristics:
a double root at 3
a pair of imaginary roots
an xintercept at 6
a root at 4 which is not a double root Answered by Penny Nom. 





Combinations 
20041122 

From Vivek: Show that
10C0 + 10C1 + 10C2 + 10C3+.....10C10 =1024 Answered by Penny Nom. 





The length of an arc 
20041121 

From Daryl: I am tying to find the arc length of a line 6' and the vertex of the arc 1' off of the line. that is all that is known Answered by Penny Nom. 





Is a square a rectangle? 
20041121 

From Carol: I am a teacher. In an FCAT sixth grade review test, there was a question to the students to draw a square and then they referred to it as a rectangle.
What is the definition that makes a rectangle a square that can be taught to the students without confusing them. Answered by Walter Whiteley. 





Proof by induction 
20041120 

From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows:
a(1) = 3 and a(k+1) = 2a(k) for k > 1.
Note: Quantities in brackets are subscripts
> means 'equal to or greater than'.
Using the recursive formula, the first 4 terms are;
a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24
The nth term a(n) = 2n1 x 3 (equation 1)
Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom. 





Solving quadratics 
20041120 

From Aaron: Can you solve the following equation (quote the value of x,y and t to 3 sig figs)
((i have changed figures so that i can work through my own example))
x^{2} + x  6 = 0
5y^{2} +19y = 3
10cos2 t + 3cos t = 4 Answered by Penny Nom. 





Construction of a cone 
20041120 

From John: I am a builder working on a project where I need to make a cone. It's a right circular cone with 15" base radius and slant angle of 30 degrees. I want to cut it out of flat sheet metal then bring the edges together to form the cone. Is this enough information? Answered by Penny Nom. 





A sequence 
20041119 

From Liucy: Find the Nth term:
10 40 90 160 250 Answered by Penny Nom. 





Volume of a box 
20041118 

From Catherine: I need to find a formula to calculate the amount of liquid would hold. maybe the volume or something. its a square box used to hold liquid on a farm . we want to measure how much liquid it can hold. Answered by Penny Nom. 





1/4 tsp salt = ??? grams 
20041116 

From Julie: if i have 1/4 teaspoon of salt how many grams does that equal Answered by Penny Nom. 





Equations involving radicals 
20041116 

From Merin:
I am quite confused about solving radical equations. This is what I understand:
___
V x3 = 3
Then you would square each side to get ride of the radical sign and then you solve the problem from there. (x=12 right?)
However, what about a problem with two radicals? For example:
___ ____
V x2 + V 3x3 = 3
No matter what I try I cant get the right answer!! Please help!!! Answered by Penny Nom. 





Interior and exterior angles of a polygon 
20041116 

From Aaron: How do you find the measure of interior and exterior angles of a regular polygon when you are given the number of sides? Answered by Walter Whiteley. 





Planting trees 
20041115 

From Heather: Design a plan of how it would be possible to plant 10 trees in 5 rows, and have 4 trees in each row. Answered by Penny Nom. 





A fixed point problem 
20041114 

From Bob: I am trying to solve an existence of fixed point problem. I need to show that a function f (on reals) with f'(x)=>2 has a fixed
point. Answered by Claude Tardif. 





An ODE 
20041110 

From David: I have a question that i really cant do, it is as follows:
The ODE dy/dx + 0.5y = 0.5e^(1.5x) ; y(5) = 2
Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 Answered by Harley Weston. 





Order of operations 
20041110 

From Andrew: I'm trying to solve this question, and I can't seem to remember the rules back from my high school days.
(40 x 8 ) / 2 + 55  15 =
Can you help me with the answer? Answered by Harley Weston. 





A 40% reduction 
20041110 

From Cathy: I'm having trouble figuring out how to figure a percentage??? it's easy to find what 40% of any given number is, but how would i accurately figure out what is the final number is when i know the number after the 40% has been removed? when i add 40% to this number it obviously is lower than it should
be. the best i could figure is;
x=?40% > x?=40% i'm all confused???? Answered by Penny Nom. 





Bedmas 
20041109 

From Fariha: i have a single line question and am not sure of the method
it would be appreciated if u could send me a method and a solution Q : 1 + 9 / 2 + 5 * 1000
would this be solved by BEDMAS? if not, why? Answered by Penny Nom. 





A standard deviation test 
20041109 

From Karen: How do you compare to see if a sample standard deviation is different than the population standard deviation? I know how to compare means, but not standard deviations. Answered by Penny Nom. 





A 306090 triangle 
20041109 

From Amy: How do you find the length of the hypotenuse of a 306090 triangle when the side opposite the 60 degree angle is 6 inches? Answered by Penny Nom. 





Factoring 
20041109 

From Rise: Q1: a^{2} + 5a + 6
I didn't really understand the purpose of the teacher's steps, but was able to get my daughter to find factors of 6 and then add them together to find which resulted in the sum of 5.
Unfortunately, this problemsolving technique did not help us to solve for the more complex problems as follows:
Q2: 9a^{3}  24a^{2} + 12a Answered by Penny Nom. 





The lcm of 5, 3, 4, 7 and 2 
20041105 

From Christine: what is the lcm of 5,3,4,7,2 Answered by Penny Nom. 





42.5 is what % of 170? 
20041105 

From Dawn: 42.5 is what % of 170? Answered by Penny Nom. 





The points of intersection of two graphs 
20041105 

From Benjamin: How do I find the points of intersection of the two functions:
1) y = 2  ex
2) y = 1 + x2 Answered by Harley Weston. 





Probabilities in poker 
20041104 

From Ben: Please can someone tell me the odds of getting a royal flush while playing texas hold em.
Please can you also let us know the odds of a royal flush while playing texas hold em if you must be dealt two of the needed cards. Answered by Chris Fisher. 





The least common denominator 
20041103 

From A student: Write the LCD for each pair of fractions.
13. 1/3,1/5
14. 2/7,1/4
15. 3/4,3/5 Answered by Penny Nom. 





The lcm of 1 and 1 
20041103 

From Nayiyan: I would like to know what is the LCM of (1) and (+1) is. Answered by Penny Nom. 





Adding 3% to get 120,000 
20041102 

From Shaun: I was asked a question by a friend of mine's kid. He asked me if you had a final figure of say 120,000, how do you work out the amount you started with if you added 3% of the starting amount, to the starting amount to get the 120,000.
Answered by Paul Betts. 





Tennis balls and probability 
20041101 

From Jeremy: I have a hopper of tennis balls that contains 25 new tennis balls and 10 old tennis balls. In the hopper the tennis balls are mixed up randomly. If i take one ball out of the hopper and hit it and then put it back and then take another ball out of the hopper and hit it and put it back, what is the probability that i hit two new tennis balls? Also a tennis ball becomes old after being hit just once. Answered by Penny Nom. 





The sides of a hexagon 
20041101 

From Timothy: I have a perfect Hexagon in which i know the measurement across is 10m. Not from point to point, but from the middle of one side directly across to the middle of the other. From that measurement, how can I determine the length of 1 side. Answered by Penny Nom. 





Multiplying two algebraic fractions 
20041031 

From A parent: Multiply:
x+2 x²4
 x 
x2 x²+x2 Answered by Harley Weston. 





Imaginary roots of a ploynomial 
20041031 

From Jennifer: how to find the roots of a polynomial equation if it would be imaginary? Answered by Harley Weston. 





GCD and LCM 
20041031 

From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom. 





The combined force of two vectors 
20041030 

From Brian: Two teams are playing push ball with a large 8 foot diameter ball. One team exerts a force represented by the vector a = 2i + 5j, and the other team exerts a force represented by the vector b = 8i3j.
1.Determine the direction of movement of the ball if the i axis is due east.
2.Determine the combined force magnitude. Answered by Harley Weston. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





Vectors in three space 
20041030 

From Jo: I have two questions that I just cannot visulise and dont know how to get started on them..!
1. Ship X is sailing North at 4m/s and Ship Y is sailing due East at 3m/s. A sailor on Ship X climbs a vertical pole at 1/2 m/s. What is the velocity of the sailor on Ship X relative to an observer on Ship Y? State it's magnitude and direction.
Not sure where to start with this one...
2. Show, using vectors, that for any tetrahedron, the segments joining the midpoints of the opposite edges are concurrent.
i know what a tetradedron is, and what I am proving but do I solve simultaneously for a specific case?? Answered by Walter Whiteley. 





Bedmas 
20041030 

From Gina: I am just curious whether Bedmas would be used in the following question as it is not in the typical Bedmas format.
Multiply 12 x 24
Add 26
Divide by 2
Subtract 7
Would we go about doing it in the sequence it is given or in Bedmas ? Answered by Penny Nom. 





The force of a 5000 tonne lorry 
20041027 

From Aaron: A 50 tonne lorry is parked on a slope with a gradient of 4%.
Due to the self weight of the lorry, what is the force
* acting down the slope
* acting normal (at right angles) to the slope Answered by Penny Nom. 





Ratios and rates 
20041027 

From Kenneth: What is the difference between a ratio and a rate? Answered by Penny Nom. 





Cube roots 
20041026 

From A parent: How do you solve the problem of finding the cubed root of (17 to the power of 3).
Can you show me each step and if you have a visual representation of this it would be very helpful.
Also can you show a step by step of finding the cubed root of 27. Visuals help a lot Answered by Penny Nom. 





20 Golfers 
20041026 

From Ian: I have 20 golfers playing over 6 days I would like to schedule all 20 golfers in 5 groups of 4 on each day here is the catch.... I would like each player to play with each other once during the 6 days. Answered by Chris Fisher. 





The point slope form of a line 
20041026 

From Jack: Given a set of ordered pairs, ie (1,1) (2,4) (3,7), how does one determine the rule f(n) other than by trial and error Answered by Penny Nom. 





Largest square inside a circle 
20041025 

From Bob: my granddaughter asked
what is the largest size square in inches
would fit in a 60 inch circle?
I believe it to be around 42.3 inches but
would like to teach her how to do it mathematically. Answered by Penny Nom. 





Square roots and inequalities 
20041025 

From Waheed: Q1. What is the simplest way of finding a square root of any number using just a pen and paper? (I am asking this question because I browsed a few sites a didn't find any method that is simpler than the one I use. so I am just curious.)
Q2. Is it possible that you take an equation and turn it into an inequality by performing same mathematical operations on both sides? Answered by Claude Tardif and Penny Nom. 





Converting coordinates 
20041025 

From Allen: I am trying to help my son with his home, but I don't remember these conversions. Please help.
1. Convert the following coordinates
Cartesian x = 7, y = 24
2. Convert the following coordinates
Polar r = 4, theta = pi / 3 Answered by Penny Nom. 





Implicit differentiation 
20041024 

From Emily: If x^3+3xy+2y^3=17, then in terms of x and y, dy/dx = Answered by Penny Nom. 





Maximize income 
20041024 

From Connie: A company that sells x units of a product generates an income (I, in dollars) which is a function of x. The income generated is described by the equation
I = (1/2)x^2 + 100x.
Discuss how to determine the number of units that must be sold so that the company can maximize its income. What is the maximum income? Answered by Penny Nom. 





Practical applications: parabolas and Pythagoras 
20041024 

From Connie: Provide two examples of real life objects that incorporate parabolic shapes. Explain the reason why the parabolic shape was used in each object.
I need at least one practical application of the Pythagorean Theorem. Answered by Penny Nom. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





An aircraft is flying directly from airport A to airport B 
20041022 

From A student: In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from airport A to airport B, which is 2000 km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i30j)km/h. Calculate
(i) the time of flight, to the nearest min
(ii) the direction of the wind. Answered by Penny Nom. 





The last digit of a large exponent 
20041020 

From Landon: How can one determine the last digit of a large exponent by hand. I have seen several examples of how to do this by breaking it up into smaller exponents, but is there a formula or some common things to look for? Answered by Penny Nom. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom. 





A 40% increase in garage space 
20041020 

From Dianna: A bus company recently expanded and no longer has enough room in its garage for all of its buses. Twelve of the buses have to be stored outside. If the company decides to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company own? Answered by Penny Nom. 





A square footage problem 
20041019 

From Jerome: I have a peice of property that is almost a triangle but not exactly about 280 frontage with the side lines at 228 and 237
I was told I had about one acre plus a little, a developer says I have 33,000 sq ft. and I would like to know what the real result is Answered by Penny Nom. 





Manipulating exponents 
20041017 

From A student: I was wondering if you can describe the steps in getting the solution to the problem below. I have the solution of 5/3 in the back of a book, but I have no idea how that answer was reached.
2raised to the 100th power + 2raised to the 98th power divided by 2raised to the 100th power  2raised to the 98th power Answered by Penny Nom. 





The third derivative 
20041015 

From Holly: Why would you ever take the third derivative? Answered by Harley Weston. 





A rate of change problem 
20041015 

From Frank: Find the rate of change of the distance between the origin and a moving point on the graph of y = x(squared) + 1 if dx/dt = 2 centimeters per second. Answered by Penny Nom. 





Two gears 
20041014 

From Lindsay: "There are two gears, a small one on the left and a larger one on the right. The gear on the right makes 1 revolution. The gear on the left makes two revolutions. Suppose the gear on the right is turned through an obtuse angle. Will the gear on the left make a full turn?" Answered by Penny Nom. 





Divisibility by 7 and 11 
20041013 

From Tammy: I'm stuck in class in Yr 7 And I'm finding it hard on our new topic Divisibility! When I try to find out what this means on Internet sites i can not understand the used symbols like algebra and so on. I'm stuck on the divisibility rules for the number 11! Answered by Penny. 





$25,000 at 11% per year 
20041013 

From A student: suppose u have $25,000 to invest and the interest rate at your bank is 11%.
1) how much money would you have at the end of EACH of the first four years?
1) i already kno that the first year w/ interest is $27,750 but how do i get the 2nd? 3rd? 4th? years? Answered by Penny. 





Pythagoras in everyday life 
20041013 

From Tiffany: I was wondering if you have any reallife uses of the pythagorean theorem that you use in your everyday life. Answered by Penny Nom. 





Cycling in the wind 
20041011 

From A student: A cyclist is travelling in the direction of 12i+5j at a speed of 39 km/h where i is a unit vector due east and j is a unit vector due north. The wind appears to the cyclist to be blowing with a velocity of (4i+j) km/h. Find, correct to 1 d.p
(a) the true speed of the wind and
(b) the bearing from which the wind is blowing
Answered by Penny Nom. 





An Octagon 
20041010 

From A parent: I am trying to determine what the size of each triangle is of a 12 foot circle consisting of 8 triangles would be. I've gotten as far as the radius being 6 feet, but cannot figure the distance. Answered by Penny Nom. 





A five digit number 
20041006 

From A parent: What is the 5 digit number in which the first 2 digits are the square of the 3rd digit and the last 2 digits are the square of the digit that is one less than the third digit? The sum of all the digits is 22. Answered by Penny Nom. 





A common tangent line 
20041005 

From Shanup: The xaxis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent. Answered by Penny Nom. 





Direct and inverse variation 
20041005 

From Abraham: Given that y varies inversely as x and x varies directly as z.If z is doubled then y is halved.Why is that true.Please explain.I'm having trouble understanding the different types of variation Answered by Penny Nom. 





Accelerating to the speed of light 
20040930 

From Lars: How long time would it take to accelerate up to the speed of light with an acceleration speed similar to 0100 seconds in 5 seconds? Answered by Penny Nom. 





A mixture problem 
20040930 

From Abraham: A chemist has one solution that is 35% pure acid and another solution that is 75% pure acid. How many cubic centimeters of each solution must be used to produce 80 cubic centimeters of solution that is 50% acid? Answered by Penny Nom. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





The area of a lot 
20040929 

From Deb: I am trying to figure out how many square feet are in a piece of property. Start at Point Athen go 140 feet norththen 100 feet due eastthen 300 feet at an angle southeast so that connecting to point A would be a straight line (right angle to first line north.) Answered by Penny Nom. 





Visitor wins or home wins 
20040929 

From Paavn and Laddi: I have a math question i am stumped on for one of my classes. The question states that there are 14 baseball games with 2 possible outcomes for each game, visitor win or home win. How many different total combinations are possible from the 14 games? Answered by Penny Nom. 





Cubic yards of concrete 
20040929 

From Tanya: We are starting up a new business and for the business we will be required to order concrete for various shapes. Right now we have a job that requires a concrete slab that a decagon it is 1403/4" from flat side to flat side, 74" from point to center and each flat side is 46" The pad should be 4" thick with 12"x12" continuous footing. Answered by Harley Weston. 





The area of a lot 
20040928 

From Stan: I own a parcel of land (lot 20) that is assessed at 9127.00 square feet and has a frontage of 99.90 feet according to the tax roll. I don't know how large my property actually is since I feel that the tax assessment and the survey map don't jive Answered by Harley Weston. 





A palindrome question 
20040928 

From Lilly: 12, 21, 13, and 31 are the only doubledigit numbers whose squares are the palindromes of the squares of the palindromes of doubledigit numbers. I was wondering why it works for these numbers, and if only these numbers work this way. Answered by Chris Fisher and Penny Nom. 





The length of a rectangle 
20040926 

From Rebecca: My question is each side of a square S is 18 inches long and the area of S is at least 3 times the area of a rectangle that is 9 inches wide. What is the greatest possible length in inches of the rectangle? Answered by Penny Nom. 





37% 
20040926 

From Andrew: how do we change 37% into a fraction Answered by Penny Nom. 





Grams to milliliters 
20040925 

From Emily: I am trying to convert 19.5g into mL assuming that it's water; density=1g/mL. I don't know where to begin. Answered by Penny Nom. 





A parallelepiped 
20040925 

From Aman: " If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,2), B is (3,6,1), and C is (4,0,1), find the coordinates of the other vertices of the parallelepiped.)" Answered by Penny Nom. 





The last digit of 2^28 
20040925 

From A student: I am currently enrolled in a math reasoning class and a math question I have to answer is determine the units digit in 3 28power. When I set up a table and keep cubing the numbers, I find a pattern with the last digits of the numbers that follow 1,3,9,7. My calculator gets to about the 19th power, and then I get an error. If I continued the pattern, would the units digit then be the last digit of 3 28th power, which would be a 7? Please let me know if I am solving this correctly and what a unit's digit actually is. Answered by Penny Nom. 





Rational expressions 
20040924 

From A student: In general, I understand rational expressions except when it comes to solving problems such as:
x+y/2xy  2x/y2x or m4/3m4 + 3m+2/43m
I am confounded by the issue of having to find a common denominator. For example, if I tried to solve these problems by multiplying both denominators they would still be uncommon. Answered by Claude Tardif. 





Supplementary angles 
20040923 

From Rosemary: Is the term supplementary angles only applicable to 2 angles (ie. a pair of angles) or can it be used when talking about 3 or more angles that add to make 180 degrees? Answered by Penny Nom. 





Incremental variance 
20040923 

From Carlos: I must keep statistical data (mean and variance) in 3 granularity levels depending on the age of the data (daily for older than 1 year, hourly for older than 1 month and quarterhour for older than 1 day). How can I calculate the resulting variance from a set of variances previously calculated supposing I have the count and mean for each member of the set? Answered by Andrei Volodin and Penny Nom. 





The volume of a pile of mulch 
20040922 

From Sam: Is there a formula to determine the cubic feet of something in a pile. IE I need to determine the cubic feet of a pile of mulch. The pile comes to a peak, so the length and width decrease as the pile increases. Answered by Penny Nom. 





Four and five digit numbers 
20040921 

From Josy:
The question I have now in front of me is....Is a 4digit number always less than a 5digit number?
Hi Josy,
The digits in order are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Thus the largest four digit number is 9999. The smallet 5 digit number is 10000.
Penny
Go to Math Central
Answered by Penny Nom. 





1,3,6,11,18,29,__ 
20040921 

From Guillermo: How do you get to the answer of this sequence
1,3,6,11,18,29,__ Answered by Claude Tardif. 





f(x) = x4 if x<2 
20040921 

From Dani: Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,2), and why does the arrow point where it does? Answered by Penny Nom. 





The method of substitution 
20040920 

From Kayla: y=x1
y=2x3 Answered by Harley Weston. 





Wages for one month 
20040920 

From Janet: if offered $10,000 or 1 cent on the first day and then doubled daily for one month which would you take ? Answered by Harley Weston. 





B={A,{A}} 
20040920 

From Muhammad: Let A be a set and let B = {A,{A}}.
(a) Explain the elements of set B (with some example)
(b) Prove that A is not a subset of B. Answered by Penny. 





The hypotenuse of a right triangle 
20040920 

From Shannon: I am trying to find the hypotenuse of a right triangle with only the length of the opposite side. What is the formula as I don't have the length of the adjacent side? Can I compute it without knowing what the other two angles are? Answered by Penny Nom. 





Fabricating with pipe 
20040919 

From Gil: I need to fabricate a 10 section, 4" pipe circle with an inside diameter of 40". I would like to know what angles would apply and how to find them, Answered by Penny Nom. 





A binomial squared 
20040919 

From John: Can you explain the steps
for me, that get you from (a  b)^{2} to a^{2} 
2ab + b^{2} Answered by Penny Nom. 





Perimeter and area of a semi_circle 
20040918 

From A student: I want to know how to find the perimeter and area of a semicircle and a quartercircle. Answered by Penny Nom. 





Zero to the zero 
20040918 

From Greta: My name is Greta, and I am a 7th grader and my test is coming up. The question I would like to ask you is why 0 elevated to 0 is unidentified. Answered by Penny. 





Driving me crazy 
20040918 

From Jerry: This is driving me crazy!!! Someone told me of a number that can be divided EQUALLY by each of the following individual numbers: 1,2,3,4,5,6,7,8,9. what is that number? Answered by Penny. 





The price of a book 
20040918 

From Dorly: If the number of toonies required to buy a book is nine more than the number of
fivedollar bills required to buy the same book, determine the cost of the book. Answered by Penny. 





A challenge 
20040917 

From Lasse: xy
xx
xyx
xxx
xyxx
"x" and "y" each represents a number.
Find out the system to make the next line Answered by Penny Nom. 





Some numbers less than 100 
20040917 

From Paul: for how many numbers less than 100 is the digit in the ones place half the digit in the tens place? Answered by Penny Nom. 





Division with and without units 
20040917 

From Kenneth: What does it indicate when the divisor has units (dollars) but not the dividend, as in 500/$10.00 or 500 is divided by $10.00?
Are the units understood to be there? Does 500/$10.00 make sense? Answered by Penny Nom. 





The length of a cut 
20040917 

From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures:
a=4squared, b=6squared.
She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif. 





Pizza for Jack? 
20040916 

From Grace: Jack is playing pool with Jim for $1 a game. He has only $2 and decides to play until he goes broke or has $5, at which point he will quit and go out for a pizza with Jim(Dutch treat). Jack knows from past experience that he beats Jim 60% of the time. What is the probability that Jack will get to eat pizza? Hints: Let A be the 6x6 matrix defined by A=[aij], where aij is the probability that Jack will have $(i1)after one game is he starts with $(j1). For example, a23  .40 since there is a 40% probability that Jack will end up with $1 after a game is he starts the game with $2 (If Jack wins 605 of the time, he must lose 40% of the time). Also, for example, a52 = 0 since there is no way jack can have $4 after one game if he had $1 at the beginning of the game. Since Jack will stop if he goes broke or accumulates $5, a11 and a66 are both 1.
Let x0 = [0 0 1 0 0 0 ] transposed, which we interpret as saying that initially Jack has $2 with a probability 1. Then Ax0 will represent the porbability of each amount of money, $0$5, after one game. What is the probability that Jack will be able to eat pizza by computing Akx0 for large k and finding a limiting value. Answered by Penny Nom. 





Volume 
20040916 

From Jonathan: I have an area of 22ft x 43 ft, 6 inches high
Sq. ft..946
sq. yds...105.1
What is the cubic feet and cubic yards for this dimension. Answered by Penny Nom. 





S is between T and V 
20040916 

From Reuben: S is between T and V. R is between S and T. T is between R and Q.
QV=18 QT=6 and TR = RS = SV Make a sketch and answer the following:
Find RS QS TS TV Answered by Penny Nom. 





The game of 24 
20040916 

From Angelica: how can you make 24 out of 7,7,6,5? Answered by Claude Tardif. 





Finding the height of a triangle 
20040914 

From A student: I have to calculate the height of a triangle.
The base is 6 (units)say ab
One of the top sides is 4 (units)say ca
The other side is 2 (units) say cb
I don't know the angles.
How to find the height? Answered by Chris Fisher and Penny Nom. 





The game of 24 
20040914 

From Alan: I was playing that math 24 game and i cant get 21,14,2,2 to equal 24 Answered by Claude Tardif. 





Crossword math puzzle 
20040914 

From Joyce and Tiffany: The puzzle name was real number vocabulary and the question is (a number that divides evenly into another what is it?). (Space in between ticmarks on a number line). Answered by Harley Weston. 





Payment plus interest 
20040914 

From Penny: Brian wants to borrow some money from Margaret.
After three years he is to pay X back plus one interest sum of 25%. If he is pays back a total of $3800, what was the original sum borrowed? Answered by Penny Nom. 





differentiate Y=X^X^X 
20040913 

From Kunle: differentiate Y=X^X^X Answered by Penny Nom. 





Making a pyramid 
20040912 

From Jacob: My name is Jacob and I am a 11th grade student trying to build a pyramid for a friend but I need a chart of some sort to show me the measurements (I learn better w\pictures) it is a square base with 18 in sides and I want the vertex to be 18in above the base I need to know as many measurements as you can give me. Answered by Penny Nom. 





A copper sphere 
20040912 

From Irfan: The radius of a copper sphere is 3cm. If a wire of 0.4 diameter is drawn by melting it,what is the length of this wire? Answered by Penny Nom. 





Three word problems 
20040912 

From Adrian: 1. Increasing area
of a field: Julia's soybean field is 3m longer than it is wide. To
increase her production, she plans to increase her to increase both the
length and width by 2m. If the new field is 46m2(2nd power) larger
than the old field, then what are the dimensions of the old field?
2. Width of a Football Field: If the perimeter of a football
field in the NFL including the end zones is 1040 ft and the field is
120 yd long, then what is the width of the field in feet?
3. Fencing dog pens Clint is constructing two adjacent rectangular
dog pens. Each pen will be three times as long as it is wide, and the
pens will share a common long side. If Clint has 65 ft of fencing, what
are the dimensions of each pen? Answered by Penny Nom. 





Number combinations 
20040910 

From Angela: I need the number of possible number combinations, both 3 and 4 digit, from 059
I know that 09 has 10000 combinations for 4 digits
I also know that 09 has 1000 combinations for 3 digits
Perhaps you could explain an easier way to figure this out rather than writing all these numbers down?? Answered by Penny Nom. 





A schedule for 6 teams 
20040910 

From Greg: I have a schedule I need to make of 6 teams. They must play each other once however no team can be the away team twice in a row. There must be 3 home games and 3 away games for each team. Answered by Penny Nom. 





105.6 is a discount of 12% from x 
20040910 

From David: If I know that 105.6 is a discount of 12% from x, how do I find x?? Answered by Penny Nom. 





1+3+5+...+(2n+1) 
20040910 

From Emma: Prove that 1+3+5+...+(2n+1)= (n+1)^{2} Answered by Penny Nom. 





Safe cracker 
20040909 

From Adam:
Franklin's friend had taken an item from him, and put it in his family's safe, when franklin went to retrieve it he came to a combination lock on the safe, with the dial numbers going from 0 to 59. Unfortunately, he wasn't sure whether there were three or four numbers in the combination, or even which direction to turn the wheel
If it takes him 15 seconds to try a single combination, how many days will it take him to to try every possible combination? Please round to the nearest day. Answered by Penny Nom. 





The 24 game 
20040909 

From Erik: Ive spent around 40 hours on this one problem. I need help. 3,3,7,7 Answered by Claide Tardif. 





A travelling salesman 
20040909 

From Liz: A salesman traveled due west from city A to city B. The distance he traveled, that is the ditance from A to B, was X miles. He returned from B to A and found that he had traveled half the distance, X/2 miles. How can that be? Answered by Chris Fisher and Penny Nom. 





Crossing a river 
20040909 

From Barb: Nine men and two boys, trekking through the jungle, need to cross a river. They have a small inflatable boat and it's easy enough to row it across the river. The boat, however, can hold no more than one man or the two boys. How can they all get across? (Hint. suppose there was only one man and two boys) Does it make math sense and what would the answer be Answered by Penny Nom and Claude Tardif. 





An inverse 
20040909 

From Hillary: I cannot figure out the inverse of this function.
f(x)= 1/2x 1 Answered by Penny Nom. 





Half way between 
20040908 

From Ben: Find the number halfway between the number shown
751,843 Answered by Penny Nom. 





The nth term 
20040908 

From Alex: What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?... Answered by Penny Nom. 





d varies inversely with g 
20040907 

From Ashlyn: d varies inversely with g when d=8 and g=2
a. write d as a function of g using function
notation.
b. find d(10). Answered by Penny Nom. 





Constructing a cone 
20040907 

From Steve: I am trying to build crayfish traps; one of the components is a cone shaped entry section.
The cone I want to make would be 12" in diameter at the base and 12" in height, from base to peak.
I need a formula to calculate the dimensions and a method of transferring the shape onto a flat piece of material.
Answered by Harley Weston. 





The intersection of planes 
20040907 

From Joshua: I was wondering about the intersection of planes. Can planes intersect? Answered by Penny Nom. 





The bar over repeating digits. 
20040907 

From Debbie: I would like to know the name given to the bar that is written over the repeating digits of a decimal. Answered by Penny Nom. 





How to dry matches 
20040906 

From Liz: The neighbors of a young man who needed seclusion for a few days offered him the keys to their cabin in Maine. Arriving there on a damp and cold autumn evening he saw that while the cabin had normal running water and electric lights, for heat it had only a potbellied stove. Fortunately, there was plenty of wood, kindling, newspaper, and matches. Being an experienced hand at making a fire, he opened the damper, put into the stove crumpled newspaper, and properly stacked the kindling and logs. The matches, however, wouldn't light. They were too damp from the humidty. The nearest town was 30 miles away, and, anyway, it was late. What next? Answered by Claude Tardif. 





(2x+5y6) + (3x4y+12) 
20040904 

From GG: I am a grade 9 student and i do not understand a question. Plz help!
OK here it is........ (2x+5y6) + (3x4y+12) Answered by Penny Nom. 





Order of operations 
20040904 

From Leanne: 6 + 3  2 x 3 = Answered by Claude Tardif. 





The distance formula 
20040904 

From Joe: Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out? Answered by Claude Tardif. 





Nine minutes 
20040902 

From A student: You have two hour glassesone measures 7 minutes and one measures 4 minutes.How can you time 9 minutes? Answered by Penny Nom. 





Cubic yards 
20040901 

From Garnet: I have the dimensions of 16 feet by 10 ft and 3 1/2 inches deep how much concrete do I need. Answered by Penny Nom. 





An isosceles trapezoid 
20040831 

From Bruce: An isosceles trapezoid with bases of lengths 12 and 16 is inscribed in a circle with a radius of 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid. Answered by Penny Nom. 





Cubic meters 
20040831 

From Brad: I have a 10' x 10' x 12" area & need to find the cubic meters, how do I do this? Answered by Penny Nom. 





Percentage change 
20040830 

From Lauren: if egg A weighed 55.4g and after 2 days it weighed 60.9g how could i calculate the percentage change in weight? Answered by Penny Nom. 





Solve for z 
20040830 

From Ana: Solve for z when 4x + 10yz = 0
solve for z if y2 + 3yz  8z  4x = 0?
Do I have to solve all of the variables in order to get z? Answered by Penny Nom. 





69 is what percentage of 113 
20040828 

From Mary: How do I work out what percentage of 113 69 is? Answered by Penny Nom. 





GCD (a + b , a^2  ab + b^2) 
20040827 

From Carol: Let a and b integer and relatively prime. Proof that:
GCD (a + b , a^2  ab + b^2) = 1 or 3 Answered by Penny Nom. 





A big number 
20040826 

From Mark: If you have $999,999,999,999,999,999,999,999,999,999.99 and you find a pennie how much is that and can you give me the name of it. Answered by Penny Nom. 





Combined operations 
20040826 

From Louise: Question 2 1/4 x 1/8 / 1 3/4 x 12 4/9 x 3 = Answered by Penny Nom. 





Percentage of a quota 
20040826 

From Jenni: I have the year to date sales of $2,042,744 and the quota is $2,257,440, how do I figure the percent quota. Answered by Penny Nom. 





The area of a quadrilateral 
20040825 

From Rich: I would like to know how to measure the area (the formula) of a quadrilateral. Answered by Penny Nom. 





The radius of a circle 
20040824 

From Peter: If you slice any circle with a line, and call the distance of the line between intersections the "y" length and the perpendicular length to the shorter side of the curve the "x" length, what is the resulting equation for the radius? Answered by Penny Nom. 





50/5x  y 
20040822 

From Rick: Niece has a question that was marked wrong but we are unable to determine how the teacher calculated and arrived at the answer? The problem was as follows:
50 / 5x  y =
x=5
y=1 Answered by Harley Weston and Leeanne Boehm. 





The area of a lot 
20040822 

From Cassie: I'm in the process of purchasing some land and I'm trying to figure out the square footage of the property. Unfortunately, it's be a while since I had to remember this type of formula. The property is 140 ft on left side, across the back it is 220.61 ft, the right side is 167.52 ft, the frontage is 105 ft. Answered by Penny Nom. 





15 cubic yards of dirt 
20040822 

From Barry: My question...what is the equivalent of 15 cubic yards of dirt? Answered by Penny Nom. 





130 cc. is ? 
20040820 

From Ayrn: 130 cc. is ?
I have to put 130cc. of petroleum in a bucket how much exactly is that?
Also 110 cc.?
I have to also put 110cc. wood alcohol in a bucket aswell! Answered by Penny Nom. 





Golfing with Norm 
20040819 

From Norm: I am organizing a golf tournament with 6 American and 6 Canadian players. We play 3 rounds of golf. Is there any way to arrange that everyone plays without playing with the same person twice. Each foursome must consist of 2 Americans and 2 Canadians with one of each in a cart. Your help would be much appreciated. Answered by Claude Tardif. 





Golfing with Sally 
20040819 

From Sally: We are a group of 8 golfers (2 foursomes) and want to golf 3 games together. How can we arrange it so that we all get to golf with each other at least once?
At another venue, we have 18 golfers (3 foursomes, 2 threesomes) and want to golf 6 games together. Same question, how can we arrange it so that we all get to golf with each other at least once? Answered by Claude Tardif. 





A division symbol 
20040818 

From William: i was wondering what the mathematical name for this division sign (÷). Answered by Penny Nom. 





A cube is inscribed inside a sphere 
20040818 

From A student: A cube is inscribed inside a sphere with radius sqrt8cm. Find the
(a) length of the cube
(b) volume of the space inside the sphere but outside the cube. Answered by Penny Nom. 





The series from i=1 to n :ai 
20040818 

From Ken: a.) Explain the difference between
the series from i=1 to n :ai
and the series j=1 to n :aj
b.) Explain the difference between
the series from i=1 to n:ai
and the series from i=1 to n :aj Answered by Penny Nom. 





Area of a triangle 
20040817 

From Barkie: I'm going into tenth grade and I have a triangle who's sides measure 3ft, 4ft, and 5ft. I need to find the area however I don't know the height, or how to get it. Answered by Chris Fisher. 





Two water jugs 
20040816 

From A student: You go to a source of water with two jugs and only two jugs. One jug has a capacity of exactly three pints and the other five pints. Both jugs are opaque (you can`t see inside them) and irregularly shaped. You have no other water containers. You do not have a scale. How can you use the two jugs and only the two jugs to measure exactly four pints of water? Answered by Penny Nom. 





Percentiles 
20040815 

From Gary: Table 1
Selected percentiles for family income in the US in 1992
1 $1,300
10 $10,200
25 $20,100
50 $36,800
75 $58,100
90 $85,000
99 $151,800
Q. The percentage of families in Table 1 with incomes below $58,100 was about? Answered by Penny Nom. 





A probability question 
20040815 

From Gary: In a law school class, the entering students averaged about 160 on the last
LSAT; the standard deviation was about 8. The historgram of the lLSAT
scores follwed the normal curve reasonable well.
Q. About what percentage of the class scored below 166?
Q. One student was 0.5 above average on the last LSAT, about what percentage
of the students had lower scores than he did? Answered by Penny Nom. 





X is due north of Y ... 
20040811 

From A student: X is due north of Y and 2km distant. Z is due east of Y and has a bearing of S35°12'E from X. How far, to the nearest metre, is Z from X? Answered by Penny Nom. 





Cubic yards of dirt 
20040811 

From A parent: How many cubic yards of dirt would it take to fill an area that is 325 feet by 325 feet and is 3 feet deep? Answered by Penny Nom. 





Acres and miles 
20040811 

From A student: How many acres are in 1 mile? Answered by Penny Nom. 





2.79 acres 
20040811 

From Helen: What would the square footage be of 2.79 acres? Answered by Penny Nom. 





Area of a hexagon 
20040810 

From RB: Hello. I need to find the Area in sq. ft. of a Hexagon with 6 equal sides, of 26' each. Answered by Penny Nom. 





A conic 
20040810 

From A student: My question is about this equation 32x*2 18y*2 64x +72y +248 =0
explain why as x goes to the infinity the graph of the conic looks like y= (3/4)X.
What I did to try to find the solution of this problem was to graph and then I thought that maybe trying to find the equation of the asymptotes I could do it, but it was useless because the equation of the asymptotes is y= +4/3(X1) 2 and that does not explain why tho conic looks like y=(3/4) x . I would really appreciate your help on this. Answered by Penny Nom. 





Constructing a triangle 
20040808 

From KV: HOW TO CONSTRUCT A TRIANGLE ABC, WHEN
ITS ALTITUDES AD,BE,CF ARE GIVEN Answered by Chris Fisher. 





A big number 
20040808 

From Carter: Can you tell me what number this is?
10,000,000,000,000,000,000,000,000,000,000,000,000
Where can I find the names for big numbers? Answered by Penny Nom. 





Limits and composite functions 
20040807 

From Sue: I have two questions, one about a limit and the other about a composite function. If you could help me, I'd really appreciate it.
1. Find the limit:
lim[x>0] (x*csc(x))
I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.
2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):
I'm having trouble with this one because x^2 + 4 isn't a perfect square.
Sue Answered by Penny Nom. 





The integrating factor method 
20040805 

From A student: Whilst using the integrating factor method, I am required to integrate a function multipled by another function.
say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.
Integral f(t)*g(t) dt or
Integral exp(kt)*g(t) dt
What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k?
More specifically, the problem and my attempted answer is in PDF format:
In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Answered by Harley Weston. 





Integrating e^sin(x) 
20040804 

From A student: I need to know that how to solve the integral " e^sin x", Answered by Harley Weston. 





Differentiation 
20040804 

From A parent: I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus:
a) f(x)=e^2^xIn(cos(8x))
b) f(x)=secx/SQRTx^4+1 Answered by Penny Nom. 





Two trig problems 
20040804 

From Tracie: sin^2x  sin x 12 = 0
sin 2x = sin x Answered by Penny Nom. 





When is the limit of f(x) undefined? 
20040803 

From Nicolasa: When is the limit of f(x) undefined? Answered by Penny Nom. 





an integer with three factors 
20040803 

From A student: What is the probability that a randomly chosen 3 digit number has exactly 3 factors Answered by Penny Nom. 





sin^2x5sinx3=0 
20040802 

From Kerri: hey my name is kerri i'm a college students and i was wondering if you could help in with this problems
sin^2x5sinx3=0 Answered by Penny Nom. 





A tangent to a hyperbola 
20040802 

From A student: The equation of a hyperbola is 32x*2 18Y*264x +72y +248=0. The equation of a tangent line to this hyperbola is y= (16/15)X + 10/3 I have been trying to find the point where this line intersects the graph. What I did was solve for x and then plugged in the result into the equation of the hyperbola, but I am getting two answers and I am supposed to get only one because the line is tangent to the graph. For this reason, I would like to know what I am doing wrong or what I have to do to know which answer is correct. Answered by Penny Nom. 





Two problems 
20040802 

From JJ: A question on my homework assignment about logs says "suppose that x=logA and y=logB & write the expression in terms of x and y"
log(A  B)
Is this even possible? It seems like a typo.
Another is: "solve for t."
12(1.221)^t = t + 3
Is this one possible? If it is, I cant figure it out. Answered by Penny Nom. 





A trig problem 
20040802 

From A student: Given that the maximum value of [sin(3y2)]^2 [cos(3y2)]^2
is k. If y>7, Find the minimum value of y for which
[Sin(3y2)]^2  [cos(3y2)]^2 =k. Answered by Penny Nom. 





Domain and range 
20040801 

From JJ: I'm checking domain and ranges of these functions. Are these right? Answered by Penny Nom. 





The law of sines 
20040801 

From Joy: How do you solve this? Do you solve this triangle using the law of sines of the law of cosines? (ASA)
A=120DEG. B=40DEG c=35 cm
I keep getting different answers. Answered by Penny Nom. 





Rate of change problems 
20040801 

From Jim: I just want to check a couple average rate of change problems because i just guessed on how to do them. Can you tell me how to do them?
the question says if f(x) = sqrt(x + 3), find f( x + rx). I got sqrt( x + rx + 3)
the other two are : f(x)= 3x1 (f(x)  f(1)) / (x1) ... I GOT 3 &
f(x)= x^3  x (f(x)  f(1)) / (x1) ... I GOT x^2 + x Answered by Penny Nom. 





Combien de litre y a t'il dans un M3 
20040730 

From Un eleve: j'aimerais savoir combien de litre y a t'il dans un M3. car je dois mettre un produit spécial dans une piscine. Answered by Claude Tardif. 





A parallelogram 
20040730 

From Keith: I'm a high school student and have been having trouble with this problem , which is based on one pair of parallel sides of a parallelogram: If AD = 6x5 and BC = 3x+7 find x. Of course both sides have to be equal. Now I know the value of x is 4 So my question is how do you get 4 from the given information. Answered by Penny Nom. 





Extraneous solutions 
20040728 

From Nicole: When I have a problem like (2x + 3)/5 = (x + 1)/6 and the question asks to check for extraneous solutions, how do you solve that? Answered by Penny Nom. 





Water in a cone 
20040728 

From A student: A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Answered by Penny Nom. 





The third side of a triangle 
20040728 

From Annette: How do you find the length of a triangle side if you know two sides? Answered by Penny Nom. 





Factoring 
20040728 

From Nicole: Can 4x2 + 19x + 12 be factored? i have tried but i cannot figure it out. Is there a way to find out if it cannot be factored before i try to work out the problem? Answered by Penny Nom. 





The intersection of two graphs 
20040728 

From JJ: Is there a way to find the intersections of these graphs algebraically?
x^2 + y = 4 & 2x  y = 1
I got (1.45, 1.9) and (3.45, 7.9) with a graphing calculator.
AND THESE...
y = 3.29x & y = 5.5(x^0.5)+ 10000
I got x at 3133 with a graphing calculator.
Answered by Penny Nom. 





x^2 = x + 2 
20040726 

From A parent: x2 = x+2
My daughter came home with this equation today and although I know the answer is x=2, i have no way of proving it by showing any working out. Answered by Penny Nom. 





The railing around a pool 
20040726 

From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom. 





The pvalue 
20040725 

From Kathy: Ms. Lisa Monnin is the budget director for the New Process Company. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.
At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the pvalue?
Having problems finding the pvalue & unsure of the formula.
Kathy Answered by Penny Nom. 





Row echelon form 
20040724 

From Michael: My name is Michael and I'm in the 11th grade. I have a Math question that I can't solve. The problem is system of equations that I need to do in augmented matrix form, find the row echelon form, and solve it by using back substitution.
2x + 3y + 7z =13
3x + 2y  5z = 22
5x+ 7y  3z = 28 Answered by Penny Nom. 





The inverse of a quintic function 
20040722 

From A student: I'm really having trouble finding out the inverse of this quintic equation. F(X)= X^{5}+3X^{3}+1.I know that this quintic has an inverse because it is one to one. But I can't find a method to solve this. Finding the inverse of a quadratic or a cubic equation is a lot easier, but with this quintc I am really lost. I even know how the graph of this equation and its inverse looks like, but I'm not sure if Iam getting the right equation. Please help me out. Answered by Penny Nom. 





Factoring 
20040719 

From A student: Factor completely:
3x3  24y3
54x6 + 16y3
16xy  4x  4y  1
0.09x2  0.16y2 Answered by Penny Nom. 





The number of blocks in a mile 
20040718 

From Valerie: I don't know if you can help me but I was wondering how many blocks are in a mile in Ocean City, New Jersey? Answered by Penny Nom. 





A proof in geometry 
20040716 

From An: Im taking a geometry course for the summer , and we just started to learn about proofs for about one week. Today in class, we started to do this one proof but didnt finish it because class ended. the problem is as follows. Answered by Penny Nom. 





Solving some quadratic equations 
20040715 

From A student: Could you please solve the following for x
x^{2}+6=5x
x^{2}+16=8x
2x+21=3x^{2} Answered by Penny Nom. 





Two vector problems 
20040714 

From Jaye: Two force, 120lb and 200lb, act on a body and make a 52 degree angle w/ ea. other. What's the magnitude of the resultant of the forces and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force? Answered by Penny Nom. 





The commuter 
20040714 

From JJ: A student who commutes 27 mi. to college remembers, after driving a few minutes, he forgot a term paper. Driving faster than usual, he returns home, gets the paper, and once again starts to school. Sketch the graph of the student's distance from home as a function of time.
Does it mean that the student drives at normal speed, drives faster to pick up the paper, and resumes normal speed to head back, or that the student drives at normal speed, then drives faster the rest of the way to college? Answered by Penny Nom. 





12(1.221)^t = t + 3 
20040714 

From Jay: This problem has me stumped since i cannot separate the t and the 3. Here it is:
12(1.221)^{t} = t + 3
It's on a logarithm worksheet, but how do i figure it out?! Answered by Harley Weston. 





Two puzzles 
20040713 

From Fred: A young man's car developed a flat tire while 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 rolled down a nearby grate. Peering through the bars of the grate the man thought 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?
It is noon, your lunch hour, but you can not 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 the sun will be shining in 36 hours? Justify your answer. Answered by Penny Nom. 





An Octagonal playhouse 
20040713 

From Levi: I'm building an octagon playhouse for my son that is 8 feet wide.
what would be the measurements of each of the eight sides. Answered by Harley Weston. 





Cubic yards 
20040712 

From A homeowner: I would like to know how many cubic yards are in the following; 20 ft wide x 80 ft long x 4 inches thick?
I am trying to figure out how much concrete I will need to pour for a driveway. Answered by Penny Nom. 





x = 2^x 
20040712 

From A student: If the graphs of y=x and y=2^{x} are drawn on the same set of axes, they will intersect when x is equal to what?
(1)1
(2)2
(3)0
(4)They won't intersect.
I know the answer is number 4 by graphing which is permitted; however, I would like to know if there is any algebraic way to do this type of problem.If yes, please show me how.Thanks. Answered by Penny Nom. 





Two Problems 
20040712 

From Justina: i cant figure out the range of this equation in interval form because the highest point seems to be a decimal. please help f(x) = x + sqrt(4x2)
.............................................................................
Building Design A circular air duct of diameter D is fit firmly into the rightangle corner where a basement wall meets the floor (see figure). Find the diameter of the largest water pipe that can be run in the rightangle corner behind the air duct. Answered by Claude Tardif and Penny Nom. 





The tangent of theta 
20040710 

From Jacob: P is a point on a unit circle with coordinates(0.6,0.8). Find tan of theta. My book shows me how to do it,"tan of theta=opp./adj.=0.8/0.6=4/3,"and leaves it as that's the answer(4/3).When do we know from a problem to find the angle measure (in this case, the angle measure of theta) and how do we know when to give something like 4/3 without converting it to the angle measure? Answered by Penny Nom. 





Four digits 
20040710 

From Rob: I am always interested to know how the for digit works. I mean, you have correctly put it that the total numbers obtain from 0000 thru 9999 are 10,000. My question is, is there any simple formula to turn this simple 4 figures of say: 1234. Answered by Penny Nom. 





The circle through three points 
20040706 

From Jim: I am a student trying to solve math problem. I'd like to calculate the radius of the circle that exactly fits any three points. If the points are (X1,Y1), (X2,Y2), and (X3,Y3), what is the radius of the circle that contains those three points? Answered by Penny Nom. 





Vectors 
20040706 

From Annie: a=3ij+2k and b=i+3j2k, determine the magnitude and direction cosines of the product vector and show that it is perpendicular to a vector c=9i+2j+2k. Answered by Chris Fisher. 





An ineqlality with absolute values 
20040705 

From Uneeza: abs(x^{2}  4x) > 3 Answered by Claude Tardif. 





Factoring integers 
20040702 

From A student: After looking at all the info I could get about NFS, I still have some questions that are unsolved:
First of all: If someone found an algorithm that has a worst case running time of N*Log(N) to factor an integer n into his divisors, would it be quicker or slower then the number field sieve algorithm?
secondly, what exactly is the time complexity of the Number Field Sieve algorithm, if I would factor an integer n? Answered by Claude Tardif. 





Choosing 5 numbers from 1,...,36 
20040630 

From A lottery player?: how many combinations are there for the numbers 1thru 36 when only using each number once in groups of five Answered by Penny Nom. 





Simplify 
20040627 

From Tiff: Simplify:
3x (x2 + 2)
(x + 2) (x + 3) Answered by Penny Nom. 





Aunt Lucy's letter 
20040627 

From Olivia: "Dear bob,
now that i am getting on (70 today). i want to give you some of my money, i shall give you a sum each year, starting now. you can choose which of the following schemes you would like me to use.
a) £100 now, £90 next year,£80 the yaer after and so on.
b) £10 now, £20 next year, £ 30 the next year and so on.
c) £10 now, 1.5 times as much next year, 1.5 times as much the year after that and so on.
d)£1 now, £2 next year, £ 4 the year after, £8 the year after and so on.
of course these schemes will only operate while i am alive. i look forward to hearing which scheme you choose and why!
Best wishes,
Aunt Lucy." Answered by Penny Nom and Claude Tardif. 





Undercapatalized small businesses 
20040626 

From Greg: Suppose that 30% of all small businesses are undercapitalized. 40% of all
undercapitalized small businesses fail and 20% of all small businesses that
are not undercapitalized fail. A small business is chosen at random. The
probability that the small business succeeds if it is undercapitalized is? Greg
Answered by Penny Nom. 





Pick a number greater than 1 
20040625 

From A student: I understand that when you pick a number greater than 1 and less than 10; multiply it by 7 and add 23, then add the digits of that number until you get a one digit number. Then multiply that number by 9, add the digits of that number until you get a one digit number, subtract 3 from that number and divide the difference by 3; that this process will always give you the result of 2. Does this have a name or theory for it as to why the answer will always be 2? Answered by Penny Nom. 





(a+b) + 5i = 9 + ai 
20040625 

From Josh: The question which someone gave you (a+b) + 5i = 9 + ai question) gave me trouble. Answered by Penny Nom. 





(ln(50/x)) / (ln(40/x)) = a 
20040621 

From Un eleve: (ln(50/x)) / (ln(40/x)) = a = constante
comment extraire la variable x ??? Answered by Claude Tardif. 





How much loam to fill a hole? 
20040619 

From Harry: Can you tell me how much loam I would need to fill a hole 15 feet in dia. x 6 inches deep. Answered by Penny Nom. 





The surface area of a pyramid 
20040619 

From Jason: I was wondering how to find the area of a pyramid when you donít know the height of the face but the height of the Pyramids highest point? Answered by Penny Nom. 





Forty balls are placed in a bag 
20040619 

From Sheila: Forty balls numbered 110 are placed in a bag and four are drawn at random. What is the probability that the first ball drawn is between 110 (inclusive) the second is between 1120, the third is between 2130 and the last is between 3140? Answered by Penny Nom. 





3+4i abd 3+4i 
20040617 

From Sandy: how would you do a question like 3+4i? is that different than just doing 3+4i? Answered by Penny Nom. 





An equation with rational terms 
20040617 

From Louise: simplify the expression
(a^{2}+n^{2})/2n = a^{2} + (a^{2}n2)/2n Answered by Penny Nom. 





Area of a lot 
20040617 

From Mike: Could you please figure out the square footage and acreage of my lot? One side is 228 feet, another is 150 feet, another is 80 feet, and the last side is 164 feet. My house is in the middle and it is 62 feet by 37 feet. Is that subtracted from the total? I would like to know this when I have to buy fertilizer.
Answered by Penny Nom. 





A garden space 
20040616 

From Carol: We have a 17' x 19' garden space. If we want it a foot high raised bed, how many cubic yards of topsoil do we need? Answered by Penny Nom. 





The height of a building 
20040616 

From Lauren: I have a homework assignment to measure a building on my school's campus. I have to stand at least 40 ft away from the building and find the angle of elevation from my feet to the top of the building. Then I have to walk at least 40 ft form that point, record the distance as X, and find the angle of elevation from my feet to the top of the building. Using X and the angles, I have to determine the height of the building. I used a protractor and a weighted string to find the angle of elevation from my eyes to the top of the building. But I haven't been able to find the way to measure the angle of elevation from my feet to the top. Answered by Penny Nom. 





Solving an equation 
20040614 

From Anthony: I was hoping that you could help me with this problem. I believe that this is a high school level problem but as an adult who has forgotten the "rules", I am stuck.
the equation is this: x=t2/(t1t2)
we know that x=5.73
t1=303
we must solve for t2 Answered by Penny Nom. 





The Number of the Beast 
20040613 

From A Heinlein reader: Most people who have an interest in mathmatics are familiar with Robert Heinlein's novel "The Number of the Beast", where 666, or ((6 to the 6th power) to the 6th power) equals 1.0315 times 10 to the 28th power, which in the novel is the number of parallel universes in the cosmos. My question is what would the number of parallel universes be if you grouped 666 the other way: (6 to the power of (6 to 6th power)). I have tried this on my calculator, but it won"t register that high. Answered by Penny Nom. 





Integers 
20040610 

From A parent: I have an odd 3 digit product. My factors are a 1digit number and either or 2 or 3digit number. My factors are odd, but neither is 1. Find my factors and my product.
There is one answer. What is it? Answered by Penny Nom. 





Choosing an investment 
20040609 

From Max: Let's say I have a list of different possible investements, and the list shows me my cost, and how much each investment will sell for.
In order to compare the investments and put them in order of relative profitability, I would want to sort them by their profits as percentages of what? Also, if each investment had an equal probability
of losing exactly 10% of the sell price before I sold would that have any relevance to the way I would calculate it? Answered by Walter Whiteley. 





Jack's social security number 
20040608 

From A student: Jack's social security number contains each of the nonzero digits exactly once. By examining the digits from left to right, he also found that 1 divides the first digit evenly, 2 divides the sum of the first two digirs evenly, 3 divides the sum of the first three digits evenly, and so on, until 9 divides the sum of all the digits evenly. What is Jack's social security number? Answered by Penny Nom. 





The sum of some positive integers 
20040607 

From A student: Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7. Answered by Penny Nom. 





What is the name of a 3D rectangle? 
20040607 

From Jack: if a cube is a 3D square, what is the name of a 3D rectangle? Answered by Penny Nom. 





The area of a pentagon 
20040606 

From Dana: HELLO, I NEED HELP IN DETERMINING THE SIZE OF A PENTAGON.
one side is 280',from both ends of the 280 'section,we have 300' lengths,from one of these 300' sections we have a 118' length,which goes over to a length of 228',will this be enough info. or should i provide more. thanks Answered by Penny Nom. 





Percentage markup 
20040604 

From A parent: if our cost is 54.00 and their cost is 117.00 what is the percentage of mark up? Answered by Penny Nom. 





A tangent to a quadratic 
20040604 

From Jem: I have a question on the tangent to a quadratic curve.
Say I have a curve y = ax^{2} + bx + c. The gradient, using the derivative of y, at any point x on the curve is: 2ax + b right? Then, for the tangent that cuts the curve at a point x, the equation of the tangent can be: y1 = (2ax + b)x1 + d.
My question is, how is the point d of this tangent determined? It is the point on the yaxis where the tangent cuts isn't it? Is there a formula for it? Answered by Penny Nom. 





The game of 24 
20040604 

From Samantha: i have the game 24 (the one where you have to use multiplication, division, addition, and subtraction to get to the answer 24) I was playing when i came across the 4 numbers 20, 17, 7, 11 and i cant seem to get 24. Answered by Claude Tardif. 





Divisors of 2n+1 and 3n+9 
20040602 

From Chris: Amy selected a positive integer N and wrote numbers 2xN+1 and 3xN+9 on a whiteboard. Boris looked at the two numbers on the whiteboard and wrote in his notebook a positive integer that divides each of them. Find all possible numbers that Boris could have written in his notebook. Answered by Chris Fisher and Penny Nom. 





Cubic yards in a pool 
20040530 

From Jerry: HAVE A AREA WHERE I HAD A 18 FOOT ROUND POOL.
THE DEEPEST PART IT WAS IN THE GROUND WAS AROUND 7 INCHES TAPERING DOWN TO AROUND 4 TO FIVE INCHES AND A LITTLE OF THE ONE SIDE ALMOST AT GROUND LEVEL...HOW MANY YARDS OF DIRT WOULD I NEED TO FILL IT IN???? IS THERE A FORMULA FOR THAT.......COULD YOU FIGURE THAT FOR ME?
Answered by Penny Mon. 





The Parliament of the land of Achronia 
20040529 

From Christine: The Parliament of the land of Achronia consists of two houses. The parliament was elected in 2003 for a period of six years beginning on Thursday, the 1st of January 2004, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every twelve days for the duration of the term, and the meetings of the second house must occur every eighteen days. For example, the second meetings of the first and the second houses were held on the 13th and 19th of January respectively. A new law can be passed on any day when both houses meet, except on a Thursday. On how many days can the parliament members pass new laws during this six year term? Answered by Penny Nom. 





112! 
20040528 

From Beatriz: 1) A bus driver collects identical sets of 5 coins from each passenger. If the totoal colledted was $21.83, how many pennies did the driver get??
2) How many terminal zero in the base 10 expression of 112! (factional) N! means N(N1)(N2) .....(2) (1). Answered by Penny Nom. 





Different infinities 
20040527 

From Plober: How can I explain to a friend (in a bar, using as a pen and a paper napkin) that the integer's infinity is 'smaller' than the irrationals's one? The demo I tried was that you couldn't match the integers with the real numbers between 0 and 1 (that 0.xxxxx replacing the Nth number from a different one... that demo), but she used my argument >: saying that you can add one to the integer's infinite, and the number I was creating was only one more...
I can't think of any other way, and I KNOW the real's cardinality is greater than the integer's one Answered by Claude Tardif and Penny Nom. 





English 
20040527 

From Chang: well my question is i was told by most of the teachers that ''think in english'' is the best way to learn english but how can i do like that do i need to know about the stucture first or do i need to learn the western culture ?
here is a sentence i have translate directly from my mother language.'' i was given an admiration of sincerity from this client on the follow up action i have done in the complaint. Answered by Claude Tardif. 





The horizontal fraction bar 
20040527 

From Kashia: What is the name of the bar that separates a numerator and that denominator? Answered by Penny Nom. 





The center of a circle 
20040526 

From Wan: I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Answered by Penny Nom. 





The base of a triangle 
20040525 

From Ralph: With a 30 degree angle at the top of a triangle and a height of 15 what is the base? Answered by Penny Nom. 





Programming without trig functions 
20040525 

From Derek: I am a programmer trying to calculate the following.
What is the formula to find the crosssectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available. Answered by Harley Weston. 





Finding bearings 
20040524 

From James: This question is about finding bearings. A boat race starts from point A, goes North to Point B, a distance of 1000 meters. The course is triangular. The bearing from point B to point C is South 70degrees West. The distance from Point B to point C is 1500 meters. Find the course bearing from C to A.
Answered by Penny Nom. 





Some trig expressions 
20040523 

From A student: Prove:
sin A + sin B = 2sin(A+B/2)cos(AB/2)
cos A  cos B = 2sin(A+B/2)sin(AB/2)
cos A + cos B = 2cos(A+B/2)cos(AB/2)
sin A  sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom. 





Volume of a box 
20040523 

From A student: The area of the top of a closed rectangular box is 252cm2, the area of the front of the box is 105cm2, and the surface of the box is 834in2 (or 5380.64cm2). What is the volume of the box? Answered by Penny Nom. 





How far apart are they? 
20040523 

From A student: 2 cars start at same loc. drive opposite direction for 6 miles then they each turn left and travel for 8 miles how far apart are they? Answered by Penny Nom. 





33 3/4 doubled 
20040522 

From A tailor: need to know how to add 33 3/4 doubled. How do I come up with the solution? I need to know for measuring garments. Usually I measure on the half meaning on the front of the garment and then double it with the measuring tape but I always get stuck when I need to measure 3/4 such as 66 3/4 doubled and etc. Can you help me figure this out easily. Answered by Penny Nom. 





The perimeter of a triangle 
20040521 

From A student: In a triangle i have the length of a line and it's opposite angle.how can i calculate perimeter?(the angles are not right) Answered by Penny Nom. 





Frieze patterns 
20040519 

From Christina: How can I prove that there are only seven unique geometric frieze patterns? Answered by Penny Nom. 





Word problems 
20040519 

From A student: why can't 2nd graders have a easy time doing word problems and drawing pictures with it
Answered by Diane Hanson. 





The dimsenions of a room 
20040518 

From Estella: I have a room that is rectangular the area is 159.5 feet, the perimeter is 51 feet what would the dimensions of the room. Answered by Penny Nom. 





Angles of elevation and depression 
20040518 

From Anjum: what is the difference between an angle of elevation and angle of depression? Answered by Penny Nom. 





The combinatiion for a keybox 
20040517 

From Darrin: I have a puzzle question based on reality. I have a realestate type keybox (Supra) that has 10 digits, 09. I am trying to figure out a methodical way to test all number combinations to it to open it. (totally legal it was taken from the trash at a jobsite since they couldn't open it!) The combination could be any or all of the digits, but any digit is only used once. This is not like a simplex lock problem where a combination of keypresses would be different i.e. 1,2,3 is the same as 1+2,3.
Any ideas? Answered by Penny Nom. 





Diagonals in a regular dodecahedron 
20040515 

From Joshua: A dodecahedron has twelve faces, all of which are regular pentagons. Three edges meet at each vertex of the dodecahedron. An interior diagonal is a segment connecting two vertices such that the segment is not an edge or along a face of the dodecagedron. How many interior diagonals does a regular dodecahedron have? Answered by Penny Nom. 





Maximizing the angle to the goal mouth 
20040515 

From Yogendra: You are running down the boundary line dribbling the ball in soccer or hockey. Investigate where in your run the angle the goal mouth makes with your position is at a maximum. Answered by Penny Nom. 





Mrs. Smith's class 
20040512 

From Amanda: Mrs. Smith's class has 35 student. Today there are 2/3 of them absent. How many are absent? present? Answered by Penny Nom. 





Subtracting fractions 
20040511 

From Filipe: Question:
_5_  __7__
6ab 8a Answered by Penny Nom. 





Area of a lot 
20040511 

From Dana: HELLO MY NAME IS DANA ,I AM AN AVERAGE JOE WITH A QUESTION THAT I CANNOT ANSWER MYSELF SO I CAME TO YOU, I HAVE A PIECE OF PROPERTY IN THE SHAPE OF AN ISOSCELES TRAPEZOID THAT IS 250 FEET ACROSS THE BACK, 100 FEET ACROSS THE FRONT AND BOTH SIDES ARE 600 FEET LONG. HOW MANY SQUARE FEET ARE IN THIS PROPERTY.?
Answered by Penny Nom. 





A pyramid 
20040511 

From Quiana: I am a student and I have the following questions I need to answer for homework:
How many sides, vertices, and edges does a pyramid have? Answered by Penny Nom. 





Three dice 
20040510 

From A student: If one has 3, 6 sided dice what is the probability of the numbers that are rolled to total 4 through 10 inclusively?
Subsequent to this, what is the probability to do this consecutively...say 3 times? Answered by Peny Nom. 





Pi 
20040510 

From Kim: I'm a 7th grader at Lakeside Middle School. And I was wondering if you can answer a question for me for my math project. I'm doing a project on pi, and my teacher said to ask an expert like you to ask about how you would use the subject, pi, in real life usage. How would you use pi in real life usage? Answered by Penny Nom. 





Why the word combinations? 
20040505 

From Megan: Why are locker combinations called locker combinations not locker permutations. The order of the numbers matter so why aren't they called locker permutations. Answered by Claude Tardif and Penny Nom. 





ChiSquared 
20040505 

From Gillian: OF75 PEOPLE, 43 ARE EXPOSED TO A VIRUS AND BECOME ILL. 11 PEOPLE ARE EXPOSED AND DO NOT BECOME ILL. 3 PEOPLE ARE NOT EXPOSED AND BECOME ILL. 18 PEOPLE ARE NOT EXPOSED AND DO NOT BECOME ILL. THE ATTACK RATE IS 80% FOR THOSE EXPOSED AND 14% FOR THOSE NOT EXPOSED. THE RELATIVE RISK IS 5.7. CAN YOU EXPLAIN TO ME HOW TO CALCULATE A CHI SQUARE TEST FROM THIS. Answered by Penny Nom. 





3x squared  27 / x + 3 
20040504 

From Stef: 3x squared  27 / x + 3 Answered by Penny Nom. 





A 3 digit number divisible by 7 
20040503 

From A student: We need to arrange 1,3 and 6 to form a 3 digit number that is divisible by 7. Answered by Penny Nom. 





Solving inequalities 
20040503 

From Joe: Let x be a real number find and graph the solution to the following sentances:
2x10+9
4X+2<15
5X+3>(x1) Answered by Peny Nom. 





A clock chimes 7 times in 7seconds 
20040502 

From Anna: A clock chimes 7 times in 7seconds. how long does it take the clock to chime 10 times? Answered by Penny Nom. 





The equation of a line 
20040430 

From Amy: Write the equation of the line that contains the point (4,6) and is perpendicular to the line y=5x+100. Answered by Penny Nom. 





Setting up an equation 
20040430 

From Matt: I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y)
and that
xy = 22
Beyond this, I don't know how to hook those 2 seemingly unrelated facts together. Answered by Penny Nom. 





The sum of 4,0,4..., 156 
20040428 

From Christina: find the requested sum of the arithmetic sequence
4,0,4..., 156 Answered by Penny Nom. 





Yards in a concrete driveway 
20040427 

From Bobbi: I am wondering how many yards of cement I need for a 49 by 45 area, 5 inches thick. I am a stay at home mom who is not very good at math and I want to pave my drive way. Also what would the yardage be for a 6 inch thick drive way with the same area. Answered by Penny Nom. 





Factoring 
20040427 

From Bipin: FACTORISE:
a to the power of 6 + b to the power of 6 Answered by Penny Nom. 





An oildrilling platform 
20040427 

From Alie: An oildrilling platform is located in the Gulf of Mexico 3.25 miles from the nearest point on shore. From a point B on the shore due east of A the bearing of the platform is S51.2W. How far is it from B to the platform? Answered by Penny Nom. 





The height of a triangle 
20040427 

From Danielle: what is the definition of height of a triangle? Answered by Penny Nom. 





Related rates and baseball 
20040426 

From Bethany: A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing? Answered by Penny Nom. 





The problem of Apollonius 
20040425 

From Mitja: There are given 2 circles lying one out of another and one point out of both circles. How to construct a circle passing through a given point and internally tangent to one and externally tangent to the other cirlce? Answered by Chris Fisher. 





A Fibonacci triangle 
20040425 

From Marcelle: Is it possible to construct a triangle with sides that are three consecutive Fibonacci numbers? Answered by Walter Whiteley. 





Water in a pipe 
20040425 

From Marlean: How much water would be in a 480 foot one inch inside diameter pipe?? In imperial gallons please. thanking you in advance for your help in this matter.
Answered by Penny Nom. 





Place Value 
20040425 

From Santosh: Q.
Write the Place value of the digits in the following numerals.
1. 5 in 54
2. 3 in 63 Answered by Penny Nom. 





Marching legion 
20040424 

From Art: A column of soldiers is 100 meters long. Their sargeant at the rear of the column gives the order to march. The sargeant marches alongside the column to its head and then back to the rear, at which point he gives the order to halt. In all, the column of soldiers has marched 100 meters. How far has the sargeant marched? I say 187.5 meters, but those who teach or who have taught mathematics tell me no. Some say much more and some different. What do you say? Answered by Penny Nom. 





Three parabolas 
20040424 

From A tutor:
I am a maths tutor. One of my year 12 students has given me this assignment. Many parts are ambiguous.
I am trying to determine the equation of the line segment AB. Given that A has an incline of 10 degrees below the horizontal, I am assuming that this parabola (although you can only see part of it) has been rotated 10 degree clockwise. Am I right in assuming this? If so, how do I derive the equation of the parabola as it will then not fit the general form y = ax squared +bx +c of a parabola.
Also, how is one expected to find the x coordinate of D without the equation of this parabola. To find the equation you need the xcoordinate and therefore be able to find another point on the parabola in order to derive the equation using simultaneous equations.
Answered by Penny Nom. 





Arrays 
20040423 

From Jan: 4x7 = 28
How many arrays can this have? How do you determine the arrays??? Answered by Penny Nom. 





square root 125 x 16 
20040423 

From Mike: how do you simplify a square root of " square root 125 x16" when x is a variable... i don't really get how to do this.... Answered by Penny Nom. 





The "22" puzzle and the "1089" puzzle 
20040422 

From Marcelle:
1. Choose 3 digits from 19
2. Make all the 2 digit numbers you can from these (6)
3. Add the 3 original digits and divide them into the sum from step 2.
The answer is always '22'. I just can't understand why. Can you please help.
Another one related to this is it:
1. Choose a three digit number ensuring the first and third digit are differnt by at least two.
2. Make the reverse three digit number and subtract the smaller one from the larger of these.
3. Take this answer and reverse it and add these two 3 digit numbers .
eg:
643  346 = 297
297 + 792 = 1089
it doesn't matter what numbers are used, the results are alwasy the same. eg 22 or 1089
Answered by Paul Betts. 





Why is ounces abbreviated oz? 
20040422 

From Someone curious: Why is ounces abbreviated oz? Answered by Chris Fisher. 





What's it called? 
20040422 

From Gerry:
I'm a father and a grandfather and have come up with a game for my offspring to play while we're on the road. When we see a license plate, the object is to be the first one to add all the numbers on it, and come up with THE one digit number that sums them up.
For example: ABC787 = 7+8+7 = 22 = 2+2 = 4
Another example is 2932 = 2+9+3+2 = 16 = 1+6 = 7
Up 'til now, I've called it just plain "Numerology", but I'm sure that there's a math term for what we're doing, and I'd sure appreciate it if you could tell me what it is!
Answered by Chris Fisher and Penny Nom. 





Surface area of a cylinder 
20040417 

From Kathryn: How do you find the radius of a cylinder when you are given only the surface area and the height of the cylinder? Answered by Penny Nom. 





The line through (4,2) and (4,8) 
20040417 

From Kim: Write an equation for the line.
Given points (4, 8) and (4,2) are on the line.
I believe m=undefined.
How do I solve for b when m is undefined, and then plug in the values for m, b, and y?
Answered by Penny Nom. 





Some factoring problems 
20040415 

From KJ: Factor these:
x^{3}+125 > (x+5)^{3}
8x^{3}27 > (?)
x^{2}+36 > (x+6)^{2}
x^{4}5x^{2}+4 > (?) Answered by Penny Nom. 





A probability density function 
20040414 

From A student: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 <= x <= 12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





A geometric sequence 
20040413 

From Michael: In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms. Answered by Penny Nom. 





Circles in a hexagon 
20040411 

From Crystal: step by step can you show me how to calculate the area of the region inside the hexagon but outside the seven circles. given the radius of each circle is one inch Answered by Penny Nom. 





Percent difference 
20040410 

From A parent: For a school science project, my son Alex is taking measurements of plant growth at regular intervals. As part of the data, he must provide the maximum percent difference observed in the categories his team has identified.
So, for example he has six plants with four measurements each. (He has more, but I'll keep it simple) For the first plant he measured 2mm, 2.4mm, 2.9mm, and 3.2mm. For the 2nd, 3rd, and 4th plants, he has similar numbers. Is there a way to calculate the maximum percent difference between any two plants in his measurements during the project? Doing it for each combination would be tedious. Answered by Penny Nom. 





Snow in the driveway 
20040409 

From Patricia: Following a severe snowstorm, Ken and Bettina Reeves must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and Bettina can clear the snow by herself in 6 hours. After Bettina has been working for 3 hours, Ken is able to join her. How much longer will it take them working together to remove the rest of the snow? Answered by Penny Nom. 





What is the nth term 
20040407 

From Jason: 1 4 10 20 35 56 84
what is the nth term Answered by Claude Tardif. 





Rational expressions 
20040406 

From Shivani: I am in 11th grade Honors Algebra II. We are currently learning about adding and subtracting rational expressions. I looked at the other questions that were similar to that of mine, but they weren't quite answering my question. I have been working on many problems to practice and see if I can come up with the correct answer, but I can't, I got like 2 out of every 7 right on my school homework. I get the easy ones, where when you have to find the LCD, it's just the other denominator. But, on others you have to really think about it. Those are hard. Here are some of the problems that I cannot get at all: (x2  3x + 1)/(x2  4)  (x2 + 2x +4)/(2  x)  (x  4) /(x  2)
The correct answer is:
(x3 + 4x2 + 7x + 17)/(x2  4) Answered by Penny Nom. 





The sum of angles in a triangle 
20040406 

From A student: How can u prove sum of angles in a triangle equal to 180 degrees? Answered by Penny Nom. 





Differences in percentages 
20040406 

From Jose:
Question:
You have two groups:
Group A has 10 people and 2 are Chinese
Group B has 12 people and 3 are Chinese
In terms of percentages what is the difference in Chinese between the two groups? In other words which group has the biggest percentage of Chinese and why?
Answered by Penny Nom. 





Trisecting an arbitrary angle 
20040406 

From Joe: Where can I submit my effort on trisecting an arbitrary angle with only a straightedge and a compass? I can do it but I do not have the smarts to prove it.S Answered by Chris Fisher. 





Ratios 
20040405 

From Tim: The ratio of W to H was 7 to 9. The ratio of H to I was 9 to 5. If the sum of the W and H exceeded twice the number of I by 12, how many were W, how were H and how many were I? Answered by Penny Nom. 





x^2/3  7 x^1/3 + 12 = 0 
20040405 

From Jackie: I am having trouble solving this question for x:
1.) x^2/3  7 x^1/3 + 12 = 0 Answered by Penny Nom. 





(3x50)+20/5=? 
20040403 

From A student: what is the answer to:
(3x50)+20/5=? Answered by Penny Nom. 





A changing rectangle 
20040403 

From A student: The width x of a rectangle is decreasing at 3 cm/s,
and its length y is increasing at 5 cm/s. At what rate
is its area A changing when x=10 and y=15? Answered by Penny Nom. 





Ratio and proportion 
20040402 

From Kenneth: The terms of a ratio in a proportion are often expressed as a is to b as c is to d.
Example: 2/4 = 6/12 this proportion represents that 2 is to 4 as 6 is to 12.
What does the "a is to b as c is to d" really represent or indicate in ratios? Answered by Claude Tardif. 





Some calculus problems 
20040401 

From Weisu:
I have questions about three word problems and one
regular problem, all dealing with derivatives.
 Find all points on xy=e^{xy} where the tangent line
is horizontal.
 The width x of a rectangle is decreasing at 3 cm/s,
and its length y is increasing at 5 cm/s. At what rate
is its area A changing when x=10 and y=15?
 A car and a truck leave the same intersection, the
truck heading north at 60 mph and the car heading west
at 55 mph. At what rate is the distance between the
car and the truck changing when the car and the truck
are 30 miles and 40 miles from the intersection,
respectively?
 The production P of a company satisfies the
equation P=x^{2} + 0.1xy + y^{2}, where x and y are
the inputs. At a certain period x=10 units and y=8
units. Estimate the change in y that should be made to
set up a decrease of 0.5 in the input x so that the
production remains the same.
If you could just give me some hints on these
questions, I'd really appreciate it. Thanks! Answered by Penny Nom. 





The intersection of two graphs 
20040331 

From Benjanim: How do I find the points of intersection of the two functions:
1) y = 2  (e^x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :) Answered by Penny Nom. 





Algebraic simplification 
20040331 

From Chris: Simplifying Exponents
Question
b^5d^2/b^3d^8 Answered by Penny Nom. 





The degree sequence of a graph 
20040331 

From Ali: How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it? Answered by Penny Nom. 





Replacement times for TV sets? 
20040331 

From Barb: Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e Answered by Andrei Volodin and Penny Nom. 





A derivative 
20040331 

From A student: What is the nth derivative of f(x) =(2x)/(1(x^{2}))? Answered by Harley Weston. 





The height of a building 
20040331 

From Nat: Two buildings are 26.3m apart. From the top of the shorter building the angle of elevation to the top of the taller building is 35.9 degrees and the angle of depression to the base of the taller building is 54.7 degrees. What is the height of the taller building? Answered by Penny Nom. 





425 cc's of a saline solution 
20040330 

From Julie: 425 cc's of a saline solution is equal to how much in lbsweight?? Answered by Harley Weston. 





n! > n^2 
20040330 

From Jose: How can you prove by mathematical induction that:
n! > n2. Answered by Penny Nom. 





A stained glass window 
20040329 

From Kay: I'm doing a stain glass project and it's on a 4 foot across octagonal window...and I'm trying to set up the pattern and I don't know how long the sides are! Answered by Penny Nom. 





Numbers around a circle 
20040328 

From Rebecca: my maths question is use the numbers 1,2,3,4,5,6 and 7 place each number in a circle so each line adds up to 12. There are seven circles, six on the outside and one in the middle. Each number lines up with the middle number and the outside numbers line up with the one directly across from it as if a line was going through the middle number circle. Answered by Penny Nom. 





Percentage difference 
20040328 

From Someone: what is the percentage difference between 157 to 251 Answered by Penny Nom. 





Maximizing the area 
20040327 

From Petey: Please could you tell me why for my coursework (where I have to find the largest area that a fence 1000m long can cover) why I should only test equilateral and isoceles triangles? We were told NOT to do right angled triangles but I was wondering why not?
Answered by Penny Nom. 





The volume of a sphere 
20040326 

From Mike: I was in class today and I learned how to calculate the volume of a sphere. I understood it easily but can't find the logic behind it. So here are my questions, in the formula why is the radius cubic and not squared? And what does 4/3 have to do with it? Answered by Penny Nom. 





z^2 = 3  4i 
20040326 

From John: Solve: Z^2 = 3  4i Answered by Harley Weston. 





Large exponents 
20040326 

From John: I
have encountered problem with the lack of memory every calculator
seems to have. No calculator, on or off the computer, I've found
has the amount of memory or writing space to calculate the sums I want
to solve. The sums are in great importance for my continued progress.
The sums are following:
16777216^1310270, 16777215^995328, 16777215^786432 and 16777215^480000 Answered by Claude Tardif. 





Sections, area and acres 
20040323 

From Tony: An acre , it can be any size right . so when they
refer to a section of a township which is 640 acres,
also 1 square mile does this mean that 1 sections
length if sqaure and there is 5,280 ft in 1 mile does
it meanthat if you took 1 side of the square of of 4 sides
the lenth would be 5,280 feet long and by multiplying
5,280 x 5,280 it would give you the square mile in
square feet. i guess what I 'm asking is what is the
perimeter of 1 acre if it was shape like a square.
sorry to make this confusing but if you can help I
would appreciate it. Answered by Penny Nom. 





Four marbles on a box 
20040322 

From Karyn: Suppose 2 solid color marbles and 2 striped marbles are placed in a box. All are the same size. If one marble is randomly drawn from the box and replaced, then a second marble is randomly drawn, what is the probability that the marble drawn both times will be striped?
I know there is a simple formula for working this out but I can't remember how.
Answered by Penny Nom. 





What's the next term? 
20040322 

From Garrett:
A friend hit me with these questions and won't tell me the answer nor how... please help? I've racked my brain and did all sorts of formulas, but I can't get it to work out... please...
What's the next number in this series...
5, 12, 17, 29, 46, ?
And this series...
12, 19, 28, 39, 52, 67, ?
and these...
ocoa, boco, oboc, dobo, odob, ?
Answered by Claude Tardif. 





BEDMAS 
20040320 

From Brad: I am in grade 7. My teacher tells me brackets always first, well i know that but, 5 (4) x 2
Does the (4) count as a bracket or is it just telling you not to minus 4 from 5 but to multiply 5 x 4 ? Am i correct? Answered by Penny Nom. 





A partial derivative 
20040319 

From Penny Nom: Is it possible to differentiate the following equation, if so could
you please explain.
S=SQRT(T(5/X^2))
I would like the derivative of S with respect to X. Answered by Harley Weston. 





A fraction of a fraction as a percent 
20040318 

From Mary: I would like to know if you could help me with this problem? Could you
take me though the steps
to this math problems.
3 =(?)% x 3
 
16 4
the question states: Finding what is the percentage of a fractional
number and another fractional number. Answered by Penny Nom. 





A water lily 
20040317 

From Inba: A water lily with a rigid stem extends one foot above the surface of the water. When pulled over, it disappears beneath the water at a distance 3 feet from where the stem originally entered the water. How deep is the pond? Answered by Penny Nom. 





Factoring x^2 + 5x + 4 
20040314 

From Keenan: how do I factor x^+5X+4? Answered by Penny Nom. 





Johann Muller 
20040314 

From A student: What major contributions to spherical trigonometry did Johann Muller make? Answered by Penny Nom. 





Baseball games 
20040314 

From Fabian: Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth.
Answered by Penny Nom. 





A new baby 
20040314 

From Jessica: I just had a baby 3weeks ago, he is in the hospital and he can come home when he is 1800 grams, well i was wondering how many pounds that is? Answered by Penny Nom. 





Some ratio problems 
20040313 

From Hossen:
1) After James spent 2/5 of his pocket money on magazines, and 1/4 of his pocket money at a football match, he had £1.75 left. How much pcket money did he have in the beginning?
2) A joint of Lamb costs £5.95 per/kg. The price per kilogram is reduced. A joint weighing 1.2kg is reduced by 50p.
A) What is the reduced price per kilogram?
c Answered by Penny Nom. 





Billions in Australia 
20040312 

From An Australian: how many million in one billion ? Answered by Penny Nom. 





Area and perimeter 
20040312 

From Sandy: The rectange has an area of M square units and a perimeter of 2M units. What is the value of x?
The length of the rectange is 3, while the width of the rectange is x1. Answered by Penny Nom. 





Sum of the angles in a pentagon 
20040311 

From Ashish: What is the sum of all the measures of the angles of a Pentagon Answered by Penny Nom. 





Distance, time and rate 
20040309 

From Peter: A car travels from one city to another at the speed of 32mph, if it had gone 4mph faster it could have made the trip in one half hour less. How far apart are the cities?
Answered by Penny Nom. 





The area of a lot 
20040309 

From Dave:
If our lot is 192.71 x 138.79 x 158.74 x 103.08
Question is what percentage of an acre is our lot?
Answered by Penny Nom. 





The factor theorem 
20040308 

From LisaMarie:
Hi, I have a career link question from gr.12 advanced functions
and intro. calculus. The equations is:
R(t) = 5(t^{4}  4t^{3} +
19/4 t^{2}  3/2 t)
The question is to apply the factor theorem
and quadratic formula to determine the times it crosses the t axis. The
only method i know of for using the factor theorem is when the last number
does not have a variable beside it so i'm not sure how you would even
use the factor theorem for this? We haven't dealt with any that have 0 as
the last number with no variable so i'm a little confused! please help!
Thank you
Answered by Penny Nom. 





A metric prefix table 
20040307 

From April: Can you tell me what the scale is for nano, micro, mega, kilo, etc.... I know that mega is 10 to the sixth power but I can't remember the other ones. Answered by Penny Nom. 





Equivalent sets 
20040306 

From A student: If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ? Answered by Penny Nom. 





The radius of a circle 
20040306 

From A student: what is the radius of a circle with the circumference of 12 inches? Answered by Penny Nom. 





The units digit of 4^478 
20040306 

From Elizabeth: What is the units digit of 4^{478}? Answered by Penny Nom. 





A fifteen sided polygon 
20040305 

From Joann: WHAT IS THE NAME OF A FIFTEEN SIDED SHAPE? Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Cosine of 35 degrees 
20040303 

From Jason: How do you find the exact solution to cosine 35 degrees. Answered by Chris Fisher. 





Proof by induction 
20040302 

From Chris: I need some help of how to solve the problem
"use the principle of mathematical induction to prove that the following are true for all positive integers"
cos(n x pi + X) = (1)^n cosX
any help would be appreciated Answered by Penny Nom. 





Volume of a fuel tank 
20040301 

From Mike: I have a fuel ank for my big truck that has a radius of 24inches and a length of 65 inches. I am trying to compute the volume of fuel in the tank. I tried pie x the radius squared times the length but no usable results.
Can you help me please? Answered by Penny Nom. 





Billions and more! and even more! 
20040301 

From Steph: What comes after undecillion? Answered by Penny Nom. 





Evennumbered roots 
20040301 

From A student: I understand that the square root is defined to be positive only. Does
the same rule apply to other evennumbered roots, such as the 4th root, or
the 6th root, etc.? Answered by Harley Weston. 





Logs 
20040229 

From Sandy: find X
3/2logb41/2logb8+logb2=logbx
my book uses prop 7 to rewrite as
logb4raised3/2logb8raised2/3+logb2=logbx; then writes
logb8logb4+logb2=logbx how did it get here? Answered by Claude Tardif. 





A dressmaker's pattern 
20040227 

From A dressmaker: Does a dressmaker's pattern for a dress, such as a skirt made up of several pieces of isosceles trapezoid, qualify as a net? How about patterns for other types of clothing or accessories e.g. jackets, handbags?Î Answered by Diane Hanson. 





Napoleon's theorem 
20040227 

From David: How do i prove this : For any triangle, if you make 3 equillateral triangles
using the sides of the the original triangle, the central points of the 3
tringles another triangle that is equillateral.z Answered by Chris Fisher and Penny Nom. 





GST and PST 
20040226 

From Mallory: I was absent on the day that my teacher taught the class how to find the GST and PST of items. I sort of understand that GST is 7% and PST is 7.5%, but our teacher said that we shouldn't combine the two to find the total amount... I'm really confused, so can you please help me?& Answered by Claude Tardif. 





Three jugs 
20040226 

From Shelly: You have three jugs: A 6 Liter, 4 Liter and a 3 Liter. Your goal is to get exactly 5 Liters of liquid in the 6 Liter jug. Your supply of liquid is unlimited and there are NO markings on the containers. You cannot do halves. Answered by Claude Tardif. 





The point where all the medians meet 
20040225 

From A student: What's the name of the point where all the medians meet? Answered by Penny Nom. 





Rearranging an expression 
20040224 

From Corey:
use the following formula to answer the question
F=9c divided by 5 plus 32
rearange the formula to solve for c
how many degrees fahrenheit would it be it it was:
0 degrees celcius
10 degrees celcius
46 degrees celcius
Answered by Penny Nom. 





An elliptic cone 
20040224 

From Ben:
I am building a model for my architecture class. I need to build a elliptic cone out of chipboard and i have no idea how to do this.
The cone needs to be 20in tall and the ellipse has a max radius of 10in and a min radius of 8in.
So my question is how do i lay this out on a piece of paper so that i can form the cone after i cut it out.
Answered by Penny Nom. 





Profit, markup and discount 
20040222 

From Kick: Using the calculation on your website, if I sell something for $885 and my cost is $296, I make $589 profit. How do I calculate the profit percent I made on that transaction?
Profit as a percentage of what it cost me?
Profit as a percentage of what I sold it for?
Answered by Penny Nom. 





A problem with logs 
20040222 

From Caitlyn: problem: ln x + ln (x2) = 1
I can solve this on the calculator, but the book wants 1+ [(sqroot)1+e]. How can I get the e? Answered by Penny Nom. 





Selecting balls from a golf bag 
20040221 

From A student: There are 5 white and 5 yellow balls in a golf bag. Two are selected randomly, and simultaneously. What is the probability that the first one or the second one will be white? Answered by Penny Nom. 





The dimensions of a rectangle 
20040221 

From Jane: A rectangular label has an area of 176cm2 and a perimeter of 54cm. Find the dimensions of the label. Answered by Penny Nom. 





Gallons in a cylinder 
20040220 

From Jim: Please advise how to use the formula I saw for determining the number of gallons in a cylinder? This is how it was written
V = pi r2 h
. does this mean pie, or 3.14 X radius squared, X the height? If so please use a standard 55 gal barrel (1' R & 3' H) for example? Answered by Penny Nom. 





Arrays 
20040219 

From A parent: please demonstrate mathematical arrays fro a 3rd grader Answered by Penny Nom. 





A worm crawling home 
20040218 

From Cindy: A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time? Answered by Penny Nom. 





Nonconvex shapes 
20040218 

From Merrill: Draw 4, 6 and 8 sided shapes so that ONE straight line can be drawn through each side Answered by Chris Fisher and Penny Nom. 





Acres and square miles 
20040217 

From Richard:
How many acres are in .17 square miles? and How many acres are in .6 square miles?
The two areas I am requesting information about are Vatican City and San Marino, the two smallest countries in the world. If I can transfer the sq. miles into acres , I can relate the size of these countries to our school grounds and the students will better understand their sizes.
Answered by Penny Nom. 





Grams and Milliliters 
20040217 

From Chantal: We have to do a "thing", and I need to convert grams into mililitres (g into mL). how can I do this? Answered by Penny Nom. 





Areas, perimeters and derivatives 
20040215 

From Geoff: A recent lecture in my calculus class led me to realize that the derivative of the area of a circle, with respect to the radius is equal to the circumfrence. This also holds true for the relationship between the volume of a sphere and the surface area of that sphere:
why do these hold true? why is it only for circular objects? Answered by Harley Weston. 





An arc on a train track 
20040215 

From A student: I'm trying to build a route in a train simulator program. I have a curve to the right (an arc, in other words) with a length of 25 meters and the radius is 1,500 meters. Let's say point P is the beginning of the curve (arc) and point Q is the end point of the arc. Then picture a tangent to point P. I need to find the length of a line perpendicular to that tangent that runs to point Q (the end of the curve/arc). Answered by Penny Nom. 





The derivative of x to the x 
20040214 

From Cher: what about the derivative of x to the power x? Answered by Penny Nom. 





The substitution method 
20040214 

From Keisha: I need to solve this problem by using the substitution method.
3x+y=1
x=2y+5
Please help me understand the method to solve. Answered by Penny Nom. 





Probabilities and olivies 
20040214 

From Annetta: A bowl contains five green olives and eight black ones. Wilma sticks a fork into a bowl and brings out two olives. What is the probability that she gets one green and one black olive? Answered by Harley Weston. 





Red riding hood 
20040214 

From Frank: Red riding hood had a number of jars to take to grandma's house. As she traveled she gave away 1/3 of them to an old lady. Then later As she walked through the forest a wolf stole 1/2 of her remaining jars. When she arrived at grandma's house she gave her 2/3 of the remaining jars. She kept 6 jars for herself. How many jars did she start out with. Answered by Diane Hanson. 





A pyramidshaped tank 
20040213 

From Annette: The base of a pyramidshaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Answered by Harley Weston. 





Fractions 
20040213 

From A parent: 12/36=?/18=4/?=?/9 Answered by Penny Nom. 





Common fractions to decimals 
20040212 

From A parent: I'm trying to help my son work with turning fractions into decimals and this seems foreigh to me after 20 years of not being in school. Can you give me a few illustrations and/or examples of how to do that?? Answered by Penny Nom. 





Profit 
20040212 

From Mohamed: if i bought some thing with 100$ and the saller told me that his profit was 30% how can i know the actual price of the good Answered by Penny Nom. 





Zero 
20040212 

From Syazwan: can you tell me who and when the number zero was
discoveredd Answered by Penny Nom. 





Three numbers are added in pairs 
20040212 

From Jane: When three numbers are added in pairs, the sums of the pairs are 22, 39, and 45. What are the three numbers? Answered by Penny Nom. 





Driving from Sarnia 
20040211 

From Jane: "Crystal drove from Sarnia at 80km/hr. Emily left Sarnia one hour later and drove along the same road at 100km/hr. How far from Sarnia did Emily overtake Crystal?" Answered by Claude Tardif. 





Digits in the decimal expansion 
20040211 

From Leslie: In the decimal expansion of 1/17 what digit is in the 1997th place? Answered by Penny Nom. 





Sums and differences 
20040210 

From David: The sum of two whole numbers is 63. The difference between the numbers is 10. Find all the possible pairs. Answered by Claude Tardif and Penny Nom. 





Three times a year 
20040209 

From Graham: What is the term for a report that is submitted three time a year or at the very least a prefix term for one third Answered by Harley Weston. 





Will be shinning in 36 hours? 
20040208 

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





Graphing lines 
20040208 

From A student: how do you solve y=1\3x+3 and y=1\3x3 by graphing? Answered by Penny Nom. 





A/30 + B/105 = (7A + 2B)/x 
20040205 

From Jim: If A/30 + B/105 = (7A + 2B)/x and A, B, and x are integers greater than 1, what must x equal? Answered by Penny Nom. 





A quadratic word problem 
20040204 

From Carl: A walkway of uniform has 72m2 and surrounds a swimming pool that is 8m wide and 10m long. Find the width of the walkway. Answered by Penny Nom. 





$20,000 at 25% compounded daily 
20040203 

From A student: Hi there, I'm tying to figure out how much interest I would pay on 20,000 if it was 25% compounded daily. Answered by Penny Nom. 





Geometric sequences 
20040203 

From Alan: hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative. Answered by Chris Fisher. 





The volume of a tetrahedron 
20040203 

From Joseph:
How do I calculate the volume of a bird tetrahedron. I'm trying to find out to get extra credit. I came with this idea while making a origami tetrahedron.
Joseph
P.S. Do you by any chance have instructions for orig ami figures. If you do, please send me some. Thanks!
Answered by Penny Nom. 





The incline of an exercise machine 
20040202 

From An exerciser: This is a question about incline percentage. On an exercise machine if the elevation is raised 3 and one half inches from a level position then what would be the incline percentage? Answered by Penny Nom. 





Angular speed 
20040201 

From Rachel: A 4 inch pulley on a motor makes 1500 revolutions/minute. It is connected to an 8 inch saw blade.
a. Find the angular speed of the pulley in radians/minute
b. Find the angular speed of the saw in radians/ minute
Answered by Harley Weston. 





Logarithms 
20040201 

From A student: Where did the word logarithmic come from? Where/whom did it originate? Answered by Harley Weston. 





Pairing boys and girls 
20040201 

From Terri: Suppose 7 boys and 7 girls are assigned to work in pairs of one boy and one girl. Explain what equation can be used and how you would use a simpler problem to solve these types of questions. Answered by Penny Nom. 





The vertex of a cone 
20040129 

From Richard: Please help me explain to my fourth graders as to why a cone has a vertex even though it does not have any straight edges. Answered by Chris Fisher. 





Intersecting a line and a curve 
20040129 

From Senthil: between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Answered by Penny Nom. 





Is a cylinder a type of prism? 
20040129 

From Rebecca: Is a cylinder a type of prism? Answered by Penny Nom. 





Order of operations 
20040128 

From John:
I am trying to find out any information concerning the development of the order of operations. for example, when (why/how) did it become the case that 2 + 3 x 5 =17, rather than 25.
any insight is appreciated. Thank you.
Answered by Penny Nom. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Sets 
20040127 

From Susan: My child has the following problems to solve, and we are puzzled.
1. Compare the subset symbols to the inequality symbols of less than or greater than.
2. If A, B & C are sets such that A has 47 elements, B has 32 elements, and C is a proper subset of B, what can you say about the number of elements in the following sets: A U B? A intersect B? B U C? and B intersect C? Answered by Penny Nom. 





The London marathon 
20040127 

From Nina: After a years training, Minnie Midriffe increased her average speed in the london marathon by 25%. By what percentage did her time decrease?o Answered by Penny Nom. 





Ounces into cubic centimeters 
20040127 

From A student: how do you convert ounces into cubic centimeters? Ex: how does 12 oz. change into cc. Answered by Penny Nom. 





Three digit combinations 
20040127 

From Kevin: how many 3 digit combinations can be made with 09. i have been told only 1,000. when i asked jeeves the response was 750 without using any digit twice. i have entered a raffle and received a ticket with 4 sets of 3 digit numbers. Answered by Penny Nom. 





Lead weights 
20040126 

From Jeff: I am making a mold for my decoy anchors. I need
10  12 lead ounce weights. How would I determine the liquid measurement for that weight? For example if I melted down 10 ounces of lead how many cups would that be or quarter cups etc?
I would like the formula if I could and good instructions on how to use the formula. Answered by Penny Nom. 





Polynomials 
20040125 

From Bruce:
A polynomial is defined as
Polynomial functions are functions that have this form:
f(x) = a_{n}x^{n} + a_{n1}x^{n1} + ... + a_{1}x + a_{0}
The value of n must be an nonnegative integer. That is, it must be
whole number; it is equal to zero or a positive integer.
The coefficients, as they are called, are a_{n}, a_{n1},
..., a_{1}, a_{0}. These
are real numbers.
Questions:
 why must n be positive?
 what are some historical facts
about the evolution of the definition?
Answered by Harley Weston. 





x^2  12x = 8 
20040124 

From Sherre: x^{2}  12x = 8 Answered by Penny Nom. 





Bundles of asphalt shingles 
20040124 

From Larry: According to my study material 4:12 multiplying factor for shingles is 1.054. The question reads as follows: A building with a floor plan of 3350 sq. ft. and a roof slope of 4:12 will require _______ bundles of standard asphalt shingles. Answered by Harley Weston. 





x^x^x^x^... 
20040123 

From Ryan: you have a number say x and it is to the power of x which is to the power of x and so on infinite times like x^x^x^x^x^x^x^... i have to figure out what x is so that the answer is always 2 Answered by Penny Nom. 





A counterfeit coin 
20040123 

From Kim: You are considering buying 45 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin? Answered by Penny Nom. 





g on Mars 
20040122 

From RC: To measure the acceleration on Mars an object is dropped from a height of 160m. It takes 10s for this object to hit the ground. What is the value for g on Mars?g Answered by Penny Nom. 





A game with some strings 
20040122 

From Trudy: A boy holds 6 pieces of strings in his hands with the ends protruding above and below. The top ends are tied together in pairs and then the lower ends are tied together in pairs. What is the probabilty that the pieces of string are all joined in one loop?
What is the probability of obtaining two loops?
Can you generalise this to solve the problem for 2n blades of grass? Answered by Andrei Volodin and Penny Nom. 





BEDMAS 
20040121 

From Jessica and her mom:
my mom and I were wondering 2 things.
1. what is the reason for having bedmas.
2. 5+54+[6x3(6+13x2) 5+9]
Answered by Penny Nom. 





A problem with sets 
20040120 

From Jason:
Given that the universal set S is the set of all sports fans, and
F={xx is a football fan}
B={xx is a basketball fan}
H={xx is a hockey fan}
a)Describe (F^B)' (f intersect b)' in words
b)Draw a Venn Diagram and shade the region that represents the set of football fans or both basketball and hockey fans.
Answered by Penny Nom. 





What is the speed of the automobile? 
20040120 

From Rita: An automobile travels toward Nashville from Cookeville. It takes 33 minutes to travel from Cookeville to Manchester, which is a 36 mile distance. If the driver continues at this pace, what is the speed of the automobile? Answered by Penny Nom. 





A parabolic arch 
20040119 

From Teresa and Robyn: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the centre of the arch Answered by Penny Nom. 





The product of any n consecutive integers 
20040118 

From Fazia: I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof. Answered by Claude Tardif. 





Combinations of 12 numbers 
20040118 

From Cheryl: I would like to know the total possible combinations using the numbers 112. We would also like to know the formula used to calculate the number of combinations. Answered by Harley Weston. 





Cubic yards in a concrete wall 
20040118 

From Danny: I am studing for my contractors exam. I am haveing truble with a few questions. I have the answer to the problems but I dont know how to get them my self. please help
How many cu. Yds. Of concrete are in a wall that is 150' long and 8'4" high an d 8' thick Answered by Penny Nom. 





Some trig problems 
20040118 

From Weisu:
I have some questions about precalculus.
(1) (2(cos(x))^2)+3sin(x)1=0
(2) sin(x)cos(x)=(1/2)
(3) 3sin(x)=1+cos(2x)
(4) tan(x)*csc(x)=csc(x)+1
(5) sin(arccsc(8/5))
(6) tan(arcsin(24/25))
(7) arccos(cos(11pi/6))
the last problem uses radian measure.
Answered by Penny Nom. 





Two consecutive negative integers 
20040117 

From Amanda: Find two consecutive negative intergers whose product is 182. Answered by Penny Nom. 





Six letter words 
20040117 

From Debora: An anthropologist discovers an isolated tribe whose written alphabet contains only six letters (call the letters A, B, C, D, E, and F). The tribe has a taboo against using the same letter twice in the same word. It's never done. If each different sequence of letters constitutes a different work in the language, what is the maximum number of six letter words that the language can employ? Answered by Penny Nom. 





Arrays of pennies 
20040117 

From Kathleen: How do I create an array of 100 pennies? Answered by Penny Nom. 





Volume of a tube 
20040114 

From Mike: where can you find how to get volume of a tube:
3 in across x 3 inch high
5 in across x 5 inch high
same formula for both. ONE will get the other. Answered by Penny Nom. 





3/8 as a decimal 
20040113 

From A student: My Math Midterm is tommorow and I am stumped... how do you turn 1 and 3/8 into a decimal... I know the answer is 1.375 but I just copied down what the teacher wrote on the board.
Oh, and what are the three cases of percents? Answered by Penny Nom. 





What is a Fact Family? 
20040113 

From Keisha: I am helping my child with his homework. The worksheet we are trying to do ask the child to choose a number from inside of a circle and then one from inside of a triangle and use the number to build a fact family. The title of the worksheet is "Building a Fact Family House". I noticed that Silver Burdett Ginn,Inc. was the publisher of the book the worksheet came from so I was on the website trying to find an answer to my question. My question is "What is a Fact Family?" Answered by Judi McDonald. 





Polynomial division 
20040113 

From Efrat:
How do we divide the following polynomials?
(x^{3} + x^{2}  x + 2) / (x + 2)
Answered by Penny Nom. 





Twelve acres 
20040113 

From Heather: I am looking at buying a property that includes 12 Acres of land and I am trying to visualize what this size is equivalent to. I have searched your site and figured out how many square feet it is but I was hoping that you could apply 12 Acres to something tangible, like a football field! Answered by Penny Nom. 





Why is the letter J used for the integers? 
20040113 

From Amanda: Why is the letter J used to represent intergers as a symbol? Answered by Penny Nom. 





The square footage of an acre 
20040112 

From Paul: What is the square footage of an acre of land assuming all four sides are
equal in length. Answered by Penny Nom. 





Permutations and combinations 
20040111 

From A student: Are there more permutations than combinations for a series of 4digit numbers with the integers 09? Can you illustrate calculations? Answered by Penny Nom. 





Cubic furlongs 
20040111 

From A student: 1 mile=8 furlongs, how many cubic furlongs in a cubic mile? Answered by Penny Nom. 





Reflex angles 
20040109 

From Sonya: My daughter is searching for examples of reflex angles. We already have the hands of a clock but still need another example. Can you help us. Answered by Chris Fisher. 





Geoboards 
20040109 

From Elissa: What is a geoboard? I have a young girl in grade eight math who has a math
question using a geoboard. Answered by Diane Hanson. 





The area of a lot 
20040109 

From Lea:
I have a problem. I am interested in purchasing a piece of property which has the following dimensions. It is 259.10 Feet on the north side x 61.20 Feet on the east side x 217.80 Feet on the south side x 196.70 Feet on the west side. It looks like an irregular rectangle shape. How do you figure out the square footage on this irregular sized property, and what is the correct square footage answer.
I have attached a survey map. Answered by Harley Weston. 





Inequalities 
20040108 

From Michael: How do you use inequalities in your job and in your everyday life? Answered by Penny Nom. 





Dividing zero by infinity 
20040108 

From Jason: What do you get when dividing zero by infinity? Our Calculus teacher was pretty sure that the expression was indeterminate from. However, if this is so...Why? Zero divded by any number (except zero) is zero, true. Any number (except infinite) over infinite is zero. So, why isn't Zero divided by infinite zero. A simpler way if I had 4 potatoes and was to split them among 2 friends, each friend would get 2 potatoes. However, if I had 0 potatoes and split them a infinite number of ways, each person would still have 0. Explain please! Answered by Penny Nom. 





Unusual occurances 
20040108 

From Martin: My wife and I have a question about the probability of something that happened to us a few years ago. So far, no one has been able to give me even an approximate answer. On my 32nd birthday, my wife and I went out to eat at local Japanese hibachi style restaurant. At the restaurant, couples/families are sat together around the hibachi where the cook performs a show. There was a fifteen minute or so wait, so my wife and I sat in the lounge waiting for our name to be called. When they called our names for the reservation, this is what happened. The first group called was the Martin family. Then they called the Francis family. We were the next family to be called, the Ashton family. My full name is Martin Francis Ashton! I think the odds of that happening to someone are very unlikely, but it did, and there is more. Next, we were all sat at the same table in that order, "Martin" family, "Francis" family, then us, the "Ashton" family. Again, it formed my full name! Answered by Penny Nom. 





Is zero even? 
20040107 

From A secretary at an elementary school: Is zero an even number? Answered by Penny Nom. 





The sides of a circle 
20040107 

From Helena: My name is Helena and I am 10 years old. On a resent math exam I was asked
the question" How many sides does a circle have?" and I wrote down none. The
teacher said the answer was one side. Answered by Chris Fisher. 





Laying decorative bricks 
20040107 

From Duk: Loren is laying decorative brick along both edges of the 21meter walkway up to his house. Each brick is 0.26 meters long. He is placing the bricks end to end. How many bricks does he need to do the job? Answered by Penny Nom. 





Factoring expressions 
20040103 

From A student:
I'm having trouble factoring expressions that aren't monic. I can do things like
x29x+8, but problems like 12x2+5x3 have me stumped.
I also have a question about factoring out common factors. In a problem like
x218x+81, wouldn't you divide by 9? But what happens to the x2, is it x2/9? Answered by Penny Nom. 





37 with four 4'2 
20040103 

From Myra: Using four fours and only four fours to get an answer of 37. Answered by Claude Tardif. 





Solving an equation 
20040103 

From A student: the question is to solve and check equations and the question is
2n + 3n + 7 = 41 Answered by Penny Nom. 





Making a windmill 
20040102 

From Matthew: I am a farmer in Ontario. It has been almost 20 years since high school. I am toying with making a windmill. The output chart for the the old generator I have is shown below. Before I tear it appart I would like to develop a formula from the chart that can predict the output at various speeds. Answered by Penny Nom. 





Four digit combinations 
20031231 

From A student: i need all 4 digit combinations using 09 please Answered by Penny Nom. 





Fractions 
20031231 

From Jae: Replace the question marks with numbers that will make the sentence true.
1.1/3=?/9=?/6
2.?/18=8/12=4/?
3. 3/?=12/?=9/?
4.?/3=?/21=?/7
5. Which problems have more than one possible answer? Why do you think this is so? Answered by Penny Nom. 





A new way to measure randomness 
20031231 

From Stephanie:
Last year, I did a science project in which I asked, "Which shuffles better, an automatic card shuffler or shuffling by hand?" To measure this I decided the "best" shuffler was the one to become random first. Last year, to measure randomness, I numbered cards 152 and had the subjects shuffle them until they broke up the rising sequences or reached 10 shuffles. (Usually 10 shuffles came first...) Anyway, I did the same thing with the automatic card shuffler, and, as hypothesized, the automatic card shuffler randomized the deck first.
This year, I have decided to continue the project. The problem is, I need a new way to measure randomness without the use of fancy computers or something. I have searched the Internet, I have posted my query on websites based on math, and I have searched the local library.
I have found many useful things on the Internet, but none of them can tell me a new way to measure randomness. I cannot do a perfect shuffle, and I am not terribly gifted in the art of using computers. If you have any information (anything will help) or advice, I would be greatly obliged. Answered by Andrei Volodin. 





The trapezoidal rule 
20031231 

From Prashanth: I have a set of XY coordinates(say 49 points),I want to find the area enclosed by the curve joining them and the axes.I do not have an equation for the curve and I am not able to fit a curve given the points.I use the trapezoidal rule
(Y1+Y2/2)*(X2X1),
Is it right? can I do this with any other method? Answered by Penny Nom. 





Ratios and proportions 
20031231 

From Frank: I would like to know how you use 'ratios and proportions' in everyday life. Answered by Penny Nom. 





Some number problems 
20031224 

From Shruthi: 1. Write 31 using 3 five times
2. Write 100 using all the 10 digits just once
. . . Answered by Penny Nom. 





Percent increase 
20031224 

From Frank: How does one figure the percent of increase or decrease in the cost of an item? Answered by Penny Nom. 





Making a cone 
20031222 

From Tracie:
I am working on a craft project at home and I have been given the following information: 16" tall and 13" diameter at base, with 1 and 1/2 " opening at top.
Is there a basic formula for creating a cone with this info?
Answered by Claude Tardif and Penny Nom. 





400, 100 and 2500 
20031221 

From A student: A person likes 400 but dislikes 300
He also likes l00 but dislikes 99
He also likes 2500 but
dislikes 2400
Which of the following does John like
900, 1000, 1100 or 2400
Answered by Penny Nom. 





The angles in a regular polygon 
20031221 

From Ernie: If i have a measure of one interior angle of a polygon, how can i find the number of sides it has? Answered by Penny Nom. 





Adding percentages 
20031219 

From Paula:
How do you add percentages
e.g 90% + 80% + 60% + 54% + 25% = ?
Answered by Penny Nom. 





Business trip 
20031219 

From Ameer: A businnessman drives from Washington, D.C., to Boston, a distance
of 442 miles, and then makes the return trip. On the way to Boston,
he drives 65 miles per hour, taking an 1hour rest stop during the
drive. After finishing his business in Boston, he make the return
trip driving at 60 miles per hour and takes a 45minute rest stop
halfway through the trip. Which leg of the journey, Washington, D.C.
to Boston, or Boston to Washington, D.C., takes the longer time? Answered by Penny Nom. 





The area of a plot of land 
20031219 

From David: I have a plot of land that I cannot find the square footage of. Actually my home sits on a large lot. Local building codes require that a home is seated on no less than 7500 square feet of land and have no less than 50ft of road frontage (the rear of the lot has 65ft of frontage on another road). I need to know if I have enough square footage to build a second home on the rear lot. The lot has five sides. Only one angle is a 90 deg. angle. The others I cannot determine. Of the 4 remaining angles, all 4 angles are obtuse, or greater than 90 deg. The dementions are 89.19' x 130' x 118.52' x 65' x 170.94'. The two legs that make the 90 deg angle are 89.19' and 170.94'. The measurements fall in order using the 90 deg angle as the point of origin and proceeding clockwise, 89.19', 130', 118.52', 65', 170.94'. I have used all the skill I can muster, however, it has been a long time since school and regretably I cannot find an answer. Answered by Penny Nom. 





Multiplier and multiplicand 
20031217 

From Karen: The K5 curriculum states that at a grade 5 level students should "understand and use the terms multiplier, multiplicand" The curriculum defines 'multiplicand' as " a number being multiplied by another number. A factor." There is no definition given for 'multiplier'
Question: Define these words are they just other words for 'factors'. If so, how important is it that students use these terms? It would seem like 'factors' would be the better choice of words to use. If multiplcand refers to eg. the first factor in the equation and the 'multiplier' the seond term, (if in fact it does) is this not confusing for students when we teach them that multiplication is commutative? Answered by Penny Nom. 





Binomial distribution 
20031217 

From Lesley: my daughter is having difficulty with the following formula
P(X=x) = ( n over x) px (1p) nx
The teacher has given them the formula but not taught them how to apply it or understand it. Answered by Penny Nom. 





The hour hand and the minute hand 
20031217 

From Minnie: When you are looking at the clock at 12:00 the hour hand and minute hand are exactly together. (one on top of the other). Between 1:00pm and 1:15pm there is another time when the hour and minute hands are exactly together again. Answered by Penny Nom. 





Factoring in 
20031216 

From Priscilla: How can you use solving by factoring in real life applications? Answered by Harley Weston. 





An elliptical race track 
20031216 

From Judy: the inner rail of a race track is a perfect ellipse. the track is a standard width all the way around. how can i prove that the outer rail is a ellipse? Answered by Penny Nom. 





How far can you see? 
20031215 

From Judy:
How far apart, assuming no obstacles, can two people stand and still see each other?
i know this deals with the curvature of earth, but i can't figure out the formulas involved.
Answered by Chris Fisher. 





(2^ 20,966,011)  1 
20031212 

From Reid: Can someone please explain, answer and/or solve this: (2^ 20,966,011)  1
I don't know what it means, my boss sent it out, I'm assuming it is to be
solved but don't know what it is, any prompt help would be appreciated, very
much so, in fact, thanks,........... Answered by Penny Nom. 





Math jobs 
20031212 

From Veronica: Do you know a couple of jobs I can get when I am older in Math? Answered by Harley Weston. 





A snowball melts 
20031211 

From Adam: A spherical snowball has diameter 10cm and density 0.75g/cm3. It is placed in a cylindrical can with diameer 12cm. After the snow melts it turns to water with density 1.0g/cm3. What will be the depth of the water in the can (to 1 decimal place)? Answered by Penny Nom. 





Diamonds and Pearls 
20031211 

From Lauren: A crown holds a total of 3080 jewels.
It is made up of diamonds and pearls.
There are 10 times as many diamonds as there are pearls.
How many pearls are there? Answered by Penny Nom. 





1/0 = ?? 
20031209 

From Lisa: One of my students asked me a fractions question. She knows that 0/1
equals 0 but does 1/0 also equal 0? Answered by Walter Whiteley and Penny Nom. 





Noneuclidean geometry 
20031208 

From Geoffrey: How can you use noneuclidean geometry to navigate on a sphere? What geometers did work in this area? Answered by Chris Fisher. 





Matrices 
20031205 

From Julie: I am doing a project and need to find some mathematiciens who had an influence in matrices. I can't seem to find any when I search online. Could you please help me with this? Answered by Judi McDonald. 





Prescription drug coverage 
20031204 

From Khadijah: Last week congressional approval was given to legislation involving prescription drug coverage for seniors. One summary of the legislation explains that it is estimated that in 2006 a senior will pay a premium of $35 per month, then pay their first $250 in pharmacy bills. After the bills reach $250, the coverage would pick up 75% of their bills that bring their total bills between the $250 and $2250 mark. After their bills reached a total of $2250, the senior would be responsible for all bills bringing their total annual bills between $2250 to $5100. Then any bills after the $5100 mark has been reached will be 95% covered by the insurance. Using this information, letís analyze the situation of a senior who accumulates $6000 in pharmacy bills over one year and has the insurance coverage. Over the course of this year, how many dollars will the senior pay? Answered by Penny Nom. 





What percentage of 6 billion is 40 million? 
20031203 

From GiGi: What percentage of 6 billion is 40 million? Answered by Penny Nom. 





The median 
20031203 

From Christiane: how do you find the median of this group of numbers:63,75,29,37,49? Answered by Penny Nom. 





NonEuclidean geometry 
20031203 

From Geoffrey: What are the applications of NonEuclidean geometry (especially hyperbolic and spherical)? Answered by Walter Whiteley. 





Four digit combinations 
20031202 

From Deen:
Question:
i have 3 numbers and i have to come up with all the possible 4digit combinations with those 3 numbers. Is there a formula for it?
Example:
given numbers are 129 and you need to break a 4 digit code. what are the posiible combinations that u can come up using the 3 numbers?
Answered by Penny Nom. 





A locus 
20031202 

From Tash:
Question:
a)Find the equation of the locus of the point P which moves so that its distance from A(1,2) is always three times its distance from B(5,6)
b) Show that this locus is a circle and states the coordinates of its centre and the length of its radius
Answered by Penny Nom. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





The area of a triangle 
20031201 

From A student: Find the Area of Triangle ABC
A(3,2)
B(4,0)
C(0,8) Answered by Penny Nom. 





Room and board fees 
20031129 

From Jennifer: A certain university wishes to determine room and board fees for the next academic year. For the current year, the fee is $3600 per student and 1800 students are living in the residence halls. Past data suggests that for every $300 increase in the semester fee, 200 fewer students will choose to live in the dorms. There are also costs to the university associated with the residence halls. The fixed costs total $2,000,000 per semester. the variable costs are currently $1000 per student but will fall $100 per student for each decrease of 100 students. Your task is to help the university determine the optimal fee. Assume linear relationships between the number of students and the fee and between the number of students and the cost per student Answered by Penny Nom. 





5.75 acres of land 
20031128 

From Susan:
We own 5.75 acres of land here in El Paso Tx.
Some one wants to buy all or some of our land...to build homes on...but.. I can't figure a few things
1. our land is Almost exactly 500x 500x500 x500 ft square proprty
based on this can you tell me the approx perimiter measurements of EACH acre
we wish to sell approx 1/2 of this 5.75 acres ...or a tad bit less.. these are all approx measurements
what I also need to know is.. how many 50ft x 100ft lots are in each (1 )Acre???
Answered by Penny Nom. 





A fish tank 
20031126 

From Bill: How do I work out the volume and weight of water in a fish tank that is 36in x 14in x 12in? Answered by Penny Nom. 





Mr.Carter is very cautious 
20031126 

From Bob: Mr.Carter is very cautious. He decides to invest in only three stocks: one low stock, one high stock, one medium stock. Given that the expected annual yields are 6% for low stock, 7% for medium stock, and 8% for high stock, he wants his investment in medium stock to be half of his total investment in low and high stock. How much should I invest in each type fo stocks to expect a total annual return fo $650 form my investments? Answered by Harley Weston. 





Area of an equilateral triangle 
20031125 

From Jared: Can you help me understand why the area of a equilateral triangle is the square root of 3 divided by 4 times the lenght of the side squared? Answered by Penny Nom. 





An inequality whose solution is all points 
20031125 

From Katie:
Hi my name is Katie and I am in the 9th grade and I would like help on this question. Is it possible to have a system of inequalities whose solution is all points?
1.I need to know why (explanation)
2.how to do it(example)
Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20031124 

From Peter: How do I calculate the volume of an irregular shaped tetrahedron where: side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom. 





Markup, profit and margin 
20031124 

From Ali: I have question regarding Margins, Markups and Profit
Purchase price = $ 10.00
Margin or Markup ?? = 40 %
Therefore Selling Price = 10/0.6 = $ 16.67
Profit ? = (16.6710)/10 *100 = 66.67%
or is the profit = (16.6710)/16.67*100 = 40 %
Can you please clarify What is Margin, Markup and Profit Answered by Penny Nom. 





Difference of squares 
20031124 

From Susie:
Factor assuming that n is a positive #
Problem: (I will give it to you in words beacuse I don't know how to do exponents on the computer.)
Fortyfive r to the 2n power minus five s to the 4n power.
I was hoping you could walk me through it not just give me the answer.
Answered by Penny Nom. 





An octagon shaped bed frame 
20031123 

From Trish: My son and I are making an octagon shaped bed frame. We are going nuts trying to figure out what angle to cut the boards to make an outline of an octagon. It seems that the 8 inside angles of the 8 "corners" are 120*, but what is the angle that the 2x6 wood should be cut so that they will angle together to form the outline of the octagon? Answered by Penny Nom. 





Laws of sines and cosines 
20031123 

From A parent: On the one side of a stream lines PA= 586.3 feet, PB = 751.6 feet are measures, angle APB being 167 degrees and 36 min. Q is a point on the opposite side of the stream. Angle PAQ=63 degress and 18 min and PBQ=49 degrees and 24 min. Find PQ. Answered by Penny Nom. 





The volume of a cube 
20031122 

From A student: i have a cube, and the line that cuts threough the middle of the cube across to the other side is 4 radical6. what is the volume of the cube? Answered by Penny Nom. 





Aristotle 
20031121 

From John:
I would like to know how aristotle was related to math.
In all my searches I have found only philosophy etc.
But not any math.
Answered by Penny Nom. 





AB/AP=AP/PB 
20031120 

From James: My name is James McBride. I'm having a difficult time with a pre calculus problem, which goes as follows: "show that AB/AP=AP/PB is equal to (1+5^1/2)/2 (one plus the sqaure root of five with the sum divided by two. I can't do the square root sign, sorry.) I have tried to solve for PB in terms of the other varialbles and then work the quadratic equation. THAT DOES NOT WORK!!!! I am befuddled. Please help me. I am a student of secondary level. Answered by Penny Nom. 





Four digit numbers 
20031120 

From Rob: Hello, I sure hope you can answer this question. I got into a discussion at work about how many possible combinations there are for a four digit number using the numbers 0 through 9. This was in reference to a discussion about the lottery. I said there was only 10,000 possible combinations. My friend said that there was many times more, but he could not remember how to figure it out. The answer and the formula would be greatly appreciated. Answered by Penny Nom. 





962 Sq. Ft. is what percent of 2656 Sq. Ft 
20031120 

From Jon: 962 Sq. Ft. is what percent of 2656 Sq. Ft Answered by Penny Nom. 





4(r2) = r(2+8) 
20031120 

From Angela: I not going to give you the problem that I have, but a problem like it.
4(r2) = r(2+8)
I get mix up trying to solve a problem like this could you help me. So that I will be able to handle the ones on my homework. Answered by Penny Nom. 





A riddle 
20031119 

From Sarah: Ok, our teacher gave us this riddle, and I cannot for the life of me figure it out. He said that there are three problems with the following proof: Answered by Penny Nom. 





Systems of equations 
20031119 

From Scott: I hope that u can help me....I
am a college student taking a class in Pre Calculus.....I have homework
due this Friday and it counts a BIG Percentage on my FINAL grade.....I
am getting mixed up and can not figure out a few problems.....Please help
me.....
Method Of Subsitution
Problem 1. y 8x = 5
x(squared) + y(squared) = 25
Problem 2. y = x(squared)  2x  6
Y = x(squared)  4
Answered by Penny Nom. 





A point and a line 
20031119 

From Meenakshi:
Given a line segment L(x_{1},y_{1})
to (x_{2},y_{2}) and a Point P(x_{3},y_{3}).
I need the formula to find a point on the line L that is closest to
the point (x_{3},y_{3}). Answered by Penny Nom. 





If 1 is neither prime nor composite... 
20031119 

From Joshua: if 1
is neither prime nor composite...what is it called? Answered by Claude Tardif and Penny Nom. 





If 1 is neither prime nor composite... 
20031119 

From Joshua: if 1
is neither prime nor composite...what is it called? Answered by Claude Tardif and Penny Nom. 





Unmatched socks 
20031117 

From Shannon:
i have 6 pairs of socks lying unmatched in my dresser drawer. Each pair is a differnt color (brown, black, red, yellow, green, purple) When i wake up in the morning, I randomly grab 2 of the loose socks and put them on without looking.
If two socks are randomly selected from the drawer, what is the probability that they match?
Answered by Andrei Volodin. 





The 4th difference 
20031117 

From Jack: If i had a sequence which was the same at the 4th difference, aka difference
to the 4th, like:
1 5 14 30 56 96
(sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1
then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an^{4}+bn^{3}+cn^{2}+dn+e Answered by Penny Nom. 





Adding fractions 
20031116 

From Ken: My name is Ken and I am taking my GED course for my High School and have not been in a class for 35 years. I am doing this for retraining. I am at the part about fractions. Here is an example that I am having trouble with.
1 3/7 + 4 2/3 + 11/21
They have no common denominators. Could you PLEASE help me. If you could send me a step by step explanation it would be greatly appreciated. Answered by Penny Nom. 





Three problems 
20031116 

From Megan: My name is Megan and I am a junior in high school. Our teacher gave us a few xtra credit questions and I need some help. Answered by Penny Nom. 





Divisibility by 7 
20031114 

From A student: how do you test a number to see if it is divisible by 7 or not? Answered by Penny Nom. 





Lines 
20031114 

From A student: What is a name that a group of lines pass through? Answered by Chris Fisher. 





root24 = 2 root6 
20031113 

From Burke: I know that all algerbra can be represented visually, for example: Y=9x+3 is a line on a two dimentional plane. Could Math Central please send me a visual representation of the proccess of simplifying square root like root24 equals 2root6 Answered by Penny Nom. 





Diagonals in an octagon 
20031113 

From Glenn: Question 1. What is the probability of choosing the longest diagonal in an octagon? Question 2. Probability of choosing the shortest? Answered by Andrei Volodin and Penny Nom. 





A trig identity 
20031112 

From A student: I can't prove this identity. Can you please help me? (1tanx)/(1+tanx)=(1sin2x)/(cos2x) Answered by Penny Nom. 





What is a number that has exactly 13 factors? 
20031109 

From Mary: What is a number that has exactly 13 factors? Answered by Penny Nom. 





Mixing Brazil nuts and cashews 
20031109 

From Bob: Cashews are sold for 1.20 per 1/4 pound and Brazil nuts are sold for $1.50 per 1/4 pound. If you mix 20lbs of Brazil nuts, how many cahsews would it take to make a mix that sells for $1.30 per 1/4 pound? Answered by Penny Nom. 





A least squares line 
20031109 

From Michelle: Hooke's Law asserts that the magnitude of the force required to hold a spring is a linear function of the extension e of the spring. That is, f = e0 + ke where k and e0 are constants depending only on the spring. The following data was collected for a spring; e: 9 , 11 , 12 , 16 , 19 f : 33 , 38 , 43 , 54 , 61 FIND the least square line f= B0 + B1x approximating this data and use it to approximate k. Answered by Penny Nom. 





Greatest Common Factor 
20031108 

From Beth: How do you use the Greatest Common Factor in addtion and subtraction of fraction? Answered by Penny Nom. 





Equal ratios 
20031107 

From A student: In the ratio 3:8=17__, can__be a whole number? Answered by Penny Nom. 





The product of the page numbers 
20031107 

From Morgan and Mom: You open a book and the product of the page numbers is 12,656. What are your page numbers? Answered by Penny Nom. 





Chisenbop 
20031106 

From Jaclyn: Hi there i was wondering if you would have any information on "counting on your fingers" or " Chisabop". Answered by Penny Nom. 





Intercepts 
20031104 

From A student: I am totally confused on how to determine intercepts of an equation and then to graph the line. For example, how to determine the intercepts of 2x3y12=0. Answered by Penny Nom. 





X bar 
20031104 

From mary: Remind me what this means:
_
X
Answered by Andrei Volodin. 





The length of a chord 
20031103 

From David: When Radius=400.00' and Arc=130.58' what is the Cord distance in feet? Answered by Penny Nom. 





A circle around an irregular polygon 
20031103 

From Dale: How do I find the properties of a circle that is drawn around an irregular polygon of (n) sides with the lenghts of each side given and all end points of the polygon lye on the circumferance of the circle? Answered by Chris Fisher. 





Solve for Q 
20031103 

From Anwaar:
The problem is: QT  X ________ + H = HT QS Answered by Peny Nom. 





Cubic yards of concrete 
20031102 

From John: The foundation is 20' X 20' and the depth is 6", there are also three footings that are 20' X 12" X 12" each. Can you show me the equation to figure out how many yards of concrete I will need to pour the footings and foundation. Answered by Harley Weston. 





Symmetries of a rhombus 
20031102 

From Tonia: why cant an equal sided rhombus have 3 lines of symmetry? you have one line of symmetry on each of the diagonals, and there should be one vertically on an angle. can you please explain the rules of symmetry to me? Answered by Walter Whiteley. 





Which one has the most factors? 
20031031 

From Kristi: Of all the whole numbers less than or equal to 5000, which one has the most factors? Answered by Claude Tardif. 





Divisibility by 2 or 5 or both 
20031030 

From Abdu: How many positive integers less than 1,001 are divisible by either 2 or 5 or both? Answered by Penny Nom. 





1/x + 1/y = 5/12 
20031030 

From Ben: 1/x +1/y =5/12, what is the sum of x and y? Answered by Penny Nom. 





12 cookies 
20031029 

From Joel: there are 12 chocolate, sugar and cinnamon cookies. the probability of choosing a chocolate cookie is 1/3. the probability of choosing a sugar cookie is 1/4 what is the probability of choosing a cinnamon cookie Answered by Penny Nom. 





A rectangle on a disk 
20031029 

From Arthur: How do I go about solving the following problem: What is the width of the largest rectangle with a length of 16 inches you can cut from a circular piece of cardboard having a 10 inch radius? Answered by Penny Nom. 





How much time? 
20031029 

From Lori: I am a elementary teacher 36 math. We have just implemented the Houghton Mifflin Math curriculum. It seems to be quite difficult for most of our students. In order to get through all the material we need to do a lesson a day. Although the students are not getting the material that fast. Should we move on without all the students understanding the material or should we wait and remediate until they get it and be behind for the year. This isn't just a few kids its most of the kids. We are also suppose to teach to all the standards so if we don't get to them the students will not do well on the standardized tests. Answered by Diane Hanson. 





Trees 
20031028 

From Ali: Is there any formula for counting the number of trees (graphs)? Answered by Denis Hanson. 





Means 
20031028 

From Abdu:
Question: 80,80,84,85,88,92,97,98 The average of the 8 numbers listed above is 88. Of the following which pair of numbers could be removed from the list without changing the average. A. 80 and 97 B. 80 and 98 C. 84 and 92 D. 84 and 97 E. 85 and 92 Answered by Andrei Volodin and Penny Nom. 





Solve for x 
20031027 

From Lonnie: i need help with solving equations and formulas such as 3x+b=6x, for x. I do not understand how you find x. Answered by Penny Nom. 





Knitting gauge and felting 
20031027 

From Sara:
I wish to create a pattern to knit an item that will then be felted, thus, shrink as a result. In order to determine the proper gauge to use in creating the item, I produced a gauge swatch, noted the original properties and then the postfelting properties. They are as follow: Before Felting: 20 stitches(width) x 20 rows(height)yielded: Gauge: 3.2 stitches(width) and 4 rows(height) = 1" Dimensions: 6.25"(width) x 5.25"(height) After Felting: 20 stitches(width) x 20 rows(height) Dimensions: 4"(width) x 3"(height) How do I calculate the percentage change in size to accurately determine the number of stitches and rows needed to produce the desired dimensions for the finished (felted) item? Answered by Penny Nom. 





A rock on a string 
20031026 

From A student: a rock on a 4' string is rotated at 80 rpm. what is the linear speed in feet per second? in miles per hour? Answered by Penny Nom. 





Maine and Nevada 
20031024 

From Jimmy:
From 1989 to 1990, the population of Nevada increased b y 157,000, and that of Maine increased by 30,000. In 1990, the population of Nevada was 1,206,152, and that of Maine was 1,233,223. If the populations of the two states continue to increase at the same rates, when will the populations of Nevada and Maine be the same? Write a verbal model for this problem Write an equation for the model Solve the equation and answer the question. Answered by Penny Nom. 





A parabola 
20031024 

From Delores: Given the vertex (4, 2) y intercept = 6 find if/where the parabola crosses the x axis? Answered by Penny Nom. 





0.810 and 0.801 
20031024 

From Ahmed:
could you please tell me what is the greatest decimal fraction formed of the digits 0, 1 , 8? Is it 0.810 or 0.801, please give me the reason of the answer in details and the references if it possible. Answered by Penny Nom. 





Odd Pythagorean triples 
20031023 

From Kathleen: in a triple can a and b be odd numbers Answered by Penny Nom. 





Arithmetic in bases other than 10 
20031022 

From Kim: how do you add, subtract, multiply and devide in base 3, base 5, etc? Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





0.3 trillion 
20031020 

From Bill: What is .3 of one trillion? Answered by Penny Nom. 





Domain of a function 
20031014 

From Karim: Find the Domain of the Function H(x) = Log3 (4x + 7)10 H(x) = log base 3 times 4X plus 7 minus 10 i am having problem solving these kinds of problems. Answered by Penny Nom. 





Pairs of prime numbers 
20031013 

From Nikolas: Use pairs of prime numbers to find all the numbers less than 50 that have only two prime factors. Make an organized list. Answered by Penny Nom. 





5x  y 
20031011 

From Candace: math problem 5xy for x=12 and y=14 do you mulitilpy 5x12 and than the answer from 14 which gives you 46? is this right Answered by Penny Nom. 





Points inside a triangle 
20031010 

From Laura:
is there a way to establish, if a given point at coordinates (x,y) is within an area defined by three other sets of coordinates forming a triangle ABC? is T(x,y) within triangle A(x,y)B(x,y)C(x,y) Answered by Chris Fisher. 





Statistics from grouped data 
20031009 

From Rebecca:
I have to use a suitable computer package (ie. Excel) to work out the mean and standard deviation of the following:
Price Range No of Houses No of Houses
£`000 Area 1 Area 2
45 and under 50 4 5
50 and under 55 7 12
55 and under 60 14 16
60 and under 70 19 18
70 and under 80 8 3
80 and under 100 5 2
I have used excel to work out mean and standard deviation before, but not in a more complicated example like this. Any advice on where to start would be greatly appreciated. Answered by Penny Nom. 





10,000 
20031008 

From Nathan: what two numbers make the product of 10,000. Neither number can end in a zero Answered by Penny Nom. 





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.Ý 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: 80Ý*ÝnÝ=ÝsquareÝnumber, 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.Ý 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 answerÝcorrect 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.Ý 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.Ý He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.Ý 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 discussionÝinvolves the daily lottery.Ý 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.ð 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.ð (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.Ý The difference is $5374.50.Ý 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. 





Quadrati 