







The modulus of a complex number 
20160729 

From Cheyenne: There's a question on my Summer Assignment I cant figure out. Here it is:
Find the absolute Value of the complex number. 5i
Please help? Answered by Penny Nom. 





Calendar arithmetic 
20160214 

From Jenalee: January 1, 2001 is Julian Day 2 451 911 (the number of days that have passed since Day 0, January 1, 4713 BC).
If Julian Day 0 was a Monday, what day of the week was January 1, 2001? Answered by Victoria West. 





A model of the sun and the Earth 
20140614 

From Lynn: There is a model of the sun that is 2 1/2 inches in diameter. This is the only clue we have! How far away is the earth from this model? Answered by Penny Nom. 





What is the value of 2((i)^(1/2))? 
20130722 

From Delilah: What is the value of 2((i)^(1/2)) ?
i.e. absolute value of 2 multiplied by square root of i. Answered by Penny Nom. 





Mod versus Rem in Turing 
20130101 

From Eric: I am a teacher teaching computer science using Turing. I am having
difficulty understanding why one would use the mod operator versus the rem
remainder operator.
Mod seems to make the resulting sign depend on the sign of the divisor,
whereas rem makes the resulting sign depend on the dividend.
Examples:
11 mod 5 = 1 and 11 rem 5 =1
11 mod 5 = 4 and 11 rem 5 = 1
11 mod 5 = 4 and 11 rem 5 =1
11 mod 5 = 1 and 11 rem 5 = 1
What I can't understand is why this would matter. For example, 11 / 5 =
2.2 and 11 / 5 = 2.2 get the same result.
So how is a remainder dependent on the sign of one of the parts?
What benefit would using one over the other have?
Any insight would be most helpful!
Eric Answered by Harley Weston. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





Modular arithmetic 
20111030 

From Kim: Hello,
I am editing a resource for students, and I think some of the answers may be incorrect.
The text I was given and my questions are in the attachment.
Any help you could give would be appreciated.
Thanks,
Kim Answered by Harley Weston. 





Sales as a function of advertising 
20101208 

From Adori: The sales S(in thousands if units) of a product after x hundred dollars is spent on advertising is given by S=10(1e^kx). Find S as a function of x if 2500 units are sold when $500 is spent on advertising. Answered by Penny Nom. 





(x^3 + 11x) is divisible by 6 
20100624 

From PT: Given that x is a nonzero integer,
how do you show that for all values of x,
(x3 + 11x) is divisible by 6?
I know it works but how do I answer the "all values of x" part?
Thanks in advance! Answered by Robert Dawson. 





A linear relationship 
20100622 

From Laura: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $300 to drive 480 miles and in June it cost her $460 to drive 800 miles.
Question: Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. Answered by Robert Dawson. 





A scale model of a city 
20100518 

From Briana: Well I have to create a three dimensional city for a geometry project and it requires us to use precise scal factor and well we want to build a medium sized city but our teacher said that If we make or buildings to high our houses would look like super small compared to the tall building were trying to figure out if we were to build a medium sized city what scale factor should we use to make the houses big enough to see and design? Answered by Walter Whiteley and Tyler Wood. 





Modelling an underpass 
20100511 

From Sue: An engineer at the Ministry of Transport is creating the plans for a new road. This road
will cross the path of a busy railway track so it will be necessary to built an underpass for this road.
This underpass will be in the shape of a parabolic arch.
The specifications include:
the road must be at least 10 m wide and it must have shoulders at least 2 m wide on either
side of the road.
there must be a clearance of 3 m over all areas of the road.
What quadratic equation could you use to model this bridge. Answered by Penny Nom. 





A model for the population of a Canadian city 
20100407 

From jess: Let t^2 represent tsquared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000? Answered by Penny Nom. 





A linear relationship 
20100224 

From Mel: This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.
h (cm) 
120 
340 
480 
600 
1040 
T (degrees C) 
14.28 
12.96 
12.12 
11.4 
8.76 
Find the gradient and vertical intercept of the function. Write the formula for T. Answered by Penny Nom. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





Commodity price increase 
20091104 

From bharat: if price of a commodity increases by x% the to keep the expenditure same
the decrease in consumption should be (x/(x+100))*100, why? Answered by Penny Nom. 





Constructing a scale model 
20090927 

From Colleen: What is the formula i need to use to find out how to state a reasonable scale in the question below;
Suppose you were constructing a model that must sit on a piece of cardboard that is 22cm by 28cm. STATE THE REASONABLE SCALE that you can use to build a model to represent the following items. Determine the dimensions of the model.
a) a rectangular prism with a length of 5m and a width of 2m? Answered by Penny Nom. 





Fitting the curve y=a*exp(b*x)+c 
20090812 

From aika: Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Answered by Robert Dawson. 





Math in everyday life 
20090803 

From Naveen: Dear sir,
We are advised to do a project on "Mathematical modeling to solve various problems
of our everyday life/environmental related problems...... Can u plz help us by mailng some
ideas, suggestion,reference to make my project successful.... Thanking you......
Waiting for your favourable reply...... Answered by Penny Nom. 





The scale for a model train 
20090313 

From Shelly: Lindy is planning to build a model of a train using a scale where 2 inches represents 25ft. If the train is 60 feet long, what is the length in inches that Lindy should build the model of the train? Answered by Stephen La Rocque and Penny Nom. 





Two modular equations 
20081008 

From Mhiko: please solve this Chinese remainder problem..and give me a solution or rule in order to solve this problem/
x=2mod15
x=1mod25 Answered by Stephen La Rocque. 





Remainders 
20080630 

From vivek: what is the remainder when 2050*2071*2095 is divided by 23 ?
this question needs to be done in as less time as possible. Answered by Penny Nom. 





The mean, the median and the mode 
20080623 

From Crystal: Hi my name is Crystal,
My question is
under what circumstances will the mean, the median, and the mode all have the same value? Answered by Stephen La Rocque and Harley Weston. 





A linear model 
20080509 

From Shelby: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of 25,195 per year with t represents the number of years since 1994? Answered by Penny Nom. 





A complex number in polar form 
20070723 

From roland: write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3  4i. Answered by Harley Weston. 





A model for a building 
20070717 

From Carl: A model for a building is 50 centimeters long, 38 centimeters wide, and 225 centimeters tall
on model 1 centimeter represents 2.5 meters.
I need to find the volume of the actual building in cubic meters,and the surface area of the building including
ceilings and floors. round to the nearest tenth of a square meter. Answered by Harley Weston. 





The "mode" of a set of numbers 
20070606 

From Anthony's mom: we have a graph: Kindergarten has 1, 1st has 5, 2nd has 4, 3rd has 3
is the mode "1st grade" because there are more children in that grade? Answered by Stephen La Rocque. 





Using a stem and leaf plot 
20070522 

From Maegan: The students in Mr.Smiths PE class collected data on the number of sit ups the students were able to do in three minutes. Use the data to create a stem and leaf plot. What is the median for the class data? range? mode? Answered by Penny Nom. 





Can you have median < mode < mean? 
20070411 

From Kaliela: Can the Median > mode > mean?
Can the Mean > Mode > Median?
I don't think either of these can occur but I'm unsure why? Answered by Penny Nom. 





A missing observation 
20070402 

From destinee: please help me my problem is 5,11,19,3,15,17,5,n find n given the following info.range:16 mode:5 median:8 mean:10 what the heck is the answer Answered by Penny Nom. 





Exponential form of complex numbers 
20070212 

From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom. 





A scale model 
20061130 

From Adrianna: 1) A model of a storage compartment is to a scale of 1:40. If the surface area of the model is 25 square centimeters, what is the surface area of the actual storage compartment?
a) The storage compartment in the last question has an actual volume of 8 cubic metres. What is the volume of the model? Answered by Penny Nom. 





A scale factor 
20060325 

From Jackie: I need a formula or step by step help to show my child how to find missing dimensions for example: The scale factor for a model is 10 inches = ________ feet
Model 39.7 in
Actual 11.9 ft Answered by Penny. 





A train model is created using a scale of 1:60 
20060101 

From Jennifer: An "n gauge " train model is created using a scale of 1:60. If an actual train engine, the "K4" an early twentiethcentury engine,is 45 feet long, what is the length of an "N gauge" model of the engine in inches? Answered by Penny Nom. 





The number is increased by the sum of its digits 
20051107 

From Ernesto: The number 1 is written on a blackboard. After each second the number on the blackboard is increased by the sum of its digits. is it possible that at some moment the number 123456 will be written on the blackboard? Answered by Claude Tardif. 





Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 
20050718 

From Ladis: Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6. Answered by Chris Fisher. 





The sum of the digits of 2^100 
20050611 

From Richard: The sum of the digits was calculated for the number 2100, then the sum of the digits was calculated for the resulting number and so on, until a single digit is left. Answered by Penny Nom. 





Divisibility of a^2 + b^2 
20050516 

From Ampa: given natural numbers a and b such that a^{2}+b^{2} is divisible by 21, prove that the same sum of squares is also divisible by 441. 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. 





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. 





Mean, median and mode 
20020908 

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





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

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





Take It! 
20020403 

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





The best linear model 
20010729 

From Rebeca: I am a student (senior) summer hire working for Dept of the Army Resource Management. I've been assisting the Analyst in developing a model to predict training costs. The technique we used was simple linear regression. Now I've been asked for my opinion in choosing the best model I feel is better. I've chosen #1. Garrison Training but I want a second opinion before I give my choice. I've taken basic statistics last year in high school and will probably be taking more this year. Could you look over the information and give me a reason my choice would not be best? The dep variabley, is Training costs in dolars per day. Model  Ind Variable X  a  b  r  sy.x  1.  Garrison Training  126.31  0.982  0.9055  117.2  2.  Local Training  212.16  1.37  0.7937  142.7  3.  Man Rig Area  116.38  2.47  0.6481  175.6  4.  Major Training  346.12  4.67  0.7280  167.2  Answered by Andrei Volodin. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





Toy bricks 
20010513 

From Sarah: A regularsized brick weighs 4 kilograms. How much will a similar toy brick, made of the same material, but all of the same dimensions of which are four times smaller, weigh? The 300metre tall Eiffel tower is made of steel and weighs 8 000 000 kg. An exact replica, made of the same material, weighs 1 kg. How high is the replica Answered by Penny Nom. 





What is the difference between Mean and Average? 
20001213 

From Julie: What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower) Answered by Patrick Maidorn and Penny Nom. 





Mode 
20000922 

From James Barton: I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others. Answered by Claue Tardif and Harley Weston. 





Finding a formula 
20000505 

From Erica Hildebrandt: If a farmer has a field and his plots are laid out in the following grid where each # represents a plot: 4  5  12  13  20  3  6  11  14  19  2  7  10  15  18  1  8  9  16  17  Of course the plot numbers aren't meaningful as I have described above. In fact they may not be numbers at all. The only constants I have are the total number of rows and columns. Using the total number of rows and columns and my current position row and column, how can I write a formula that tells me column 3 row 3 = 10, column 4 row 2 = 14, etc. I can see the pattern but can't quite get the formula. I believe I will need 2 different formulas one for even and one for odd rows. Answered by Paul Betts and Penny Nom. 





A model area 
19991215 

From John Ost: Hello, I am a college student taking an elementary math course I need if possible assistance to developing an area model 36 x 25 that shows each of the four separate partial products. I must know how to do the computation 36x25 showing each of the four partial products separately, and indicate how each corresponds to the drawing that is required of the area model. Answered by Penny Nom. 





Mean, median and mode 
19991207 

From J William Morning: Using the data values 2,2,10,6,5, determine the median, mode and mean. Answered by Penny Nom. 





Linear models 
19991109 

From Helen Moreno: What is a linear model? Answered by Harley Weston. 





Mean, median and mode 
19991106 

From Rick: I have five number places and the mean and median are both "0". The mode is greater than the mean. The sum of the absolute values of all of the numbers is 20. The smallest number is 4 less than the next smallest number. What are the five numbers. (negative integers can be used) All of the numbers are integers. Answered by Penny Nom. 





Divisibility by 9 
19990221 

From Razzi: I've been having a hard time trying to solve the following problem and I was wondering if you could help me. For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b). Answered by Chris Fisher and Harley Weston. 





Modular Arithmetic 
19990204 

From Leslie Kupper: I am trying to do a project on modular arithmetic. I was wondering if there were any websites that include a sample lesson plan on modular arithmetic for any grade level. Let me know where and how to find them. Thanks. Answered by Harley Weston. 





Absolute value of i 
19990106 

From Wayne Bagley: I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Answered by Harley Weston. 





A Logic Problem 
19980607 

From Anthony Bacigalupo: My name is Anthony Bacigalupo and I take Sequential ][ Math and am taking a practice regents. When doing a logic problem, I encountered the following statements, where I am trying to prove P ( I left out steps unrelated to the question).... Answered by Chris Fisher. 





Clock Arithmetic. 
19980309 

From Joann Dixon: What is clock mathematics? Answered by Patrick Maidorn. 





Arithmétique modulaire 
20080110 

From hausknecht: ma grand mère a entre 60 et 80 ans.il y a un an son âge était un multiple de 3.dans deux ans son âge sera un multiple de 2,de 3 et de 9.cette année , c'est un multiple de 5.quel est l'âge de ma grand mère? Answered by Claude Tardif. 





mod n 
20050426 

From Jean: Réecrire (5A27)en base 16 changer en base 8
( (2n)!+ 1) (mod n)
(1764n) (mod n)
(n+1)exposant 78355 (mod n)
PPCM(n!+1 , n!) Answered by Claude Tardif. 





le système RSA 
20050219 

From Un eleve: Je suis actuellement en classe préparatoire MP au lycée Henri Poincaré de Nancy et je souhaiterais obtenir des informations sur l'exponentiation modulaire car je réalise un TIPE sur la cryptographie et plus particulièrement le système RSA. pourriezvous m'indiquez en quoi consiste l'exponentiation modulaire et comment cela fonctionne. Answered by Claude Tardif. 

