







The square root of a large number 
20100119 

From darlene: I understand the simple process, like 12 is the root to 144 but what happens when the number is 42563. Without a calculator how does a person figure this out during a timed test? Answered by Robert Dawson. 





The product of two numbers is 2400 
20081016 

From belinda: The product of two numbers is 2400, one number is 20 more than the other number. what are the two numbers? Answered by Penny Nom. 





Compatible numbers 
20080925 

From Katie: I am having trouble remembering how to find compatible numbers used to find the estimate in the foloowing problem. Can you please help me solve it and explain it to me? My son is in 5th grade and I need help. Thank you. Here is the problem: 2,752 / 28 estimate: 90 Answered by Penny Nom. 





The cube root of a really big number 
20080717 

From Pete: Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator? Answered by Harley Weston. 





Estimate the cube root of 270 
20080311 

From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the NewtonRaphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston. 





The irrationality of PI 
20070807 

From Matthew: I have what I like to think of as a rather interesting question that I can't explain confidently for the life of me.
If we take a circle with a radius of 1 and we calculate the circumference, we can use 2 pi R.
Doing this calculation results in a circumference of 6.28318530717~ which goes on forever.
However, if you were to take a that same circle in the real world, say with radius 1cm and wrap a string around
it, and then measure the string, you don't get 6.28~, you get something like 6.2, a much more finite distance. The length
of the string is not an irrational number, like the math claims it to be. Answered by Claude Tardiff and Stephen La Rocque. 





Fill in the blanks 
20061004 

From Justin: 1. To find out about how much, you can
2. The  states that the sum is the same no matter who you group the addends. Answered by Stephen La Rocque. 





How many digits? 
20050607 

From Floren: The numbers 2^{1989} and 5^{1989} are written one after another. How many digits in all are there? Answered by Claude Tardif. 





50^99 and 99! 
20050523 

From Romel: Which number is greater, 50^{99} or 99! Answered by Claude Tardif. 





How do you estimate the equation of a parabola? 
20021201 

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





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

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





Dan is 4 inches taller than Mike. 
20020904 

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





A sample size problem 
20011028 

From Charles: The U.S Transportation Dept. will randomly sample traffic reports to estimate the proportion of accidents involving people over the age of 70. The Dept. has no advance estimate of this proportion. how many reports should the dept select to be atleast 97% confident that the estimate is within .01 of the true proportion? Answered by Harley Weston. 





Linear regression 
20010801 

From A student and a mother: My mom is taking a correspondence course in Simple Linear Regression and Correlation Analysis and we've been arguing about the relationship between the correlation rxy and standard estimate of errorSy.x. I took statistics last year in high school and I remember something about the Sy.x being proportionate to the r. Are they inversely related, directly related, not related, or can only range from 0 to 1.00? Her book doesn't say very much and I believe they are inversely related. She says they're directly related. Answered by Chris Fisher and Penny Nom. 





A confidence interval 
20010426 

From Kim: A poll asked 1528 adults if they were in favor of the death penalty, 1238 said yes, find 99% confidence level for percent of all adult who are in favor of the death penalty. Answered by Andrei Volodin. 





Estimating the time to complete a job 
20001203 

From Jack Hook: I'm a contractor and need to estimate how much time it will take me to do a specific job. A previous job I did was 6,480.16 Square Feet and I was able to paint it in 31.5 hours. In estimating my next job, how many hours will it take me to paint 11,000 Sqare Feet. Answered by Penny Nom. 





Sample variance 
20000416 

From Jonathan Freeman: I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand? Answered by Harley Weston. 





Estimates 
20000411 

From Sue Jordan: I am looking for examples of estimates for underestimating and overestimating. When would you do each one. For my child age 11 6th grade. Answered by Penny Nom. 





Area of an irregular shaped objects. 
19990407 

From Jesse Townsend: How do I find the surface area of an irregulary shaped object such as someone's knee from the thigh to shin? Thanks. Answered by Walter Whiteley. 





The bricklayers formula 
19981124 

From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston. 





A Monte Carlo Procedure 
19970423 

From Donna Hall: A irregularly shaped object of unknown area A is located in the unit square 0<=x<=1. Consider a random point uniformly distributed over the square. Let X = 1 if the point lies inside the object and X = 0 otherwise. Show that E(X) = A. How could A be estimated from a sequence of n independent points uniformly distributed over the square? How would you use the central limit theorem to gauge the probable size of the error of the estimate. Answered by Harley Weston. 





Approximating pi. 
19961104 

From Ben Dixon: How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference? Answered by Chris Fisher. 





Approximating roots. 
19961104 

From Ben Dixon: How do you calculate a square root? eg the square root of 2.There is obviously some sort of successive approximation type algorithm for doing it to however many decimal places is required, but what is the algorithm? Answered by Harley Weston. 

