







Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom. 





A proof by contraposition 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, then x>=e. I understand the approach very well but I do not understand why if x=e then x>=e. If it is so then why not x=
Thanks in advance!'
Rahul. Answered by Penny Nom. 





The test for some disease is 99% accurate 
20100224 

From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher. 





4digit positive numbers 
20100215 

From marjon: Find the sum of all the 4digit positive numbers with no zero digit. Answered by Penny Nom. 





The intervals where the function is positive and negative 
20100110 

From Ron: Hello
I'm trying to find out the intervals where the function is positive and negative.
It's for a polynomial function y= (x+2)^2 (x2) and y= (x+1)(x+4)(x3)
I have tried the right and left side of each xintercepts, but I still don't understand the
results
thank you for your help Answered by Penny Nom. 





A number base that's not a positive integer 
20091211 

From Nick: Is it possible for a number to have a base that's not a positive integer?
Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.
Thank you.
Nick Answered by Robert Dawson and Claude Tardif. 





Percent increase from a negative number to a positive number 
20090421 

From Brian: I have no problem calculating year over year net profits but am having trouble when it comes to a negative.
2007 Net Profit = 110,333.00
2008 Net Profit = 66,054.00
Brian Answered by Harley Weston. 





Comparing positive and negative fractions 
20090324 

From Christyrose: Hello. I am a sixth grade math student and i need help on how to compare negative and positive fractions.
Here is is:
3/4 2/3 7/10 5/6
I'm not sure how to do the negative parts because i was absent for a couple days. Thank you!
Christyrose Answered by Penny Nom. 





A product of positive and negative numbers 
20081003 

From kaylou: Suppose you were given 13 numbers and asked to find their product.
Seven of the numbers were positive, and the rest were negative.
Would your product be positive or negative? Why? Answered by Penny Nom. 





Right Sided Limit of an Exponential Function 
20080729 

From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x
which look like this lim x^sinx
x>0+ Answered by Harley Weston. 





Three consecutive positive integers 
20080720 

From AC: find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third Answered by Penny Nom. 





Probability of H.I.V. tests 
20070507 

From Danielle: A medical test detects H.I.V. Among those who have H.I.V., the test will detect the disease with probability 0.95; among those who do NOT have H.I.V., the test will falsely claim that H.I.V. is present with probability 0.0125. Among those who take this test, 4% have H.I.V. The test is given to Lucille, and indicates that she has H.I.V. What is the probability that Lucille actually has H.I.V.? Answered by Stephen La Rocque. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





Whole numbers 
20051010 

From Kirk: Can the sum of two or more whole numbers be less than any of those numbers? Answered by Penny Nom. 





Adding positive and negative numbers 
20050903 

From Billy: 46 + 24 =
38 + 22 =
19  20 = Answered by Penny Nom. 





Strategies for teaching operations with positive and negative decimal numbers 
20050202 

From Erin: I am wondering if you can suggest any strategies for teaching operations with positive and negative decimal numbers that do not rely on rules that must be memorized? Answered by Diane Hanson. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





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. 





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. 





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. 





Negative times negative is positive 
20011026 

From Mary: I have a question about adding and multiplying positive and negative numbers. When we add two negative numbers the answer is negative BUT when we multiply two negative numbers the answer is positive. I don't understand. Why? Answered by Penny Nom. 





A sequence of even terms 
20010429 

From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and Penny Nom. 





False Positives 
20001029 

From James: A rare disease infected 1 in 1000 people in the population. A test for the disease is accurate 99% of the time when given to an infected person and also when given to a heathy person.  Fill out a twotier tree diagram and find the probability of the false positive(i.e the conditional probabily of being healty even when tested postive by the test) Comment on the result?
 ...
Answered by Penny Nom. 





(mn + m + n)/(m^2 + n^2) = 1 
20000724 

From William: Find all pair of positive integers m and n such that mn + m + n divides m^{2} + n^{2} = 1. Answered by Peny Nom. 





Natural numbers 
20000412 

From Sara: What is a natural number??? Answered by Penny Nom. 





Whole numbers 
19991202 

From Patty: I'm in a 5th grade class, please explaine what whole numbers are..... Answered by Penny Nom. 





Is zero positive? 
19990903 

From Shah: Is zero a positive integer? Answered by Penny Nom. 





Division by a negative 
19990819 

From Sangeeta B.: 56/8 Answered by Penny Nom. 

