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Percentage change in productivity 2017-03-15
From Sunni:
I'm working on a graph and I need to find the percentage of increase from one figure to another. How do I do that? For instance our department started with a workload of 1773 in Jan and ended with 341 in Dec. In addition to that we received 2088 new items from Jan - Dec with an average of 5 workers. How do I find the percentage of increased productivity if any?
Answered by Penny Nom.
A triple product 2016-10-03
From sam:
Let a and b are vectors such that
Vector a = (1,1,2)
Vector b = (2,-1,1)
And let vector c be a unit vector such that triple product of a,b,c is minimum . We have to find the value of c.

I thought triple product of a b, c means the volume occupied by parallelepiped. And we have to do volume minimum

Answered by Penny Nom.
Two quadratic polynomials 2014-10-28
From khushboo:
The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd' and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'. find the numerical value of a+b+c+d where a, b, c and d are non zero integers.
Answered by Penny Nom.
Expand and simplify [x-3][x+3] 2014-07-16
From symion:
Expand and simplify [x-3][x+3]
Answered by Penny Nom.
Dt[sin t tan (t^2+1)] 2012-02-21
From Ayu:
Dt[sin t tan (t^2+1)]

Answered by Harley Weston.
A product of 1 000 000 2010-11-19
From Sharron:
There are many pairs of numbers that when multiplied together give a product of 1 000 000. However, there is one pair, and only one pair, of whole numbers that contain no zero digits and has a product of 1 000 000. What are these two numbers?
Answered by Stephen La Rocque.
Arrays 2010-09-09
From Susan:
I'm a lawyer but evidently incredibly stupid at 4th grade math. . . .Question: cover a tabletop with 9 rows of square tiles with 9 squares in each row. How many tiles cover the tabletop? Then, the paper shows a 9x9 array and asks how it is used to solve the problem. My daughter wrote 9x9=81. The next question is "what are the products of the two smaller arrays?" ???? There are no other arrays - are we to make smaller arrays from the 9x9? how?
Answered by Robert Dawson.
Adding five positive integers that have a product of 48 2010-04-27
From Lorraine:
What is the smallest possible sum that can be obtained by adding five positive integers that have a product of 48.
Answered by Chris Fisher.
The product of two integers their LCM and their HCF 2009-02-15
From Anonymous:
Two numbers have LCM = 60. If their product is 180, what is their HCF?
Answered by Harley Weston.
(a x b) intersect (b x a) 2009-01-08
From sean:
is it possible to have two sets such that n((a X b) intersect (b X a) =3
Answered by Harley Weston.
The product of two numbers is 2400 2008-10-16
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.
A product of positive and negative numbers 2008-10-03
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.
Product of Two-Digit Numbers 2008-07-31
From pete:
The number 4641 can be expressed as the product of two two-digit whole numbers. What is the sum of these two numbers?
Answered by Janice Cotcher.
Sum and product of the roots of a quadratic 2008-07-03
From Gautam:
If a and b are the roots of x^2+px+1=0 and c and d are the roots of x^2+qx+1=0
prove that

Answered by Harley Weston.
Product of Two Integers 2008-06-25
From devin:
two consecutive integer have a product of 240. what are they
Answered by Penny Nom.
The product of the roots 2008-03-19
From Rebecca:
Determine the product of the roots of the equation (x-1)(x-2) + (x-2)(x-5)=0
Answered by Penny Nom.
The sum and product of the roots of a quadratic 2008-03-16
From Katelyn:
Write the quadratic equation....

Sum of the roots = 16
Product of the roots = -80

Answered by Penny Nom.
The product of two numbers is 1,000,000,000 2008-03-14
From Henry:
What two numbers that don't in zero when multiplied equals 1,000,000,000 and same with 1,000,000,000,000,000,000.
Answered by Penny Nom.
Percentage change 2007-08-19
From nona:
If inputs increase by 30% and outputs increase by 15%, what is the percentage change in productivity?
Answered by Stephen La Rocque.
Scalar triple product and volume of a general tetrahedron 2007-08-03
From Anurag:
how do you prove that volume of tetrahedron= 1/12 times scalar triple product of vectors a,b and c?
Answered by Stephen La Rocque.
If the product of A,B,C is 15834, what is A+B+C? 2007-03-10
From rachel:
if the product of A,B,C is 15834, what is A+B+C?
Answered by Penny Nom.
An octagonal bird house 2007-01-13
From Soren:
I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew!
Answered by Harley Weston.
Products with symbols 2007-01-09
From Jennifer:
Find the product of each

Answered by Penny Nom.
The product of of two rotations 2006-12-17
From Katie:
Is the product of of two rotations over a different center point always a translation?
Answered by Walter Whiteley.
The sum of two numbers is 30 2006-11-03
From GG:
The sum of two numbers is 30 and the product of the same two numbers is 221. Find the two numbers.
Answered by Stephen La Rocque.
The product of polynomials 2006-07-13
From Lynne:
If you multiply two polynomials, what can you say about the degree of their product? What exponent applies here?
Answered by Stephen La Rocque.
A product equals a sum 2005-03-27
From Tor:
Can you please help me with a general formula for the following system:

and how will you prove the formula?

Answered by Penny Nom.
A 3-digit product 2005-02-25
From A student:
I have an odd 3- digit product. My factors are a 1 digit number and either a 2 or 3 digit number. My factors are odd, but neither is 1. Find my factors and my product.
Answered by Penny Nom.
Vectors 2004-07-06
From Annie:
a=3i-j+2k and b=i+3j-2k, 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.
The product of any n consecutive integers 2004-01-18
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.
Pairs of prime numbers 2003-10-13
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.
10,000 2003-10-08
From Nathan:
what two numbers make the product of 10,000. Neither number can end in a zero
Answered by Penny Nom.
The product of four consecutive integers is 3024. 2003-04-25
From pillar:
The product of four consecutive integers is 3024. What are those numbers.
Answered by Penny Nom.
1575 2003-03-13
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.
X times Y equals ten million 2003-02-26
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.
Multiplying vectors 2001-10-22
From Murray:
Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b)
Answered by Harley Weston.
The solutions of a quadratic 2001-01-30
From A student:
  1. Show that the product of the solutions of ax2 + bx + c = 0 is c/a.

  2. For each equation under the given condition, (a) find k and
    (b) find the other solution.
    kx2 - 2x + k = 0; one solution is -3

Answered by Penny Nom.
Multiplying decimals 2000-10-16
From Lily:
I need help with mutiplying decimals (example) 2.28*0.48( * = times).
Answered by Harley Weston.
10 000 000 = a x b 2000-03-06
From Spencer Jaffe:
What two numbers that don't end in zero, multiplied equal 10,000,000.
Answered by Claude tardif.
A negative times a negative 2000-02-29
From Michael J. Butler :
I have reviewed the answer in relation to the question of why (-3)x(-2)=6; however, I am still not able to properly explain the reasoning to my son, Jonathan, who is in grade 7. I want him to understand the reason for the rule that the multiplication or division of two negative numbers equals a positive number. Can you help?
Answered by Chris Fisher.
Area of a triangle from vertex coordinates 1999-04-21
From Mark Tyler:
I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too.

I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula:

A = abs((x1-x2)*(y1-y3)-(y1-y2)*(x1-x3)) for triangle (x1,y1)(x2,y2)(x3,y3)

I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long.

Regardless, it may be fun for the kids, even if it's not on the curriculum.
Answered by Walter Whitley.

A Sum or Product of Fractions 1998-10-06
From Emily Robb:
Find a pair of fractions that when they are multiplyed and added the sum /product is the same
Answered by Penny Nom.
Matrices 1998-03-10
From Ksya:
  1. A and B are matrices. If A^n=B^n, can we say A=B or det(A)=det(B) or det(A)^n=det(B)^n ? Any conditions ???

  2. If B^(-1) is the inverse of B, where B is a matrices. Can we say [(B^(-1))^n][B^n]=I, where I is identity matrices? Any conditions???

Answered by Doug Farenick.
Mathematical Induction and the Derivative 1997-03-18
From Shuling Chong:
"Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n."

Any educated tries are appreciated.
Answered by Penny Nom.

(-3)x(-2) 1995-10-25
From Azmat:
Why is (-3)x(-2) = 6?
Answered by Herley Weston and Ed Giesbrecht.
Quel serait le cout total de production de 500 entrees 2006-06-10
From Suzanne:
Chaque operateur traite des donnees pendant 7 heures 1/2 par jour, et peut s'acquitter d'une demande en 3 heures et 3/4. Combien d'operateurs faudra-t-il pour traiter 50 demandes en 1 jour.

Vous etes surveillant a l'entree des donnees. Pour atteindre vos objectifs vous engagez temporairement 2 commis a un salaire de 10$ et a raison de 8 heures par jour. Si chaque personne peut produire 50 entrees par jour, quel serait le cout total de production de 500 entrees.

Answered by Claude Tardif.



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