Note: * = infinite
Suppose that the function f:[0,*)->R is continuous and strictly increasing, with f(0) = 0 and f([0,*)) = [0,*). Then define
F(x) = the integral from 0 to x of f and
G(x) = the integral from 0 to x of f^-1 for all x>=0
(a)...

Suppose that the matrix A is a linear operator on R(2) represented in the standard basis {i,j}, by the matrix
mat(A)= [-1 3;2 4].
Find a new basis in which A is diagonalized.

How many 5 card poker hands are there? Note a deck of 52 cards is assumed.

Let X be a txk matrix whose columns are linearly independent. Let M=I-X(X'X)^(-1)X'. Show that M is symmetric and idempotent.

1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2)
2) Find the volume of the solid bounded above and below by the cone (z^2) = (x^2) + (y^2), and the side by y=0 and y= square root(4-(x^2...

Five cats can catch 5 mice in 5 minutes. At this rate, how many cats are needed to catch 100 mice in 100 minutes? (Hint: it is not 100.)

4-terms - NOT factored by grouping.
Factor out greatest common factor. 2-terms together. Get down to 3 terms first.
4t(xt+yt)+4t(x+y)-24x-24y

Look at the model you found for the data on the number of shopping centers and retail sales for the North Central states.
a. Make a plot of the residuals versus the independent variable.
b. From the plot, does it appear that a linear model is a...

Tom and Jim decided to play the following game for points. A single die is rolled. If it shows a non-prime number, Tom receives points equal to two times the number of dots showing. If it shows a prime number, Tom loses points equal to three times...

In order to test a new car, an automobile manufacturer wants to select 4 employees to test drive the car for one year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability t...