Compute $A-B^T$ if

$$\begin{equation*}A=\begin{bmatrix}3&&-1&&2&&4\\1&&5&&-6&&-2\end{bmatrix},B=\begin{bmatrix}-4&&0\\ 2&&5\\ -1&&-3\\ 0&&2 \end{bmatrix}\end{equation*}$$

Use long division to find the quotient. Show your work.

$$\frac{6x^4 + 3x^3 + 13x^2 – x – 5}{3x^2 – 1}.$$

The scores of Katie’s first seven tests are listed: 90, 85, 80, 90, 95, 90, 100. What is the range of the scores?

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. an arrangement of the letters in the word intercept.

A report in the New England Journal of Medicine notes growing evidence that the herb Aristolochia fangchi can cause urinary tract cancer in those who take it. Suppose you are asked to design an experiment to study this claim. Imagine that you have data on urinary tract cancers in subjects who have used this herb and similar subjects who have not used it and that you can measure incidences of cancer and precancerous lesions in these subjects. State the null and alternative hypotheses you would use in your study.

Find a unit vector in the direction in which f decreases most rapidly at P, and find the rate of change of f at P in that direction f(x, y)=

$$e^{xy}$$

; P(2, 3)

Find the slope of the line that passes through each pair of points. (-4, 3), (-2, 1)

Reduce:

$$\frac { 500 } { 1000 }$$

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). Malcolm has two options for membership to a golf club. Option A has an annual cost of $3300 for unlimited golf. Option B has an annual cost of$1500 plus $40 for each round of golf. How many rounds of golf would Malcolm have to play in a year for the two options to cost the same?

Perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defind as follows If an operation is not defined, state the reason,

$$A = \left[ \begin{array} { r r } { 0 } & { 2 } \\ { - 1 } & { 3 } \\ { 1 } & { 0 } \end{array} \right] \quad B = \left[ \begin{array} { r r } { 4 } & { 1 } \\ { - 6 } & { - 2 } \end{array} \right] \quad C = \left[ \begin{array} { r r } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$$

$$A ( B + C )$$

The servicing of a machine requires two separate steps, with the time needed for the first step being an exponential random variable with mean .2 hour and the time for the second step being an independent exponential random variable with mean .3 hour. If a repair person has 20 machines to service, approximate the probability that all the work can be completed in 8 hours.

Moises saves 8% of his weekly paycheck in his savings account. He deposited $18.80 from his last paycheck into his savings account. Which is the best estimate of the total amount of Moises’s last paycheck? (A)$26, (B) $100, (C)$160, (D) $200

Write < or > in the box. $0 \div ( - 49 ) \ ? \ 49 \div ( - 1 )$

List all the subsets of each set.

$$\{ - 2,2 \}$$