Find the standard matrix of the linear transformation T, and use it to determine whether T is onto. $T:R^3\to R$ defined by

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\end{pmatrix} =2x_1-5x_2+4x_3.\end{equation*}$$

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ∫ sin² 2x cos 2x dx = 1/3sin³ 2x + C

Simplify each expression. $2 ^ { 4 } \div 8 + 5$

True or False. Resource prices provide information to producers that allows them to use resources in a way that maximizes their value.

Use prime factorization to subtract these fractions: 1/18 - 1/30

Write the integral as a sum of integrals without absolute values and evaluate.

$$\int _ { 0 } ^ { \pi } | \cos x | d x$$

Fill in each blank so that the resulting statement is true. In order to factor

$$7 x ^ { 2 } - 23 x + 6$$

begin by finding two first terms whose product is _____ and two last terms whose product is _____.

A 4-person leadership committee is randomly chosen from a group of 24 candidates. Ten of the candidates are men, and 14 are women. What is the probability that the committee is all male or all female?

Solve the compound inequality, if possible. Graph the solution set (if one exists) and write it using interval notation.

$$- 6 < f ( x ) \leq 0 \text { where } f ( x ) = 3 x - 9$$

Verify that

$$y _ { 1 } ( x ) = e ^ { x } \cos 2 x , y _ { 2 } = e ^ { x } \sin 2 x , \text { and }y _ { 3 } = e ^ { 3 x }$$

are solutions to the differential equation

$$y ^ { \prime \prime \prime } - 5 y ^ { \prime \prime } + 11 y ^ { \prime } - 15 y = 0$$

and show that

$$\left| \begin{array} { l l l } { y _ { 1 } } & { y _ { 2 } } & { y _ { 3 } } \\ { y _ { 1 } ^ { \prime } } & { y _ { 2 } ^ { \prime } } & { y _ { 3 } ^ { \prime } } \\ { y _ { 1 } ^ { \prime \prime } } & { y _ { 2 } ^ { \prime \prime } } & { y _ { 3 } ^ { \prime \prime } } \end{array} \right|$$

is nonzero on any interval.

Give equations for ellipses and tell how many units up or down and to the right or left each ellipse is to be shifted. Find an equation for the new ellipse, and find the new foci, vertices, and center.

$$\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 2 } = 1 , \quad \text { right } 2 , \text { up } 3$$

use a graphing utility to graph f, g, and y = x in the same viewing window to verify geometrically that is the inverse function of f (Be sure to restrict the domain of f properly.) f(x) = tan x, g(x) = arctan x

A sales representative receives an annual salary s, an average commission each month c, and a bonus b for each sales goal that she reaches. a. Write an algebraic expression to represent her total earnings in one year if she receives four equal bonuses. b. Suppose her annual salary is $52,000 and her average commission is$1225 per month. If each of the four bonuses equals $1150, what does she earn annually?

Write each polynomial in simplest form. Use algebra tiles to help. $-x^{2}+4 x+2+2 x^{2}-x$