Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. There are the same number of permutations of {1, 2, 3, 4} of even parity as there are of odd parity.

Determine the general solution to the linear system

$$\mathbf { x } ^ { \prime } = A \mathbf { x }$$

for the given matrix A.

$$\left[ \begin{array} { r r } { 3 } & { 13 } \\ { - 1 } & { - 3 } \end{array} \right].$$

What is the Ratio Test inconclusive for summation n=1 to infinite (-3)^n-1/n^1/2 (that is, it fails to give a definite answer)?

If c and d are different positive integers and

$$4c + d = 26,$$

what is the sum of all possible values of c?

$$A \ 6 \\ B \ 10 \\ C \ 15 \\ D \ 21$$

Find general solutions of the differential equation. Primes denote derivatives with respect to $x$.

$$4 y ^ { \prime \prime } + 8 y ^ { \prime } + 3 y = 0$$

Acid or subtract. $\frac { 6 r s } { r ^ { 2 } s ^ { 2 } } + \frac { 18 r } { r ^ { 2 } s ^ { 2 } }$

Of the seventeen students in Angela's class, eight play in the school band. What fraction of the total number of students in Angela's class are in the band?

Evaluate or simplify each expression without using a calculator.

$$\log 10 ^ { 7 }$$

Find the positive radian measure of the angle that the second hand of a clock moves through in the given time.

$$4 \text { minutes and } 25 \text { seconds }$$

What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?

Make the following conversions:

$$2500 ^ { \circ } \mathrm { F }$$

to K

For the function, give the new function rule after the given transformation.

$$f ( x ) = \left\{ \begin{array} { l l } { 3 x ^ { 2 } } & { \text { if } x < 1 } \\ { - 2 x + 4 } & { \text { if } x \geq 1 } \end{array} \right.$$

after a vertical stretch by a factor of 5

use a graphing utility to graph the quadratic function. Find the x-intercept(s) of the graph and compare them with the solutions of the corresponding quadratic equation when f(x) = 0. f(x) = x^2 - 4x

Solve the inequality and graph the solution. $\frac{3}{8}+x \leq \frac{5}{16}$