A bag contains number slips numbered 1 to 9. Determine whether the events are independent or dependent, and find the indicated probability. selecting 2 even numbers when 2 slips are chosen without replacement.

Perform the indicated operations. |-11|-|-5|-|7|+|-2|

Let G = (V, E) be a loop-free connected undirected graph with $|V| \geq 3.$ If G has no articulation points, prove that G has no pendant vertices.

AVS Industries has determined that the combined fixed and variable expenses for the production and sale of 800,000 items are $24,000,000. What is the price at the breakeven point for this Item?

Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why.

$$\begin{bmatrix} x & 2y & z \\ r/4 & -s & -5t \end{bmatrix} = \begin{bmatrix} -2 & 10 & -9 \\ 12 & -4 & 5 \end{bmatrix}$$

Davinder ( D ) and Mikhail ( M ) were 2 miles apart when they began walking toward each other. D walks at a constant rate of 3.7 miles per hour, and M walks at a constant rate of 4.3 miles per hour. When they started, D's dog, who runs at a constant rate of 6 miles per hour, ran to M and then turned back and ran to D. If the dog continued to run back and forth until D and M met and the dog lost no time turning around, how far did it run?

Consider the following linear system.

$$\left\{ \begin{array} { c } { x + y = 3 } \\ { 3 x - y = 1 } \end{array} \right.$$

(a) Express the system as a matrix equation AX = B. (b) If a linear system is expressed as a matrix equation AX = B, how do we solve the system? Solve the system in part (a).

The binomial coefficient $\binom{n}{k}$ is the number of k-element subsets of an n-element set. Here is another way to think of $\binom{n}{k}$. Let A be an n-element set and suppose we have we supply of labels; we have k labels that say "good" and n-k labels that say "bad". In how many ways can we affix exactly one label to each element of A?

The _ of a plane wave is perpendicular to the direction of motion of this wave.

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between the product of six and a number and negative two times the number

Find the indefinite integral.

$$\int \sqrt[3]{\tan x} \sec ^{2} x d x$$

Find $\mathcal L^{-1}\left\{ F(s)\right\}$ for the function $F$ defined below.

$$F(s)=\frac{e^{-2 s}-2 e^{-5 s}}{s^{3}}$$

Suppose we have a sinusoidal current i(t) that has an rms value of 5 A, has a period of 10 ms, and reaches a positive peak at t = 3 ms. Write an expression for i(t).

For problem

$$\overrightarrow{\textbf{x}}'=\begin{bmatrix}1&4\\2&3\end{bmatrix}\overrightarrow{\textbf{x}}+\begin{bmatrix}t\\2t\end{bmatrix}$$

, construct appropriate diagonalizing matrices, decouple the linear system, then solve the nonhomogeneous system.