Use properties of determinants to evaluate the given determinant by inspection. Explain your reasoning.

$$\left| \begin{array} { r r r } { 1 } & { 1 } & { 1 } \\ { 3 } & { 0 } & { - 2 } \\ { 2 } & { 2 } & { 2 } \end{array} \right|$$

Find the derivatives of the functions. Assume that a and k are constants. $f ( \theta ) = e ^ { k \theta } - 1$

Solve each equation. Check your solution.

$$4w + 10 = 6 w - 13$$

List the prime numbers between 80 and 90.

Assume the signals listed are solutions of the given difference equation. Determine if the signals form a basis for the solution space of the equation. Justify your answers using appropriate theorems. $1^{k},(-1)^{k} ; y_{k+4}-2 y_{k+2}+y_{k}=0$.

a. Rewrite the equation in a rotated x'y'-system without an x'y'-term. b. Express the equation involving x' and y' in the standard form of a conic section. c. Use the rotated system to graph the equation.

$$x ^ { 2 } + x y + y ^ { 2 } - 1 = 0$$

Determine whether or not the given vectors are perpendicular. (4, -2, -4), (1, -2, 2)

Evaluate the following determinants:

$$\left|\begin{array}{rr}3 & 5 \\ -2 & -3\end{array}\right|$$

Asample of 20 engineers employed with a company for three years has been rank ordered with respect to managerial potential. Some of the engineers attended the company’s management-development course, others attended an off-site management-development program at a local university, and the remainder did not attend any program. Use the following rankings and $\alpha =$ .025 to test for a significant difference in the managerial potential of the three groups.

$$\begin{matrix} \text{No Program} & \text{Company Program} & \text{Off-Site Program}\\ \text{16} & \text{12} & \text{7}\\ \text{9} & \text{20} & \text{1}\\ \text{10} & \text{17} & \text{4}\\ \text{15} & \text{19} & \text{2}\\ \text{11} & \text{6} & \text{3}\\ \text{13} & \text{18} & \text{8}\\ \text{ } & \text{14} & \text{5}\\ \end{matrix}$$

What genre is "Of Mice and Men" book?

Summarize the events at the end of the story. Do you think it is an effective ending? Explain.

Describe a dilation with center (0, 0) that would produce an image such that every image point is closer to (0, 0) than its corresponding preimage point.

As an avid biker, you’ve come to realize that your top speed is really an air speed, not a ground speed, because air resistance is very noticeable when you ride fast. You like to ride at top speed for exactly an hour every day, and you know that on a calm day, you can ride 20 km before having to turn around and come back the same way. Today, though, you have a 20-km/h head wind for the first leg of the trip (which of course is a tailwind on the way back). You must be back home in an hour, so you look at your map.

A coin is tossed and a number cube is rolled. What is the probability of heads and a number greater than three?