In the opening scene, you learn that Emily is unhappy. How might Emily's face, posture, and actions show this?

If $z=\operatorname{cis} \alpha,$ in polar form and hence determine the modulus and argument of 1 + z.

Determine two linearly independent power series solutions to the given differential equation centered at x = 0. Also determine the radius of convergence of the series solutions.

$$y ^ { \prime \prime } - y = 0.$$

Let $f : R \rightarrow S$ be a ring homomorphism from the ring $R$ to the ring $S$ with $f\left(1_{R}\right)=1_{S}$ . Verify the details that $s r=s f(r)$ defines a right $R$ -action on $S$ under which $S$ is an $(S, R)$ - bimodule.

(a) How does Madame Loisel change over the ten years she works to pay off the cost of the necklace? (b) Analyze: What actually causes her to change?

Show all possible ways that each integer can be written as the product of two positive factors.

$$53$$

A scientist observes that over several decades, fence posts placed in soil on a slope became tilted. Have erosion, deposition, or both occurred in this area? Use evidence to explain how you know.

Elementary school students wrote the following stories. For each situation, write a sentence that shows how two quantities in the situation are related. It is possible that you can describe several relationships in each situation. a. An airplane is flying miles high over Siberia, hundreds of miles from any help. Suddenly, the fuel tank ruptures and fuel starts steadily leaking out. b. A motor home has a water tank that holds a large amount of water. Each shower takes 5 gallons of water. c. You have $5 and you buy candy bars at 50 cents each. d. A class starts off with 16 students. Two students stop coming every week.

State whether the relation represents a function.

$$\begin{matrix} \text{x} & \text{2} & \text{3} & \text{2} & \text{3} & \text{2}\\ \text{y} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \end{matrix}$$

Simplify the equation. Then solve the equation by factoring. $2 x(x-2)=-3(x-2)$ _____.

Find the result (in BCD format) of adding the BCD numbers: 1. 10010011.0101 and 00110111.0001; 2. 01011000.1000 and 10001001.1001

Completely factor each expression. 14 − 8m

At a time when energy conservation is so important, some scientists think closer scrutiny should be given to the cost (in energy) of producing various forms of food. Suppose you wish to compare the mean amount of oil required to produce 1 acre of corn versus 1 acre of cauliflower. The readings (in barrels of oil per acre), based on 20-acre plots, seven for each crop, are shown in the table:

Corn: 5.6 7.1 4.5 6.0 7.9 4.8 5.7 Cauliflower: 15.9 13.4 17.6 16.8 15.8 16.3 17.1

a. Use these data to find a 90% confidence interval for the difference between the mean amounts of oil required to produce these two crops. b. Based on the interval in part a, is there evidence of a difference in the average amount of oil required to produce these two crops? Explain.

Find the quotient and remainder for: a. $\frac{x^{3}+2 x^{2}+x-3}{x^{2}+x+1}$ b. $\frac{3 x^{2}-x}{x^{2}-1}$ c. $\frac{3 x^{3}+x-1}{x^{2}+1}$ d. $\frac{x-4}{x^{2}+2 x-1}$