Solve by the method of your choice. Two teachers have driven to school in separate cars. When they arrive, there are seven empty spaces in the parking lot. They each choose a parking space. How many outcomes are possible?

The Fernandez family drove 273 miles in 5.25 hours. How far would they have driven at that rate in 4 hours? (A) 208 miles (B) 220 miles (C) 280 miles (D) 358 miles

A stretched string of length L is observed to vibrate in five equal segments when driven by a 630-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in three segments?

Lisa Carr fills up her car's gas tank and drives off. The table shows the numbers of gallons of gas left in the tank at various numbers of miles driven.

Find the coefficient of determination and the correlation coefficient again by calculating $S S_{\text {dev }}$ and $S S_{\text {res }}$ directly from their definitions. Do the answers agree with the results in the previous part?

Shields Company is preparing its interim report for the second quarter ending June 30. The following payments were made during the first two quarters:

$$\begin{array}{lcr} \text { Expenditure } & \text { Date } & \text { Amount } \\ \hline \text { Annual advertising } & \text { January } & \$ 800,000 \\ \text { Property tax for the fiscal year } & \text { February } & 350,000 \\ \text { Annual equipment repairs } & \text { March } & 260,000 \\ \text { One-time research and development fee to consultant } & \text { May } & 96,000 \end{array}$$

For each expenditure, indicate the amount that would be reported in the quarterly income statements for the periods ending March 31, June 30, September 30, and December 31.

Which lettered pair of words-a, $b, c, d$, or $e$-most nearly expresses the same relationship as the capitalized pair? Write the letter of your answer in the space provided.

ABSCOND : DEPART

a. state : proclaim

b. grant : withhold

c. conceal : reveal

d. conspire : agree

e. declare : announce

An automobile is driven down a straight highway such that after

$$0 \leq t \leq 12$$

seconds it is s=4.5

$$t^2$$

feet from its initial position. Find the instantaneous velocity of the car at t=6.

In the following paragraph, identify each underlined phrase by writing above it PART for participial phrase or GER for gerund phrase.

$\underline{Determined\ and\ driven\ toward\ her\ goals}$, Butcher raises her own dogs.

In an investigation by V. A. Tucker and K. Schmidt-Koenig, it was determined that the energy E expended by a bird in flight varies with the speed v (km/hr) of the bird. For a particular kind of parakeet, the energy expenditure changes at a rate given by $\frac{d E}{d v}=\frac{0.31 v^{2}-471.75}{v^{2}}$ for v > 0 where E is given in joules per gram mass per kilometer. Observations indicate that the parakeet tends to fly at the speed $v_{\min }$ that minimizes E. a. What is the most economical speed $v_{\min } ?$ b. Suppose that when the parakeet flies at the most economical speed $v_{\min }$ its energy expenditure is $E_{\min }.$ Use this information to find E(v) for v > 0 in terms of $E_{\min }.$

Plot a velocity resonance curve for a driven, damped oscillator with Q = 6, and show that the full width of the curve between the points corresponding to $\dot{x}_{\max } / \sqrt{2}$ is approximately equal to $\omega_{0} / 6.$

A car tire is pressurized to $35\ \text{psi}$ in Michigan when the temperature is $-10^{\circ} \mathrm{F}$. The car is driven to Arizona, where the temperature on the highway, and in the tire, reaches $150^{\circ} \mathrm{F}$. Estimate the maximum pressure in the tire.

Lincoln High School's swim team finished the

$$4 \times 100$$

-meter freestyle relay in 5 minutes 18 seconds. Prospect High School's swim team finished the race in 5 minutes 7 seconds. Write an integer that represents Lincoln's finish compared to Prospect's finish.

The diameter of a car’s tire is 60 cm. While the car is being driven, the tire picks up a nail. How high above the ground is the nail after the car has travelled 1 km?

Shields Company is preparing its interim report for the second quarter ending June 30. The following payments were made during the first two quarters:

$$\begin{array}{lcr} \text { Expenditure } & \text { Date } & \text { Amount } \\ \hline \text { Annual advertising } & \text { January } & \$ 800,000 \\ \text { Property tax for the fiscal year } & \text { February } & 350,000 \\ \text { Annual equipment repairs } & \text { March } & 260,000 \\ \text { One-time research and development fee to consultant } & \text { May } & 96,000 \end{array}$$

For each expenditure, indicate the amount that would be reported in the quarterly income statements for the periods ending March 31, June 30, September 30, and December 31.