A piston $/$ cylinder has $15\ \mathrm{ft}$ of liquid $70 \mathrm{~F}$ water on top of the piston $(m=0)$ with a cross-sectional area of $1\ \mathrm{ft}^2$. Air let in under the piston rises and pushes the water out over the top edge. Determine the work needed to push all the water out and plot the process in a $P-V$ diagram.

Data collected on investments in Broadway shows the number of investors, total invested, name of the show, and profit/loss after one year.

When you organize data in a spreadsheet, it is necessary to lay it out as a data table. Demonstrate how you would lay out this data. Indicate the headings of columns and what would be found in each row.

Before a strike in 1994, the median salary of the 746 major league baseball players was about $500,000. The lowest salary was about$100,000 and the highest was over $5,000,000. Choose one option and explain: (i) The owners were paying out around$ $746 \times \$ 500,000 = \$ 373 \text { million }$ $per year in salaries to the players. (ii) The owners were paying out substantially less than$373 million per year to the players. (iii) The owners were paying out substantially more than $373 million per year to the players.

Read each sentence and decide if the underlined number should be spelled out. If it should, write the spelled-out form above it. If the number is already correct, write $C$ above it.

Example 1. $\underline{152}$ (One hundred fifty-two) students auditioned for the marching band.

The temperature should not drop below $\underline{32}$ degrees tonight.

A manufacturer of lightbulbs wants to produce bulbs that last about $700$ hours but, of course, some bulbs burn out faster than others. Let $F(t)$ be the fraction of the company's bulbs that burn out before $t$ hours, so $F(t)$ always lies between $0$ and $1$ .

What is the meaning of the derivative $r(t)=F^{\prime}(t)$ ?

Read each sentence and decide if the underlined number should be spelled out. If it should, write the spelled-out form above it. If the number is already correct, write $C$ above it.

Example 1. $\underline{152}$ (One hundred fifty-two) students auditioned for the marching band.

The next rest area is $\underline{100}$ miles away.

You have 10 pairs of socks, five black and five blue, but they are not paired up. Instead, they are all mixed up in a drawer. It's early in the morning, and you don't want to turn on the lights in your dark room. How many socks must you pull out to guarantee that you have a pair of one color? How many must you pull out to have two good pairs (each pair is the same color)? How many must you pull out to be certain you have a pair of black socks?

The speed, s, in metres per second, of water flowing out of a hole near the bottom of a tank relates to the height, h, in metres, of the water above the hole by the formula $s=\sqrt{2gh}$ . In the formula, g represents the acceleration due to gravity, 9.8 m/$s^2$. At what height is the water flowing out a speed of 9 m/s?

A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let $F ( t )$ be the fraction of the company's bulbs that burn out before t hours, so $F ( t )$ always lies between 0 and 1. What is the meaning of the derivative $r ( t ) = F' ( t )$ ?

For each sentence, if the underlined pronoun is correct write C above it. If it is not correct, cross it out and write the correct form of the pronoun above it.

Example 1. My choice for the student delegate will be $\overset{\textit{\color{#c34632}{she}}}{{\underline{\sout{\text{her}}}}}$.

It wasn’t $\underline{\text{I}}$ who left the baseball equipment out on the field.

Assume all variables are binomial. (Note: If values are not found in Previous Table . use the binomial formula.)
High School Dropouts Approximately $10.3\%$ of American high school students drop out of school before graduation. Choose $10$ students entering high school at random. Find the probability that
No more than $2$ drop out

Answer the next two questions based on the following scenario. Bank #1 receives a $\$20,000$ deposit from a customer. Bank #1 then loans out all its excess reserves of $\$18,000$, which are deposited into Bank #2. Bank #2 loans out all its excess reserves, as does Bank #3, and so on.

If the process described previously continues throughout the banking system until all excess reserves are loaned out, the total change in the money supply resulting from the $\$20,000$ deposit would be

a. $\$18,000$.

b. $\$20,000$.

c. $\$38,000$.

d. $\$200,000$.

In a calorimetry experiment, 0.50 kg of a metal at $100^{\circ} \mathrm{C}$ is added to 0.50 kg of water at $20^{\circ} \mathrm{C}$ in an aluminum calorimeter cup. The cup has a mass of 0.250 kg. (a) If some water splashed out of the cup when the metal was added, the measured specific heat will appear to be (1) higher, (2) the same, (3) lower than the value calculated for the case in which the water does not splash out. Why? (b) If the final temperature of the mixture is $25^{\circ} \mathrm{C}$ and no water splashed out, what is the specific heat of the metal?

A large tank is filled with water when an outflow valve is opened at $t=0$. Water flows out at a rate, in $\mathrm{gal} / \mathrm{min}$, given by $Q^{\prime}(t)=0.1\left(100-t^2\right)$, for $0 \leq t \leq 10$. a. Find the amount of water $Q(t)$ that has flowed out of the tank after $t$ minutes, given the initial condition $Q(0)=0$. b. Graph the flow function $Q$, for $0 \leq t \leq 10$. c. How much water flows out of the tank in $10 \mathrm{~min}$ ?