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.

Write the integers from 1 through 100 in 10 lines of 10 numbers each. (a) Cross out the number 1. Cross out all multiples of 2 other than 2 itself. Do the same for 3, 5, and 7. (b) Of what type are the remaining numbers? Explain why this is the only type of number left.

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 value of ^∞∫0 r(t) dt? Why?

The volume of water in a tank t min after it starts draining is $V(t)=350(20-t)^{2} \mathrm{L}$.

How fast is the water draining out after 5 min? after 15 min?

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.

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.

[Related to the Apply the Concept on page 270] An opinion columnist for bloomberg.com observed, “A lot of people seem to think that committed, long-term shareholders should get more say than those who can bail out at any moment.”

What does the columnist mean by a shareholder who can bail out at any moment?

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.

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.

Circle the letter of the choice that describes an action potential.
a. Reversal of charges due to the flow of positive ions into a neuron
b. Increase in negative ions in a neuron due to the flow of potassium out of the cell
c. Change to a negative charge due to the flow of sodium ions out of a neuron
d. Reversal of charges due to the flow of negative ions into a neuron

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?

GENERAL: Airplane Flight Delays For flights from U.S. airports, the "taxi-out" time (the number of minutes between leaving the gate and takeoff) can be approximated by an exponential random variable with mean 20 . Find the probability that for a given flight the taxi-out time is more than:

a. 1 hour ( 60 minutes)

b. 3 hours ( 180 minutes)

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 $10 \mathrm{~min}$ ?

Consider a bivariate normal distribution with $\mu 1=1, \mu 2=3, \sigma 11=2, \sigma 22=1$ and $\rho 12=-.8$. (a) Write out the bivariate normal density. (b) Write out the squared statistical distance expression $(x-\mu)^{\prime} \Sigma-1(x-\mu)$ as a quadratic function of $x_{1}$ and $x_{2}$.