Set up the payoff matrix. You must decide whether to attack your opponent by sea or air, and your opponent must simultaneously decide whether to mount an all-out air defense, an all-out coastal defense (against an attack from the sea) or a combined air and coastal defense. If there is no defense for your mode of attack, you win 100 points. If your attack is met by a shared air and coastal defense, you win 50 points. If your attack is met by an all-out defense, you lose 200 points.

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. $\$200,000$.

a) Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if the tiles are red, green, or gray, so that no two red tiles are adjacent and tiles of the same color are considered indistinguishable. b) What are the initial conditions for the recurrence relation in part (a)? c) How many ways are there to lay out a path of seven tiles as described in part (a)?

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?

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.

Consider a room air conditioner using a Carnot cycle at maximum theoretical efficiency and operating between the temperatures of $18.0^{\circ} \mathrm{C}$ (indoors) and $35.0^{\circ} \mathrm{C}$ (outdoors). For each $1.00 \mathrm{~J}$ of heat flowing out of the room into the air conditioner: a) How much heat flows out of the air conditioner to the outdoors?

Zoom out sufficiently far so that the graph appears as a line. What equation does this line appear to have? (Note that the points at which the function is not continuous are not readily seen when you zoom out.)

$$f(x)=-\frac{x^{3}-2x^{2}+2}{2x^{2}}$$

$$g(x)= -\frac{1}{2}x+1-\frac{1}{x^{2}}$$

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.

In the sentence below, correct any errors in the use of comparisons. Cross out any unnecessary words. Insert any missing word by inserting a caret (^) and writing the word above it. If the sentence is already correct, write C at the end.

Then I carefully cut out the pieces with my dad’s jigsaw, which is the most perfect tool for the job.

A box contains four white and eight black balls. You pick out a ball with your left hand and don’t look at it. Then you pick out a ball with your right hand and don’t look at it.

Next, you look at the ball in your right hand and it is black. Now what is the probability that the ball in your left hand is white?

Identify an advertisement for a product you would consider buying. If the ad appeared in a newspaper or magazine, cut it out and bring it to class. If it appeared online, print it out. If it was aired on the radio or television, either record the ad or write a description of it and bring it to class. Answer the following questions about your ad:

What product or service does the ad promote?

Imagine that you are out of school and have started working and saving. You want to keep from using credit cards or unnecessary loans as much as possible, so you make savings plans for major purchases and expenses.

Why is saving up for major purchases and expenses better than using credit cards or taking out loans?

Zoom out sufficiently far so that the graph appears as a line. What equation does this line appear to have? (Note that the points at which the function is not continuous are not readily seen when you zoom out.)
$f(x)=-\dfrac{x^3-2 x^2+2}{2 x^2}$

$$g(x)=-\dfrac{1}{2} x+1-\dfrac{1}{x^2}$$

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 $10 \mathrm{~min}$ ?