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)?

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?

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.

Mai needs to be at the auditorium by $\underline{6:00}$ P.M. for rehearsal.

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

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 $10 \mathrm{~min}$ ?

Design an RC high-pass filter that passes a signal with frequency $5.00 \mathrm{kHz}$, has a ratio $V_{\text {out }} / V_{\text {in }}=0.500$, and has an impedance of $1.00 \mathrm{k} \Omega$ at very high frequencies. b) What is the phase of $V_{\text {out }}$ relative to $V_{\text {in }}$ at the frequency of $5.00 \mathrm{kHz}$ ?

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

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?

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.

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?

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?

A television advertisement shows a lawyer in a bathing suit coming out of a lake. He says, "If you're in over your head because of bad debts, let us bail you out. We're the best firm in the state." Should there be any restrictions on ads like this? If so, what? Should there be other restrictions on ads? If so, what should they be?

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?

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?