Which of the following are exact numbers?

The elevation of Breckenridge, Colorado, is 9600 ft$.

The table gives the number of millions of individuals in the U.S. civilian noninstitutional population 16 years and older who are non-White or Hispanic for the years 2000 and projected to 2050.

a. Find a power function y = f(x) modeling this population as a function of the number of years after 1990.

b. Graph the model on the same axes with the scatter plot of the data to determine whether the model is a good fit to the data.

c. What does the model predict that this population will be in 2033?

Choose the letter of the best answer. A star system in which one star blocks the light from another is called a(n) a. open cluster. b. quasar. c. binary star. d. eclipsing binary.

Develop an explicit formula for the toothpick sequence using the first term and the common difference. The first term of the sequence is $a_{1}=8$. The second term is $a_2 = 8 + 6$. The third term is $a_3 = 8 + 6 + 6$, or $a_3 = 8 + 2(6).$ a. Write an expression for the fourth term using the value of $a_1$ and the common difference. $a_4= ?$ b. Express regularity in repeated reasoning. Use the patterns you have observed to determine the 15th term. Justify your reasoning. $a_{15} = ?$ c. Write an expression that can be used to find the nth term of the toothpick sequence. $a_n= ?$

In the past, the mean lifetime of diesel engine injection pumps has been 12,000 operating hours. A new injection pump is available that is promoted as lasting longer than the old version. In a test of 50 of the new pumps, the lifetimes are as listed in data file XR10113. Based on the sample data, and using the $0.025$ level of significance, examine the possibility that the new pumps might have a mean life that is no more than that of the old design. Identify and interpret the $p$-value for the test.

GENERAL: Learning A person can memorize words at the rate of $3 / \sqrt{t}$ words per minute.

a. Find a formula for the total number of words that can be memorized in t minutes. [Hint: Evaluate C so that 0 words have been memorized at time t=0. ]

b. Use the formula that you found in part (a) to find the total number of words that can be memorized in 25 minutes.

Modeling Data A department store manager wants to estimate the number of customers that enter the store from noon until closing at $9$ P.M. The table shows the number of customers $N$ entering the store during a randomly selected minute each hour from $t-1$ to $t,$ with $t=0$ corresponding to noon.

(b) Estimate the total number of customers entering the store between noon and $9$ P.M.

On a clear day, the distance d in miles you can see across the ocean from a height of h feet is given by $h=\frac{2}{3} d^2$. Jaime is learning to parasail with his friends. If beginning parasailers usually go up about 150 feet, how far can Jaime see when he is in the air?

Let

$$\left.\begin{aligned} \mathbf { u } & = a _ { 1 } \mathbf { i } + b _ { 1 } \mathbf { j } \\ \mathbf { v } & = a _ { 2 } \mathbf { i } + b _ { 2 } \mathbf { j } \\ \mathbf { w } & = a _ { 3 } \mathbf { i } + b _ { 3 } \mathbf { j }. \end{aligned} \right.$$

Prove each property by obtaining the vector on each side of the equation. Have you proved a distributive, associative, or commutative property of vectors?

$$c ( \mathbf { u } + \mathbf { v } ) = c \mathbf { u } + c \mathbf { v }$$

The purchase of a "collector's item" is often made in hopes the item will increase in value. In 1998, Mark purchased a 1909-S VDB Lincoln Cent (in fair condition) for $\$ 150$. By the year 2004, its value had grown to $\$ 190$.

(a) Use the relation (time since purchase, value) with $t=0$ corresponding to 1998 to find a linear equation modeling the value of the coin.

(b) Discuss what the slope and $y$-intercept indicate in this context.

(c) How much was the penny worth in 2009?

(d) How many years after purchase will the penny's value exceed $250?

(e) If the penny is now worth$170, how many years has Mark owned the penny?

Tickets for the school football game cost five dollars for adults and three dollars for students. In order to buy new helmets, at least $9000 worth of tickets must be sold. Write an inequality that describes the total number of tickets that must be sold in order to buy new helmets.

In the previous example we showed that the rabbit and wolf populations satisfy the differential equation

$$\dfrac{dW}{dR} = \dfrac{-0.02W + 0.00002RW}{0.08R - 0.001RW}$$

By solving this separable differential equation, show that

$$\dfrac{R^{0.02}W^{0.08}}{e^{0.00002R}e^{0.001W}} = C$$

where $C$ is a constant. It is impossible to solve this equation for $W$ as an explicit function of $R$ (or vice versa). If you have a computer algebra system that graphs implicitly defined curves, use this equation and your CAS to draw the solution curve that passes through the point (1000, 40) and compare with the figure.

A patient needs to learn how to administer a subcutaneous injection. Which of the following reflects that the patient is ready to learn?

1. Describing difficulties a family member has had in taking insulin
2. Expressing the importance of learning the skill correctly
3. Being able to see and understand the markings on the syringe
4. Having the dexterity needed to prepare and inject the medication

Learning. The time $T$ (in minutes) it takes a person to learn a list of length $n$ is

$$T(n)=0.08n^{3}-1.2n^{2}+6n\quad n\geq0$$

(A) When is the rate of change of $T$ with respect to the length of the list increasing? Decreasing?

(B) Where does the graph of $T$ have inflection points?

(C ) Graph $T$ and $T'$ on the same coordinate system.

(D) What is the minimum value of $T'(n)$?