Look up the prime interest rate, corporate bond rate, and interest rate on 10-year U.S. government bonds today in a newspaper such as The Wall Street Journal, the business section of your local daily, or the Internet. List some of the differences between these three rates.

Consider the impurity level data. Construct a 99% CI on the mean difference between the two testing procedures. Use it to answer the question posed. Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown in the following tabulation. Is there sufficient evidence to conclude that both tests give the same mean impurity level, using $\alpha = 0.01?$

$$\begin{matrix} \text{Specimen} & \text{Test 1} & \text{Test 2} & \text{Specimen} & \text{Test 1} & \text{Test 2}\\ \text{1} & \text{1.2} & \text{1.4} & \text{5} & \text{1.7} & \text{2.0}\\ \text{2} & \text{1.3} & \text{1.7} & \text{6} & \text{1.8} & \text{2.1}\\ \text{3} & \text{1.5} & \text{1.5} & \text{7} & \text{1.4} & \text{1.7}\\ \text{4} & \text{1.4} & \text{1.3} & \text{8} & \text{1.3} & \text{1.6}\\ \end{matrix}$$

A group of 20 high school students is volunteering to help elderly members of their community. Each student will be assigned a job based on requests received for help. There are 8 requests for raking leaves, 7 requests for running errands, and 5 requests for washing windows.

One way to count the number of possible job assignments is to find the number of permutations of $8 L$ 's (for "leaves"), 7 E's (for "errands"), and $5 \mathrm{~W}$ 's (for "windows"). Use this method to write the number of possible job assignments first as an expression involving factorials and then as a simple number.

Now suppose that the corporate tax is (Tc) = .35. Demonstrate that when River Cruises borrows the $250,000, the combined after-tax income of its debtholders and equity holders increases (compared to all-equity financing) by 35% of the firm’s interest expense regardless of the state of the economy.

Sketch the graph of $f(x)=2-2 \sin x$ on the interval $[0, \pi / 2]$. (a) Find the distance from the origin to the y-intercept and the distance from the origin to the x-intercept. (b) Write the distance d from the origin to a point on the graph of f as a function of x. Use your graphing utility to graph d and find the minimum distance. (c) Use calculus and the zero or root feature of a graphing utility to find the value of that minimizes the function d on the interval $[0, \pi / 2]$. What is the minimum distance? (Submitted by Tim Chapell, Penn Valley Community College, Kansas City, MO)

The average number of hours of television watched per week by women over age 55 is 48 hours. Men over the age of 55 watch an average of 43 hours of television per week. Random samples of 40 men and 40 women from a large retirement community yielded the following results. At the $0.01$ level of significance, can it be concluded that women watch more television per week than men?

Round answers to the nearest tenth of a percent. Sascha owns stock in Lewis Corp and she bought a $1,000 corporate bond. The bond pays 6.34% annual interest. Sascha's stock is worth$46 per share, and it pays a $2 annual dividend. What is the yield?

It is estimated that t years fom now, the population of a certain suburban community will be $p(t)=20-\frac{6}{t+1}$ thousand. An environmental study indicates that the average daily level of carbon monoxide in the air will be $c(p)=0.5 \sqrt{p^{2}+p+58}$ parts per million when the population is p thousand. a. At what rate will the level of carbon monoxide be changing with respect to population when the population is 18 thousand people? b. At what rate will the carbon monoxide level be changing with respect to time 2 years from now? Will the level be increasing or decreasing at this time?

A small spherical bead is used as a controlled drug-release capsule in the gastrointestinal system (i.e., your stomach. In this particular case, a 0.10-cm diameter bead has a uniform initial concentration of 0.20 mmole/L of the drug griseofulvin (species A). The diffusion coefficient of griseofulvin within the bead material is $1.5 \times 10^{-7} \mathrm{cm}^{2} / \mathrm{s}$. Upon release from the bead, the drug is immediately consumed so that the surface concentration is essentially zero. a. Using the concentration-time charts, determine the time it will take for concentration of the griseofulvin in the center of the bead to reach 10% of its initial value. b. Using the infinite series analytical solution for $c_{A}(r, t),$ determine the time it will take for concentration of the griseofulvin in the center of the bead to reach 10% of its initial value, and then plot out the concentration profile from r = 0 (center) to r = R (surface). Carry out your calculations on a computer spreadsheet.

Test your understanding of the corporate income statement and the statement of stockholders’ equity by answering the following questions. Which of the following items is most closely related to prior-period adjustments? a. Retained earnings b. Earnings per share c. Preferred stock dividends d. Accounting changes

The durations (minutes) of $26$ electric power outages in the community of Sonando Heights over the past five years are shown below. (a) Find the mean, median, and mode. (b) Are the mean and median about the same? (c) Is the mode a good measure of center for this data set? Explain. (d) Is the distribution skewed? Explain.

$$\begin{array}{rrrrrrrrrrrrr}32 & 44 & 25 & 66 & 27 & 12 & 62 & 9 & 51 & 4 & 17 & 50 & 35 \\ 99 & 30 & 21 & 12 & 53 & 25 & 2 & 18 & 24 & 84 & 30 & 17 & 17\end{array}$$

The drug Lipitor (atorvastatin) is used to treat high cholesterol. In a clinical trial of Lipitor, 47 of 863 treated subjects experienced headaches (based on data from Pfizer). The accompanying TI-83 / 84 Plus calculator data shows results from a test of the claim that fewer than 10% of treated subjects experience headaches.

$$\begin{matrix} \text{1-PropZTest}\\ \text{prop<.1}\\ \text{z=-4.45929186}\\ \text{p=4.1151493e-6}\\ \text{$\hat p$=.0544611819}\\ \text{n=863}\\ \end{matrix}$$

			Use the normal distribution as an approximation to the binomial distribution. Use a 0.05 significance level and answer the following:	What is the test statistic?

You are contacted by a project organizer for a university computer science fair. The project organizer asks you to hold a forum that discusses the origins of the Linux operating system, including how it has evolved and continues to develop. The main focus of this forum is to encourage university students toward participating in the open source community; therefore, it should detail the philosophy, major features, and methods of the hacker culture. Prepare a bulleted list of the major topics that you will discuss, and write down some sample questions that you anticipate from the participants as well as your responses.

Every corporation has a governing board of directors. The number of individuals on a board varies from one corporation to another. One of the authors of the article “Does Optimal Corporate Board Size Exist? An Empirical Analysis” (J. of Applied Finance, 2010: 57–69) provided the accompanying data on the number of directors on each board in a random sample of 204 corporations.

$$\begin{matrix} \text{No. directors:} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9}\\ \text{Frequency:} & \text{3} & \text{12} & \text{13} & \text{25} & \text{24} & \text{42}\\ \text{No. directors:} & \text{10} & \text{11} & \text{12} & \text{13} & \text{14} & \text{15}\\ \text{Frequency:} & \text{23} & \text{19} & \text{16} & \text{11} & \text{5} & \text{4}\\ \text{No. directors:} & \text{16} & \text{17} & \text{21} & \text{24} & \text{32}\\ \text{Frequency:} & \text{1} & \text{3} & \text{1} & \text{1} & \text{1}\\ \end{matrix}$$

Construct a histogram of the data based on relative frequencies and comment on any interesting features.