A realtor wants to sell some riverfront lots. To set a fair price for them, he studies several similar riverfront lots nearby that were sold recently. The table shows the area of the lots (in hundreds of square feet) and their selling prices (in thousands of dollars).

$$\begin{matrix} \text{Square Footage} & \text{Price}\\ \text{189} & \text{240}\\ \text{232} & \text{260}\\ \text{172} & \text{230}\\ \text{195} & \text{230}\\ \text{240} & \text{280}\\ \text{210} & \text{260}\\ \text{200} & \text{240}\\ \text{230} & \text{250}\\ \text{191} & \text{241}\\ \text{198} & \text{255}\\ \end{matrix}$$

a. Create a scatter plot for the data. Does it appear to have a linear trend? b. The coefficient of determination for the data is found to be equal to $r^2 = 0.673.$ Explain what that means in terms of association of the price of the lot and its area. c. Calculate a regression line for the data.

A subtle form of racial discrimination in housing is "racial steering." Racial steering occurs when real estate agents show prospective buyers only homes in neighborhoods already dominated by that family's race. This violates the Fair Housing Act of 1968. According to an article in Chance magazine (Vol. 14, no. 2 [2001]), tenants at a large apartment complex recently filed a lawsuit alleging racial steering. The complex is divided into two parts: Section A and Section B. The plaintiffs claimed that white potential renters were steered to Section A, while African-Americans were steered to Section B. The table displays the data that were presented in court to show the locations of recently rented apartments. Do you think there is evidence of racial steering?

$$\begin{array}{|l|cc|c|}\hline &\text { New Renters } \\ \hline & \text { White } & \text { Black } & \text { Total } \\ \hline \text { Section A } & 87 & 8 & 95 \\ \text { Section B } & 83 & 34 & 117 \\ \hline \text { Total } & 170 & 42 & 212 \\ \hline\end{array}$$

Let $X_1, . . . , X_n$ be i.i.d. with mean $\mu$, variance $\sigma^2$, and MGF $M$. Let

$$Z _ { n } = \sqrt { n } ( \frac { \overline { X } _ { n } - \mu } { \sigma } )$$

(a) Show that $Z_n$ is a standardized quantity, i.e., it has mean 0 and variance 1. (b) Find the MGF of $Z_n$ in terms of $M$, the MGF of each $X_j$ .

You are working as the triage nurse in the emergency department at a busy tertiary care center. A woman comes in complaining of very heavy vaginal bleeding and extreme pain. S.K. is single, $47$ years of age, and has been bleeding for $24$ hours, soaking a pad an hour. She works in a law firm as a paralegal and was embarrassed yesterday when she leaked around her pad and stained a chair in the conference room. She has two sexual partners currently and has been relying on condoms for birth control. She thinks her last menstrual period was $2$ months ago, but they have been irregular and she is not sure. She has had some occasional spotting during the past $6$ months. She states she is afraid of the amount of bleeding in the past $24$ hours.

What precautions do you need to take while administering the meperidine (Demerol)?

Western States Supply, Inc. (WSS), consists of 3 divisions—California, Northwest, and Southwest—that operate as if they were independent companies. Each division has its own sales force and production facilities. Each division manager is responsible for sales, cost of operations, acquisition and fi nancing of divisional assets, and working capital management. WSS corporate management evaluates the performance of each division and its managers on the basis of ROI.

Southwest has just been awarded a contract for a product that uses a component manufactured by outside suppliers as well as by Northwest, which is operating well below capacity. Southwest used a cost figure of $37 for the component in preparing its bid for the new product. Northwest supplied this cost fi gure in response to Southwest’s request for the average variable cost of the component; it represents the standard variable manufacturing cost and variable marketing costs.

Northwest’s regular selling price for the component that Southwest needs is$65. Northwest’s management indicated that it could supply Southwest the required quantities of the component at the regular selling price less variable selling and distribution expenses. Southwest management responded by offering to pay standard variable manufacturing cost plus 25 percent.

The two divisions have been unable to agree on a transfer price. Corporate management has never established a transfer price policy. The corporate controller suggested a price equal to the standard full manufacturing cost (that is, no selling and distribution expenses) plus a 20 percent markup. The two division managers rejected this price because each considered it grossly unfair.

The unit cost structure for the Northwest component and the suggested prices follow.

Required
Should WSS’s corporate management become involved in this transfer price controversy? Explain your answer.

Pelamed Pharmaceuticals has EBIT of $\$ 133$ million in $2006$. In addition, Pelamed has interest expenses of $\$ 49$ million and a corporate tax rate of $35 \%$.

a. What is Pelamed's $2006$ net income?

b. What is the total of Pelamed's $2006$ net income and interest payments?

c. If Pelamed had no interest expenses, what would its $2006$ net income be? How does it compare to your answer in part (b)?

d. What is the amount of Pelamed's interest tax shield in $2006$?

On January 15, the end of the first biweekly pay period of the year, North Company’s payroll register showed that its employees earned $35,000 of sales salaries. Withholdings from the employees’ salaries include FICA Social Security taxes at the rate of 6.2%, FICA Medicare taxes at the rate of 1.45%,$6,500 of federal income taxes, $772.50 of medical insurance deductions, and$120 of union dues. No employee earned more than $7,000 in this first period. Prepare the journal entry to record North Company’s January 15 (employee) payroll expenses and liabilities. (Round amounts to cents.)

Use systems of equations to work the following applied problem.

An investor wants to invest $30,000 in corporate bonds that are rated AAA, A, and B. The lower rated ones pay higher interest, but pose a higher risk as well. The average yield is 5% on AAA bonds, 6% on A bonds, and 10% on B bonds. Being conservative, the investor wants to have twice as much in AAA bonds as in B bonds. How much should she invest in each type of bond to have an interest income of$2000?

Diversified Industries manufactures sump-pumps. Its most popular product is called the Super Soaker, which has a retail price of $1,200 and costs$540 to manufacture. It sells the Super Soaker on a standalone basis directly to businesses. Diversified also provides installation services for these commercial customers, who want an emergency pumping capability (with regular and back-up generator power) at their businesses. Diversified also distributes the Super Soaker through a consignment agreement with Menards. Income data for the first quarter of 2017 from operations other than the Super Soaker are as follows.

$$\begin{array}{lrr} \text{Revenues }&\text{\$\hspace{5pt}9,500,000}\\ \text{Expenses }&\text{7,750,000}\\ \end{array}$$

Diversified has the following information related to two Super Soaker revenue arrangements during the first quarter of 2017.

1. Diversified sells 30 Super Soakers to businesses in flood-prone areas for a total contract price of $54,600. In addition to the pumps, Diversified also provides installation (at a cost of$150 per pump). On a standalone basis, the fair value of this service is $200 per unit installed. The contract payment also includes a$10 per month service plan for the pumps for 3 years after installation (Diversified’s cost to provide this service is $7 per month). The Super Soakers are delivered and installed on March 1, 2017, and full payment is made to Diversified. Any discount is applied to the pump/installation bundle.
2. Diversified ships 300 Super Soakers to Menards on consignment. By March 31, 2017, Menards has sold two-thirds of the consigned merchandise at the listed price of$1,200 per unit. Menards notifies Diversified of the sales, retains a 5% commission, and remits the cash due Diversified.

Accounting Determine Diversified Industries’ 2017 first-quarter net income. (Ignore taxes.)

Analysis Determine free cash flow (see Chapter 5) for Diversified Industries for the first quarter of 2017. In the first quarter, Diversified had depreciation expense of $175,000 and a net increase in working capital (change in accounts receivable and accounts payable) of$250,000. In the first quarter, capital expenditures were $500,000; Diversified paid dividends of$120,000.

Principles Explain how the five-step revenue recognition process, when applied to Diversified’s two revenue arrangements, reflects the concept of control in the definition of an asset and trade-offs between relevance and faithful representation.

The following data were collected in two studies of the reaction $2 \mathrm { A } + \mathrm { B } \longrightarrow \mathrm { C } + \mathrm { D }$ where $\text {Rate} = \frac { - d [ \mathrm { A } ] } { d t }$

$$\begin{matrix} & {Experiment 1} & {Experiment 2}\\ \text{Time (s)} & {[ \mathrm { A } ] ( M ) \times 10 ^ { - 2 }} & {[ \mathrm { A } ] ( M ) \times 10 ^ { - 2 }}\\ \hline \text{0} & \text{10.00} & \text{10.00}\\ \text{20.} & \text{6.67} & \text{5.00}\\ \text{40.} & \text{5.00} & \text{3.33}\\ \text{60.} & \text{4.00} & \text{2.50}\\ \text{80.} & \text{3.33} & \text{2.00}\\ \text{100.} & \text{2.86} & \text{1.67}\\ \text{120.} & \text{2.50} & \text{1.43}\\ \end{matrix}$$

In experiment $1 , [ B ] _ { 0 } = 5.0$ M. In experiment $2 , \left[ \left. B \right| _ { 0 } =10.0\ \mathrm { M }.\right.$ Give the rate law and value for k for this reaction.

In a diagnostic procedure, a patient in a hospital ingests 80 mCi of gold $-198\left(t_{1 / 2}=2.7 \text { days }\right) .$ What is the activity at the end of one month, assuming none of the gold is eliminated from the body by biological functions?

Consider the growth of the following virus. A new virus has been created and is distributed to 100 computers in a company via a corporate E-mail. From these workstations the virus continues to spread. Let t=0 be the time of the first 100 infections, and at t=17 minutes the population of infected computers grows to 200. Assume the anti-virus companies are not able to identify the virus or slow its progress for 24 hours, allowing the virus to grow exponentially.

What will the population be after a full 24 hours?

Choose a corporate bond listed on the New York Stock Exchange. Use Moody's Industrial Manuals (available at many public libraries) or Moody's online at www.moodys.com to answer the following questions about this bond.

a. What is Moody's rating for the bond?

b. What is the purpose of the bond?

c. Does the bond have a call provision?

d. What collateral, if any, has been pledged as security for the bond?

Based on the information studied, would the bond be a good investment for you? Why or why not?

ETHICS PROBLEM Bond rating agencies have invested significant sums of money in an effort to determine which quantitative and nonquantitative factors best predict bond defaults. Furthermore, some of the raters invest time and money to meet privately with corporate personnel to get nonpublic information that is used in assigning the issue's bond rating. To recoup those costs, some bond rating agencies have tied their ratings to the purchase of additional services. Do you believe that this is an acceptable practice? Defend your position.