A physics instructor wants to produce a double-slit interference pattern large enough for her class to see. For the size of the room, she decides that the distance between successive bright fringes on the screen should be at least $2.50 \mathrm{~cm}$. If the slits have a separation $d=0.0220 \mathrm{~mm}$, what is the minimum distance from the slits to the screen when $632.8 \mathrm{~nm}$ light from a $\mathrm{He}-\mathrm{Ne}$ laser is used?

Job Satisfaction. A study reported in the Journal of Small Business Management concluded that self-employed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with $1-5$ response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18 to 90 , is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction for lawyers, physical therapists, cabinetmakers, and systems analysts. The results obtained for a sample of 10 individuals from each profession follow.

$$\begin{array}{cccc} \text { Lawyer } & \text { Physical Therapist } & \text { Cabinetmaker } & \text { Systems Analyst } \\ 44 & 55 & 54 & 44 \\ 42 & 78 & 65 & 73 \\ 74 & 80 & 79 & 71 \\ 42 & 86 & 69 & 60 \\ 53 & 60 & 79 & 64 \\ 50 & 59 & 64 & 66 \\ 45 & 62 & 59 & 41 \\ 48 & 52 & 78 & 55 \\ 64 & 55 & 84 & 76 \\ 38 & 50 & 60 & 62 \end{array}$$

At the = 5 .05 level of significance, test for any difference in the job satisfaction among the four professions.

Discuss the ethical choices in the situations below. In each instance, describe the ethical dilemma, determine the alternative courses of action, and tell what you would do.

1. You are the payroll accountant for a small business. A friend asks you how much another employee is paid per hour.

2. As an accountant for the branch office of a wholesale supplier, you discover that several of the receipts the branch manager has submitted for reimbursement as selling expenses actually stem from nights out with his spouse.

3. You are an accountant in the purchasing department of a construction company. When you arrive home from work on December 22, you find a large ham in a box marked “Happy Holidays—It’s a pleasure to work with you.” The gift is from a supplier who has bid on a contract your employer plans to award next week.

4. As an auditor with one year’s experience at a local CPA firm, you are expected to complete a certain part of an audit in 20 hours. Because of your lack of experience, you know you cannot finish the job within that time. Rather than admit this, you are thinking about working late to finish the job and not telling anyone.

5. You are a tax accountant at a local CPA firm. You help your neighbor fill out her tax return, and she pays you $200 in cash. Because there is no record of this transaction, you are considering not reporting it on your tax return.

6. The accounting firm for which you work as a CPA has just won a new client, a firm in which you own 200 shares of stock that you received as an inheritance from your grandmother. Because it is only a small number of shares and you think the company will be very successful, you are considering not disclosing the investment.

You work for the Plains State Bank as an analyst specializing in the financial statements of small businesses seeking loans from the bank. Digit Retail Enterprises Inc. provides you with its balance sheet for December 31, 2012 and 2013 (Exhibit 6.21), and its income statement for 2013 (Exhibit 6.22). Digit Retail Enterprises, Inc., acquired no new property, plant, and equipment during the year.

$$\begin{array}{lcc} &\textbf{Digit Retail Enterprises, Inc.}\\ &\textbf{Balance Sheet}\\ &\textbf{(Problem 33)}\\ &&\textbf{December}&\textbf{December}\\ &&\textbf{31, 2013}&\textbf{31, 2012}\\ \text{ASSETS}\\ \textbf{Current Assets}\\ \text{Cash}&&\$ 50,000&\$ 36,000\\ \text{Accounts Receivable}&&38,000&23,000\\ \text{Notes Receivable}&&—&7,500\\ \text{Interest Receivable}&&—&100\\ \text{Merchandise Inventory}&&65,000&48,000\\ \text{Prepaid Insurance}&&12,000&9,000\\ \text{Prepaid Rent}&&—&\underline{2,000}\\ \quad\text{Total Current Assets}&&\underline{\$165,000}&\underline{\$125,600}\\ \textbf{Property, Plant, and Equipment}&&&\\ \text{At Cost}&&\$ 90,000&\$100,000\\ \text{Less Accumulated Depreciation}&&\underline{(35,000)}&\underline{(20,000)}\\ \text{Net}&&\underline{\$ 55,000}&\underline{\$ 80,000}\\ \quad\text{Total Assets}&&\underline{\underline{\$220,000}}&\underline{\underline{\$205,600}}\\ \\ \text{LIABILITIES AND SHAREHOLDER’S EQUITY}\\ \textbf{Current Liabilities}\\ \text{Accounts Payable—Merchandise Suppliers}&&\$ 20,000&\$ 18,000\\ \text{Salaries Payable}&&2,800&2,100\\ \text{Rent Payable}&&3,000&—\\ \text{Advances from Customers}&&6,100&8,500\\ \text{Note Payable}&&5,500&—\\ \text{Dividends Payable}&&2,600&4,200\\ \text{Other Current Liabilities}&&\underline{3,700}&\underline{1,300}\\ \quad\text{Total Current Liabilities}&&\underline{\$ 43,700}&\underline{\$ 34,100}\\ \textbf{Shareholders’ Equity}&&&\\ \text{Common Stock}&&\$164,500&\$160,000\\ \text{Retained Earnings}&&11,800&11,500\\ \text{Total Shareholders’ Equity}&&\underline{\$176,300}&\underline{\$171,500}\\ \text{Total Liabilities and Shareholders' Equity}&&\underline{\underline{\$220,000}}&\underline{\underline{\$205,600}}\\ \end{array}$$

$$\begin{array}{lr} &\textbf{Digit Retail Enterprises, Inc.}\\ &\textbf{Balance Sheet}\\ &\textbf{(Problem 33)}\\ &&\textbf{December}&\textbf{December}\\ \text{Sales Revenue}&\$270,000\\ \text{Gain on Sale of Property, Plant, and Equipment}&3,200\\ \text{Interest Revenue}&\underline{200}\\ \quad\text{Total Revenues}&\underline{\$273,400}\\ \textbf{Less Expenses:}&\\ \text{Cost of Goods Sold}&\$145,000\\ \text{Salaries Expense}&68,000\\ \text{Rent Expense}&12,000\\ \text{Insurance Expense}&5,000\\ \text{Depreciation Expense}&20,000\\ \text{Other Expenses}&\underline{13,800}\\ \quad\text{Total Expenses}&\underline{\$263,800}\\ \text{Net Income}&\underline{\underline{\$ 9,600}}\\ \end{array}$$

g. Calculate the amount of dividends paid during 2013.

Complete the problem.

$$\begin{array}{|c| c c c c c c c |c|}\hline \small \textbf{Total} &\small \textbf{(Selling Price per Share} & \times & \small\textbf{Number of Shares} & - & \small\textbf{Commission)}& =& \small\textbf{Net Sale} &\small \textbf{Amount of}\\ \small\textbf{Paid} & & & & & & & &\small\textbf{Profit or Loss}\\ \hline \$380 & (\small \$2 \frac{1}{2} & \times & 200) & - & \$26.45 &=& ? & ?\\ \hline \end{array}$$

The change in the size of businesses in a certain Canadian city from one year to the next can be described by a Markov chain. The businesses are classified into three categories based on size: small (2-10 employees), medium (11-43 employees), and large (44 or more employees). The transition matrix for a 1-year period is given below.

$$\begin{array}{l} \\ Small \\ Medium \\ Large \end{array} \left[\begin{array}{ccc} \text { Small } & \text { Medium } & \text { Large } \\ 0.9216 & 0.0780 & 0.0004 \\ 0.0460 & 0.8959 & 0.0581 \\ 0.0003 & 0.0301 & 0.9696 \end{array}\right]$$

Suppose that in 2015, there were 2094 small, 2363 medium, and 2378 large businesses. Based on this model, find the number of businesses of each type that would be expected in each of the following years. (a) 2016 (b) 2017 (c) Write the transition matrix for a 2-year period. Based on your answer to part (c), what percent of medium businesses are in each of the following categories after 2 years? (d) Small businesses (e) Large businesses.

Each student in a physics lab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature $r = 40$ cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.

After completing his Certified Financial Planner designation (CFP), Andre was excited about the prospects of working with small business owners and their employees regarding retirement planning. Andre wanted to show the value of an annuity program as one of the viable investment options in a salary reduction retirement plan. In addition, he wanted to demonstrate the substantial tax benefits that annuities can provide. For instance, qualified annuities (by definition) not only reduce your current taxable salary, they also accumulate earnings on a tax-deferred basis-meaning you don't pay taxes on the earnings until they are withdrawn. Andre was developing a spreadsheet to show the way that annuities could grow using various rates of return.

Using the same information from Exercise earlier and assuming a $25 \%$ tax bracket, what would be the net effect of investing at $8 \%$ for $20$ years if taxes on the earnings were paid from the investment fund each year? How would this compare if no taxes had to be paid, such as in a tax-deferred annuity at $8 \%$ for $20$ years?

The Large Hadron Collider. In 2012, the Large Hadron Collider confirmed the existence of the Higgs boson with a mass of 125 GeV. Research this particle and its discovery: Why is the Higgs boson so interesting to physicists? What is its role in the standard model of particle physics? Why are some physicists a little disappointed that the Higgs particle appears to be almost exactly what they expected? An upgraded Large Hadron Collider was turned on in 2015. Has it made any further discoveries?

The simplest cost function is the linear cost function, $C(x) = mx + b$, where the y-intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item produced. Suppose that a small bicycle manufacturer has daily fixed costs of $1800 and each bicycle costs$90 to manufacture. Graph the model.

Focal length and angular velocity A cylindrical container, partially filled with mercury, is rotated about its axis so that the angular speed of each cross section is $\omega$ radians/second. From physics, the function $f$, whose graph generates the inside surface of the mercury (see the figure), is given by

$$f(x)=\frac{1}{64} \omega^2 x^2+k,$$

where $k$ is a constant. Determine the angular speed $\omega$ that will result in a focal length of $2$ feet.

A small business called The Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit, and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity; but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production, and, at the same time, payments from customers were often delayed until the product was shipped. Unable to deliver on orders, the company became so strapped for cash that employee paychecks began to bounce. Finally, out of cash, the company ceased operations entirely 3 years later.

What are some of the actions that a small company like The Grandmother Calendar Company can take if it finds itself in a situation in which growth in sales outstrips production capacity and available financial resources? What other options (besides expansion of capacity) are available to a company when orders exceed capacity?

CarryALL, Inc., makes and sells small cargo trailers to individuals and small businesses. Since its opening in 1990, it has allocated indirect costs (IDC) to its three manufacturing plants based on direct materials cost per unit. Each plant builds different models and sizes. Because of advances in automation and materials, Judy, the CFO, plans to use build-time per unit as the new basis. Build-time is the average number of work-hours to complete a trailer. However, she initially wants to determine what the allocation would have been this year had the build-time basis been used prior to the incorporation of new technology and materials. The data shown below represents average costs and times. Use this data and the bases indicated to determine the allocation rates and IDC allocation of $1,000,000 for this year for the three bases.$

$$\begin{array}{lcccc} \text { Plant } & \text { New York } & \text { Virginia } & \text { Tennessee } & \text { Total } \\ \hline \text { Direct material cost, } & 20,000 & 12,700 & 18,600 & 51,300 \\ \text { \$ per unit } & & & & \\ \text { Previous build-time } & 400 & 415 & 580 & 1395 \\ \text { per unit, work-hours } & & & & \\ \text { New build-time per } & 425 & 355 & 480 & 1260\\ \text { unit, work-hours } & & & & \\ \hline \end{array}$$

$

Solve. Find the cost per mile to the nearest cent.

$$\begin{array}{|c c c c c c c c c c c|} \hline \small\textbf{(Total Daily Cost}& + & \small\textbf{Total Mileage Cost} & +& \small\textbf{Gasoline Cost} & = & \small\textbf{Total Cost)} & \div & \small\textbf{Miles} & = & \small\textbf{Cost per}\\ & & & & & & & &\small\textbf{Driven} & & \small\textbf{Mile}\\ \hline (\$160.00 & + & \$94.00 & + & \$23.89 & = & ?) & \div & 500 & = & ? \\ \hline \end{array}$$