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.

A single firm in a perfectly competitive market is relatively small compared to the rest of the market. What does this mean? How “small” is “small”?

In physics it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft/sec from a rooftop 112 feet high is $s=s(t)=-16 t^{2}+96 t+112$ where t is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground. When does the ball strike the ground? That is, how long is the ball in the air?

The exercise describes a number of business ventures. Write the cost function, C. A company that manufactures small canoes has a fixed cost of $18,000. It costs$20 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.)

Ortel Telecom sells telecommunication products and services to a variety of small businesses. Two of Ortel’s key clients are Square and Cloudburst, both fast-growing technology start-ups located in New York City. Ortel has compiled information regarding its transactions with Square and Cloudburst for 2017, as well as its expectations regarding their interactions over the next 3 years: Ortel’s transactions with Square and Cloudburst are in cash. Assume that they occur at year-end. Ortel is headquartered in the Cayman Islands and pays no income taxes. The owners of Ortel insist on a required rate of return of 12%. Required: 1. What is the expected net cash flow from Square and Cloudburst for the next 3 years? 2. Based on the net present value from cash flows over the next 3 years, is Cloudburst or Square a more valuable customer for Ortel? 3. Cloudburst threatens to switch to another supplier unless Ortel gives a 10% price reduction on all sales starting in 2018. Calculate the 3-year NPV of Cloudburst after incorporating the 10% discount. Should Ortel continue to transact with Cloudburst? What other factors should it consider before making its final decision?

$$\begin{matrix} \text{ } & \text{Expected Annual Percentage Increase} & \text{2017}\\ \text{ } & \text{Square } & \text{Cloudburst} & \text{Square} & \text{Cloudburst}\\ \text{Sales Revenues} & \text{6 \\\%} & \text{5.5 \\\%} & \text{\$ 567.000} & \text{\$ 3.510.000}\\ \text{Cost of Sales} & \text{5 \\\%} & \text{4.5 \\\%} & \text{\$ 364.800} & \text{\$ 3.060.000}\\ \text{Net cash flow} & \text{ } & \text{ } & \text{\$ 202.200} & \text{\$ 450.000}\\ \end{matrix}$$

Find the total paid.

$$\begin{array}{|c| c c c c c c c c c|} \hline \small\textbf{Company} & \small\textbf{(Number of Shares} & \times & \small\textbf{Cost per Share} & = & \small\textbf{Cost of Stock)} & + & \small\textbf{Commission} & = & \small\textbf{Total Paid}\\ \hline \text{ICN Br} & (500 & \times & \small \$73 \frac{1}{4} & = & ?) & + & \$318.00 &=& ?\\ \hline \end{array}$$

Betty owns a small store. The store has been losing money for some time. Because she is the sole owner of the business, her personal assets are at risk. Explain to Betty the differences among Chapters 7, 11 , and 13 bankruptcies. Which type of bankruptcy would you recommend and why?

The hyperbolic cosine of x, denoted by $\cosh x$, is defined by

$$\cosh x=\frac{1}{2}\left(e^r+e^{-r}\right) \text {. }$$

This function occurs often in physics and probability theory. The graph of $y=\cosh x$ is called a catenary.

(a) Use differentiation and the definition of a Taylor series to compute the first four nonzero terms in the Taylor series of $\cosh x$ at x=0.

(b) Use the known Taylor series for $e^x$ to obtain the Taylor series for $\cosh x$ at x=0.

You start a small bee-keeping business, spending $\$ 500$ for equipment and bees. You figure it will cost $\$ 1.25$ per pound to collect, clean, bottle, and label the honey. How many pounds of honey must you produce before your average cost per pound is $\$ 1.79$?

List an appropriate SI base unit (with a prefix as needed) for measuring the following: a. the time it takes to play a CD in your stereo, b. the mass of a sports car, c. the length of a soccer field, d. the diameter of a large pizza, e. the mass of a single slice of pepperoni, f. a semester at your school, g. the distance from your home to your school, h. your mass, i. the length of your physics lab room, j. your height.

Your small remodeling business has two work vehicles. One is a small passenger car used for job site visits and for other general business purposes. The other is a heavy truck used to haul equipment. The car gets 25 miles per gallon (mpg). The truck gets 10 mpg. You want to improve gas mileage to save money, and you have enough money to upgrade one vehicle. The upgrade cost will be the same for both vehicles. An upgraded car will get $40 \mathrm{mpg}$; an upgraded truck will get 12.5 mpg. The cost of gasoline is 2.65 per gallon. Assuming an upgrade is a good idea in the first place, which one should you upgrade to? Both vehicles are driven by 12,000 miles per year.

The small fingerlike projections covering the plicae of the small intestines are called _______.

Elite Service Company is a very profitable small business. It has not, however, given much consideration to internal control. For example, in an attempt to keep clerical and office expenses to a minimum, the company has combined the jobs of cashier and bookkeeper. As a result, Steve Evans handles all cash receipts, keeps the accounting records, and prepares the monthly bank reconciliations.

The balance per the bank statement on March 31, 2014, was $5,931.51. Outstanding checks were: No. 206 for$358.53, No. 441 for $292, No. 590 for$283.00, No. 781 for $286.00, No. 782 for$319.47, and No. 783 for $303.14. Included with the statement was a credit memorandum of$175 indicating the collection of a note receivable for Elite Service Company by the bank on March 21. This memorandum has not been recorded by Elite Service.

The company’s ledger showed one cash account with a balance of $6,889.53. The balance included undeposited cash on hand. Because of the lack of internal controls, Steve took for personal use all of the undeposited receipts in excess of$1,591.63. He then prepared the following bank reconciliation in an effort to conceal his theft of cash.

$$\begin{array}{lrr} \text{Cash balance per books, March 31}&&\text{\$\hspace{1pt}6,889.53}\\ \text{Add: Outstanding checks}\\ \qquad\text{No. 781}&\text{\$\hspace{1pt}286.00}\\ \qquad\text{No. 782}&\text{319.47}\\ \qquad\text{No. 783}&\underline{\text{\hspace{5pt}303.14}}&\underline{\text{\hspace{16pt}808.61}}\\ &&\text{7,698.14}\\ \text{Less: Undeposited receipts}&&\underline{\text{\hspace{8pt}1,591.63}}\\ \text{Unadjusted balance per bank, March 31}&&\text{6,106.51}\\ \text{Less: Bank credit memorandum}&&\underline{\text{\hspace{16pt}175.00}}\\ \text{Cash balance per bank statement, March 31}&&\underline{\underline{\text{\$\hspace{1pt}5,931.51 }}}\\ \end{array}$$

Instructions

(b) Indicate the three ways that Steve attempted to conceal the theft and the dollar amount involved in each method.

Presented below are five independent situations.

(b) Al Bolt, a college student looking for summer employment, opened a bait shop in a small shed at a local marina.

Instructions

In each case, explain what form of organization the business is likely to take—sole proprietorship, partnership, or corporation. Give reasons for your choice.