In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing$700,000 if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdict to be 0.8. a. Find the expected value of the amount the company can lose by taking the case to court. b. Should the company settle out of court?

A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $300,000 if successful and a yearly loss of$100,000 otherwise. The probability of success is $\frac{1}{2}$. If the second mall is selected, it is estimated that the yearly profit will be $200,000 if successful; otherwise, the annual loss will be$60,000. The probability of success at the second mall is $\frac{3}{4}$. Which mall should be chosen in order to maximize the expected profit?

A construction company is planning to bid on a building contract. The bid costs the company $\$1500$. The probability that the bid is accepted is $\frac{1}{5}$. If the bid is accepted, the company will make $\$40,000$ minus the cost of the bid. Find the expected value in this situation. Describe what this value means.

Consider a political discussion group consisting of 5 Democrats, 6 Republicans, and 4 Ind epend ents. Suppose that two group members are randomly selected, in succession, to attend a political conven tion. Find the probability of selecting two Republicans.

Use the Fundamental Counting Principle. In the Cambridge Encyclopedia of Language (Cambridge University Press, 1987), author David Crystal presents five sentences that make a reasonable paragraph regardless of their order. The sentences are as follows:

• Mark had told him about the foxes.
• John looked out of the window.
• Could it be a fox?
• However, nobody had seen one for months.
• He thought he saw a shape in the bushes. In how many different orders can the five sentences be arranged?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Here’s my dilemma: I can accept a $1000 bill or play a dice game ten times. For each roll of the single die, I win$500 for rolling 1 or 2. I win $200 for rolling 3. I lose$300 for rolling 4, 5, or 6. Based on expected value, I should accept the $1000 bill.

Involve computing expected values in games of chance. For many years, organized crime ran a numbers game that is now run legally by many state governments. The player selects a three-digit number from 000 to 999. There are 1000 such numbers. A bet of $1 is placed on a number, say number 115. If the number is selected, the player wins$500. If any other number is selected, the player wins nothing. Find the expected value for this game and describe what this means.

In the case of Rochin v. California, the Supreme Court ruled that the _____.

a) 5th Amendment was violated

b) 1st Amendment was violated

c) 14th Amendment was violated

d) 2nd Amendment was violated

When, in a criminal court, a defendant is found “not guilty,” is the court saying with certainty that he or she is innocent? Explain.

A subsidiary of Elektra Electronics manufactures graphing calculators. Management determines that the daily cost C(x) (in dollars) of producing these calculators is $C(x)=0.0001 x^{3}-0.08 x^{2}+40 x+5000$ where x is the number of calculators produced. Find the inflection point of the function C, and interpret your result.

A large mountain can slightly affect the direction of “down” as determined by a plumb line. Assume that we can model a mountain as a sphere of radius R = 2.00 km and density (mass per unit volume) 2.6 × 10³ kg/m³. Assume also that we hang a 0.50 m plumb line at a distance of 3R from the sphere’s center and such that the sphere pulls horizontally on the lower end. How far would the lower end move toward the sphere?

Information taken from Bonita Bay Supply's financial statements is provided in the Working Papers.

Calculate the following efficiency measures and market ratios for the current year and the prior year. Round percentage calculations to the nearest 0.1%, dollar amounts to the nearest $0.01, and the price-earnings ratio to the nearest tenth.

Earnings per share

A service that repairs air conditioners sells maintenance agreements for $80 a year. The average cost for repairing an air conditioner is$350 and 1 in every 100 people who purchase maintenance agreements have air conditioners that require repair. Find the service’s expected profit per maintenance agreement.

The following information was taken from the financial statements of Tolbert Inc. for December 31 of the current fiscal year:

$$\begin{array}{lr} \text { Common stock, } \$ 20 \text { par (no change during the year) } & \$ 10,000,000 \\ \text { Preferred \$4 stock, } \$ 40 \text { par (no change during the year) } & 2,500,000 \end{array}$$

The net income was $1,750,000 and the declared dividends on the common stock were$1,125,000 for the current year. The market price of the common stock is $45 per share. For the common stock, determine the earnings per share. Round to one decimal place, except earnings per share, which should be rounded to two decimal places