# Liberty MATH 114 Test 2 Answers Complete Solutions

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A group of n people win a total of $7 million from a state lottery drawing. Let f(n) be each person’s share (in millions of dollars). Write a variation equation in the given variables. State the value of the variation constant k.

Write a variation equation in the given variables.

State the value of the variation constant k.

Suppose that a CD is about to be released. Let n=f(a) be the number of CDs (in millions) to be sold, where a is the advertising budget (in thousands dollars). A graph of f is sketched in the figure.

a. Is f an increasing function? Explain.

b. Does the number of CDs sold vary directly as the amount of money spent on advertising? Explain.

c. Compare the meanings of these two statements: “One quantity varies directly as another quantity.” “One quantity will increase if the other quantity increases.” Choose the correct answer.

y varies directly as the square of R. If y is 9 when R is 5, find y when R is 10.

a) Write the variation.

b) Find y when R is 10.

a) How are these two variables related?

b) The quantity indicated is

x varies inversely as the square of P. If x is 7 when P is 6, find x when P is 2.

a) Write the variation.

b) Find x when P is

a) How are these two variables related?

b) The quantity indicated is

The interest on an investment varies directly as the rate of interest. If the interest is

$57 when the interest rate is 10%, find the interest when the rate is 4.9%.

The interest when the rate of interest is

If the temperature is constant, the pressure of a gas in a container varies inversely as the volume of the container. If the pressure is 40 pounds per square foot in a container with 6 cubic feet, what is the pressure in a container with 5.5 cubic feet?

## STATUS

The distance that a spring will stretch varies directly as the force applied to the spring. A force of 50 pounds is needed to stretch a spring 5 inches. What force is required to stretch the spring 23 inches?

Company XYZ closed at $52.25 per share with a P/E ratio of 13.72. Answer the following questions.

a. How much were earnings per share?

b. Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?

a. How much were earnings per share?

b. Based on the fact that Company XYZ stock historically trades at an average P/E ratio of 12-14, does the stock price seem overpriced, underpriced, or about right?

Company XYZ closed at $103.91 per share with a P/E ratio of 14.32. Answer the following questions.

a. How much were earnings per share?

b. Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?

a. How much were earnings per share?

b. Based on the fact that Company XYZ stock historically trades at an average P/E ratio of 12-14, does the stock price seem overpriced, underpriced, or about right?

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

The price per gallon of gasoline has risen from only a quarter in 1918 to nearly $3 in 2009, thereby making it much more difficult for the poor to afford fuel for their cars.