We now have $5,000 in assets and are given a choice between investment 1 and investment 2. With investment 1, 80% of the time weincrease our asset position by$295,000, and 20% of the time we increase our asset position by $95,000. With investment 2, 50% of the time we increase our asset position by$595,000, and 50% of the time we increase our asset position by $5,000. Our utility function for final asset position x is u(x). We are given the following values for u(x): u(0) = 0, u(640,000) = .80, u(810,000) = .90, u(0) = 0, u(90,000) = .30, u(1,000,000) = 1, u(490,000) = .7. a. Are we risk-averse, risk-seeking, or risk-neutral? Explain. b. Will we prefer investment 1 or investment 2?

Fill in the blanks. Given a relation in x and y, if to each value of x in the domain there corresponds exactly one value of in the range, y is said to be a _____ of x. We call x the independent _____ and y the _____ variable.

Convert each rectangular equation to a polar equation that expresses f in terms of

$$\theta.$$

$$2 x + 3 y = 8$$

Evaluate the expression when a=16, b=8, and c=7. 3a+2.1(4)

Simplify the function. List any restrictions on the domain.

$$f ( x ) = \frac { x ^ { 2 } + 6 x - 16 } { x ^ { 2 } - 4 }$$

The region below the curve y=1/sqrt(4+x^2) from x=0 to x=2 is revolved avbout the x-axis. Find the volume of the resulting solid

A car goes into a skid and gradually comes to a stop, accelerating at a constant rate. At the midpoint of the skid, how much of its kinetic energy has it lost?

Let the domain of the function

$$f(x) = \frac { 1 } { 5 } x - 12$$

be {-5, 0, 10}. What is the range? F. {-5, 0, 10} G. {0, 12, 13} H. {-13, -12, -11} I. {-13, -12, -10}

Find an equation of the curve that satisfies the given conditions. At each point (x, y) on the curve the slope equals the square of the distance between the point and the y-axis; the point (−1, 2) is on the curve.

Simplify

$$\frac { x ^ { 16 } - 1 } { x - 1 }$$

by long division and by factoring. Which method do you prefer? Explain your answer.

Suppose my utility function for asset position x is given by u(x) = ln x. a. Am I risk-averse, risk-neutral, or risk-seeking? b. I now have $20,000 and am considering the following two lotteries: L1: With probability 1, I lose$1,000. L2: With probability .9, I gain $0. With probability .1, I lose$10,000. Determine which lottery I prefer and the risk premium of L2.

Sam wants to bicycle a total of 600 miles to prepare for a race. He will bicycle 15 miles each day. How many days must he bicycle to reach his goal? A. 40 days B. 50 days C. 300 days D. 585 days

Briefly explain the significance of Second Great Awakening.

Use the x- and y-intercepts to graph each linear equation.

$$3x - 4y = 12$$