An individual with unit initial wealth will construct a portfolio consisting of fractions 1 − α of a risk-free asset and α of a risky asset. The risk-free asset has return rate rf , a known constant.
The risky asset has return rate r1, a random variable with expected value rbar1 and variance σ1^2 . The return rate for the portfolio is the random variable r = (1 − α)rf + αr1.
Assume utility function U(x) = x − (1/3)x^2 for the individual.

a) Find formulas for E[r] and for E[r^2] in terms of α, rf , rbar1, and σ1^2.
b) After one year the utility of the wealth is U(1 + r). Write out the formula for E[U (1 + r)] = E[ 1 + r −(1/3)(1 + r)^2] in terms of α, rf , rbar1 and σ1^2 .
c) If rf = (1/40), rbar1 = (1/20) and σ1 = (1/5), find α for the portfolio of maximum expected utility.

Peyton's field hockey team wins 4 games out of every 7 games played. her team lost 9 games. how many games did peyton's team play?

3. simplify. 312⋅312 4. rewrite n√xm using a rational expression.

When constructing a perpendicular line through a point off a line, how can you verify that the lines constructed are perpendicular? check the angles used in the construction with a straightedge to ensure consistency. check the distance along the lines at several places with a compass to ensure they are the same length. check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. check the distance between the lines at several places with a compass to ensure they are equidistant. question 2(multiple choice worth 1 points) (01.03 lc) which of the following steps is included in the construction of a perpendicular line through a point on a line? connect arcs that are above and below the given line with a straightedge. connect arcs that are above the original line with a straightedge. create arcs on either side of a point that is off the given line. create a copied angle by using the first two lines as the original angle.