91Ó°ÊÓ

Suppose that you inherit 10,000 dollar. The will states how you must invest the money. Some (or all) of the money must be invested in stocks and bonds. The requirements are that at least 3000 dollar be invested in bonds, with expected returns of 0.08 dollar per dollar, and at least 2000 dollar be invested in stocks, with expected returns of 0.12 dollar per dollar. Because the stocks are medium risk, the final stipulation requires that the investment in bonds should never be less than the investment in stocks. How should the money be invested so as to maximize your expected returns?

write the partial fraction decomposition of each rational expression. $$ \frac{6 x^{2}-x+1}{x^{3}+x^{2}+x+1} $$

In Exercises \(29-42,\) solve each system by the method of your choice. $$ \left\\{\begin{array}{l} x-3 y=-5 \\ x^{2}+y^{2}-25=0 \end{array}\right. $$

In Exercises \(43-46,\) let \(x\) represent one number and let \(y\) represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is \(7 .\) If one number is subtracted from the other, their difference is \(-1 .\) Find the numbers.

perform each long division and write the partial fraction decomposition of the remainder term. $$ \frac{x^{5}}{x^{2}-4 x+4} $$

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A system of two equations in two variables whose graphs are two circles must have at least two real ordered-pair solutions.

When a crew rows with the current, it travels 16 miles in 2 hours. Against the current, the crew rows 8 miles in 2 hours. Let \(x=\) the crew's rowing rate in still water and let \(y=\) the rate of the current. The following chart summarizes this information: Find the rate of rowing in still water and the rate of the current. (TABLE CAN'T COPY)

What does a solid line mean in the graph of an inequality?