Rafael has decided to retire once he has $1,000,000 in his retirement account. At the end of each year, he will contribute $7,000 to the account, which is expected to provide an annual return of 6.2%. How many years will it take until he can retire

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.

Which of the following statements is correct? stockholders should generally be happier than bondholders to have managers invest in risky projects with high potential returns as opposed to safe projects with lower expected returns. potential conflicts between stockholders and bondholders are increased if a firm's bonds are convertible into its common stock. takeovers are most likely to be attempted if the target firm’s stock price is above its intrinsic value. one advantage of operating a business as a corporation is that stockholders can deduct their pro rata share of the taxes the firm pays, thereby eliminating the double taxation investors would face in a partnership.

The third program provides families with $50 in food stamps each week, redeemable for both perishable and nonperishable food. the fourth policy instead provides a family with a box of nonperishable foods each week, worth $50. use two graphs to illustrate that a family may be indifferent between the two programs, but will never prefer the $50 box of nonperishable foods over the $50 in food stamps. state your answer and use a consumer choice model for perishable food and nonperishable food to graphically justify your choice.