Two smart students form a study group in some math class where homework is handed in jointly by each group. in the last homework of the semester, each of the two students can choose to either work ("w") or party ("p"). if at least one of them solves the homework that week (chooses "w"), then they will both receive 10 points. but solving the homework incurs a substantial effort, worth −7 points for a student doing it alone, and an effort worth −2 points for each student, if both students work together. partying involves no effort, and if both students party, they both receive 0 points. assume that the students do not communicate prior to deciding whether they will work or party. write this situation as a matrix game and determine all nash equilibria.

Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). however, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). what is the future value of a 13-year annuity of $2,800 per period where payments come at the beginning of each period? the interest rate is 9 percent. use appendix c for an approximate answer, but calculate your final answer using the formula and financial calculator methods. to find the future value of an annuity due when using the appendix tables, add 1 to n and subtract 1 from the tabular value. for example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to appendix c for n = 6 and i = 10 percent. look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716)

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.

The purpose of safety stock is to: a. eliminate the possibility of a stockout. b. control the likelihood of a stockout due to variable demand and/or lead time. c. eliminate the likelihood of a stockout due to erroneous inventory tally. d. protect the firm from a sudden decrease in demand. e. replace failed units with good ones.