Max stamp approves study abroad documents for the university. students must wait in line with their forms outside max's office. one student at a time is allowed in his office and max takes precisely 15 minutes to evaluate each student’s set of documents. on average 2 students per hour go to his office and they spend on average 160 minutes trying to get their forms approved (time waiting in queue plus time in max’s office having him evaluate their documents).

Information on gerken power co., is shown below. assume the company’s tax rate is 40 percent. debt: 9,400 8.4 percent coupon bonds outstanding, $1,000 par value, 21 years to maturity, selling for 100.5 percent of par; the bonds make semiannual payments. common stock: 219,000 shares outstanding, selling for $83.90 per share; beta is 1.24. preferred stock: 12,900 shares of 5.95 percent preferred stock outstanding, currently selling for $97.10 per share. market: 7.2 percent market risk premium and 5 percent risk-free rate. required: calculate the company's wacc. (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.) wacc %

Onsider the following subscription behavior information from genie, a web site that provides tools for constructing a family tree (ancestor search). subscriptions cost $9.99 per month, but you are charged for the entire year at the time of purchase. there is a one-year minimum term when you sign up for the service. once purchased, subscriptions are set to renew automatically unless the subscriber cancels them. when a membership renews, it renews for a one-year term and again you are charged for the entire year. there are no variable costs associated with providing this service to an individual customer, but genie does engage in customer relationship activities that they believe will increase customer retention. these customer relationship activities cost genie about $10 per year per customer. based on a sample of 1000 customers that joined genie five years ago, near the time when the company was founded, they were able to determine how many of those customers remained subscribers in the second year, third year etc. based on this information, genie calculated the average annual retention rate to be 20%. genie uses an annual discount rate of 8%. a. last year, genie spent $10,000 placing advertisements on google. genie management believes that these advertisements were responsible for about 300 new subscribers. would you recommend to genie management that they purchase more google ads? b. suppose a newly-introduced loyalty program increases the number of customers that remained to 30%. does this new data change your answer to 9.a? c. do you have any hesitations or concerns about making recommendations to management based on your above estimate of customer lifetime value?

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.