Twelve years ago, the archer corporation borrowed $6,200,000. since then, cumulative inflation has been 80 percent (a compound rate of approximately 5 percent per year). a. when the firm repays the original $6,200,000 loan this year, what will be the effective purchasing power of the $6,200,000? (hint: divide the loan amount by one plus cumulative inflation.) (do not round intermediate calculations and round your answer to the nearest whole dollar.) b. to maintain the original $6,200,000 purchasing power, how much should the lender be repaid? (hint: multiply the loan amount by one plus cumulative inflation.) (do not round intermediate calculations and round your answer to the nearest whole dollar.)

Nellie lumpkin, who suffered from dementia, was admitted to the picayune convalescent center, a nursing home. because of her mental condition, her daughter, beverly mcdaniel, signed the admissions agreement. it included a clause requiring the par- ties to submit any dispute to arbitration. after lumpkin left the center two years later, she filed a suit against picayune to recover damages for mistreatment and malpractice. [covenant health & rehabilitation of picayune, lp v. lumpkin, 23 so.2d 1092 (miss. app. 2009)] (see page 91.) 1. is it ethical for this dispute—involving negligent medical care, not a breach of a commercial contract—to be forced into arbitration? why or why not? discuss whether medical facilities should be able to impose arbitration when there is generally no bargaining over such terms.

At a student café, there are equal numbers of two types of customers with the following values. the café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i. e., she cannot price-discriminate). students with early classes students without early classes coffee 70 60 banana 51 101 the marginal cost of coffee is 10 and the marginal cost of a banana is 40. the café owner is considering three pricing strategies: 1. mixed bundling: price bundle of coffee and a banana for 161, or just a coffee for 70. 2. price separately: offer coffee at 60, price a banana at 101. 3. bundle only: coffee and a banana for 121. do not offer goods separately. assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle. for simplicity, assume there is just one student with an early class, and one student without an early class. price strategy revenue from pricing strategy cost from pricing strategy profit from pricing strategy 1. mixed bundling $ $ $ 2. price separately $ $ $ 3. bundle only $ $ $ pricing strategy yields the highest profit for the café owner.

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.