Theo just won a prize that will pay him $12,000 a year for 12 years, starting at the end of Year 12. What is the current value of this prize if the discount rate is 9 percent, compounded annually?

(05.04 mc) a 2012 report from the u.s. surgeon general stated: "another common practice is strategically locating tobacco-related marketing materials where young children will be exposed to them. tobacco industry executives acknowledge that products and advertising should be placed at eye level (pollay 2007), but in california, 48% of stores had at least one cigarette marketing item at or below 3 feet from the floor (feighery et al. 2001)." it was also noted that 25% of cigarette displays were next to candy. in addition, a national study found that about one-third of the stores had tobacco ads at low heights. after california banned counter displays, some stores place cigarettes in transparent displays so product brands could still be seen. why did some stores use transparent units to display the cigarettes? (3 points) to comply with the new rules while still encouraging cigarette purchases via visual exposure to ensure children and minors are not exposed to cigarettes and their eye-catching packaging to minimize exposure to humidity, extending the shelf life of the cigarettes' tobacco to reduce the occurrence of shoplifting, since cigarettes are high-revenue items

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.

Suppose farmer lane grows and sells cotton in a perfectly competitive industry. the market price of cotton is $1.64 per kilogram, and his marginal cost of production is $1.44 per kilogram, which increases with output. assume farmer lane is currently earning a profit. can farmer lane do anything to increase his profit in the short run? farmer lane: a. cannot do anything to increase his profit. b. may or may not be able to increase his profit. c. can increase his profit by raising his price. d. can increase his profit by producing more output. e. can increase his profit by shutting down.