Durran has recently acquired a rare art piece that he plans to put on display in his private collection. He estimates that revenues generated from donations and admissions tickets to see the new exhibit will be $23,000 per year for the next five years. If he requires a rate of return of 7%, how much are the expected cash flows worth for him today

The leading producer of cell phone backup batteries, jumpstart, has achieved great success because they produce high-quality battery backups that are not too expensive. even so, another company that produces lower-quality batteries at the same price has also achieved some success, but not as much as jumpstart. also, in general, the price of backup batteries has declined because of economies of scale and learning. in addition, jumpstart has added complementary assets, such as a carrying case. considering all of these factors, the backup battery industry is most likely in the introduction stage. growth stage. shakeout stage. maturity stage.

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.

Amanager of a store that sells and installs spas wants to prepare a forecast for january and june of next year. her forecasts are a combination of trend and seasonality. she uses the following equation to estimate the trend component of monthly demand: ft = 30+5t, where t = 1 in january of this year. seasonal relatives are 0.60 for january and 1.50 for june. what demands should she predict for january and june of next year