On january 3, 2006, hamm enterprises was granted a patent on a product. on january 8, 2021, to protect its patent, hamm purchased a patent on a competing product that originally was issued on january 15, 2010. because of its unique plant, hamm does not feel that the competing patent can be used in producing a product. the cost of acquiring the competing patent should be:
a) amortized over a maximum period of 12 years.
b) amortized over a maximum period of 8 years.
c) expensed in 2019.
d) amortized over a maximum period of 20 years.

Burke enterprises is considering a machine costing $30 billion that will result in initial after-tax cash savings of $3.7 billion at the end of the first year, and these savings will grow at a rate of 2 percent per year for 11 years. after 11 years, the company can sell the parts for $5 billion. burke has a target debt/equity ratio of 1.2, a beta of 1.79. you estimate that the return on the market is 7.5% and t-bills are currently yielding 2.5%. burke has two issuances of bonds outstanding. the first has 200,000 bonds trading at 98% of par, with coupons of 5%, face of $1000, and maturity of 5 years. the second has 500,000 bonds trading at par, with coupons of 7.5%, face of $1000, and maturity of 12 years. kate, the ceo, usually applies an adjustment factor to the discount rate of +2 for such highly innovative projects. should the company take on the project?

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.

Zeta corporation is a manufacturer of sports caps, which require soft fabric. the standards for each cap allow 2.00 yards of soft fabric, at a cost of $2.00 per yard. during the month of january, the company purchased 25,000 yards of soft fabric at $2.10 per yard, to produce 12,000 caps. what is zeta corporation's materials price variance for the month of january?