Jack recommends his new keurig coffee machine to his friend jill. jill buys her own keurig and loves it - studies show that she is now significantly more likely to recommend the keurig coffee machine to another person. what is this effect called?

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.

Stosch company's balance sheet reported assets of $112,000, liabilities of $29,000 and common stock of $26,000 as of december 31, year 1. if retained earnings on the balance sheet as of december 31, year 2, amount to $74,000 and stosch paid a $28,000 dividend during year 2, then the amount of net income for year 2 was which of the following? a)$23,000 b) $35,000 c) $12,000 d)$42,000

(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?