Corporation A receives a dividend from Corporation B. It includes the dividend in gross income for tax purposes but includes a pro-rata portion of B's earnings in its financial accounting income. If A has accounted for the dividend correctly (using the general rule), how much of B's stock does A own

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

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.

Security a has a higher standard deviation of returns than security b. we would expect that: (i) security a would have a risk premium equal to security b. (ii) the likely range of returns for security a in any given year would be higher than the likely range of returns for security b. (iii) the sharpe ratio of a will be higher than the sharpe ratio of b. (a) i only (b) i and ii only (c) ii and iii only (d) i, ii and iii