Suppose there are 12-year, 14-year, and 16-year cicadas that all appear this year. after how many years will all three types of cicadas appear together again? how do you know?

David and darlene jasper have one child, sam, who is 6 years old (birthdate july 1, 2011). the jaspers reside at 4639 honeysuckle lane, los angeles, ca 90248. david's social security number is 577-11-3311, darlene's is 477-98-4731, and sam's is 589-22-1142. david's birthdate is may 29, 1984 and darlene's birthday is january 31, 1986. david and darlene's earnings and withholdings for 2017 are:

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.

Which of the following would classify as a general education requirement