Cindy wishes to arrange her coins into $x$ piles, each consisting of the same number of coins, $y$. each pile will have more than one coin and no pile will have all the coins. if there are 13 possible values for $y$ given all of the restrictions, what is the smallest number of coins she could have?

The master manufacturing company has just announced a tender offer for its own common stock. master is offering to buy up to 100% of the company's stock at $20 per share contingent on at least 64% of the outstanding shares being tendered. after the announcement of the offer, the stock closed on the nyse up 2.50 at $18.75. a customer has 100 shares of master stock in his cash account. the customer tells you that he wishes to "cash out" his position. you should recommend that the customer:

If the ceo of a large, diversified, firm were filling out a fitness report on a division manager (i.e., "grading" the manager), which of the following situations would be likely to cause the manager to receive a better grade? in all cases, assume that other things are held constant.a. the division's basic earning power ratio is above the average of other firms in its industry.b. the division's total assets turnover ratio is below the average for other firms in its industry.c. the division's debt ratio is above the average for other firms in the industry.d. the division's inventory turnover is 6, whereas the average for its competitors is 8.e. the division's dso (days' sales outstanding) is 40, whereas the average for its competitors is 30.

White truffles are a very prized and rare edible fungus that grow naturally in the countryside near alba, italy. suppose that it costs $200 per day to search for white truffles. on an average day, the total number of white truffles (t) found in alba is t = 20x − x 2 , where x is the number of people searching for white truffles on that day. white truffles can be sold for $100 each. if there is no regulation, how many more people will be searching for white truffles than the socially optimal number?