Define the following sample spaces. define notations as necessary. i. number of black hole mergers detected since ligo openedii. time (in days) until ligo observes the first black hole merger(b)[3 pts]what type of variables are the following?

i. the cause of the gravitational waves observed, which can be either a black hole or aneutron star merger
ii. number of gravitational wave detections observed
iii. time (in days) until ligo first detects a gravity wave signal.

Andy purchases only two goods, apples (a) and kumquats (k). he has an income of $125 and can buy apples at $5 per pound and kumquats at $5 per pound. his utility function is u(a, k) = 6a + 2k. what is his marginal utility for apples and his marginal utility for kumquats? andy's marginal utility for apples (mu subscript a) is mu subscript aequals 6 and his marginal utility for kumquats (mu subscript k) is

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?

Utilization will always be lower than efficiency because: a. effective capacity is greater than design capacityb. expected output is less than actual output. c. effective capacity equals design capacity. d. effective capacity is less than design capacity. e. expected output is less than rated capacity.