Avending machine dispensing books of stamps accepts only one dollar coins, 1 dollar bills and 5 dollar bills. a) find a recurrence relation for the number of ways to deposit n dollars in the vending machine, where the order in which the coins and bills are deposited matters. b) what are initial conditions? c) how many ways are there to deposit $10 for a book of stamps?

In 2015, lori assigned a paid-up whole life insurance policy to an irrevocable life insurance trust (ilit) for the benefit of her three children. the ilit contained a crummey provision for the benefit of each child. at the time of the transfer, the whole life insurance policy was valued at $200,000, and since lori had not made any other taxable gifts during her lifetime, she did not owe any gift tax. lori died in 2016, and the face value of the whole life insurance policy of $2,000,000 was paid to the ilit. regarding this transfer, how much is included in lori’s gross estate at her death?

An increase in the market price of men's haircuts, from $16 per haircut to $26 per haircut, initially causes a local barbershop to have its employees work overtime to increase the number of daily haircuts provided from 20 to 25. when the $26 market price remains unchanged for several weeks and all other things remain equal as well, the barbershop hires additional employees and provides 40 haircuts per day. what is the short-run price elasticity of supply? nothing (your answer should have two decimal places.) what is the long-run price elasticity of supply? nothing (your answer should have two decimal places.)

Qwest airlines has implemented a program to recycle all plastic drink cups used on their aircraft. their goal is to generate $7 million by the end of the recycle program's five-year life. each recycled cup can be sold for $0.005 (1/2 cent). a. how many cups must be recycled annually to meet this goal? assume uniform annual plastic cup usage and a 0% interest rate. b. repeat part (a) when the annual interest rate is 12%. c. why is the answer to part (b) less than the answer to part (a)?