A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed.

a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer
b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes
c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers

John and daphne are saving for their daughter ellen's college education. ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). college tuition and expenses at state u. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).so far, john and daphne have accumulated $15,000 in their college savings account (at t = 0). their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. they expect their investment account to earn 9%. how large must the annual payments at t = 5, 6, and 7 be to cover ellen's anticipated college costs? a. $1,965.21b. $2,068.64c. $2,177.51d. $2,292.12e. $2,412.76