Given a machine with time span T and a set of jobs each having a profit pi and required time ti, the goal is to maximize the summed profit of jobs scheduled on the machine. Consider the following algorithm for job scheduling: Sort the jobs in decreasing order by pi/ti and schedule them until you cannot fit more. Prove or disprove the correctness of this greedy algorithm

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount s present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) find the amount of money accrued at the end of 3 years when $4000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (round your answer to the nearest cent.) $ (b) in how many years will the initial sum deposited have doubled? (round your answer to the nearest year.) years (c) use a calculator to compare the amount obtained in part (a) with the amount s = 4000 1 + 1 4 (0.0575) 3(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.) s = $

Need true or false 1 2 3 4 5 6 7 8

Suppose the number of equipment sales and service contracts that a store sold during the last six (6) months for treadmills and exercise bikes was as follows: treadmill exercise bike total sold 185 123 service contracts 67 55 the store can only sell a service contract on a new piece of equipment. of the 185 treadmills sold, 67 included a service contract and 118 did not.