An automatic filling machine is used to fill two-litre bottles of cola. The machine's output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of .01 litres. Output is monitored using means of samples of five observations. a) Determine the two-sigma upper and lower control limits for the sample means. b) If the means for 6 samples are: 2.005, 2.001, 1.998, 2.002, 1.995, and 1.999, is the process in control?

Trey morgan is an employee who is paid monthly. for the month of january of the current year, he earned a total of $4,538. the fica tax for social security is 6.2% of the first $118,500 earned each calendar year, and the fica tax rate for medicare is 1.45% of all earnings for both the employee and the employer. the amount of federal income tax withheld from his earnings was $680.70. his net pay for the month is .

When it is 4: 00 a.m. in halifax, it is 1: 00 p.m. in karachi, and when it is 9: 00 a.m. in karachi, it is 5: 00 a.m. in warsaw. mary left halifax to fly to karachi, but she accidentally left her watch on warsaw time. according to mary’s watch, she left halifax at 9: 40 p.m. on monday. the local time when she arrived at karachi was 3: 00 p.m. tuesday. how long was mary’s flight? a. 9 hours, 20 minutes b. 13 hours, 20 minutes c. 14 hours, 20 minutes d. 17 hours, 20 minutes

Assume a competitive firm faces a market price of $60, a cost curve of c = 0.003q^3 + 25q + 750, and a marginal cost of curve of: mc = 0.009q^2 + 25.the firm's profit maximizing output level (to the nearest tenth) is , and the profit (to the nearest penny) at this output level is $ will cause the market supply to (shift right/shift left). this will continue until the price is equal to the minimum average cost of $