In order to determine if the time required for students to take a final exam is excessive, five students were selected at random from each of six classes. If the process average is 123.77 minutes and the average range is 66.83 minutes, the upper and lower control limits of a 3- sigma R-chart are O UCL = 133.6, LCL = 0 O UCL = 96, LCL = 0 O UCL = 152.3, LCL = 0 O UCL = 141, LCL = 0

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.

Tri fecta, a partnership, had revenues of $369,000 in its first year of operations. the partnership has not collected on $45,000 of its sales and still owes $39,500 on $155,000 of merchandise it purchased. there was no inventory on hand at the end of the year. the partnership paid $27,000 in salaries. the partners invested $48,000 in the business and $23,000 was borrowed on a five-year note. the partnership paid $2,070 in interest that was the amount owed for the year and paid $9,500 for a two-year insurance policy on the first day of business. compute net income for the first year for tri fecta.

Amonopolist’s inverse demand function is p = 150 – 3q. the company produces output at two facilities; the marginal cost of producing at facility 1 is mc1(q1) = 6q1, and the marginal cost of producing at facility 2 is mc2(q2) = 2q2.a. provide the equation for the monopolist’s marginal revenue function. (hint: recall that q1 + q2 = q.)mr(q) = 150 - 6 q1 - 3 q2b. determine the profit-maximizing level of output for each facility.output for facility 1: output for facility 2: c. determine the profit-maximizing price.$