1. A family has a 30-year, $225,000 mortgage at 3.9% compounded monthly. Find: a. the monthly payment b. the unpaid balance after 15 years c. the equity built up in the home after 22 years' worth of payments are made and the value of the home is calculated as $295,000 d. the total interest paid on the loan at the 30-year point (last payment is made) Answers: a. ____________ b. _____________ c. _____________ d. ____________ 2. Solve the following system of linear equations using substitution, elimination by addition, or augmented matrix methods (your choice, but you must show all work to get any credit): 7 x+2 y=4 2 x +3 y=11 Answer: _________________________________ 3. Ogunquit Craftsmen's Guild makes bookcases and desks. Each bookcase requires 5 workhours for assembling and 4 work-hours for finishing. Each desk requires 10 work-hours for assembling and 3 work-hours for finishing. The profit realized per bookcase is $40. The profit realized per desk is $75. The MAXIMUM work-hours available per month for assembling is 600 and for finishing is 240. a. How many bookcases and desks should be manufactured each month to make maximum profit? (You may give your answer algebraically or graphically) 1 b. What is the associated maximum monthly profit? Answer: (a) _____________ bookcases, _____________ desks (b) Maximum monthly profit: __________________ 4. A survey of 800 small businesses indicates that 250 own a videoconferencing system, 420 own projection equipment, and 180 own both videoconferencing and projection equipment. How many own either projection equipment or a videoconferencing system but not both? Answer: _______________________________ 5. The times needed (in minutes) to check out 12 randomly selected customers at a large supermarket during the store's busiest time are: 4.6 11.9 10.2 8.4 2 9.4 8.8 6.1 11.4 8.8 9.1 6.7 13.2 a. Find the sample mean, median, and mode(s) (if it/they exist(s)) Answer: mean ____________ median _____________ mode _____________ b. Find the sample variance s2 and sample standard deviation s : Answer: s2 = _____________________ 3 s = ___________________________