1. Car Sales: Of the cars sold during the month of July, 90 had air conditioning, 100 had automatic transmissions, and 75 had power steering. Five cars had all three of these extras. Twenty cars had none of these extras. Twenty cars had only air conditioning; 60 cars had only automatic transmissions; and 30 cars had only power steering. Ten cars had both automatic transmission and power steering.
a) How many cars had both power steering and a/c?
b) How many had both auto and a/c?
c) How many had neither power steering nor auto?
d) How many cars were sold in July?
e) How many had automatic transmission or air conditioning or both?
2. Ten grams of sugar are added to a 40g serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mix?
3. For a certain commodity the demand equation is given by D = -3p + 20. At a price of $1, four units of the commodity are supplied. If the supply equation is linear and the market price is $4, find the supply equation
4. Calculate the first four terms of the recursively defined sequence:
tn+1 = (tn)2 - tn : t1 = -2
5. Last Friday, Formax cinemas sold a total of 170 movie tickets. Tickets can be bought in one of 3 ways : a child admission costs $5, student admission is $6 and regular admissions are $8.50. Proceeds totaled $970. The number of child tickets sold was double that of student tickets.
Write a system of equations that can be used to find the number of each type of tickets sold. You may use any method (Crammers rule, Inverse matrix, ERO'S) to solve the system of equations.
6. A retired couple has up to $30000 to invest in fixed-income securities. Their broker recommends investing in two bonds: one a AAA bond yielding 8%; the other a B+ bond paying 12%.After some consideration, the couple decides to invest at most $12000 in the B+-rated bond and at least $6000 in the AAA bond. They also want the amount invested in the AAA bond to exceed or equal the amount invested in the B+ bond. What should the broker recommend if the couple wants to maximize the return on their investment?
7. Use Cramer's Rule to solve the system of linear equations for x.
2x + y + z = 6
x - y - z = -3
3x + y + 2z = 7
8. The Pearl Company plans to market a new product. Based on its market studies, Pearl estimates that it can sell 5500 units in 2017.The selling price will be $2 per unit. Variable costs are estimated to be 40% of the selling price. Fixed costs are estimated to be $6000.What is the break-even point?