1. C: The mean value is calculated as the sum of the values (175) divided by the number of values (7). The standard deviation, s, of the sample set is calculated as the square root of the difference between the average of the actual values squared and the square of the average value.
2. C: Multiplication of (x – 3) by (x – 4) yields the quadratic formula (x2 – 7x + 12). When multiplied by the third factor (x + 7), this produces the formula x3 – 37x + 84.
3. C. The correct answer is $30.16 per share. To compute this weighted average, multiply the number of shares purchased per stock by the stock price. Then, add these totals together and divide by the total number of shares. Marjorie bought 100 shares of Microsoft at $45.14, 100 shares of Apple Computer at $16.90, and 200 shares of Garmin at $29.30. So, the total amount that she spent was
She obtained a total of 400 shares of stock. So, the average cost per share is
4. C: If the region within the circle is the probability of the event A, then the region outside if the circle must represent the probability of “not A”. That is, of A not occurring.
5. D: Rafael’s profit on each computer is given by the difference between the price he pays and the price he charges his customer, or $800-$450. If he sells n computers in a month, his total profit will be n times this difference, or n(800-450). However, it is necessary to subtract his fixed costs of $3000 from this to compute his final profit per month.
6. A: Each glass of lemonade costs 10?, or $0.10, so that g glasses will cost g×$0.10. To this, add Bob’s fixed cost of $45, giving the expression in A.
7. B: Profit equals (tickets sold) x (price) – cost. The number of tickets sold is given by the equation in Question 12. Multiplying this expression by price, p, gives 25,000p-0.1p3, and subtracting cost gives the expression in Choice B.
8. B: To calculate S, calculate the discount and subtract it from the original price, p. The discount is 33% of p, or 0.33p. Thus, S=p-0.33p.
9. D: Let = the price of truck A and that of truck B. Similarly let and represent the gas mileage obtained by each truck. The total cost of driving a truck n miles is
To determine the break-even mileage, set the two cost equations equal to one another and solve for n:
Plugging in the given values:
10. D: The formula for book value is (face amount – discount) = book value. The total face amount of the bonds is $20,000,000 (2,000 x $10,000) and the discount is 1% (7%-6%), or $200,000. Therefore, $20,000,000 – $19,800,000 = $200,000.