Printer P prints at the constant rate of x seconds per page, and printer Q prints at the constant rate of y seconds per page. If both printers print at their respective rates, then, in terms of x and y, what is the total number of pages the two printers print in 1 hour?
Answer(s): A
1 hour = 3600 seconds.Printer P prints 1 page every x seconds, so in 3600 seconds it printsPrinter Q prints 1 page every y seconds, so in 3600 seconds it printsTotal pages in 1 hour are
FILL BLANKThe length of a diagonal of a square is 72. What is the perimeter of the square?
For a square, diagonal = side × 2.Perimeter = 4 × 7 = 28.
What percent of the integers between 1 and 650, inclusive, are less than 14?
Answer(s): B
Integers from 1 to 650 inclusive: 650 numbers.Integers less than 14 in this range: 1 through 13, which is 13 numbers.
Which of the following is a value of x for which x12 - x10 + x8 - x6 > 0?
Factor: x12 - x10 + x8 - x6 = x6(x6 - x4 + x2 - 1).Let t = x2. Then x6 - x4 + x2 - 1 = t3 - t2 + t - 1 = (t - 1)(t2 + 1).So the expression becomes x6(x2 - 1)(x4 + 1).x6 0 and x4 + 1 > 0 for all real x, so the expression is > 0 exactly when x2 - 1 > 0, i.e., |x| > 1.Only x = -2 satisfies this.
FILL BLANKAn order for bottles of vitamins from an online store costs $12.04 per bottle plus a shipping cost of $4.80 regardless of the number of bottles ordered. Over the past month, the store has received 100 orders for bottles of vitamins. The standard deviation of the numbers of bottles per order for the 100 orders is 1.5 bottles. What is the standard deviation of the 100 costs for the orders? (Enter your answer as an integer or a decimal in the answer box.)
Let n be the number of bottles in an order. The cost is C = 12.04n + 4.80.Adding 4.80 to every order does not change the standard deviation (SD).Multiplying by 12.04 multiplies SD by 12.04.So SDC = 12.04 × SDn = 12.04 × 1.5 = 18.06.
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