FILL BLANKThe integer n is greater than 1, and set S = {5 - n, 5 - n2, 5 + n). If the difference between the greatest number in S and the least number in S is 72, what is the value of n? (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)
Answer(s): A
To determine the greatest and least numbers in the set, we need to compare the three values:5 - n5 - n25 + nWe know that the greatest number will have the highest value, and the least number will have the lowest value.Since n is greater than 1, we will try different values of n to find the one that satisfies the condition that the difference between the greatest and least numbers is 72.Try n = 9:The three numbers in the set are:5 - n = 5 - 9 = -45 - n2 = 5 - 92 = 5 - 81 = -765 + n = 5 + 9 = 14The greatest number is 14, and the least number is -76. The difference is:14 - (-76) = 14 + 76 = 90Since this is not 72, n = 9 is not the correct value.Try n = 8:The three numbers in the set are:5 - n = 5 - 8 = -35 - n2 = 5 - 82 = 5 - 64 = -595 + n = 5 + 8 = 13The greatest number is 13, and the least number is -59. The difference is:13 - (-59) = 13 + 59 = 72This is the correct difference. Thus, the value of n is 8.
FILL BLANKLast year the value of one share of a stock increased by 10 percent during the first half of the year, and the value of one share of the stock increased by 50 percent during the entire year. What was the percent increase in the value of one share of the stock during the second half of the year?Give your answer to the nearest whole percent. (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)
In the first half of the year, the value of the stock increased by 10 percent. So, the value of the stock at the end of the first half of the year is:Value after first half = x + 0.10x = 1.10xThe value of the stock increased by 50 percent during the entire year, so the value of the stock at the end of the year is:Value after second half = x + 0.50x = 1.50xThe value at the end of the first half is 1.10x, and the value at the end of the year is 1.50x. The increase during the second half of the year is:Increase during second half = 1.50x - 1.10x = 0.40xThe percent increase during the second half of the year is:Rounding to the nearest whole percent, the percent increase in the value of one share of the stock during the second half of the year is 36 percent.
FILL BLANKThe width of rectangle R is of the length. If the area of R is 84, what is the perimeter of R? (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)
Let the length of rectangle R be L, and the width be W. We are told that:The area of the rectangle is given as 84, so:Area = L × W = 843L2 = 588L2 = 196The perimeter P of a rectangle is given by:P = 2L + 2WP = 2(14) + 2(6) = 28 + 12 = 40
FILL BLANKGreg's weekly salary is $187, which is 15 percent less than Karla's weekly salary. If Karla's weekly salary increases by 10 percent, by what percent must Greg's weekly salary increase in order to equal Karla's new weekly salary?Give your answer to the nearest tenth of a percent. (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)
Since Greg's salary is 15% less than Karla's salary, let Karla's original salary be K. This means:Greg's salary = Karla's salary - 15% of Karla's salary187 = K - 0.15K187 = 0.85KK = 220Karla's salary increases by 10%, so her new salary is:New Karla's salary = 220 + 10% of 220220 + (0.10 × 220) = 220 + 22 = 242Greg's salary must increase from 187 to 242. The percentage increase is:
FILL BLANKThe circle shown has center O and radius 11. If PR = 12, what is the area of triangle PQR?Give your answer to the nearest 10. (Enter your answer as an integer or a decimal in the answer box.Backspace to erase.)
Radius of the circle = 11Diameter (QR) = 2 × 11 = 22Leg PR = 12Since QR is the diameter, and PQR is a right triangle, we can use the Pythagorean Theorem to find PQ.Compute the Area of Triangle PQR:Area 110
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