Set Q has 83 members.Quantity AThe number of subsets of Q that have 40 members or 41 membersQuantity BThe number of subsets of Q that have 42 members or 43 members
Answer(s): C
Because for any positive integer n,Hence
The value of a certain stock was N dollars when it was purchased. For the 3 one-year periods beginning with the date of purchase, the value of the stock at the end of each one-year period was 20 percent less than its value at the beginning of that period.Which of the following is closest to the value, in dollars, of the stock at the end of the 3 one-year periods?
Each year the stock loses 20% of its value, so it retains 80% = 0.80 of the value it had at the beginning of that year.After three successive one-year periods:N × 0.803 = N × 0.512 0.50N
The figure shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.The random variable W is normally distributed with mean 50 and standard deviation 9.Which of the following is closest to the value of W at the 25th percentile of the distribution?
Answer(s): D
On the normal-curve sketch, the first 16 % of the distribution lies to the left of m - d (2 % + 14 %).The 25th percentile is therefore 9% farther to the right (25 % - 16 % = 9 %) within the 34 % band that stretches from m - d to m.Hence the 25th-percentile point is about 0.26d to the right of m - d:m - d + 0.26d = m - 0.74dWith m = 50 and d = 9:50 - 0.74(9) 50 - 6.7 44.Thus, the value at the 25th percentile is closest to 44.
If a-2 + 6a-1 +9 = 0, then a =
Answer(s): A
We need to solve a2 + 6a-1 + 9 = 0Multiply by a(a 0):a3 + 9a + 6 = 0Numerically solving a3 + 9a + 6 = 0 gives one real root a -0.638Among the listed options the value closest to -0.638 is = -0.667
What is the units digit of 22222?
Powers of 2 repeat their units digits in a cycle of length 4:21 = 2 (mod 10)22 = 4 (mod 10)23 = 8 (mod 10)24 = 6 (mod 10)25 = 2 (mod 10)Thus, the units digit depends on the exponent mod 4.Compute 22222 mod 4:22222 ÷ 4 = 5555 remainder 2,so, 22222 2 (mod4).The remainder 2 corresponds to the second entry in the cycle, which has units digit 4.
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