R1: -3, -2, -1R2: 1, 2, 3R1: -3, -2, -1, 1, 2, 3The standard deviations of the numbers in the lists R1, R2, and R3 are s1, s2, and s3, respectively. Which of the following is true?
Answer(s): B
Standard deviation measures how spread out the numbers are from the average (mean) of the list.If the numbers are close together, the standard deviation is small.If they are far apart, it is large.It is always positive or zero, but never negative.Compare R1 and R2R1 = {-3, -2, -1} Mean = -2R2 = {1, 2, 3} Mean = 2The numbers in both lists are spaced the same distance from their means:Each list has three numbersThey are equally spaced (1 unit apart)So, spread is the sameThat means s1 = s2Look at R3 = {-3, -2, -1, 1, 2, 3}This list has 6 numbers, from -3 to 3 (excluding 0).The mean = 0The values are more spread out than in R1 or R2So the standard deviation is largerThat means s3 > s1 = s2Eliminate wrong answers:s1 < 0 Impossible s1 = s2 True s2 > s1 False (they are equal)s3 = 0 False (spread exists)s1 + s2 = 0 False (they are both positive)
Which of the following is equivalent to y3 < y?
Answer(s): E
y3 - y < 0y(y2 - 1) < 0y(y - 1)(y + 1) < 0The factors are zero at y = -1, 0, 1.So the number line is divided into intervals:(-, -1), (-1, 0), (0, 1), (1, )We check the sign of y(y - 1)(y + 1):y < -1: pick y = -2(-2)(-3)(-1) = (-)(-)(-) = negative inequality holds-1 < y < 0: pick y = -0.5(-0.5)(-1.5)(0.5) = (-)(-)(+) = positive inequality does not hold 0 < y < 1: pick y = 0.5(0.5)(-0.5)(1.5) = (+)(-)(+) = negative inequality holds y > 1: pick y = 2(2)(1)(3) = positive inequality does not holdThe inequality holds when y < -1 or 0 < y < 1
If the product of integers a, b, c, and d is an even integer, which of the following statements about a, b, c,and d must be true?
A product is even if at least one factor is even. We don't need two evens. We don't need any restriction on odds. Zero would also make the product even (since 0 is even).
The SeaVille Oceanfront Hotel has two types of rooms; 70 percent of the rooms are standard rooms and the rest are deluxe rooms. Of the standard rooms, 10 percent have an ocean view, and of the deluxe rooms, 80 percent have an ocean view. If one room with an ocean view is to be selected at random, approximately what is the probability that the room selected will be a standard room?
Answer(s): C
Let total rooms = 100 (easy to work with).Standard rooms = 70Deluxe rooms = 30Standard ocean view = 10% of 70 = 7Deluxe ocean view = 80% of 30 = 24Total ocean-view rooms = 7 + 24 = 31
FILL BLANKMarion works as a salesperson at a clothing boutique. Her total daily earnings consist of a base daily salary of $120 and a commission equal to 10 percent of her daily sales. Marion's daily sales for Thursday were $800, and her total daily earnings for Friday were twice her total daily earnings for Thursday. What were Marion's daily sales for Friday?
Answer(s): A
Thursday:Daily sales = $800Commission = 10% of 800 = $80Total earnings (Thursday) = 120 + 80 = $200Friday:Total earnings = 2 × Thursday's earnings = 2 × 200 = $400Let x = Friday's sales120 + 0.10x = 4000.10x = 280x = 2800
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