and xy ≠ 0Quantity AxQuantity By
Answer(s): B
Multiply both sides by xy (allowed since xy 0):y - x = 1y = x + 1y > x
Six patients have undergone a certain operation. In the graph above, p(x) denotes the probability that exactly x of the patients will have recovered within one month.Quantity AThe probability that at least 2 and at most 4 patients will have recovered within one monthQuantity BThe probability that at least 1 and at most 3 patients will have recovered within one month
Answer(s): A
Quantity A:Probability that at least 2 and at most 4 patients recover:p(2) + p(3) + p(4) = 0.234 + 0.314 + 0.234 = 0.782Quantity B:Probability that at least 1 and at most 3 patients recover:p(1) + p(2) + p(3) = 0.093 + 0.234 + 0.314 = 0.641
x > 0Quantity Ax percent of 30Quantity B30 percent of x
Answer(s): C
A certain rectangular solid has height g and a base with dimensions 8 by 10. A certain right circular cylinder has height h, diameter 10, and the same volume as the rectangular solid.Quantity AgQuantity Bh
Volume of rectangular solidBase = 8 × 10 = 80Height = gSo, volume = 80gVolume of cylinderDiameter = 10 radius = 5Base area = (52) = 25Height = hSo, volume = 25hEquating volumes80g = 25hCompare g and hg < h
Quantity AxQuantity B
Answer(s): D
x - 2 = (x - 2)2(x - 2)2 - (x - 2) = 0(x - 2)((x - 2) - 1) = 0(x - 2)(x - 3) = 0x = 2 or x = 3Since we're given x 2, both x = 2 and x = 3 are valid. Since both values of x are possible, and they give different outcomes, the relationship cannot be determined without knowing which x is used.
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