In the xy-plane, line k is the of and line m has slope 2.If lines k and m have the same y-intercept, what is the x-intercept of line m?
Answer(s): E
Line k:Its y-intercept is 3.Line m has the same y-intercept and slope -2, so y = -2x + 3.Set y = 0 to find the x-intercept:
A stone was dropped into a still poad and produced concentric circular ripples on the surface of the water. The radius of the outermost ripple increased at a constant rate of x feet per second.If the area of the circular region enclosed by the outermost ripple was 400 square feet 10 seconds after the stone hit the water, what is the value of x?
Answer(s): B
Area of the outermost ripple after 10 seconds:A = 400 = r2So, r2 = 400 > r2 400 > r = 20Radius increases at a constant rate x feet per second, so after 10 seconds:r = 10xSet equal to 20:10x = 20 > x = 2.
Quantity AQuantity B2
Answer(s): C
In the right triangle, the hypotenuse is 2 and the base is 1, so the other leg is . Thus a = arctan = 60°and b = arcsin = 30°; therefore a/b = 60/30 = 2, equal to Quantity B.
Quantity AThe number of positive integers less than 50 that are the product of 2 different prime numbers greater than 2Quantity B5
Prime numbers greater than 2 are: 3, 5, 7, 11, 13, ...We list all products of two different such primes that are less than 50:3×5 = 153×7 = 213×11 = 333×13 = 395×7 = 35These 5 numbers are all below 50 and meet the conditions, so Quantity A = 5.
Of 20 tickets purchased for a concert, 12 tickets were purchased at prices from $60 to $80 each and the remaining 8 tickets were purchased at prices from $30 to $40 each.Quantity AThe average (arithmetic mean) price of the 20 ticketsQuantity BThe median price of the 20 tickets
The 8 cheapest tickets are between $30$40, and the 12 costlier tickets are between $60$80.In the ordered list of 20 prices, the 10th and 11th values (which determine the median) are both in the higher- price group, so the median is at least $60.The average, however, must be pulled below the median because:12 prices are high ($60$80),8 prices are much lower ($30$40).Even if all high tickets are $80 and all low tickets are $40, the average is:But in that case the median is 80, so the average is still lower.In every valid price assignment, the lower-price tickets reduce the mean below the median.Therefore, the median price (Quantity B) is always greater than the average (Quantity A).
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