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If x is a positive integer, what is the value of x?(1) The first nonzero digit in the decimal expansion of $$\frac{1}{x！} $$is in the hundredths place.(2) The first nonzero digit in the decimal expansion of$${1}\over{{(x+1)！}}$$ is in the thousandths place.
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Four concentric circles share the same center. The smallest circle has a radius of 1 inch. For n greater than 1, the area of the nth smallest circle in square inches,$$A_{n} $$, is given by $$A_{n}=A_{n-1}+(2n-1) \pi $$ What is the sum of the areas of the four circles, divided by the sum of their circumferences, in inches?
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Two positive numbers differ by 12 and their reciprocals differ by$$\frac{4}{5}$$ What is their product?
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If a, b, and c are positive integers, what is the remainder after b-a is divided by 3?(1)$$a=c^{3}$$(2)$$b={(c+1)}^{3}$$
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If $${{1}\over{x+2}}={{1}\over{x-2}}+{{1}\over{x+1}}$$, which of the following is a possible value of x?
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If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12) + 11 is
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Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?
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KMFPS
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$$x^{8}-y^{8}=$$
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Skier Lindsey Vonn completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. She then rides a chairlift back up the mountain the same distance at an average speed of (x - 8) meters per second. If the ride up the mountain took 135 seconds longer than her run down the mountain, what was her average speed, in meters per second, during her downhill run?
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The tens digit of$$6^{17}$$ is
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x is replaced by 1 - x everywhere in the expression $$\frac{1}{x}-{{1}\over{1-x}}$$, with$$x\neq0$$and$$x\neq1$$ and . If the result is then multiplied by$$x^{2}-x$$ , the outcome equals
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At the beginning of year 1, an investor puts p dollars into an investment whose value increases at a variable rate of $$x_n%$$per year, where n is an integer ranging from 1 to 3 indicating the year. If $$85\lt{x_n}\lt110$$ for all n between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between
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An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?
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If x and y are integers and x< y, what is the value of x + y?(1)$$x^{Y}=4$$(2) |x| = |y|
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A "Sophie Germain" prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is
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In the xy-plane, region Q consists of all points (x, y) such that$$x^{2}+y^{2}\le{100}$$ . Is the point (a, b) in region Q?(1)a + b = 14(2)a>b
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If $${v}\neq{0}$$,is$$ \mid w\mid$$<$$\mid v \mid$$?(1)$$\frac{w}{v}<{1}$$(2)$$\frac{w^2}{v^2}<{1}$$
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What is the 99th digit after the decimal point in the decimal expansion of$$\frac{2}{9}+\frac{3}{11}$$ ?
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$$\frac{3}{8}$$ of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. $$\frac{1}{2}$$ of all students are in Albanian, $$\frac{5}{8}$$ are in Bardic, and $$\frac{3}{4}$$ are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
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Although the initial setup of generators and a power grid by Edison and JP Morgan was rather costly, the electrification of lighting in lower Manhattan doubled work efficiency when the energy costs were cut in half.
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