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PREP07 Test 2
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If $$(2^x)(2^y) = 8$$ and $$(9^x)(3^y) = 81$$, then (x, y) =
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190603
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Mary has two methods to depart from A to C. The first one is A-B-C with speed of 80 meters per hour, and the other one is A-C with speed of 60 meters per hour. How many hours Mary used in A-C less than used in A-B-C?
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190321
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Five spaces will be filled with numbers 1-5 at random and use each number only once. What's the probability that these 5 numbers are arranged in order from large to small or from small to large?
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191031
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A has worked for 18 hours and B has worked for 6 hours. A is three times more efficient than B. So , what the fraction of (A + B) 's total workload is B's total workload ?
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Mary, Jane, and Lucy are typing a manuscript and are capable of completing the whole manuscript in $${2}\frac{1}{2}$$ hours if they work together. If Mary alone can type the same manuscript in 10 hours, and Jane is capable of typing the complete manuscript in 6 hours, in how many hours can Lucy type the whole manuscript?
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190302
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There are four small circles tangent to each other. The small circles are all inscribed in a large circle, as shown in the figure. The radii of small circles are all r. What is the ratio of the side length of the square formed by the line connecting four small circle centers to the diameter of the large circle?
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If the sequence $${x}_{1}$$, $${x}_{2}$$, $${x}_{3}$$, ..., $${x}_{n}$$, ... is such that $${x}_{1}={3}$$ and $${x}_{n+1}={2}{x}_{n}-{1}$$ for $$n\ge 1$$, then $${x}_{20}-{x}_{19}=$$
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Magoosh
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$$(1\frac{1}{6})$$x$$(1\frac{11}{21})$$=
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What is the value of $${t}^{-1}$$ ?(1) $${t}^{-2}<{1}$$(2) $${t}^{-3}=\frac{1}{27}$$
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1/x<1/x³？
（1）x>0
（2）x<1
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OG19-数学分册
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$$\frac{1}{3- \frac{1}{3- \frac{1}{3-1}}}$$=
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190310
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$$\frac{1}{(2n-1)!} - \frac{1}{(2n+1)!} = \frac{an^2+bn+c}{(2n+1)!}$$.a+b+c=?
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Ready4
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If k is negative, which of the following must also be negative?
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190310 还原机经选题: 文字题&几何 730高分节-数学测试
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54x,y12 is a six digit number. x,y can be 3, 5, or 8. The value of x and y may be the same. What's the probability that the number can be divided by eight?
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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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Magoosh
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A box contains 10 balls numbered from 1 to 10 inclusive. If Ann removes a ball at random and replaces it, and then Jane removes a ball at random, what is the probability that both women removed the same ball?
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A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow. If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?
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PREP07 Test 2
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 The figure shown represents a board with four rows of pegs, and at the bottom of the board are four cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end up in cell 2 ?
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PREP07 Test 1
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If $$\frac{x}{y}=\frac{2}{3}, then \frac{(x-y)}{x}=$$
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