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In a certain English class, $$\frac1 4$$ of the number of girls is equal to $$\frac1 6$$ of the total number of students. What is the ratio of the number of boys to the number of girls in the class?
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排列组合
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If a certain coin is flipped, the probability that the coin will land heads is $$\frac1 2$$. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
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If $$\frac{x}{y}=\frac{3}{2}$$,then $$\frac{x-y}{x}=$$
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0---:-|---:--|-:--:-|--:---|-:----1On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the least possible distance between any two of the tick marks?
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300难题
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For each positive integer k,let $$a_k$$= (1 +$$\frac{1}{k+1}$$). Is the product $$a_1$$, $$a_2$$...,$$a_n$$ an integer?
1. n +1 is a multiple of 3.
2. n is a multiple of 2.
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190124
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Which of the following options satisfy $$x^{-9}$$ - $$x^{-8}$$ > 0?
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190321
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$$\sqrt{x}+\frac{1}{ \sqrt{x} }=2$$.x = ?
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190113
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$$[3(x)^{-1}+3(y)^{-1}]{-1}$$=?
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190310
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$$(x^2+bx-1)(x^2-bx+1)=x^4-9x^2+6x-1$$.b>0,b=?
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OG16 OG17 OG18 OG19 OG20 OG2022
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Which of the following expressions can be written as an integer?(1) $$(\sqrt{82}+\sqrt{82})^{2}$$(2) $$({82})(\sqrt{82})$$(3) $$\frac{(\sqrt{82})(\sqrt{82})}{82}$$
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PREP07 Test 2
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A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?
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190124
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$$\sqrt{24}$$+$$\sqrt{12}$$=2a$$\sqrt{3}$$.a=?
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Is x negative?(1)$${x}^{3}(1-{x}^{2})<{0}$$(2)$${x}^{2}-1<{0}$$
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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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Is the sum of $${p}^{2}$$ and $${q}^{2}$$ greater than 1?(1) p is greater than $$\frac{1}{2}$$.(2) q is greater than $$\frac{1}{2}$$.
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190124
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$$( \sqrt{2}-1)^{-1}$$=?
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OG18-数学分册
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The sequence $$s_{1}$$, $$s_{2}$$, $$s_{3}$$, ...$$s_{n}$$,... is such that $$s_{n} = \frac{1}{n} - \frac{1}{n +1}$$ for all integers $$n\ge 1$$. If k is a positive integer, is the sum of the first k terms of the sequence greater than $$\frac{9}{10}$$?(1) k > 10(2) k < 19
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PREP07 Test 1
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for any integer k from 1 to 10, inclusion, the kth of a certain sequence is given by $$(-1)^{k+1}(\frac1 {2^k})$$. If T is the sum of the first 10 terms of the sequence, then T is:
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300难题
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What is the value of x ?
1.$$x^{4} +x^{2}$$ +1=$$\frac{1}{x^{4} +x^{2} +1}$$
2.$$x^{3}+x^{2}$$=0
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$$\frac {1}{1+(\frac{1}{2+\frac1 3})}$$=
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