idx int64 6 996 | query stringlengths 45 642 | response stringlengths 1.99k 33.2k | solution stringlengths 1 7 | token_ids listlengths 480 9.26k | logprobs listlengths 480 9.26k |
|---|---|---|---|---|---|
818 | Which number from the set \(\{1,2,3,4,5,6,7,8,9,10,11\}\) must be removed so that the mean (average) of the numbers remaining in the set is 6.1?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8 | Okay, so I have this problem here: I need to figure out which number from the set {1,2,3,4,5,6,7,8,9,10,11} has to be removed so that the average of the remaining numbers is 6.1. The options are 4,5,6,7, or 8. Let me think step by step.
First, I remember that the average is the sum of the numbers divided by how many n... | 5 | [
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463 | Tapanga and Corey have 66 candies together. However, Tapanga has 8 more candies than Corey. How many candies does Corey have? | Okay, so Tapanga and Corey together have 66 candies. And Tapanga has 8 more candies than Corey. I need to find out how many candies Corey has. Hmm, let's see.
Alright, let me start by breaking down the problem. Let's denote the number of candies Corey has as a variable. Let's say Corey has C candies. Then, since Tapa... | 29 | [
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101 | "Given the binomial distribution $\\xi\\sim B(4, \\frac{1}{2})$, the value of the variance $D\\xi$ i(...TRUNCATED) | "Okay, so I need to find the variance of a binomial distribution given by ξ ~ B(4, 1/2). Hmm, let m(...TRUNCATED) | 1 | [33413,11,779,358,1205,311,1505,279,33373,315,264,9736,21524,8141,2728,555,8008,122,4056,426,7,19,11(...TRUNCATED) | [-0.020743101835250854,-0.000010371154530730564,-0.07893876731395721,-0.000014781842764932662,-0.112(...TRUNCATED) |
942 | "After learning about \"removing the denominator,\" student Min Hui tried to calculate $\\frac{3}{5}(...TRUNCATED) | "Okay, let me try to figure this out. So the question is about whether Min Hui's method of \"removin(...TRUNCATED) | 1 | [33413,11,1095,757,1456,311,7216,420,704,13,2100,279,3488,374,922,3508,3468,473,2005,596,1749,315,33(...TRUNCATED) | [-0.0069510783068835735,-2.264974000354414e-6,-0.6827404499053955,-0.8981736898422241,-0.16232967376(...TRUNCATED) |
164 | Given $x^{2}+y^{2}=4$ and $\left(x-y\right)^{2}=5$, find $\left(x+y\right)^{2}$. | "Okay, so I need to find (x + y)² given that x² + y² = 4 and (x - y)² = 5. Hmm, let me think abo(...TRUNCATED) | 3 | [33413,11,779,358,1205,311,1505,320,87,489,379,8,30556,2728,430,865,30556,489,379,30556,284,220,19,3(...TRUNCATED) | [-0.05518987029790878,-2.264974000354414e-6,-0.252037912607193,-1.1920928244535389e-7,-0.82840776443(...TRUNCATED) |
194 | "A teacher asks her class what the value of $\\left(5^2-4^2\\right)^3$ is. What is the value of the(...TRUNCATED) | "Okay, so the teacher asked the class to find the value of (5² - 4²)³. Hmm, let me think about ho(...TRUNCATED) | 729 | [33413,11,779,279,11326,4691,279,538,311,1505,279,907,315,320,20,30556,482,220,19,30556,8,44301,13,8(...TRUNCATED) | [-0.012952128425240517,-5.602820692729438e-6,-0.3218311369419098,-0.055015452206134796,-0.2812575697(...TRUNCATED) |
302 | "Given that the square root of $a+1$ is $\\pm 2$, and the cube root of $2a+b-2$ is $2$, find the ari(...TRUNCATED) | "Okay, let me try to solve this problem step by step. So, the problem says:\n\n\"Given that the squa(...TRUNCATED) | 5 | [33413,11,1095,757,1456,311,11886,420,3575,3094,555,3094,13,2100,11,279,3575,2795,1473,1,22818,430,2(...TRUNCATED) | [-0.04936204478144646,-4.291525328881107e-6,-0.6931921243667603,-1.053743839263916,-0.28188785910606(...TRUNCATED) |
334 | "Given the proposition \"$a > b$ implies $ac^{2} > bc^{2}$\", determine the number of true statement(...TRUNCATED) | "Okay, so I need to figure out how many of the converse, negation, and contrapositive of the stateme(...TRUNCATED) | 2 | [33413,11,779,358,1205,311,7216,704,1268,1690,315,279,95340,11,4277,367,11,323,6155,31515,3486,315,2(...TRUNCATED) | [-0.03397848457098007,-1.9073468138230965e-6,-0.3869125545024872,-0.00012361239350866526,-0.20142844(...TRUNCATED) |
729 | "The \"Stacked Multiplication\" problem in the important work \"Detailed Explanation of the Nine Cha(...TRUNCATED) | "Okay, so I need to figure out the 15th term of this second-order arithmetic sequence given the firs(...TRUNCATED) | 198 | [33413,11,779,358,1205,311,7216,704,279,220,868,339,4751,315,420,2132,24747,35884,8668,2728,279,1176(...TRUNCATED) | [-0.04375249519944191,-8.34461570775602e-6,-0.34928926825523376,-0.00004362964682513848,-0.316352754(...TRUNCATED) |
103 | Evaluate the integral $$\int_{0}^{2}(2-|1-x|)dx=\_\_\_\_\_\_.$$ | "Okay, so I need to evaluate the integral from 0 to 2 of (2 minus the absolute value of (1 minus x))(...TRUNCATED) | 3 | [33413,11,779,358,1205,311,15806,279,26154,505,220,15,311,220,17,315,320,17,28382,279,10973,907,315,(...TRUNCATED) | [-0.043360237032175064,-2.3841830625315197e-6,-0.03604317456483841,0.0,-0.06994067877531052,0.0,-0.0(...TRUNCATED) |
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