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15,574
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nSimplify the sum \\( (...TRUNCATED)
["<think>\nOkay, so I need to simplify the sum \\( \\large\\sum_{i=0}^{50} \\binom{100}{2i} \\). Hmm(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
[ 1, 1, 1, 1, 264, 264, 264, 264, 446, 446, 446, 446, 712, 712, 712, 712 ]
940
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nJohn needs to catch a(...TRUNCATED)
["<think>\nOkay, let me try to figure out this problem. So, there's a train that arrives randomly be(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 221, 221, 221, 221, 468, 468, 468, 468, 678, 678, 678, 678 ]
2,818
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nDetermine the range o(...TRUNCATED)
["<think>\nOkay, let's see. I need to find the range of values for \\( a + b \\) such that \\( a \\c(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]
[ 1, 1, 1, 1, 357, 357, 357, 357, 550, 550, 550, 550, 716, 716, 716, 716 ]
9,467
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nEvaluate the limit: \(...TRUNCATED)
["<think>\nOkay, so I need to find the limit as x approaches 0 of (square root of 1 + 4x minus 1 min(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 ]
[ 1, 1, 1, 1, 235, 235, 235, 235, 537, 537, 537, 537, 707, 707, 707, 707 ]
558
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nA ball was floating i(...TRUNCATED)
["<think>\nOkay, so I need to find the radius of a ball that was floating on the lake and then remov(...TRUNCATED)
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
[ 1, 1, 1, 1, 293, 293, 293, 293, 476, 476, 476, 476, 705, 705, 705, 705 ]
6,621
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nDetermine the dimensi(...TRUNCATED)
["<think>\nOkay, so I need to figure out the dimension of the vector space H_n, which consists of n(...TRUNCATED)
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0 ]
[ 1, 1, 1, 1, 313, 313, 313, 313, 467, 467, 467, 467, 758, 758, 758, 758 ]
4,240
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nAt the World Meteorol(...TRUNCATED)
["<think>\nOkay, let me try to figure out this problem. Alright, so there's this World Meteorologica(...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 373, 373, 373, 373, 569, 569, 569, 569, 732, 732, 732, 732 ]
9,065
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nFind the eccentricity(...TRUNCATED)
["Okay, so I need to find the eccentricity of the conic section represented by the equation 10x - 2x(...TRUNCATED)
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
[ 1, 1, 1, 1, 408, 408, 408, 408, 488, 488, 488, 488, 763, 763, 763, 763 ]
26,066
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nFind the seven soluti(...TRUNCATED)
["Okay, so I need to find the seven solutions to the congruence x^7 ≡ 1 mod 29. I remember that 2 (...TRUNCATED)
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 1, 309, 309, 309, 309, 579, 579, 579, 579, 678, 678, 678, 678 ]
21,024
"<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n<|im_start|>user\nEvaluate the limit \\(...TRUNCATED)
["<think>\nOkay, so I need to evaluate the limit as x approaches 0 from the positive side of the exp(...TRUNCATED)
[ 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ]
[ 1, 1, 1, 1, 365, 365, 365, 365, 425, 425, 425, 425, 742, 742, 742, 742 ]
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