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train · 47.7k rows

problem stringlengths 14 2k	images unknown	answer stringlengths 9 199
<image> As shown in the figure, in the square $OABC$, is $OB$ perpendicular to $AC$? (Answer "Yes" or "No")	137,80,78,71,13,10,26,10,0,0,0,13,73,72,68,82,0,0,2,247,0,0,2,91,8,2,0,0,0,239,195,44,121,0,0,165,163,73,68,65,84,120,156,236,221,103,92,20,87,251,55,240,89,202,178,160,52,93,17,11,162,168,136,177,99,23,53,198,26,123,73,140,49,198,222,147,168,177,195,178,192,2,11,8,26,53,104,140,209,68,141,177,38,118,99,215,196,134,21,177,96,65,68,4,17,69,64,169,82,22,150,125,94,204,253,156,255,4,16,129,45,83,246,247,125,113,127,230,28,150,153,43,183,204,236,53,167,138,150,47,95,190,98,197,10,10,0,0,0,64,88,76,216,14,0,0,0,0,64,47,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,132,44,7,0,0,0,132,9,89,14,0,0,0,8,19,178,28,0,0,0,16,38,100,57,0,0,0,32,76,200,114,0,0,0,64,152,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,132,44,7,0,0,0,132,9,89,14,0,0,0,8,19,178,28,0,0,0,16,38,100,57,0,0,0,32,76,200,114,0,0,0,64,152,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,132,44,7,0,0,0,132,9,89,14,0,0,0,8,19,178,28,0,0,0,16,38,100,57,0,0,0,32,76,200,114,0,0,0,64,152,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,132,44,7,0,0,0,132,9,89,14,0,0,0,8,19,178,28,0,0,0,16,38,100,57,0,0,0,32,76,200,114,0,0,0,64,152,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,132,44,7,0,0,0,132,9,89,14,0,0,0,8,19,178,28,0,0,0,16,38,100,57,0,0,0,32,76,200,114,0,0,0,64,152,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,132,44,7,0,0,0,132,9,89,14,0,0,0,8,19,178,28,0,0,0,16,38,100,57,0,0,0,32,76,200,114,0,0,0,64,152,144,229,0,0,0,128,48,33,203,1,0,0,0,97,66,150,3,0,0,0,194,100,198,118,0,0,80,101,233,233,233,37,37,37,164,152,154,154,170,209,104,74,125,198,206,206,206,194,194,130,89,20,139,197,6,138,15,0,128,27,144,229,0,176,47,59,59,187,160,160,224,245,235,215,133,133,133,217,217,217,153,153,153,5,5,5,105,105,105,121,121,121,185,185,185,111,223,190,45,44,44,76,79,79,215,213,229,106,214,172,105,101,101,37,149,74,37,18,137,189,189,189,181,181,181,165,165,101,157,58,117,36,18,137,173,173,45,157,30,57,56,56,232,234,114,0,0,108,65,150,3,96,56,89,89,89,175,95,191,78,77,77,37,255,75,31,20,21,21,25,50,140,220,220,220,220,220,220,212,212,212,138,63,38,149,74,29,28,28,234,214,173,75,255,47,57,48,76,144,0,0,218,67,150,3,160,23,57,57,57,9,9,9,9,9,9,47,95,190,36,105,77,65,65,1,219,113,85,65,122,122,122,122,122,250,195,135,15,75,213,147,116,167,126,253,250,13,27,54,108,220,184,177,163,163,35,43,17,2,0,84,12,89,14,128,14,168,213,234,231,207,159,63,127,254,60,62,62,62,41,41,233,233,211,167,25,25,25,186,58,185,173,173,173,133,133,5,179,17,69,42,149,154,152,252,223,212,129,114,123,151,178,178,178,10,11,11,73,49,35,35,131,180,24,101,101,101,21,20,20,124,176,45,231,125,232,38,168,232,232,104,82,99,105,105,233,228,228,212,180,105,211,70,141,26,53,110,220,184,113,227,198,53,106,212,168,222,201,1,0,116,8,89,14,64,117,20,20,20,60,126,252,248,233,211,167,79,159,62,77,74,74,74,74,74,82,171,213,213,56,143,181,181,181,131,131,67,157,58,117,106,212,168,33,149,74,45,44,44,106,213,170,85,179,102,77,122,160,140,165,165,165,173,173,173,206,131,39,10,10,10,200,48,160,244,244,244,188,188,188,156,156,28,122,24,80,90,90,218,235,215,175,43,57,24,40,63,63,63,54,54,54,54,54,150,212,72,165,82,23,23,151,134,13,27,54,111,222,188,69,139,22,82,169,84,111,255,17,0,0,239,133,44,7,160,178,210,211,211,31,61,122,20,19,19,243,224,193,131,132,132,4,230,44,167,15,178,180,180,44,59,192,165,110,221,186,86,86,86,250,11,248,131,36,18,137,68,34,169,96,160,177,90,173,38,227,135,232,78,55,186,248,193,150,42,186,183,235,198,141,27,116,177,78,157,58,110,110,110,31,125,244,81,203,150,45,155,52,105,34,18,137,116,249,159,1,0,240,30,200,114,0,222,75,163,209,60,123,246,236,209,255,151,150,150,86,201,95,180,181,181,117,113,113,161,187,111,156,157,157,235,214,173,107,109,109,173,215,80,245,196,212,212,180,94,189,122,245,234,213,43,85,175,82,169,94,191,126,157,156,156,156,152,152,72,119,210,189,120,241,162,130,243,164,165,165,165,165,165,93,186,116,137,162,40,75,75,75,55,55,55,58,233,105,209,162,133,68,34,209,227,127,0,0,24,55,100,57,0,165,61,127,254,60,50,50,242,238,221,187,49,49,49,249,249,249,31,252,188,88,44,166,7,225,54,105,210,164,81,163,70,46,46,46,122,237,102,226,2,177,88,236,228,228,228,228,228,212,173,91,55,186,166,176,176,48,41,41,41,62,62,62,49,49,49,49,49,241,217,179,103,57,57,57,229,254,110,126,126,254,237,219,183,111,223,190,77,81,148,72,36,106,210,164,73,219,182,109,59,118,236,248,209,71,31,153,155,155,27,238,191,1,0,140,0,178,28,0,138,250,255,95,189,81,81,81,81,81,81,31,28,140,66,127,55,183,108,217,178,101,203,150,141,27,55,118,114,114,66,23,140,133,133,69,179,102,205,154,53,107,70,106,50,50,50,158,62,125,250,228,201,147,135,15,31,62,126,252,184,220,249,101,26,141,38,62,62,62,62,62,254,208,161,67,18,137,164,117,235,214,157,59,119,238,208,161,3,38,109,1,128,78,32,203,1,163,246,236,217,179,91,183,110,69,69,69,61,122,244,168,226,225,195,18,137,164,69,139,22,31,125,244,17,221,219,98,105,105,105,176,32,121,202,222,222,190,83,167,78,157,58,117,162,254,127,223,223,131,7,15,98,98,98,30,61,122,84,110,30,89,80,80,16,25,25,25,25,25,73,81,84,131,6,13,220,2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The below problem is with the following images: <image> Given a poll that identifies the proportions of high-income and low-income voters who support a decrease in taxes, determine the sample size needed to achieve a margin of error of ±0.02 at the 95% confidence interval.	255,216,255,225,5,100,69,120,105,102,0,0,77,77,0,42,0,0,0,8,0,12,1,0,0,3,0,0,0,1,2,32,0,0,1,1,0,3,0,0,0,1,0,108,0,0,1,2,0,3,0,0,0,3,0,0,0,158,1,6,0,3,0,0,0,1,0,2,0,0,1,18,0,3,0,0,0,1,0,1,0,0,1,21,0,3,0,0,0,1,0,3,0,0,1,26,0,5,0,0,0,1,0,0,0,164,1,27,0,5,0,0,0,1,0,0,0,172,1,40,0,3,0,0,0,1,0,2,0,0,1,49,0,2,0,0,0,34,0,0,0,180,1,50,0,2,0,0,0,20,0,0,0,214,135,105,0,4,0,0,0,1,0,0,0,236,0,0,1,36,0,8,0,8,0,8,0,45,198,192,0,0,39,16,0,45,198,192,0,0,39,16,65,100,111,98,101,32,80,104,111,116,111,115,104,111,112,32,67,67,32,50,48,49,55,32,40,87,105,110,100,111,119,115,41,0,50,48,50,48,58,48,49,58,48,55,32,49,54,58,49,49,58,51,50,0,0,0,0,4,144,0,0,7,0,0,0,4,48,50,50,49,160,1,0,3,0,0,0,1,255,255,0,0,160,2,0,4,0,0,0,1,0,0,1,16,160,3,0,4,0,0,0,1,0,0,0,54,0,0,0,0,0,0,0,6,1,3,0,3,0,0,0,1,0,6,0,0,1,26,0,5,0,0,0,1,0,0,1,114,1,27,0,5,0,0,0,1,0,0,1,122,1,40,0,3,0,0,0,1,0,2,0,0,2,1,0,4,0,0,0,1,0,0,1,130,2,2,0,4,0,0,0,1,0,0,3,218,0,0,0,0,0,0,0,72,0,0,0,1,0,0,0,72,0,0,0,1,255,216,255,237,0,12,65,100,111,98,101,95,67,77,0,2,255,238,0,14,65,100,111,98,101,0,100,128,0,0,0,1,255,219,0,132,0,12,8,8,8,9,8,12,9,9,12,17,11,10,11,17,21,15,12,12,15,21,24,19,19,21,19,19,24,17,12,12,12,12,12,12,17,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,1,13,11,11,13,14,13,16,14,14,16,20,14,14,14,20,20,14,14,14,14,20,17,12,12,12,12,12,17,17,12,12,12,12,12,12,17,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,255,192,0,17,8,0,13,0,65,3,1,34,0,2,17,1,3,17,1,255,221,0,4,0,5,255,196,1,63,0,0,1,5,1,1,1,1,1,1,0,0,0,0,0,0,0,3,0,1,2,4,5,6,7,8,9,10,11,1,0,1,5,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,2,3,4,5,6,7,8,9,10,11,16,0,1,4,1,3,2,4,2,5,7,6,8,5,3,12,51,1,0,2,17,3,4,33,18,49,5,65,81,97,19,34,113,129,50,6,20,145,161,177,66,35,36,21,82,193,98,51,52,114,130,209,67,7,37,146,83,240,225,241,99,115,53,22,162,178,131,38,68,147,84,100,69,194,163,116,54,23,210,85,226,101,242,179,132,195,211,117,227,243,70,39,148,164,133,180,149,196,212,228,244,165,181,197,213,229,245,86,102,118,134,150,166,182,198,214,230,246,55,71,87,103,119,135,151,167,183,199,215,231,247,17,0,2,2,1,2,4,4,3,4,5,6,7,7,6,5,53,1,0,2,17,3,33,49,18,4,65,81,97,113,34,19,5,50,129,145,20,161,177,66,35,193,82,209,240,51,36,98,225,114,130,146,67,83,21,99,115,52,241,37,6,22,162,178,131,7,38,53,194,210,68,147,84,163,23,100,69,85,54,116,101,226,242,179,132,195,211,117,227,243,70,148,164,133,180,149,196,212,228,244,165,181,197,213,229,245,86,102,118,134,150,166,182,198,214,230,246,39,55,71,87,103,119,135,151,167,183,199,255,218,0,12,3,1,0,2,17,3,17,0,63,0,244,124,78,175,139,151,143,110,77,65,254,157,71,73,110,182,15,77,153,45,125,12,4,189,254,165,54,49,236,255,0,8,170,89,157,110,69,212,101,83,148,42,197,178,189,107,16,231,106,108,99,158,28,198,100,82,235,119,122,79,250,95,161,126,55,163,255,0,106,108,244,239,31,217,223,106,108,236,245,189,43,118,248,122,123,153,246,175,248,63,231,125,63,89,29,194,105,34,130,26,118,159,76,128,8,6,61,190,217,110,239,243,146,83,131,110,73,182,170,176,29,149,141,145,109,52,203,154,247,189,182,155,131,77,117,58,193,233,222,255,0,77,204,183,215,251,71,167,190,171,169,103,232,236,251,79,234,250,7,172,116,188,42,234,162,252,128,215,138,152,253,90,126,132,56,122,174,244,235,99,24,207,209,89,254,14,165,30,152,58,135,218,73,189,223,163,216,239,180,49,173,110,207,180,122,134,92,203,28,239,180,108,244,118,250,45,117,95,204,122,95,225,22,145,244,247,107,27,187,76,74,74,104,85,214,168,177,129,237,173,238,222,203,223,88,110,210,92,49,236,110,54,214,55,112,253,37,239,177,158,146,7,252,231,192,24,246,228,57,175,2,168,253,24,18,247,29,150,222,237,141,209,158,159,165,143,115,217,103,169,250,95,79,254,35,214,211,253,91,211,252,207,78,15,134,216,159,119,253,36,238,244,99,223,182,37,188,196,110,145,233,127,107,126,207,77,37,33,200,234,20,208,105,107,193,221,125,141,168,9,0,53,206,1,193,182,188,187,99,29,238,246,51,233,219,254,9,82,111,214,76,39,87,91,195,30,209,110,232,222,90,208,208,209,91,183,88,253,219,91,252,253,123,255,0,209,126,177,234,255,0,70,185,93,198,253,159,180,250,27,35,214,178,103,159,87,115,189,127,167,238,245,61,68,103,122,16,237,219,35,93,211,28,123,183,110,255,0,193,18,83,145,255,0,58,106,255,0,184,25,95,248,7,254,245,36,180,255,0,201,255,0,240,63,244,82,73,79,255,217,255,237,13,20,80,104,111,116,111,115,104,111,112,32,51,46,48,0,56,66,73,77,4,4,0,0,0,0,0,23,28,1,90,0,3,27,37,71,28,1,90,0,3,27,37,71,28,2,0,0,2,0,0,0,56,66,73,77,4,37,0,0,0,0,0,16,199,93,23,229,116,181,110,245,219,190,57,148,192,233,121,92,56,66,73,77,4,58,0,0,0,0,0,247,0,0,0,16,0,0,0,1,0,0,0,0,0,11,112,114,105,110,116,79,117,116,112,117,116,0,0,0,5,0,0,0,0,80,115,116,83,98,111,111,108,1,0,0,0,0,73,110,116,101,101,110,117,109,0,0,0,0,73,110,116,101,0,0,0,0,67,108,114,109,0,0,0,15,112,114,105,110,116,83,105,120,116,101,101,110,66,105,116,98,111,111,108,0,0,0,0,11,112,114,105,110,116,101,114,78,97,109,101,84,69,88,84,0,0,0,10,0,65,0,100,0,111,0,98,0,101,0,32,0,80,0,68,0,70,0,0,0,0,0,15,112,114,105,110,116,80,114,111,111,102,83,101,116,117,112,79,98,106,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<image>As shown in the figure, if D and E are points on sides AB and AC of △ABC respectively, and ∠AED = ∠B, AD = 3, AC = 6, DB = 5, then the length of AE is ().	137,80,78,71,13,10,26,10,0,0,0,13,73,72,68,82,0,0,0,126,0,0,0,103,8,2,0,0,0,73,152,97,140,0,0,13,123,73,68,65,84,120,156,237,93,95,108,219,68,24,63,151,149,160,17,20,193,10,203,67,85,39,109,42,2,12,41,83,169,40,26,194,125,88,214,193,226,53,136,77,3,105,210,50,52,232,16,72,52,244,143,42,241,144,241,196,159,173,106,95,144,72,82,180,189,128,82,254,173,67,169,182,226,76,114,52,96,41,65,100,72,149,90,68,194,210,238,129,84,69,52,104,147,72,186,144,227,225,214,171,103,59,142,99,59,105,211,230,247,16,57,231,187,207,151,95,62,127,119,247,125,223,217,4,132,16,212,160,20,161,80,200,108,54,183,180,180,40,104,91,167,121,111,182,20,236,118,187,226,182,53,234,149,99,112,112,144,166,105,101,42,15,0,32,106,6,71,25,124,62,95,115,115,179,221,110,87,76,96,77,235,149,32,145,72,0,0,204,102,51,77,211,138,133,212,168,87,2,175,215,251,250,235,175,3,0,172,86,171,98,33,53,234,75,134,207,231,59,125,250,52,65,16,22,139,69,141,156,109,90,117,104,139,0,153,26,100,223,67,161,208,31,127,252,161,88,84,141,250,18,144,72,36,220,110,247,183,223,126,139,190,170,225,29,0,0,96,13,50,144,207,231,7,6,6,16,99,241,120,28,66,136,7,216,193,193,65,101,50,107,147,75,85,128,16,18,4,161,172,109,109,152,149,133,66,10,170,152,119,80,163,94,38,138,82,172,192,120,212,168,47,13,225,112,248,179,207,62,19,150,43,80,255,26,245,37,32,24,12,118,117,117,205,204,204,0,69,106,206,67,141,122,185,8,4,2,111,188,241,134,219,237,142,199,227,64,157,149,191,3,173,166,95,155,15,249,124,30,31,251,124,62,146,36,103,103,103,167,167,167,109,54,155,38,242,107,212,23,199,232,232,168,213,106,77,38,147,16,194,84,42,101,48,24,52,17,91,163,190,8,60,30,207,227,143,63,254,231,159,127,226,18,157,78,151,78,167,213,75,174,217,122,41,184,221,238,96,48,248,227,143,63,26,141,70,92,104,177,88,174,95,191,174,94,120,141,250,130,112,185,92,177,88,140,101,89,131,193,192,45,111,109,109,77,38,147,234,229,215,220,103,34,200,229,114,175,188,242,74,38,147,153,154,154,210,233,116,188,179,38,147,105,126,126,94,253,85,106,90,207,71,54,155,125,241,197,23,1,0,19,19,19,66,222,1,0,38,147,73,19,173,175,81,127,23,110,221,186,213,213,213,213,208,208,240,197,23,95,220,115,207,61,162,117,72,146,156,155,155,83,127,173,26,245,107,248,231,159,127,58,59,59,119,239,222,125,246,236,89,137,21,83,77,235,53,198,226,226,226,158,61,123,28,14,199,200,200,8,183,28,10,28,6,38,147,73,147,25,206,22,157,215,115,87,170,16,194,100,50,105,181,90,71,70,70,100,54,111,104,104,72,165,82,42,251,176,21,181,30,222,29,223,152,155,155,163,40,170,175,175,175,183,183,87,162,9,247,171,197,98,81,111,115,182,34,245,4,177,22,155,187,118,237,154,221,110,255,240,195,15,79,156,56,81,168,62,20,132,162,72,146,84,79,253,22,157,215,35,42,167,167,167,157,78,231,216,216,216,129,3,7,138,86,230,194,108,54,215,180,94,57,194,225,176,211,233,28,31,31,151,230,93,20,38,147,9,185,142,17,160,34,223,253,22,165,126,114,114,242,229,151,95,158,152,152,120,238,185,231,228,16,199,171,99,50,153,126,255,253,119,252,21,223,22,165,253,7,42,135,233,106,68,32,16,104,108,108,140,197,98,37,181,226,78,138,102,103,103,73,146,84,217,141,45,71,189,223,239,71,203,81,53,66,50,153,140,78,167,203,229,114,106,132,108,45,234,185,65,15,153,224,173,0,48,208,36,71,77,103,182,144,173,63,117,234,148,223,239,103,89,150,36,73,249,173,10,121,20,212,187,19,170,134,122,184,58,130,65,69,211,9,20,244,248,225,135,31,118,238,220,169,73,127,212,207,47,171,102,94,143,181,79,65,42,192,241,227,199,175,95,191,206,178,172,94,175,7,234,178,245,48,72,146,84,233,201,169,26,173,7,0,116,119,119,19,119,163,104,147,255,254,251,239,240,225,195,127,253,245,215,212,212,20,226,29,148,254,231,9,239,51,8,161,217,108,86,233,58,174,38,234,47,92,184,64,211,52,74,244,133,16,14,12,12,72,147,152,205,102,157,78,39,65,16,19,19,19,247,222,123,175,226,235,10,175,66,16,132,201,100,90,88,88,80,44,19,84,17,245,88,245,240,142,189,143,62,250,136,166,233,193,193,65,209,250,188,160,135,6,25,75,119,131,231,58,86,48,2,85,13,245,4,65,48,12,195,219,187,100,181,90,69,239,122,110,208,163,76,253,105,106,106,90,94,94,206,102,179,184,123,165,74,216,208,212,243,84,137,97,152,125,251,246,113,75,68,119,51,161,160,7,77,211,188,160,135,80,160,26,16,4,97,54,155,213,140,180,27,154,122,158,42,157,62,125,122,239,222,189,220,146,120,60,206,187,15,230,231,231,59,59,59,95,123,237,53,143,199,83,84,160,26,64,8,213,166,38,168,89,143,85,18,241,120,124,96,96,0,29,163,21,38,242,29,50,12,131,235,32,215,138,223,239,175,76,151,122,122,122,62,249,228,19,252,181,208,186,183,16,170,102,94,31,10,133,176,121,65,202,235,118,187,105,154,70,247,193,207,63,255,188,109,219,54,135,195,49,60,60,124,228,200,17,168,197,204,189,40,120,243,203,146,175,168,177,38,148,13,96,117,255,24,92,213,119,154,166,209,215,100,50,169,215,235,183,111,223,254,205,55,223,84,178,75,129,64,192,233,116,42,110,94,5,212,51,12,35,84,40,174,157,97,89,246,225,135,31,182,217,108,86,171,245,151,95,126,169,88,199,162,209,40,78,248,70,214,166,36,155,83,5,212,139,2,255,200,96,48,104,52,26,35,145,8,132,240,204,153,51,122,189,254,253,247,223,23,173,89,84,84,169,72,167,211,106,18,190,171,149,122,4,97,208,99,102,10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<image> A $p$-$n$ junction includes $p$-type silicon, with donor atom density $N_D$, adjacent to $n$-type silicon, with acceptor atom density $N_A$. Near the junction, free electrons from the $n$ side have diffused into the $p$ side while free holes from the $p$ side have diffused into the $n$ side, leaving a “depletion region” of width $W$ where there are no free charge carriers. The width of the depletion region on the $n$ side is $a_n$, and the width of the depletion region on the $p$ side is $a_p$. Each depleted region has a constant charge density with magnitude equal to the corresponding donor atom density. Assume there is no net charge outside the depleted regions. Define an $x$-axis pointing from the $p$ side toward the $n$ side with the origin at the center of the junction. An electric field $\vec{E} = -E\hat{\imath}$ has developed in the depletion region, stabilizing the diffusion. Question: The $p$ side is doped with boron atoms with density $N_A = 1.00 \times 10^{16}\ cm^{-3}$. The $n$ side is doped with arsenic atoms with density $N_D = 5.00 \times 10^{16}\ cm^{-3}$. The $n$ side depletion depth is $a_n = 55.0\ nm$. What is the $p$ side depletion depth $a_p$? Choices: A: "275nm" B: "399nm" C: "250nm" D: "0.350nm"	137,80,78,71,13,10,26,10,0,0,0,13,73,72,68,82,0,0,3,236,0,0,1,234,8,2,0,0,0,17,125,83,235,0,0,12,75,105,67,67,80,73,67,67,32,80,114,111,102,105,108,101,0,0,72,137,149,87,7,88,83,201,22,158,91,82,33,4,8,68,64,74,232,77,16,145,18,64,74,8,45,128,244,34,136,74,72,2,132,18,99,66,80,177,163,139,10,174,93,68,176,162,171,32,138,29,16,177,97,87,22,197,238,90,22,11,42,43,235,98,193,174,188,9,1,116,217,87,190,55,223,55,119,254,251,207,153,127,206,57,119,230,222,59,0,208,219,249,82,105,14,170,9,64,174,36,79,22,19,236,207,26,151,148,204,34,117,2,28,16,1,10,28,1,129,47,144,75,57,81,81,225,0,150,129,246,239,229,221,77,128,40,219,107,14,74,173,127,246,255,215,162,37,20,201,5,0,32,81,16,167,9,229,130,92,136,15,2,128,55,9,164,178,60,0,136,82,200,155,79,205,147,42,241,106,136,117,100,208,65,136,171,148,56,67,133,155,148,56,77,133,175,244,217,196,197,112,33,126,2,0,89,157,207,151,101,0,160,209,13,121,86,190,32,3,234,208,97,180,192,73,34,20,75,32,246,131,216,39,55,119,178,16,226,185,16,219,64,27,56,39,93,169,207,78,251,65,39,227,111,154,105,131,154,124,126,198,32,86,197,210,87,200,1,98,185,52,135,63,253,255,76,199,255,46,185,57,138,129,57,172,97,85,207,148,133,196,40,99,134,121,123,146,61,57,76,137,213,33,254,32,73,139,136,132,88,27,0,20,23,11,251,236,149,152,153,169,8,137,87,217,163,54,2,57,23,230,12,48,33,30,35,207,137,229,245,243,49,66,126,64,24,196,134,16,167,75,114,34,194,251,109,10,211,197,65,74,27,152,63,180,76,156,199,139,131,88,15,226,42,145,60,48,182,223,230,132,108,114,204,192,188,55,211,101,92,78,63,255,156,47,235,243,65,169,255,77,145,29,207,81,233,99,218,153,34,94,191,62,230,88,144,25,151,8,49,21,226,128,124,113,66,4,196,26,16,71,200,179,99,195,250,109,82,10,50,185,17,3,54,50,69,140,50,22,11,136,101,34,73,176,191,74,31,43,77,151,5,197,244,219,239,204,149,15,196,142,157,200,20,243,34,250,241,213,188,204,184,16,85,174,176,39,2,126,159,255,48,22,172,91,36,225,196,15,232,136,228,227,194,7,98,17,138,2,2,85,177,227,100,145,36,62,86,197,227,122,210,60,255,24,213,88,220,78,154,19,213,111,143,251,139,114,130,149,188,25,196,113,242,252,216,129,177,249,121,112,113,170,244,241,34,105,94,84,156,202,79,188,60,139,31,26,165,242,7,223,11,194,1,23,4,0,22,80,192,154,6,38,131,44,32,110,237,170,239,130,119,170,158,32,192,7,50,144,1,68,192,161,159,25,24,145,216,215,35,129,215,88,80,0,254,132,72,4,228,131,227,252,251,122,69,32,31,242,95,135,176,74,78,60,200,169,174,14,32,189,191,79,169,146,13,158,66,156,11,194,64,14,188,87,244,41,73,6,61,72,0,79,32,35,254,135,71,124,88,5,48,134,28,88,149,253,255,158,31,96,191,51,28,200,132,247,51,138,129,25,89,244,1,75,98,32,49,128,24,66,12,34,218,226,6,184,15,238,133,135,195,171,31,172,206,56,27,247,24,136,227,187,61,225,41,161,141,240,136,112,131,208,78,184,51,73,92,40,27,226,229,88,208,14,245,131,250,243,147,246,99,126,112,43,168,233,138,251,227,222,80,29,42,227,76,220,0,56,224,46,112,30,14,238,11,103,118,133,44,183,223,111,101,86,88,67,180,255,22,193,15,79,168,223,142,226,68,65,41,195,40,126,20,155,161,35,53,236,52,92,7,85,148,185,254,49,63,42,95,211,6,243,205,29,236,25,58,63,247,135,236,11,97,27,54,212,18,91,132,29,192,206,97,39,177,11,88,19,86,15,88,216,113,172,1,107,193,142,42,241,224,138,123,210,183,226,6,102,139,233,243,39,27,234,12,93,51,223,159,172,50,147,114,167,26,167,78,167,47,170,190,60,209,180,60,229,102,228,78,150,78,151,137,51,50,243,88,28,248,197,16,177,120,18,129,227,8,150,179,147,179,43,0,202,239,143,234,245,246,38,186,239,187,130,48,91,190,115,243,127,7,192,251,120,111,111,239,145,239,92,232,113,0,246,185,195,87,194,225,239,156,13,27,126,90,212,0,56,127,88,160,144,229,171,56,92,121,33,192,55,7,29,238,62,125,96,12,204,129,13,140,199,25,184,1,47,224,7,2,65,40,136,4,113,32,9,76,132,222,103,194,117,46,3,83,193,76,48,15,20,129,18,176,28,172,1,229,96,19,216,10,170,192,110,176,31,212,131,38,112,18,156,5,151,192,21,112,3,220,133,171,167,3,188,0,221,224,29,248,140,32,8,9,161,33,12,68,31,49,65,44,17,123,196,25,97,35,62,72,32,18,142,196,32,73,72,42,146,129,72,16,5,50,19,153,143,148,32,43,145,114,100,11,82,141,236,67,14,35,39,145,11,72,27,114,7,121,136,116,34,175,145,79,40,134,170,163,58,168,17,106,133,142,68,217,40,7,13,67,227,208,9,104,6,58,5,45,64,23,160,75,209,50,180,18,221,133,214,161,39,209,75,232,13,180,29,125,129,246,96,0,83,195,152,152,41,230,128,177,49,46,22,137,37,99,233,152,12,155,141,21,99,165,88,37,86,139,53,194,231,124,13,107,199,186,176,143,56,17,103,224,44,220,1,174,224,16,60,30,23,224,83,240,217,248,18,188,28,175,194,235,240,211,248,53,252,33,222,141,127,35,208,8,134,4,123,130,39,129,71,24,71,200,32,76,37,20,17,74,9,219,9,135,8,103,224,94,234,32,188,35,18,137,76,162,53,209,29,238,197,36,98,22,113,6,113,9,113,3,113,15,241,4,177,141,248,152,216,67,34,145,244,73,246,36,111,82,36,137,79,202,35,21,145,214,145,118,145,142,147,174,146,58,72,31,200,106,100,19,178,51,57,136,156,76,150,144,11,201,165,228,157,228,99,228,171,228,103,228,207,20,77,138,37,197,147,18,73,17,82,166,83,150,81,182,81,26,41,151,41,29,148,207,84,45,170,53,213,155,26,71,205,162,206,163,150,81,107,169,10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<image> After subtracting all tiny purple metallic cylinders and all blue metallic spheres, how many objects remain?	137,80,78,71,13,10,26,10,0,0,0,13,73,72,68,82,0,0,1,224,0,0,1,64,8,6,0,0,0,100,200,175,123,0,1,0,0,73,68,65,84,120,156,124,253,201,142,109,75,146,37,136,45,209,125,204,238,189,175,241,222,163,205,202,42,38,178,50,171,10,100,49,65,128,179,250,1,2,252,0,126,67,13,73,128,224,136,31,64,128,3,206,248,5,245,7,4,8,18,156,114,72,16,69,176,218,136,172,140,200,240,140,72,15,15,111,222,123,183,179,115,182,10,7,42,75,214,210,109,55,105,142,231,215,236,156,221,168,74,187,68,84,84,52,254,243,255,252,63,207,204,4,2,64,2,99,4,50,1,32,145,9,68,0,153,192,113,28,152,115,2,72,68,12,204,57,49,70,96,206,68,68,96,206,137,136,216,238,231,15,159,19,17,245,123,32,115,174,75,34,0,172,215,207,92,207,226,223,89,55,230,156,136,17,245,41,214,189,8,140,8,100,143,179,38,208,215,172,247,71,4,142,99,96,206,196,156,179,126,159,0,128,99,28,56,207,147,183,32,16,200,186,183,159,22,209,52,224,243,214,179,247,119,113,220,125,205,156,61,183,227,24,120,60,206,162,193,122,127,112,146,136,166,199,186,47,23,173,115,22,241,128,108,90,250,59,214,223,153,89,4,94,207,230,216,73,75,94,199,207,0,52,221,250,126,0,78,61,206,27,0,198,24,152,231,89,35,200,245,36,255,110,158,253,140,166,98,241,130,114,16,49,234,111,254,14,251,126,61,199,231,145,38,135,148,43,159,111,4,48,198,129,199,227,129,81,114,33,30,56,173,178,158,85,52,15,27,101,141,131,207,151,188,244,48,16,35,90,86,214,51,36,83,124,143,116,132,122,113,246,124,155,95,153,136,49,122,60,175,105,253,250,157,148,69,190,111,158,39,98,140,150,155,150,199,250,63,234,161,207,113,206,44,94,115,24,137,49,70,127,207,57,103,38,110,183,163,230,151,69,19,93,231,63,99,4,206,115,26,29,163,231,223,252,140,104,89,35,109,35,128,17,3,231,156,95,120,166,248,179,228,55,90,6,19,137,156,217,215,44,89,225,51,162,231,116,149,19,241,118,17,57,34,22,221,166,100,44,90,214,70,141,63,55,59,69,222,81,87,68,219,168,207,1,32,49,168,119,246,156,204,108,187,115,165,183,143,151,54,84,252,145,60,143,8,156,53,103,14,120,206,217,60,229,120,129,40,219,118,148,252,69,143,243,106,155,124,28,155,221,121,101,223,118,222,209,110,81,6,156,223,188,246,245,179,73,135,101,103,125,28,228,27,245,62,182,57,69,235,6,255,38,109,150,12,28,226,23,100,215,22,41,104,155,162,229,121,183,73,70,143,82,194,158,91,241,144,188,113,94,93,52,182,125,158,243,143,215,187,76,190,166,63,253,101,201,66,154,161,231,23,36,46,93,97,4,150,163,106,225,90,130,77,165,71,38,110,183,91,51,178,239,55,135,27,112,199,158,155,129,201,204,205,249,102,78,52,233,22,247,205,112,200,208,36,118,195,227,215,24,167,113,158,167,17,133,115,11,156,243,44,195,40,231,78,5,68,44,7,15,190,163,31,71,67,30,198,164,40,197,201,50,14,89,128,97,141,229,60,151,18,57,211,16,116,139,2,20,153,107,228,143,243,236,241,32,98,163,163,207,143,66,40,191,236,130,176,27,163,108,138,166,28,102,234,247,118,242,180,74,245,221,121,158,253,93,196,88,128,40,151,96,201,249,74,88,41,15,14,22,4,230,70,191,98,241,173,140,117,9,42,202,177,186,65,92,207,212,147,22,13,202,33,69,232,153,40,96,145,128,12,216,114,88,89,70,203,73,68,57,118,165,20,95,221,225,46,217,245,241,22,233,76,214,19,199,56,218,65,52,173,32,89,146,145,75,209,240,194,54,202,51,232,128,154,118,146,39,93,131,254,156,243,228,181,11,184,148,162,27,143,105,192,200,63,242,226,24,163,156,234,14,102,221,65,211,80,206,83,198,169,245,181,233,132,126,231,197,230,3,192,230,124,221,208,147,255,253,238,126,255,68,164,174,213,61,110,75,102,59,17,142,69,0,185,200,61,162,157,35,54,103,83,32,172,236,3,121,180,211,119,32,98,148,76,138,231,40,121,225,124,57,15,218,167,227,56,48,79,167,243,10,4,56,135,163,198,115,158,39,168,151,82,61,57,241,0,237,161,156,119,130,78,209,228,181,245,8,112,157,108,17,203,169,103,182,93,155,5,30,28,140,17,200,132,28,99,46,29,114,185,152,211,236,72,221,71,7,189,129,25,148,239,48,190,219,168,46,124,21,152,157,246,183,222,177,3,129,136,197,215,81,254,161,121,188,201,129,128,1,109,3,74,159,103,235,202,236,251,253,157,203,94,159,101,15,142,246,91,45,27,101,139,104,247,58,176,4,233,185,207,205,117,147,207,31,114,60,33,150,53,128,146,177,161,225,0,162,21,78,84,81,36,193,219,162,62,59,142,131,164,222,24,70,1,222,25,147,134,254,53,248,227,24,245,78,180,35,111,199,110,136,149,2,31,109,68,163,199,76,134,3,105,232,85,66,198,203,230,204,14,47,92,88,221,9,237,64,162,148,166,12,158,43,42,127,70,8,49,182,112,115,52,253,254,0,149,48,32,65,4,106,76,33,193,94,136,216,159,221,211,218,158,75,71,196,119,83,128,91,129,128,87,14,99,129,7,19,70,82,189,104,228,17,99,3,176,226,11,17,103,214,184,228,32,197,104,206,171,21,209,120,72,128,66,99,177,71,210,142,178,229,188,250,186,8,60,206,179,101,106,140,21,109,101,189,131,202,198,144,81,10,63,250,122,242,53,98,180,227,34,50,111,25,51,195,208,227,198,138,84,34,68,39,119,46,84,100,201,175,161,127,160,163,99,143,78,245,222,245,93,108,52,220,141,227,201,108,75,27,24,58,64,201,214,162,41,233,204,57,135,57,16,201,39,141,50,223,195,235,228,214,164,31,128,233,54,89,10,233,167,198,114,25,63,24,237,9,60,161,238,155,238,168,7,1,157,64,33,29,125,230,50,140,206,79,122,49,151,77,32,218,9,236,17,208,122,150,211,253,106,52,233,84,93,79,71,56,16,208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The below problem is with the following images: <image> A large sunshade umbrella, when the canopy is fully opened, can be approximately regarded as a conical shape. Its slant height is 2.5m, and the height is 1.5m. Calculate the area of the fabric required to make this sunshade umbrella, ignoring the seams.	137,80,78,71,13,10,26,10,0,0,0,13,73,72,68,82,0,0,0,135,0,0,0,112,8,2,0,0,0,187,18,244,252,0,0,20,149,73,68,65,84,120,156,237,93,127,76,83,215,23,191,175,48,126,24,39,176,49,69,130,22,254,24,52,113,209,226,50,121,184,140,66,102,180,16,13,37,49,195,250,135,22,178,69,230,246,7,115,51,43,75,104,65,51,113,26,81,163,14,205,150,47,197,101,148,45,179,160,147,138,38,90,59,18,91,183,12,112,91,214,154,205,22,129,173,232,6,40,67,91,196,246,126,255,184,243,250,246,222,235,235,107,233,143,199,230,231,143,230,245,190,251,238,61,239,158,123,206,61,247,220,115,239,35,32,132,96,78,193,235,245,198,197,197,209,18,119,238,220,121,228,200,17,151,203,149,150,150,22,19,170,194,11,98,206,113,133,9,143,199,51,127,254,124,0,192,203,47,191,220,213,213,245,47,96,204,156,225,10,132,144,32,8,116,237,243,249,68,34,17,190,85,81,81,145,152,152,152,151,151,87,80,80,240,201,39,159,232,245,250,164,164,164,24,145,25,30,196,199,154,0,190,192,44,161,93,87,85,85,149,151,151,59,157,78,0,64,89,89,217,244,244,180,82,169,236,236,236,4,255,100,36,96,240,82,200,152,27,84,210,128,219,186,174,174,46,47,47,79,165,82,225,148,138,138,138,242,242,242,170,170,42,148,205,231,243,225,167,230,10,75,192,28,210,96,76,104,181,90,0,64,99,99,35,77,38,0,0,26,141,6,0,176,107,215,46,86,211,64,248,152,51,221,135,6,157,78,55,52,52,212,216,216,8,254,169,208,16,118,237,218,245,215,95,127,29,60,120,112,46,178,4,0,0,224,28,132,94,175,175,172,172,228,200,224,245,122,33,132,42,149,170,181,181,21,165,248,124,190,40,16,22,46,8,157,43,184,53,81,67,67,8,187,187,187,21,10,133,219,237,198,41,16,66,141,70,163,209,104,240,95,116,203,237,118,43,20,138,238,238,238,40,210,27,30,8,221,6,195,218,9,141,213,86,171,117,223,190,125,61,61,61,220,182,47,202,156,148,148,164,215,235,75,74,74,50,51,51,165,82,105,228,137,13,27,230,210,184,50,48,48,160,86,171,187,186,186,248,79,71,146,146,146,140,70,227,155,111,190,105,183,219,169,246,24,0,0,82,204,28,218,173,216,35,214,194,202,23,14,135,131,36,73,151,203,21,218,179,50,153,204,225,112,248,203,32,180,81,103,110,112,133,163,89,121,54,168,205,102,35,73,114,124,124,28,63,130,126,169,131,147,112,32,104,174,248,124,62,175,215,59,62,62,46,147,201,250,251,251,121,62,245,240,225,67,214,244,254,254,254,130,130,2,183,219,29,54,250,34,6,225,114,5,245,101,183,219,77,146,36,55,75,188,94,47,205,6,243,7,86,251,77,128,16,238,104,79,16,132,199,227,81,42,149,245,245,245,220,22,20,127,87,74,89,89,89,101,101,229,214,173,91,5,238,125,137,37,113,76,203,7,66,72,77,84,42,149,91,182,108,41,43,43,11,99,165,175,189,246,90,73,73,73,77,77,77,24,203,12,59,98,233,7,131,143,252,87,172,222,220,234,234,234,162,162,34,149,74,5,252,172,116,205,6,28,62,52,33,32,150,178,130,59,4,141,37,16,194,186,186,186,220,220,92,196,18,102,134,217,163,177,177,113,104,104,72,167,211,97,150,196,176,119,50,17,123,159,49,83,80,112,71,142,116,213,21,21,21,91,182,108,169,168,168,160,165,199,94,128,98,102,103,248,65,107,107,171,74,165,10,246,41,158,54,24,13,130,117,148,197,222,15,6,41,29,243,139,47,190,232,233,233,233,232,232,136,206,186,97,82,82,210,255,254,247,191,138,138,10,228,40,19,206,98,101,236,137,192,44,49,26,141,29,29,29,58,157,46,154,181,167,165,165,117,118,118,86,85,85,57,157,78,129,176,4,0,193,104,48,139,197,34,147,201,162,63,191,67,213,5,116,148,69,25,81,226,10,173,173,105,206,171,254,254,126,153,76,134,156,84,179,193,108,156,140,33,211,128,220,66,179,167,138,154,45,122,178,226,143,184,217,56,131,249,215,194,7,88,94,67,120,150,191,136,243,161,48,218,26,140,70,61,85,117,204,166,65,67,179,193,152,232,238,238,150,203,229,254,238,82,41,244,249,124,84,223,51,2,147,55,94,175,55,4,157,28,237,241,141,58,162,78,76,76,168,84,170,67,135,14,229,228,228,0,182,160,136,232,3,57,202,170,171,171,89,239,66,202,220,142,32,8,68,48,117,30,138,223,14,82,38,200,212,87,198,254,36,200,57,77,140,153,213,225,241,120,202,202,202,14,31,62,140,76,210,88,145,193,132,74,165,202,205,205,173,171,171,99,222,98,53,210,122,123,123,17,135,222,123,239,61,214,2,103,102,102,86,172,88,129,242,156,63,127,30,240,153,165,6,43,92,33,131,42,200,104,250,102,52,26,161,80,215,157,212,106,245,222,189,123,169,41,172,10,118,104,104,104,199,142,29,232,130,32,136,35,71,142,48,31,209,233,116,54,155,13,167,204,204,204,44,95,190,60,43,43,107,106,106,74,163,209,160,11,179,217,12,0,64,13,2,163,169,193,168,29,13,57,131,75,75,75,169,157,35,106,148,240,65,83,83,147,221,110,167,78,158,152,189,27,66,120,253,250,245,3,7,14,0,0,150,44,89,210,218,218,122,238,220,57,240,168,163,227,71,166,167,167,37,18,9,120,36,34,241,241,241,223,127,255,61,73,146,95,125,245,213,202,149,43,83,82,82,44,22,203,233,211,167,79,158,60,233,112,56,80,201,81,213,96,72,83,161,200,96,236,125,66,220,18,194,160,66,67,107,107,107,71,71,135,209,104,244,151,129,32,136,53,107,214,224,191,217,217,217,232,5,241,144,3,0,232,237,237,221,182,109,27,65,16,70,163,17,37,66,8,175,92,185,146,147,147,51,53,53,245,226,139,47,222,189,123,247,204,153,51,7,14,28,64,28,253,27,97,148,122,154,46,98,53,63,212,106,117,83,83,83,24,43,69,168,175,175,175,175,175,247,71,9,127,208,204,42,183,219,45,151,203,77,38,1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"<image>\nAs shown in the figure, the edge length of the cube $$ABCD-A_1B_1C_1D_1$$ is 1, and $$E$$,(...TRUNCATED)	"iVBORw0KGgoAAAANSUhEUgAAATYAAAE7CAIAAADYQDogAACBCElEQVR4nO2dd5hdVdXw1z719umTnhBIQhUpitKbgKBAkKpiAQX(...TRUNCATED)	\boxed{1}
"<image>/n<image>/nBased on the given images, answer the following question.\n\nIn the diagram, the (...TRUNCATED)	"/9j/2wCEAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDIBCQk(...TRUNCATED)	\boxed{C}
"<image>/nBased on the given images, answer the following question.\n\nGiven that line l has an incl(...TRUNCATED)	"/9j/2wCEAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDIBCQk(...TRUNCATED)	\boxed{A}
"Based on the figure, which reconstruction technique appears to be the most robust against adversari(...TRUNCATED)	"/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDA(...TRUNCATED)	\boxed{C}

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