| [ |
| { |
| "index": 3, |
| "pred_answer": "\\text{IV}", |
| "gt_answer": "III", |
| "correct": false |
| }, |
| { |
| "index": 5, |
| "pred_answer": "23.5\\ \\text{cm}", |
| "gt_answer": "22.8cm", |
| "correct": false |
| }, |
| { |
| "index": 6, |
| "pred_answer": "300\\ \\text{m}", |
| "gt_answer": "320m", |
| "correct": false |
| }, |
| { |
| "index": 7, |
| "pred_answer": "9.9\\ \\text{m/s}", |
| "gt_answer": "4.1m/s", |
| "correct": false |
| }, |
| { |
| "index": 8, |
| "pred_answer": "40.0\\ \\text{m}", |
| "gt_answer": "41.3m", |
| "correct": false |
| }, |
| { |
| "index": 9, |
| "pred_answer": "-5800\\ \\text{m}", |
| "gt_answer": "537m", |
| "correct": false |
| }, |
| { |
| "index": 10, |
| "pred_answer": "\\text{The graph represents blood velocity as a sinusoid with amplitude }0.8\\text{ m/s and period }1.0\\text{ s.}", |
| "gt_answer": "the acceleration of the blood is greatest in magnitude at about 0.10 s.", |
| "correct": false |
| }, |
| { |
| "index": 11, |
| "pred_answer": "12.75\\ \\text{m/s}", |
| "gt_answer": "1.29m/s", |
| "correct": false |
| }, |
| { |
| "index": 13, |
| "pred_answer": "110\\ \\text{mph}", |
| "gt_answer": "120m/s", |
| "correct": false |
| }, |
| { |
| "index": 16, |
| "pred_answer": "1.14\\ \\text{m/s}", |
| "gt_answer": "1.5m/s", |
| "correct": false |
| }, |
| { |
| "index": 17, |
| "pred_answer": null, |
| "gt_answer": "3\\sqrt{gD} to 3.13\\sqrt{gD}", |
| "correct": false |
| }, |
| { |
| "index": 23, |
| "pred_answer": "2.0\\ \\text{kg}", |
| "gt_answer": "26.7kg", |
| "correct": false |
| }, |
| { |
| "index": 24, |
| "pred_answer": "\\frac{F}{g}", |
| "gt_answer": "5.30kg", |
| "correct": false |
| }, |
| { |
| "index": 27, |
| "pred_answer": "152\\ \\text{N}", |
| "gt_answer": "46.3kN", |
| "correct": false |
| }, |
| { |
| "index": 28, |
| "pred_answer": "w\\sqrt2", |
| "gt_answer": "3.35w", |
| "correct": false |
| }, |
| { |
| "index": 30, |
| "pred_answer": "137\\ \\text{N}", |
| "gt_answer": "191N", |
| "correct": false |
| }, |
| { |
| "index": 31, |
| "pred_answer": "144.6\\ \\text{N down the incline}", |
| "gt_answer": "146N", |
| "correct": false |
| }, |
| { |
| "index": 32, |
| "pred_answer": "0\\ \\text{m/s}^2", |
| "gt_answer": "-2.13 \\( \\text{m/s}^2 \\)", |
| "correct": false |
| }, |
| { |
| "index": 33, |
| "pred_answer": "1000\\ \\text{N}", |
| "gt_answer": "30.4N", |
| "correct": false |
| }, |
| { |
| "index": 36, |
| "pred_answer": "3360\\ \\text{N}", |
| "gt_answer": "6400N", |
| "correct": false |
| }, |
| { |
| "index": 39, |
| "pred_answer": "0.800\\ \\text{N}", |
| "gt_answer": "0.700mg", |
| "correct": false |
| }, |
| { |
| "index": 40, |
| "pred_answer": "1.80\\ \\text{m/s}", |
| "gt_answer": "12.3m/s", |
| "correct": false |
| }, |
| { |
| "index": 42, |
| "pred_answer": "0.920\\ \\text{m/s}", |
| "gt_answer": "1.78m/s", |
| "correct": false |
| }, |
| { |
| "index": 43, |
| "pred_answer": "160\\ \\text{N}", |
| "gt_answer": "15.0N", |
| "correct": false |
| }, |
| { |
| "index": 44, |
| "pred_answer": "26\\ \\text{N}", |
| "gt_answer": "1.80N", |
| "correct": false |
| }, |
| { |
| "index": 45, |
| "pred_answer": "10.0\\text{ N}", |
| "gt_answer": "249N", |
| "correct": false |
| }, |
| { |
| "index": 46, |
| "pred_answer": "mg_A", |
| "gt_answer": "3.0N", |
| "correct": false |
| }, |
| { |
| "index": 48, |
| "pred_answer": "880\\ \\text{N}", |
| "gt_answer": "424N", |
| "correct": false |
| }, |
| { |
| "index": 49, |
| "pred_answer": "\\frac{m_2}{m_1+m_2}g", |
| "gt_answer": "\\( \\frac{2m_2g}{4m_1 + m_2}\\)", |
| "correct": false |
| }, |
| { |
| "index": 50, |
| "pred_answer": "6.0\\ \\text{kg}", |
| "gt_answer": "39.0kg", |
| "correct": false |
| }, |
| { |
| "index": 56, |
| "pred_answer": "a_x = M\\frac{2mg}{1 + 2Mg - m\\sin\\alpha}", |
| "gt_answer": "\\( \\frac{gM}{(M + m) \\tan \\alpha + (M / \\tan \\alpha)} \\)", |
| "correct": false |
| }, |
| { |
| "index": 64, |
| "pred_answer": "50.0\\ \\text{N}", |
| "gt_answer": "637N", |
| "correct": false |
| }, |
| { |
| "index": 69, |
| "pred_answer": "12\\ \\text{m}", |
| "gt_answer": "142m", |
| "correct": false |
| }, |
| { |
| "index": 70, |
| "pred_answer": "6.26\\ \\text{m/s}", |
| "gt_answer": "4.4m/s", |
| "correct": false |
| }, |
| { |
| "index": 71, |
| "pred_answer": "-0.58\\ \\text{J}", |
| "gt_answer": "-0.83J", |
| "correct": false |
| }, |
| { |
| "index": 72, |
| "pred_answer": "12.0\\ \\text{m}", |
| "gt_answer": "\\(\\frac{\\left(v_0^2/2g\\right)+L\\sin\\alpha}{\\sin\\beta+\\mu_r\\cos\\beta}\\)", |
| "correct": false |
| }, |
| { |
| "index": 73, |
| "pred_answer": "33.5\\ \\text{m}", |
| "gt_answer": "25.6m", |
| "correct": false |
| }, |
| { |
| "index": 74, |
| "pred_answer": "1", |
| "gt_answer": "19.6%", |
| "correct": false |
| }, |
| { |
| "index": 78, |
| "pred_answer": "107.88\\ \\text{m}", |
| "gt_answer": "5.7m", |
| "correct": false |
| }, |
| { |
| "index": 84, |
| "pred_answer": "0.0127\\ \\text{rad}", |
| "gt_answer": "17.7 rad", |
| "correct": false |
| }, |
| { |
| "index": 85, |
| "pred_answer": "5.77\\ \\text{m/s}", |
| "gt_answer": "8.04m/s", |
| "correct": false |
| }, |
| { |
| "index": 86, |
| "pred_answer": "9.90\\ \\text{m/s}", |
| "gt_answer": "3.07m/s", |
| "correct": false |
| }, |
| { |
| "index": 87, |
| "pred_answer": "3.87\\ \\text{m/s}", |
| "gt_answer": "3.40m/s", |
| "correct": false |
| }, |
| { |
| "index": 88, |
| "pred_answer": "\\frac{1}{5}\\pi R^2 h^2", |
| "gt_answer": "\\(\\frac{3}{10} MR^2\\)", |
| "correct": false |
| }, |
| { |
| "index": 92, |
| "pred_answer": "2.26\\ \\text{m}", |
| "gt_answer": "3.76m", |
| "correct": false |
| }, |
| { |
| "index": 93, |
| "pred_answer": "1.2\\ \\text{s}", |
| "gt_answer": "3.27s", |
| "correct": false |
| }, |
| { |
| "index": 94, |
| "pred_answer": "0.841\\ \\text{rad/s}", |
| "gt_answer": "5.70 rad/s", |
| "correct": false |
| }, |
| { |
| "index": 96, |
| "pred_answer": "10.6\\ \\text{N}", |
| "gt_answer": "1300N", |
| "correct": false |
| }, |
| { |
| "index": 99, |
| "pred_answer": "H_0", |
| "gt_answer": "\\(\\frac{3}{5} H_0\\)", |
| "correct": false |
| }, |
| { |
| "index": 101, |
| "pred_answer": "31.3\\ \\text{m/s}", |
| "gt_answer": "29.0m/s", |
| "correct": false |
| }, |
| { |
| "index": 103, |
| "pred_answer": "-7.8", |
| "gt_answer": "4.50", |
| "correct": false |
| }, |
| { |
| "index": 105, |
| "pred_answer": null, |
| "gt_answer": "55m", |
| "correct": false |
| }, |
| { |
| "index": 106, |
| "pred_answer": "10\\ \\text{s}", |
| "gt_answer": "10s", |
| "correct": false |
| }, |
| { |
| "index": 108, |
| "pred_answer": "37.0\\ \\text{m/s}", |
| "gt_answer": "\\( 45^{\\circ} \\)", |
| "correct": false |
| }, |
| { |
| "index": 110, |
| "pred_answer": "0.9\\ \\text{N}", |
| "gt_answer": "0.90N", |
| "correct": false |
| }, |
| { |
| "index": 111, |
| "pred_answer": "mg\\cos\\alpha", |
| "gt_answer": "\\( w \\cos \\alpha \\)", |
| "correct": false |
| }, |
| { |
| "index": 112, |
| "pred_answer": "W_2 = m(g\\sin 15^\\circ)", |
| "gt_answer": "\\( w_2 = w_1 \\sin 15^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 115, |
| "pred_answer": "738\\ \\text{N}", |
| "gt_answer": "390N", |
| "correct": false |
| }, |
| { |
| "index": 117, |
| "pred_answer": null, |
| "gt_answer": "\\( 2\\pi \\sqrt{\\frac{L \\cos \\beta}{g}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 118, |
| "pred_answer": "3390\\ \\text{N}", |
| "gt_answer": "79000N", |
| "correct": false |
| }, |
| { |
| "index": 119, |
| "pred_answer": "7.67\\ \\text{m/s}", |
| "gt_answer": "7.67m/s", |
| "correct": false |
| }, |
| { |
| "index": 123, |
| "pred_answer": "480\\ \\text{m/s}", |
| "gt_answer": "\\( \\frac{m_{\\text{B}} + m_{\\text{W}}}{m_{\\text{B}}} \\sqrt{2gh} \\)", |
| "correct": false |
| }, |
| { |
| "index": 124, |
| "pred_answer": "1.20\\ \\text{m/s}", |
| "gt_answer": "4.47m/s", |
| "correct": false |
| }, |
| { |
| "index": 129, |
| "pred_answer": "1.33\\ \\text{rad/s}", |
| "gt_answer": "\\(v/R\\)", |
| "correct": false |
| }, |
| { |
| "index": 131, |
| "pred_answer": "672\\ \\text{N}\\cdot\\text{m (upward)}", |
| "gt_answer": "\\( 680 \\text{ N} \\cdot \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 132, |
| "pred_answer": null, |
| "gt_answer": "\\( \\sqrt{\\frac{4}{3}gh} \\)", |
| "correct": false |
| }, |
| { |
| "index": 137, |
| "pred_answer": "0\\ \\text{m/s}^2", |
| "gt_answer": "\\( 48000 \\text{ m/s}^2 \\)", |
| "correct": false |
| }, |
| { |
| "index": 139, |
| "pred_answer": "0.0025\\ \\text{Wb}", |
| "gt_answer": "\\( 0.00035 \\ \\text{Wb} \\)", |
| "correct": false |
| }, |
| { |
| "index": 142, |
| "pred_answer": "0.0159\\ \\text{Hz}", |
| "gt_answer": "\\( 410 \\, \\text{Hz} \\)", |
| "correct": false |
| }, |
| { |
| "index": 143, |
| "pred_answer": "0.10\\ \\text{mV}", |
| "gt_answer": "\\( 0.00025 \\, \\text{V} \\)", |
| "correct": false |
| }, |
| { |
| "index": 146, |
| "pred_answer": "0.20\\ \\text{A}", |
| "gt_answer": "\\( \\Delta V_{\\text{bat}}/R \\)", |
| "correct": false |
| }, |
| { |
| "index": 147, |
| "pred_answer": "\\left(\\frac{\\mu_0 I}{2\\pi d}\\right) l v", |
| "gt_answer": "\\( (\\mu v_0 I / 2\\pi) \\ln[(d+l)/d] \\)", |
| "correct": false |
| }, |
| { |
| "index": 148, |
| "pred_answer": "3.4\\ \\text{s}", |
| "gt_answer": "\\( 0.1 \\, \\text{s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 149, |
| "pred_answer": "2.2\\times 10^{-7}\\ \\mathrm{H/m}", |
| "gt_answer": "\\( 0.36 \\, \\mu\\text{H/m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 150, |
| "pred_answer": "6\\sqrt{3}\\text{ V}", |
| "gt_answer": "\\( -10\\,\\text{V} \\)", |
| "correct": false |
| }, |
| { |
| "index": 152, |
| "pred_answer": "V_0", |
| "gt_answer": "\\( V_\\text{R} \\to \\mathcal{E}_0 \\)", |
| "correct": false |
| }, |
| { |
| "index": 153, |
| "pred_answer": "159292\\ \\text{Hz}", |
| "gt_answer": "\\( 5000 \\text{ Hz} \\)", |
| "correct": false |
| }, |
| { |
| "index": 154, |
| "pred_answer": "10^{4}\\ \\text{T}, \\text{into the page}", |
| "gt_answer": "\\( 46 \\text{ mT} \\)", |
| "correct": false |
| }, |
| { |
| "index": 155, |
| "pred_answer": "0.136\\ \\text{km/s}", |
| "gt_answer": "\\( 252000 \\text{ m/s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 160, |
| "pred_answer": "0.00025", |
| "gt_answer": "\\( 0.005 \\)", |
| "correct": false |
| }, |
| { |
| "index": 162, |
| "pred_answer": "4c", |
| "gt_answer": "0.13", |
| "correct": false |
| }, |
| { |
| "index": 163, |
| "pred_answer": "74\\ \\text{cm}", |
| "gt_answer": "\\( 440000000000.0000610352 \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 167, |
| "pred_answer": "0.13\\ \\text{m/s}", |
| "gt_answer": "\\[ 24 \\text{ m/s} \\]", |
| "correct": false |
| }, |
| { |
| "index": 168, |
| "pred_answer": "0\\ \\text{m/s}", |
| "gt_answer": "\\[ 0 \\text{ m/s} \\]", |
| "correct": false |
| }, |
| { |
| "index": 170, |
| "pred_answer": "32\\ \\text{m}", |
| "gt_answer": "28m", |
| "correct": false |
| }, |
| { |
| "index": 176, |
| "pred_answer": "100\\text{ N}", |
| "gt_answer": "\\( 9.5 \\text{ N} \\)", |
| "correct": false |
| }, |
| { |
| "index": 177, |
| "pred_answer": "14.3\\ \\text{m/s}", |
| "gt_answer": "\\( 0.944 \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 178, |
| "pred_answer": "115.4\\ \\text{m}\\,\\hat{i}+66.8\\ \\text{m}\\,\\hat{j}", |
| "gt_answer": "\\( 14300 \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 179, |
| "pred_answer": "12.0\\ \\text{km/h}", |
| "gt_answer": "\\( 15.0 \\text{ km/h} \\)", |
| "correct": false |
| }, |
| { |
| "index": 180, |
| "pred_answer": "0.198\\ \\text{N}", |
| "gt_answer": "\\( 0.078 \\text{ N} \\)", |
| "correct": false |
| }, |
| { |
| "index": 182, |
| "pred_answer": null, |
| "gt_answer": "\\( d \\tan \\theta_i - \\frac{gd^2}{2v_i^2 \\cos^2 \\theta_i} \\)", |
| "correct": false |
| }, |
| { |
| "index": 189, |
| "pred_answer": "127\\ \\text{km/h}", |
| "gt_answer": "\\( 68.8 \\text{ km/h} \\)", |
| "correct": false |
| }, |
| { |
| "index": 192, |
| "pred_answer": "2", |
| "gt_answer": "0.949", |
| "correct": false |
| }, |
| { |
| "index": 193, |
| "pred_answer": "22.5^\\circ", |
| "gt_answer": "\\( \\theta' = 22.3^{\\circ} \\)", |
| "correct": false |
| }, |
| { |
| "index": 195, |
| "pred_answer": "1.25\\ \\text{m}", |
| "gt_answer": "\\( 1.94 \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 196, |
| "pred_answer": "0.011\\ \\text{s}", |
| "gt_answer": "\\( 0.000000000106 \\text{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 197, |
| "pred_answer": "12.0\\ \\text{cm}", |
| "gt_answer": "\\( 6.30 \\text{ cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 202, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "\\( 67.2^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 203, |
| "pred_answer": "39.4^\\circ", |
| "gt_answer": "\\( 2.83^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 204, |
| "pred_answer": "2.00\\ \\text{mm}", |
| "gt_answer": "\\( \\frac{nd}{n-1} \\)", |
| "correct": false |
| }, |
| { |
| "index": 205, |
| "pred_answer": "32.3^\\circ", |
| "gt_answer": "\\( 25.7^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 208, |
| "pred_answer": "48.0^\\circ", |
| "gt_answer": "\\( 27.5^{\\circ} \\)", |
| "correct": false |
| }, |
| { |
| "index": 210, |
| "pred_answer": "\\theta=\\tan^{-1}\\!\\left(\\frac{n_1}{n}\\right)", |
| "gt_answer": "\\( \\sin^{-1}\\left[n\\sin\\left(\\sin^{-1}\\frac{L}{R} - \\sin^{-1}\\frac{L}{nR}\\right)\\right] \\)", |
| "correct": false |
| }, |
| { |
| "index": 211, |
| "pred_answer": "0.77", |
| "gt_answer": "1.44", |
| "correct": false |
| }, |
| { |
| "index": 212, |
| "pred_answer": "1.65", |
| "gt_answer": "1.93", |
| "correct": false |
| }, |
| { |
| "index": 213, |
| "pred_answer": "33.4^\\circ", |
| "gt_answer": "\\( 38.7^{\\circ} \\)", |
| "correct": false |
| }, |
| { |
| "index": 215, |
| "pred_answer": "5.00\\times10^{-7}\\ \\text{s}", |
| "gt_answer": "\\( 3.40 \\text{ ns} \\)", |
| "correct": false |
| }, |
| { |
| "index": 217, |
| "pred_answer": "0.05\\ \\text{s}", |
| "gt_answer": "\\( \\frac{\\pi}{8\\omega} \\)", |
| "correct": false |
| }, |
| { |
| "index": 218, |
| "pred_answer": "1.0\\ \\text{m}", |
| "gt_answer": "\\( p_1 + h \\)", |
| "correct": false |
| }, |
| { |
| "index": 221, |
| "pred_answer": "-1.00\\ \\text{D}", |
| "gt_answer": "\\( +0.667 \\text{ diopters} \\)", |
| "correct": false |
| }, |
| { |
| "index": 222, |
| "pred_answer": "+2.00", |
| "gt_answer": "-0.800", |
| "correct": false |
| }, |
| { |
| "index": 224, |
| "pred_answer": "14.6\\ \\text{mm}", |
| "gt_answer": "\\( 10.7 \\text{ cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 225, |
| "pred_answer": "+1.0\\ \\text{m}", |
| "gt_answer": "\\( +11.7 \\text{ cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 227, |
| "pred_answer": "56.6\\ \\text{m}", |
| "gt_answer": "\\( 56.4 \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 231, |
| "pred_answer": "1.6c", |
| "gt_answer": "\\( 0.700c \\)", |
| "correct": false |
| }, |
| { |
| "index": 232, |
| "pred_answer": "R \\approx 7.89\\times 10^{14}\\ \\text{m}", |
| "gt_answer": "\\( 39400 \\text{ m/s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 234, |
| "pred_answer": "6.62606957\\times 10^{-34}\\ \\mathrm{J·s}", |
| "gt_answer": "\\( 0 \\text{ J} \\cdot \\text{s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 235, |
| "pred_answer": "161000000000000\\ \\text{s}^{-1}", |
| "gt_answer": "\\( 725000000000000 \\)", |
| "correct": false |
| }, |
| { |
| "index": 237, |
| "pred_answer": "75.63\\ \\text{nm}", |
| "gt_answer": "\\( 378 \\text{ nm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 238, |
| "pred_answer": "0.0001", |
| "gt_answer": "0.090", |
| "correct": false |
| }, |
| { |
| "index": 240, |
| "pred_answer": "-k\\frac{p}{r}", |
| "gt_answer": "\\( U = \\frac{-2p^2}{4\\pi\\epsilon_0 r^3} - \\frac{2p^2}{4\\pi\\epsilon_0 d^3} \\)", |
| "correct": false |
| }, |
| { |
| "index": 242, |
| "pred_answer": "80.9^\\circ", |
| "gt_answer": "\\(0.0000994 \\, \\text{rad}\\)", |
| "correct": false |
| }, |
| { |
| "index": 243, |
| "pred_answer": "2000\\ \\text{Hz}", |
| "gt_answer": "\\(2.00 \\, \\text{kHz}\\)", |
| "correct": false |
| }, |
| { |
| "index": 244, |
| "pred_answer": "21.3^\\circ", |
| "gt_answer": "\\( 3.30^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 246, |
| "pred_answer": "0.282\\ \\text{s}", |
| "gt_answer": "\\( 174 \\text{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 249, |
| "pred_answer": null, |
| "gt_answer": "\\( 0 \\text{ kg} \\cdot \\text{m/s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 250, |
| "pred_answer": "0.204\\ \\text{nm}", |
| "gt_answer": "\\( 0.218 \\text{ nm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 251, |
| "pred_answer": "0.389", |
| "gt_answer": "0.0103", |
| "correct": false |
| }, |
| { |
| "index": 252, |
| "pred_answer": "0.01", |
| "gt_answer": "0.908", |
| "correct": false |
| }, |
| { |
| "index": 254, |
| "pred_answer": "127.5\\ \\text{nm}", |
| "gt_answer": "365 nm", |
| "correct": false |
| }, |
| { |
| "index": 256, |
| "pred_answer": "2.78\\times 10^{-48}\\ \\text{kg·m}^2", |
| "gt_answer": "\\(0 \\text{ kg} \\cdot \\text{m}^2\\)", |
| "correct": false |
| }, |
| { |
| "index": 260, |
| "pred_answer": "0.125", |
| "gt_answer": "\\(\\frac{1}{4} \\sin^2 \\theta\\)", |
| "correct": false |
| }, |
| { |
| "index": 261, |
| "pred_answer": "0.81", |
| "gt_answer": "\\(\\sin^2(\\omega_0 t / 2)\\)", |
| "correct": false |
| }, |
| { |
| "index": 262, |
| "pred_answer": "0.5000000000000001", |
| "gt_answer": "\\(\\frac{4 \\sqrt{E} \\sqrt{E - V_0}}{(\\sqrt{E} + \\sqrt{E - V_0})^2}\\)", |
| "correct": false |
| }, |
| { |
| "index": 264, |
| "pred_answer": "-\\frac{V_0}{2}", |
| "gt_answer": "\\( 2V_0 \\)", |
| "correct": false |
| }, |
| { |
| "index": 265, |
| "pred_answer": "0.98c", |
| "gt_answer": "\\(0.987c\\)", |
| "correct": false |
| }, |
| { |
| "index": 266, |
| "pred_answer": "\\nu'=\\nu\\left(1+\\frac{m_ec^2}{h}\\cos^2\\theta\\right)", |
| "gt_answer": "\\[ \\frac{\\nu}{1 + \\frac{h\\nu}{m_0 c^2} (1 - \\cos \\theta)} \\]", |
| "correct": false |
| }, |
| { |
| "index": 268, |
| "pred_answer": "\\frac{1}{10}", |
| "gt_answer": "\\[ \\frac{17}{81} \\]", |
| "correct": false |
| }, |
| { |
| "index": 269, |
| "pred_answer": "4.69\\times 10^{-25}\\ \\text{J}", |
| "gt_answer": "\\( 0.000000000000684 \\text{ J} \\)", |
| "correct": false |
| }, |
| { |
| "index": 272, |
| "pred_answer": "553\\ \\text{MeV}", |
| "gt_answer": "\\( 78.9 \\text{ MeV} \\)", |
| "correct": false |
| }, |
| { |
| "index": 274, |
| "pred_answer": "12.1^\\circ", |
| "gt_answer": "\\( 12.7^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 275, |
| "pred_answer": "35.3^\\circ", |
| "gt_answer": "\\( 34.4^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 276, |
| "pred_answer": "1.33\\times 10^7\\ \\text{m/s}", |
| "gt_answer": "\\( 0.95c \\)", |
| "correct": false |
| }, |
| { |
| "index": 282, |
| "pred_answer": "0.044\\ \\text{m}", |
| "gt_answer": "\\( 0.05021 \\text{rev} \\)", |
| "correct": false |
| }, |
| { |
| "index": 283, |
| "pred_answer": "1.0\\ \\text{mA}", |
| "gt_answer": "\\( (1/16)A \\)", |
| "correct": false |
| }, |
| { |
| "index": 284, |
| "pred_answer": null, |
| "gt_answer": "\\(V_0\\sqrt{C/L} \\)", |
| "correct": false |
| }, |
| { |
| "index": 285, |
| "pred_answer": null, |
| "gt_answer": "$C_1 / (1 - \\omega R C_1)$", |
| "correct": false |
| }, |
| { |
| "index": 286, |
| "pred_answer": "V_0", |
| "gt_answer": "\\( \\frac{C_1}{C_1+C_2}V_0 \\)", |
| "correct": false |
| }, |
| { |
| "index": 290, |
| "pred_answer": "12\\ \\text{V}", |
| "gt_answer": "\\(V_{\\text{DC}\\)", |
| "correct": false |
| }, |
| { |
| "index": 291, |
| "pred_answer": "5\\ \\text{ft}", |
| "gt_answer": "\\( 1.3 \\text{ ft} \\)", |
| "correct": false |
| }, |
| { |
| "index": 293, |
| "pred_answer": "0.00000000333\\ \\text{s}", |
| "gt_answer": "\\( 0.11 t_0 \\)", |
| "correct": false |
| }, |
| { |
| "index": 305, |
| "pred_answer": "\\frac{I_t}{I_0}=\\left(1-R\\right)\\left(\\frac{\\sin d\\sin\\theta}{d\\sin\\theta}\\right)^2", |
| "gt_answer": "\\( \\frac{T^4}{2R^2(1-\\cos(4\\pi D/\\lambda)) + T^4} \\)", |
| "correct": false |
| }, |
| { |
| "index": 306, |
| "pred_answer": "0.21\\,\\lambda", |
| "gt_answer": "\\( \\omega \\frac{F_2}{F_1} \\frac{\\cos \\theta_i}{\\cos \\theta_d} \\)", |
| "correct": false |
| }, |
| { |
| "index": 308, |
| "pred_answer": "\\boldsymbol E(t)=-\\frac{1}{c}\\boldsymbol a", |
| "gt_answer": "\\( \\frac{a \\sin \\theta}{(1 - \\beta \\cos \\theta)^3} \\boldsymbol{e}_x \\)", |
| "correct": false |
| }, |
| { |
| "index": 312, |
| "pred_answer": "P_0", |
| "gt_answer": "\\( P_0/2 \\)", |
| "correct": false |
| }, |
| { |
| "index": 313, |
| "pred_answer": null, |
| "gt_answer": "\\( \\sqrt{(P_0 A/L_0 + K)/m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 315, |
| "pred_answer": "4", |
| "gt_answer": "1", |
| "correct": false |
| }, |
| { |
| "index": 317, |
| "pred_answer": "1140\\ \\text{V}", |
| "gt_answer": "\\( \\frac{d^2}{lcq_e} \\frac{\\sqrt{3mc^2kT}}{t} \\)", |
| "correct": false |
| }, |
| { |
| "index": 319, |
| "pred_answer": "0.51", |
| "gt_answer": "\\( 66\\% \\)", |
| "correct": false |
| }, |
| { |
| "index": 320, |
| "pred_answer": "0.025\\ \\text{J/K}", |
| "gt_answer": "\\( 27.8 \\mathrm{ J K}^{-1} \\)", |
| "correct": false |
| }, |
| { |
| "index": 322, |
| "pred_answer": "0.0037\\ \\text{m}^3/\\text{s}", |
| "gt_answer": "\\( 2.8 \\mathrm{ m}^3 \\mathrm{ s}^{-1} \\)", |
| "correct": false |
| }, |
| { |
| "index": 323, |
| "pred_answer": "0\\ \\text{J/K}", |
| "gt_answer": "0", |
| "correct": false |
| }, |
| { |
| "index": 324, |
| "pred_answer": "109\\ \\text{Hz}", |
| "gt_answer": "\\( \\frac{1}{2\\pi} \\sqrt{\\frac{T}{m} \\frac{l}{x(l-x)}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 327, |
| "pred_answer": "3", |
| "gt_answer": "2", |
| "correct": false |
| }, |
| { |
| "index": 332, |
| "pred_answer": "-\\frac{\\sigma_2-\\sigma_1}{\\epsilon_0}", |
| "gt_answer": "\\[ \\phi(P) = \\frac{\\lambda}{4\\pi\\epsilon_0} \\ln \\left[ \\frac{l_2 + \\sqrt{r^2 + l_2^2}}{-l_1 + \\sqrt{r^2 + l_1^2}} \\right] \\]", |
| "correct": false |
| }, |
| { |
| "index": 333, |
| "pred_answer": "1.5\\times 10^7\\ \\text{N/C}", |
| "gt_answer": "\\[ \\left( \\frac{\\lambda}{2\\pi \\epsilon_0 r} \\right) \\boldsymbol{e}_r \\]", |
| "correct": false |
| }, |
| { |
| "index": 334, |
| "pred_answer": "413000\\ \\text{V}", |
| "gt_answer": "\\[ \\frac{1}{2\\pi\\epsilon_0} \\left[ \\frac{q+q'}{r_c} - q' \\left( \\frac{1}{r_b} - \\frac{1}{r_a} \\right) \\right] \\]", |
| "correct": false |
| }, |
| { |
| "index": 336, |
| "pred_answer": "\\lambda A", |
| "gt_answer": "\\[ -\\frac{4}{9} \\epsilon_0 k x^{-2/3} \\]", |
| "correct": false |
| }, |
| { |
| "index": 337, |
| "pred_answer": "-\\frac{kQ}{a}", |
| "gt_answer": "\\[ \\frac{1}{4\\pi\\epsilon_0} \\frac{q}{b} \\]", |
| "correct": false |
| }, |
| { |
| "index": 340, |
| "pred_answer": null, |
| "gt_answer": "\\[ 0.000000011 \\mathrm{C\\,m^{-2}} \\]", |
| "correct": false |
| }, |
| { |
| "index": 342, |
| "pred_answer": "2686.7^\\circ\\text{C}", |
| "gt_answer": "\\[ 20.53^\\circ\\text{C} \\]", |
| "correct": false |
| }, |
| { |
| "index": 347, |
| "pred_answer": "14\\ \\mu\\text{T}", |
| "gt_answer": "\\( dj/2\\epsilon_0c^2 \\)", |
| "correct": false |
| }, |
| { |
| "index": 348, |
| "pred_answer": "\\mathbf{B}=\\left(\\frac{\\omega B_0}{v}\\right)\\cos(\\omega t)\\,\\mathbf{k}", |
| "gt_answer": "\\[ \\frac{\\sigma v}{2\\epsilon_0 c^2} \\boldsymbol{e}_x \\]", |
| "correct": false |
| }, |
| { |
| "index": 354, |
| "pred_answer": "267000000000000", |
| "gt_answer": "\\( 4000000 \\text{ photons} \\)", |
| "correct": false |
| }, |
| { |
| "index": 356, |
| "pred_answer": "0.46\\ \\text{s}", |
| "gt_answer": "\\( k_1+k_2 \\)", |
| "correct": false |
| }, |
| { |
| "index": 360, |
| "pred_answer": "1", |
| "gt_answer": "1.000289", |
| "correct": false |
| }, |
| { |
| "index": 362, |
| "pred_answer": "-\\frac{1}{k}", |
| "gt_answer": "\\( \\frac{1}{3} \\)", |
| "correct": false |
| }, |
| { |
| "index": 365, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "\\( 18.8^\\circ \\)", |
| "correct": false |
| }, |
| { |
| "index": 366, |
| "pred_answer": "24", |
| "gt_answer": "5", |
| "correct": false |
| }, |
| { |
| "index": 368, |
| "pred_answer": "0.75\\ \\text{s}", |
| "gt_answer": "\\( 0.4 \\text{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 371, |
| "pred_answer": null, |
| "gt_answer": "\\( 2\\pi \\sqrt{\\frac{d}{\\mu g}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 374, |
| "pred_answer": null, |
| "gt_answer": "\\( 2\\pi \\sqrt{\\frac{m + \\frac{J}{R^2}}{k}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 377, |
| "pred_answer": "y(x,t)=f(-ut).", |
| "gt_answer": "\\( 3\\cos4\\pi\\left(t + \\frac{x}{20}\\right)\\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 378, |
| "pred_answer": "y(t)=0.2\\sin(2\\pi t)\\ \\text{m}", |
| "gt_answer": "\\( 0.2\\cos\\left(2\\pi t - \\frac{\\pi}{2}\\right)\\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 379, |
| "pred_answer": "0.0000048\\ \\text{m}", |
| "gt_answer": "\\( 2 \\left[\\sqrt{4(H+h)^2 + d^2} - \\sqrt{4H^2 + d^2}\\right] \\)", |
| "correct": false |
| }, |
| { |
| "index": 380, |
| "pred_answer": "0", |
| "gt_answer": "\\( A \\cos\\omega t \\)", |
| "correct": false |
| }, |
| { |
| "index": 383, |
| "pred_answer": "58.2\\ \\text{m/s}", |
| "gt_answer": "\\( 0.25 \\text{ m/s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 384, |
| "pred_answer": "27^\\circ", |
| "gt_answer": "\\( \\arcsin \\frac{\\sqrt{n_2^2 - n_1^2}}{n_0} \\)", |
| "correct": false |
| }, |
| { |
| "index": 385, |
| "pred_answer": "2.00\\ \\text{cm}", |
| "gt_answer": "\\( 10 \\text{ cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 389, |
| "pred_answer": "12", |
| "gt_answer": "8", |
| "correct": false |
| }, |
| { |
| "index": 392, |
| "pred_answer": "0.999958", |
| "gt_answer": "1.00029", |
| "correct": false |
| }, |
| { |
| "index": 393, |
| "pred_answer": "30^\\circ", |
| "gt_answer": "\\( 11^\\circ 30' \\)", |
| "correct": false |
| }, |
| { |
| "index": 395, |
| "pred_answer": "90^\\circ", |
| "gt_answer": "\\( 19^\\circ 45' \\)", |
| "correct": false |
| }, |
| { |
| "index": 398, |
| "pred_answer": "32.6^\\circ", |
| "gt_answer": "\\( \\frac{\\alpha + \\delta_{\\text{min}}}{2} \\)", |
| "correct": false |
| }, |
| { |
| "index": 399, |
| "pred_answer": "\\frac{h}{d}", |
| "gt_answer": "\\( \\sqrt{1 + \\left(\\frac{2h}{d}\\right)^2} \\)", |
| "correct": false |
| }, |
| { |
| "index": 401, |
| "pred_answer": "2.236\\ \\text{cm}", |
| "gt_answer": "\\( d \\left( 1 - \\frac{1}{n} \\right) \\)", |
| "correct": false |
| }, |
| { |
| "index": 402, |
| "pred_answer": "P_1O + OP_2 = 2R", |
| "gt_answer": "\\( (b^2 + R^2 + 2bR \\cos\\theta)^2 + (b^2 + R^2 - 2bR \\cos\\theta)^2 \\)", |
| "correct": false |
| }, |
| { |
| "index": 403, |
| "pred_answer": null, |
| "gt_answer": "\\( n_0 - \\frac{r^2}{2fd} \\)", |
| "correct": false |
| }, |
| { |
| "index": 404, |
| "pred_answer": "5.0\\text{ cm}", |
| "gt_answer": "\\( 11.3 \\, \\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 405, |
| "pred_answer": "2.121", |
| "gt_answer": "2", |
| "correct": false |
| }, |
| { |
| "index": 406, |
| "pred_answer": "1.330", |
| "gt_answer": "\\( \\frac{D_2}{D_1} \\)", |
| "correct": false |
| }, |
| { |
| "index": 407, |
| "pred_answer": "40\\text{ cm}", |
| "gt_answer": "\\( 12 \\, \\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 409, |
| "pred_answer": "\\text{real}", |
| "gt_answer": "\\( 2\\left(\\delta+\\frac{D}{n}\\right) \\)", |
| "correct": false |
| }, |
| { |
| "index": 410, |
| "pred_answer": "140\\text{ cm}", |
| "gt_answer": "\\( 30 \\, \\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 411, |
| "pred_answer": "1.11", |
| "gt_answer": "1", |
| "correct": false |
| }, |
| { |
| "index": 415, |
| "pred_answer": "10.0\\ \\text{cm}", |
| "gt_answer": "\\( 0.3 \\, \\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 417, |
| "pred_answer": "2.00\\ \\text{mm}", |
| "gt_answer": "\\( 20.3 \\, \\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 418, |
| "pred_answer": "-2.00\\ \\text{m}", |
| "gt_answer": "\\( 60 \\, \\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 419, |
| "pred_answer": "2.0", |
| "gt_answer": "-0.375", |
| "correct": false |
| }, |
| { |
| "index": 421, |
| "pred_answer": "12.0\\ \\text{mm}", |
| "gt_answer": "\\( 36.00 \\, \\text{m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 422, |
| "pred_answer": "n = n_g", |
| "gt_answer": "\\( \\sqrt{n_{\\text{g}}^2 - \\sin^2 i'} \\)", |
| "correct": false |
| }, |
| { |
| "index": 423, |
| "pred_answer": "37^\\circ", |
| "gt_answer": "\\( 0.0213 \\, (\\text{rad}) \\)", |
| "correct": false |
| }, |
| { |
| "index": 425, |
| "pred_answer": "-112\\text{ cm}", |
| "gt_answer": "\\( \\frac{1}{2.2} \\text{ cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 428, |
| "pred_answer": "5.65\\pi \\ \\text{rad}", |
| "gt_answer": "\\( 480000 \\text{ (rad)} \\)", |
| "correct": false |
| }, |
| { |
| "index": 431, |
| "pred_answer": "1.7", |
| "gt_answer": "1.52", |
| "correct": false |
| }, |
| { |
| "index": 432, |
| "pred_answer": "0.26\\ \\text{m}", |
| "gt_answer": "\\( D\\sqrt{2\\left(1 - \\frac{j\\lambda}{t}\\right)} \\)", |
| "correct": false |
| }, |
| { |
| "index": 436, |
| "pred_answer": "14.8\\ \\text{mm}", |
| "gt_answer": "\\( 13.5(\\text{mm}) \\)", |
| "correct": false |
| }, |
| { |
| "index": 438, |
| "pred_answer": "60\\text{ mm}", |
| "gt_answer": "\\( 90\\text{mm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 439, |
| "pred_answer": "2.0\\ \\text{cm}", |
| "gt_answer": "\\( 0.12(\\text{cm}) \\)", |
| "correct": false |
| }, |
| { |
| "index": 440, |
| "pred_answer": "h", |
| "gt_answer": "\\( 0.3\\text{(mm)} \\)", |
| "correct": false |
| }, |
| { |
| "index": 441, |
| "pred_answer": "15\\text{ cm}", |
| "gt_answer": "\\( 2\\text{cm} \\)", |
| "correct": false |
| }, |
| { |
| "index": 443, |
| "pred_answer": "2", |
| "gt_answer": "4", |
| "correct": false |
| }, |
| { |
| "index": 445, |
| "pred_answer": "1.0", |
| "gt_answer": "1.5", |
| "correct": false |
| }, |
| { |
| "index": 447, |
| "pred_answer": "0.50\\ \\text{mm}", |
| "gt_answer": "\\( 0.6328(\\mu\\text{m}) \\)", |
| "correct": false |
| }, |
| { |
| "index": 448, |
| "pred_answer": "0.003125\\ \\text{mm}", |
| "gt_answer": "\\( \\frac{\\lambda}{2 \\sin \\alpha \\sin \\beta} \\)", |
| "correct": false |
| }, |
| { |
| "index": 450, |
| "pred_answer": "0.00018\\ \\text{m}", |
| "gt_answer": "\\( 1.625(\\text{mm}) \\)", |
| "correct": false |
| }, |
| { |
| "index": 453, |
| "pred_answer": "\\lambda", |
| "gt_answer": "\\( \\left(k + \\frac{1}{2}\\right)\\frac{\\lambda}{n-1}\\)", |
| "correct": false |
| }, |
| { |
| "index": 456, |
| "pred_answer": "\\frac{2\\pi v}{\\hbar}+\\frac{mgH}{\\hbar}", |
| "gt_answer": "\\( v \\left(1 + \\frac{gH}{c^2}\\right) \\)", |
| "correct": false |
| }, |
| { |
| "index": 461, |
| "pred_answer": "10\\,\\mu\\text{s}", |
| "gt_answer": "\\( \\textbf{10}^\\textbf{9} \\textbf{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 462, |
| "pred_answer": "220\\text{ k}\\Omega", |
| "gt_answer": "\\( \\textbf{1.85} \\times \\textbf{10}^\\textbf{5} \\textbf{\\Omega} \\)", |
| "correct": false |
| }, |
| { |
| "index": 463, |
| "pred_answer": "4069", |
| "gt_answer": "42", |
| "correct": false |
| }, |
| { |
| "index": 465, |
| "pred_answer": "400000000000000", |
| "gt_answer": "\\( \\frac{1}{\\lambda} [\\alpha - (\\alpha - \\lambda \\textbf{N}_0)\\textbf{e}^{-\\lambda t}] \\)", |
| "correct": false |
| }, |
| { |
| "index": 469, |
| "pred_answer": "0\\ \\text{N/C}", |
| "gt_answer": "0", |
| "correct": false |
| }, |
| { |
| "index": 471, |
| "pred_answer": null, |
| "gt_answer": "\\( 3\\epsilon_0 vB \\cos \\theta' \\)", |
| "correct": false |
| }, |
| { |
| "index": 474, |
| "pred_answer": "0.99999999999999999999999999999999\\,c", |
| "gt_answer": "\\( : 0.198c \\)", |
| "correct": false |
| }, |
| { |
| "index": 476, |
| "pred_answer": "0.0000156\\ \\text{s}", |
| "gt_answer": "\\( \\frac{L}{c} \\sqrt{\\frac{v+c}{c-v}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 477, |
| "pred_answer": "0", |
| "gt_answer": "\\( \\frac{2 l_0 \\Delta t}{(\\Delta t)^2 + \\frac{l_0^2}{c^2}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 480, |
| "pred_answer": "\\frac{l}{u}", |
| "gt_answer": "\\( \\frac{l(c^2 + uv)}{uc^2 \\sqrt{1-(v/c)^2}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 481, |
| "pred_answer": "1.225\\, l_0", |
| "gt_answer": "\\( \\frac{l_0(c^2 - v^2)}{c^2 + v^2} \\)", |
| "correct": false |
| }, |
| { |
| "index": 482, |
| "pred_answer": "2.236\\,c", |
| "gt_answer": "\\( 4720 \\text{ km}\\cdot\\text{s}^{-1} \\)", |
| "correct": false |
| }, |
| { |
| "index": 484, |
| "pred_answer": "0.00238\\ \\text{s}", |
| "gt_answer": "\\( \\frac{L_0/\\gamma + l_0}{\\nu} \\)", |
| "correct": false |
| }, |
| { |
| "index": 485, |
| "pred_answer": "20\\ \\text{m s}^{-2}", |
| "gt_answer": "\\( 1.97 \\text{year} \\)", |
| "correct": false |
| }, |
| { |
| "index": 486, |
| "pred_answer": "5\\ \\text{s}", |
| "gt_answer": "\\( 8 \\text{ s} \\)", |
| "correct": false |
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| { |
| "index": 487, |
| "pred_answer": "1.8\\times 10^{-7}\\ \\text{h}", |
| "gt_answer": "\\( -0.000033 \\text{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 489, |
| "pred_answer": "2.88\\ \\text{s}", |
| "gt_answer": "\\( 2.93 \\text{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 491, |
| "pred_answer": "0.412", |
| "gt_answer": "\\( 4 \\text{ s} \\)", |
| "correct": false |
| }, |
| { |
| "index": 492, |
| "pred_answer": "0.26\\ \\text{MeV}", |
| "gt_answer": "\\( 0.000000000000007 \\text{ J} \\)", |
| "correct": false |
| }, |
| { |
| "index": 493, |
| "pred_answer": "431\\ \\text{nm}", |
| "gt_answer": "\\( 0.000000649 \\text{ m} \\)", |
| "correct": false |
| }, |
| { |
| "index": 495, |
| "pred_answer": "m A", |
| "gt_answer": "\\( \\frac{n^2 h^2}{4mL^3} \\)", |
| "correct": false |
| }, |
| { |
| "index": 499, |
| "pred_answer": "\\frac{(v - v_0)^2}{2g}", |
| "gt_answer": "\\( \\frac{c^2}{g} \\left(\\frac{1}{\\sqrt{1+(v/c)^2}} - 1\\right) \\)", |
| "correct": false |
| }, |
| { |
| "index": 500, |
| "pred_answer": "4640000000", |
| "gt_answer": "\\( \\left(\\frac{1+v/c}{1-v/c}\\right)^n \\)", |
| "correct": false |
| }, |
| { |
| "index": 502, |
| "pred_answer": "\\frac{l_0}{v}", |
| "gt_answer": "\\( \\frac{l_0 \\left(1 + \\frac{u_0 v}{c^2}\\right)}{u_0 \\sqrt{1 - \\frac{v^2}{c^2}}} \\)", |
| "correct": false |
| }, |
| { |
| "index": 503, |
| "pred_answer": "232400000\\ \\text{m/s}", |
| "gt_answer": "\\( 0.78c \\)", |
| "correct": false |
| }, |
| { |
| "index": 506, |
| "pred_answer": "12.6\\ \\text{seconds}", |
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| "correct": false |
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| { |
| "index": 510, |
| "pred_answer": "5.6\\ \\text{N}", |
| "gt_answer": "6.6kN", |
| "correct": false |
| }, |
| { |
| "index": 511, |
| "pred_answer": "5.61\\ \\text{N},\\ 4.38\\ \\text{N}", |
| "gt_answer": "50N", |
| "correct": false |
| }, |
| { |
| "index": 512, |
| "pred_answer": "4330\\ \\text{N}", |
| "gt_answer": "7600N", |
| "correct": false |
| }, |
| { |
| "index": 513, |
| "pred_answer": "1.60\\ \\text{m}", |
| "gt_answer": "0.8m", |
| "correct": false |
| }, |
| { |
| "index": 518, |
| "pred_answer": "135\\text{ N}", |
| "gt_answer": "140N", |
| "correct": false |
| }, |
| { |
| "index": 519, |
| "pred_answer": "0.50\\ \\text{m}", |
| "gt_answer": "49.9cm", |
| "correct": false |
| }, |
| { |
| "index": 520, |
| "pred_answer": "73.2\\text{ N (upward)}", |
| "gt_answer": "474N", |
| "correct": false |
| }, |
| { |
| "index": 521, |
| "pred_answer": "125\\ \\text{mm}", |
| "gt_answer": "4.4mm", |
| "correct": false |
| }, |
| { |
| "index": 524, |
| "pred_answer": "0.452", |
| "gt_answer": "0.473", |
| "correct": false |
| }, |
| { |
| "index": 527, |
| "pred_answer": "0.26\\ \\text{N}", |
| "gt_answer": "0.848N", |
| "correct": false |
| }, |
| { |
| "index": 529, |
| "pred_answer": "0.480\\ \\text{m}", |
| "gt_answer": "1.92m", |
| "correct": false |
| }, |
| { |
| "index": 531, |
| "pred_answer": "5.625\\ \\text{m}", |
| "gt_answer": "0.44m", |
| "correct": false |
| }, |
| { |
| "index": 532, |
| "pred_answer": "287\\ \\text{N}", |
| "gt_answer": "400N", |
| "correct": false |
| }, |
| { |
| "index": 535, |
| "pred_answer": "1100\\ \\text{Pa}", |
| "gt_answer": "921Pa", |
| "correct": false |
| }, |
| { |
| "index": 537, |
| "pred_answer": "13.9\\text{ cm}", |
| "gt_answer": "13.9cm", |
| "correct": false |
| }, |
| { |
| "index": 538, |
| "pred_answer": "-0.35\\ \\text{N}", |
| "gt_answer": "8.2kg", |
| "correct": false |
| }, |
| { |
| "index": 539, |
| "pred_answer": "3.2\\ \\text{kPa}", |
| "gt_answer": "69700Pa", |
| "correct": false |
| }, |
| { |
| "index": 540, |
| "pred_answer": "P_2 = P_1 - 100\\text{ Pa}", |
| "gt_answer": "0.000000025N", |
| "correct": false |
| }, |
| { |
| "index": 543, |
| "pred_answer": "5.94\\times 10^{-10}\\ \\text{N·m}^2", |
| "gt_answer": "0.0000191\\, \\text{N} \\cdot \\text{m/rad}", |
| "correct": false |
| }, |
| { |
| "index": 545, |
| "pred_answer": "23.0\\text{ cm}", |
| "gt_answer": "45cm", |
| "correct": false |
| }, |
| { |
| "index": 546, |
| "pred_answer": "1.816\\ \\text{m}", |
| "gt_answer": "25m", |
| "correct": false |
| }, |
| { |
| "index": 547, |
| "pred_answer": "0.0000135\\ \\text{kg}", |
| "gt_answer": "18.5g", |
| "correct": false |
| }, |
| { |
| "index": 549, |
| "pred_answer": "48.6\\ \\text{m}", |
| "gt_answer": "90.8m", |
| "correct": false |
| }, |
| { |
| "index": 552, |
| "pred_answer": "630\\ \\text{Hz}", |
| "gt_answer": "375Hz", |
| "correct": false |
| }, |
| { |
| "index": 553, |
| "pred_answer": "12.0\\ \\text{Hz}", |
| "gt_answer": "27.3Hz", |
| "correct": false |
| }, |
| { |
| "index": 554, |
| "pred_answer": "12.73\\ \\text{Hz}", |
| "gt_answer": "86Hz", |
| "correct": false |
| }, |
| { |
| "index": 555, |
| "pred_answer": "0.625\\ \\text{m}", |
| "gt_answer": "0.242m", |
| "correct": false |
| }, |
| { |
| "index": 556, |
| "pred_answer": null, |
| "gt_answer": "340000J/kg", |
| "correct": false |
| }, |
| { |
| "index": 557, |
| "pred_answer": "0.65\\ \\text{m}", |
| "gt_answer": "1m", |
| "correct": false |
| }, |
| { |
| "index": 558, |
| "pred_answer": "1.00\\ \\text{m}", |
| "gt_answer": "1.74m", |
| "correct": false |
| }, |
| { |
| "index": 559, |
| "pred_answer": "\\frac{m a^2}{2}", |
| "gt_answer": "0\\, kg*{m}^2", |
| "correct": false |
| }, |
| { |
| "index": 561, |
| "pred_answer": "73\\ \\text{J}", |
| "gt_answer": "53J", |
| "correct": false |
| }, |
| { |
| "index": 563, |
| "pred_answer": "0\\ \\text{J}", |
| "gt_answer": "0J", |
| "correct": false |
| }, |
| { |
| "index": 566, |
| "pred_answer": "23.6\\ \\text{J}", |
| "gt_answer": "-1950J", |
| "correct": false |
| }, |
| { |
| "index": 567, |
| "pred_answer": "0.20\\ \\text{L}", |
| "gt_answer": "0.8L", |
| "correct": false |
| }, |
| { |
| "index": 571, |
| "pred_answer": "-30.4\\%", |
| "gt_answer": "31.9\\%", |
| "correct": false |
| }, |
| { |
| "index": 572, |
| "pred_answer": "6100\\ \\text{J}", |
| "gt_answer": "220J", |
| "correct": false |
| }, |
| { |
| "index": 573, |
| "pred_answer": "1.00", |
| "gt_answer": "10.5\\%", |
| "correct": false |
| }, |
| { |
| "index": 574, |
| "pred_answer": "0.50", |
| "gt_answer": "8.7\\%", |
| "correct": false |
| }, |
| { |
| "index": 575, |
| "pred_answer": "60\\%", |
| "gt_answer": "8.7\\%", |
| "correct": false |
| }, |
| { |
| "index": 576, |
| "pred_answer": "0", |
| "gt_answer": "11.1\\%", |
| "correct": false |
| }, |
| { |
| "index": 578, |
| "pred_answer": "33.3\\%", |
| "gt_answer": "6.25\\%", |
| "correct": false |
| }, |
| { |
| "index": 579, |
| "pred_answer": "1.6\\ \\text{MW}", |
| "gt_answer": "153kW", |
| "correct": false |
| }, |
| { |
| "index": 580, |
| "pred_answer": "4.8\\ \\mu\\text{A}", |
| "gt_answer": "0.24mV", |
| "correct": false |
| }, |
| { |
| "index": 581, |
| "pred_answer": "0.200\\ \\text{V (clockwise)}", |
| "gt_answer": "0.435V", |
| "correct": false |
| }, |
| { |
| "index": 583, |
| "pred_answer": "0.000031\\ \\text{V/m}", |
| "gt_answer": "0.0002V/m", |
| "correct": false |
| }, |
| { |
| "index": 584, |
| "pred_answer": null, |
| "gt_answer": "25\\ \\mu\\mathrm{H}", |
| "correct": false |
| }, |
| { |
| "index": 587, |
| "pred_answer": "637\\ \\Omega", |
| "gt_answer": "80\\ \\Omega\\", |
| "correct": false |
| }, |
| { |
| "index": 589, |
| "pred_answer": "1.1\\times 10^{-9}\\ \\text{T}", |
| "gt_answer": "0.0000000000817T", |
| "correct": false |
| }, |
| { |
| "index": 590, |
| "pred_answer": "180\\ \\text{W/m}^2", |
| "gt_answer": "5.6kW", |
| "correct": false |
| }, |
| { |
| "index": 591, |
| "pred_answer": "\\begin{array}{l}\n\\text{Reflected ray direction: } 60^\\circ\\text{ from normal} \\\\\n\\text{Refracted ray direction: } 40.9^\\circ\\text{ from normal}\n\\end{array}", |
| "gt_answer": "49.3^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 592, |
| "pred_answer": "48.8^\\circ", |
| "gt_answer": "53.1^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 597, |
| "pred_answer": "1.00\\ \\text{m}", |
| "gt_answer": "1.5m", |
| "correct": false |
| }, |
| { |
| "index": 601, |
| "pred_answer": "1.90\\times 10^{-6}\\ \\text{m}", |
| "gt_answer": "633nm", |
| "correct": false |
| }, |
| { |
| "index": 602, |
| "pred_answer": "0.068\\ \\text{mm}", |
| "gt_answer": "633nm", |
| "correct": false |
| }, |
| { |
| "index": 604, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "60.0^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 605, |
| "pred_answer": "1.5", |
| "gt_answer": "1.59", |
| "correct": false |
| }, |
| { |
| "index": 610, |
| "pred_answer": "40\\text{ cm}", |
| "gt_answer": "8.3cm", |
| "correct": false |
| }, |
| { |
| "index": 617, |
| "pred_answer": "0.663\\ \\text{m}", |
| "gt_answer": "6.1m", |
| "correct": false |
| }, |
| { |
| "index": 619, |
| "pred_answer": "15\\text{ cm}", |
| "gt_answer": "30cm", |
| "correct": false |
| }, |
| { |
| "index": 624, |
| "pred_answer": "10^\\circ", |
| "gt_answer": "20^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 629, |
| "pred_answer": "1.50", |
| "gt_answer": "1.58", |
| "correct": false |
| }, |
| { |
| "index": 631, |
| "pred_answer": "10\\text{ cm}", |
| "gt_answer": "15cm", |
| "correct": false |
| }, |
| { |
| "index": 633, |
| "pred_answer": "-8", |
| "gt_answer": "2.5", |
| "correct": false |
| }, |
| { |
| "index": 636, |
| "pred_answer": "269700\\ \\text{N}", |
| "gt_answer": "0N", |
| "correct": false |
| }, |
| { |
| "index": 638, |
| "pred_answer": "1800\\ \\text{N}", |
| "gt_answer": "0.00018N", |
| "correct": false |
| }, |
| { |
| "index": 639, |
| "pred_answer": "8.4\\times 10^{-11}\\ \\mathrm{N}", |
| "gt_answer": "0.0043N", |
| "correct": false |
| }, |
| { |
| "index": 640, |
| "pred_answer": "710000\\ \\text{N}", |
| "gt_answer": "0.0073N", |
| "correct": false |
| }, |
| { |
| "index": 641, |
| "pred_answer": "8.99\\times 10^{-15}\\ \\text{N}", |
| "gt_answer": "0.0002N", |
| "correct": false |
| }, |
| { |
| "index": 643, |
| "pred_answer": "-1.0\\ \\text{nC}", |
| "gt_answer": "0.68nC", |
| "correct": false |
| }, |
| { |
| "index": 649, |
| "pred_answer": "25\\ \\text{nC}", |
| "gt_answer": "14^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 650, |
| "pred_answer": "0.0000001\\ \\text{kg}", |
| "gt_answer": "4.1g", |
| "correct": false |
| }, |
| { |
| "index": 652, |
| "pred_answer": "2.0\\times 10^{7}\\ \\text{m/s}", |
| "gt_answer": "33000000m/s", |
| "correct": false |
| }, |
| { |
| "index": 654, |
| "pred_answer": "-630000\\ \\text{rad/s}^2", |
| "gt_answer": "5rad/s^2", |
| "correct": false |
| }, |
| { |
| "index": 656, |
| "pred_answer": "-1.60\\times 10^{-19}\\ \\text{C}", |
| "gt_answer": "-0.0000000000099C", |
| "correct": false |
| }, |
| { |
| "index": 657, |
| "pred_answer": "1080\\ \\text{N/C}", |
| "gt_answer": "7600N/C", |
| "correct": false |
| }, |
| { |
| "index": 660, |
| "pred_answer": "0\\ \\text{N/C}", |
| "gt_answer": "7600N/C", |
| "correct": false |
| }, |
| { |
| "index": 664, |
| "pred_answer": "4700\\ \\text{N/C}", |
| "gt_answer": "98000N/C", |
| "correct": false |
| }, |
| { |
| "index": 667, |
| "pred_answer": "16000\\ \\text{V/m}", |
| "gt_answer": "2.5mm", |
| "correct": false |
| }, |
| { |
| "index": 669, |
| "pred_answer": "50\\ \\text{N/C}", |
| "gt_answer": "5N/C", |
| "correct": false |
| }, |
| { |
| "index": 670, |
| "pred_answer": "1800000\\ \\text{N/C}", |
| "gt_answer": "-5N/C", |
| "correct": false |
| }, |
| { |
| "index": 674, |
| "pred_answer": "2060\\ \\text{N/C}", |
| "gt_answer": "1400N/C", |
| "correct": false |
| }, |
| { |
| "index": 675, |
| "pred_answer": "0", |
| "gt_answer": "0N m^2/C", |
| "correct": false |
| }, |
| { |
| "index": 677, |
| "pred_answer": "114\\ \\text{N}\\cdot\\text{m}^2/\\text{C}", |
| "gt_answer": "110N m^2/C", |
| "correct": false |
| }, |
| { |
| "index": 682, |
| "pred_answer": "43000000\\ \\text{m/s}", |
| "gt_answer": "1000 m/s", |
| "correct": false |
| }, |
| { |
| "index": 684, |
| "pred_answer": "9.0\\times10^{-16}\\ \\text{J}", |
| "gt_answer": "0J", |
| "correct": false |
| }, |
| { |
| "index": 693, |
| "pred_answer": "4.0\\ \\text{m/s}", |
| "gt_answer": "0.49m/s", |
| "correct": false |
| }, |
| { |
| "index": 694, |
| "pred_answer": "138000000\\ \\text{m/s}", |
| "gt_answer": "100000m/s", |
| "correct": false |
| }, |
| { |
| "index": 695, |
| "pred_answer": "316000\\ \\text{m/s}", |
| "gt_answer": "296000m/s", |
| "correct": false |
| }, |
| { |
| "index": 696, |
| "pred_answer": "225\\ \\text{V}", |
| "gt_answer": "2100V", |
| "correct": false |
| }, |
| { |
| "index": 697, |
| "pred_answer": "-133\\ \\text{V}", |
| "gt_answer": "-200V", |
| "correct": false |
| }, |
| { |
| "index": 703, |
| "pred_answer": "30\\ \\text{V}", |
| "gt_answer": "-70V", |
| "correct": false |
| }, |
| { |
| "index": 704, |
| "pred_answer": "E_x = -5\\ \\text{V/m}", |
| "gt_answer": "-5V/m", |
| "correct": false |
| }, |
| { |
| "index": 705, |
| "pred_answer": "2500\\ \\text{V/m}", |
| "gt_answer": "3750V/m", |
| "correct": false |
| }, |
| { |
| "index": 707, |
| "pred_answer": "63\\,\\mu\\text{F}", |
| "gt_answer": "25\\ \\mu\\mathrm{F}", |
| "correct": false |
| }, |
| { |
| "index": 708, |
| "pred_answer": "660\\ \\mu\\text{C}", |
| "gt_answer": "60\\ \\mu\\mathrm{C}", |
| "correct": false |
| }, |
| { |
| "index": 709, |
| "pred_answer": "162\\,\\mu\\text{C}", |
| "gt_answer": "16\\ \\mu\\mathrm{C}", |
| "correct": false |
| }, |
| { |
| "index": 711, |
| "pred_answer": "0.000048\\ \\text{J}", |
| "gt_answer": "314J", |
| "correct": false |
| }, |
| { |
| "index": 712, |
| "pred_answer": "10000000000\\ \\text{J}", |
| "gt_answer": "1300J", |
| "correct": false |
| }, |
| { |
| "index": 713, |
| "pred_answer": "40500\\text{ mm}", |
| "gt_answer": "60cm", |
| "correct": false |
| }, |
| { |
| "index": 714, |
| "pred_answer": "1\\ \\text{cm}", |
| "gt_answer": "3.8cm", |
| "correct": false |
| }, |
| { |
| "index": 715, |
| "pred_answer": "75^\\circ\\text{C}", |
| "gt_answer": "1556^\\circ C", |
| "correct": false |
| }, |
| { |
| "index": 716, |
| "pred_answer": "1200\\ \\text{K}", |
| "gt_answer": "3246^\\circ C", |
| "correct": false |
| }, |
| { |
| "index": 720, |
| "pred_answer": "2.88\\ \\text{mmHg}", |
| "gt_answer": "24cm", |
| "correct": false |
| }, |
| { |
| "index": 721, |
| "pred_answer": "690\\ \\text{K}", |
| "gt_answer": "657^\\circ C", |
| "correct": false |
| }, |
| { |
| "index": 724, |
| "pred_answer": "200000\\ \\text{K}", |
| "gt_answer": "338K", |
| "correct": false |
| }, |
| { |
| "index": 726, |
| "pred_answer": "2.25\\ \\text{cm}", |
| "gt_answer": "22.7cm", |
| "correct": false |
| }, |
| { |
| "index": 727, |
| "pred_answer": "1.46\\ \\text{mm}", |
| "gt_answer": "1cm", |
| "correct": false |
| }, |
| { |
| "index": 728, |
| "pred_answer": "480\\ \\text{kPa}", |
| "gt_answer": "500000\\ Pa", |
| "correct": false |
| }, |
| { |
| "index": 729, |
| "pred_answer": "52.4\\ \\text{m/s}", |
| "gt_answer": "4.9m/s", |
| "correct": false |
| }, |
| { |
| "index": 733, |
| "pred_answer": "758\\ \\text{kPa}", |
| "gt_answer": "156.2 kPa", |
| "correct": false |
| }, |
| { |
| "index": 737, |
| "pred_answer": "0.998\\ \\text{m}^3", |
| "gt_answer": "19910kg", |
| "correct": false |
| }, |
| { |
| "index": 738, |
| "pred_answer": "2.95\\ \\text{m}", |
| "gt_answer": "50cm", |
| "correct": false |
| }, |
| { |
| "index": 740, |
| "pred_answer": "103480\\ \\text{Pa}", |
| "gt_answer": "125.2kPa", |
| "correct": false |
| }, |
| { |
| "index": 742, |
| "pred_answer": "0\\ \\text{kPa}", |
| "gt_answer": "25.84kPa", |
| "correct": false |
| }, |
| { |
| "index": 743, |
| "pred_answer": "0.106\\ \\text{N}", |
| "gt_answer": "880kN", |
| "correct": false |
| }, |
| { |
| "index": 744, |
| "pred_answer": "59\\ \\text{kPa}", |
| "gt_answer": "370kPa", |
| "correct": false |
| }, |
| { |
| "index": 747, |
| "pred_answer": "460\\ \\text{kPa}", |
| "gt_answer": "515.3kPa", |
| "correct": false |
| }, |
| { |
| "index": 752, |
| "pred_answer": "400\\ \\text{Pa}", |
| "gt_answer": "3.33MPa", |
| "correct": false |
| }, |
| { |
| "index": 755, |
| "pred_answer": "0.9978\\,c", |
| "gt_answer": "0.0198c", |
| "correct": false |
| }, |
| { |
| "index": 760, |
| "pred_answer": "0.000000000000608\\ \\text{nm}", |
| "gt_answer": "5.7V", |
| "correct": false |
| }, |
| { |
| "index": 761, |
| "pred_answer": "42\\ \\text{m/s}", |
| "gt_answer": "-5m/s", |
| "correct": false |
| }, |
| { |
| "index": 762, |
| "pred_answer": "500\\ \\text{cm}", |
| "gt_answer": "8cm", |
| "correct": false |
| }, |
| { |
| "index": 764, |
| "pred_answer": "16\\ \\text{m/s}", |
| "gt_answer": "30 \\mathrm{m/s}", |
| "correct": false |
| }, |
| { |
| "index": 766, |
| "pred_answer": "90^\\circ", |
| "gt_answer": "63^\\circ ", |
| "correct": false |
| }, |
| { |
| "index": 773, |
| "pred_answer": "10\\ \\text{m/s}", |
| "gt_answer": "13.3 \\mathrm{m/s}", |
| "correct": false |
| }, |
| { |
| "index": 774, |
| "pred_answer": "8.1\\ \\text{m}", |
| "gt_answer": "3.7m", |
| "correct": false |
| }, |
| { |
| "index": 778, |
| "pred_answer": "30\\ \\text{rpm}", |
| "gt_answer": "98rmp", |
| "correct": false |
| }, |
| { |
| "index": 780, |
| "pred_answer": "14.8\\ \\text{m/s}", |
| "gt_answer": "4.8 \\mathrm{m/s}", |
| "correct": false |
| }, |
| { |
| "index": 782, |
| "pred_answer": "\\frac{1}{5}", |
| "gt_answer": "0.48", |
| "correct": false |
| }, |
| { |
| "index": 786, |
| "pred_answer": "0.5\\ \\text{N}", |
| "gt_answer": "3.6N", |
| "correct": false |
| }, |
| { |
| "index": 788, |
| "pred_answer": "87\\ \\text{N}", |
| "gt_answer": "94N", |
| "correct": false |
| }, |
| { |
| "index": 789, |
| "pred_answer": "72\\ \\text{N}", |
| "gt_answer": "12N", |
| "correct": false |
| }, |
| { |
| "index": 790, |
| "pred_answer": "-4\\ \\text{m/s}^2", |
| "gt_answer": "0 \\mathrm{m/s}^2", |
| "correct": false |
| }, |
| { |
| "index": 791, |
| "pred_answer": "19.6\\ \\text{N}", |
| "gt_answer": "1035N", |
| "correct": false |
| }, |
| { |
| "index": 792, |
| "pred_answer": "4\\ \\text{m/s}", |
| "gt_answer": "9 \\mathrm{m/s}", |
| "correct": false |
| }, |
| { |
| "index": 793, |
| "pred_answer": "6\\ \\text{N}", |
| "gt_answer": "4376N", |
| "correct": false |
| }, |
| { |
| "index": 794, |
| "pred_answer": "4.2\\ \\text{kg}", |
| "gt_answer": "77kg", |
| "correct": false |
| }, |
| { |
| "index": 797, |
| "pred_answer": "1.41\\ \\text{kg}", |
| "gt_answer": "9.6N", |
| "correct": false |
| }, |
| { |
| "index": 798, |
| "pred_answer": "10.4\\ \\text{m/s}^2", |
| "gt_answer": "13 \\mathrm{m/s}^2", |
| "correct": false |
| }, |
| { |
| "index": 799, |
| "pred_answer": "24000\\ \\mathrm{m/s^2}", |
| "gt_answer": "3.9 \\mathrm{m/s}^2", |
| "correct": false |
| }, |
| { |
| "index": 802, |
| "pred_answer": "1.25\\ \\text{m}^3", |
| "gt_answer": "287.7 m^3", |
| "correct": false |
| }, |
| { |
| "index": 803, |
| "pred_answer": null, |
| "gt_answer": "587 kJ", |
| "correct": false |
| }, |
| { |
| "index": 805, |
| "pred_answer": "185.4^\\circ\\text{C}", |
| "gt_answer": "25\\circ\\text{C}", |
| "correct": false |
| }, |
| { |
| "index": 807, |
| "pred_answer": "10.7\\ \\text{kJ}", |
| "gt_answer": "220.7 kJ", |
| "correct": false |
| }, |
| { |
| "index": 809, |
| "pred_answer": "298\\ \\text{K}", |
| "gt_answer": "668 k", |
| "correct": false |
| }, |
| { |
| "index": 810, |
| "pred_answer": "275\\ \\text{m/s}", |
| "gt_answer": "13.63 m/s", |
| "correct": false |
| }, |
| { |
| "index": 812, |
| "pred_answer": "1.247\\ \\text{kJ}", |
| "gt_answer": "25961 kJ", |
| "correct": false |
| }, |
| { |
| "index": 813, |
| "pred_answer": "3.35\\times 10^5\\ \\text{J}", |
| "gt_answer": "725 kJ", |
| "correct": false |
| }, |
| { |
| "index": 814, |
| "pred_answer": "-147.4\\ \\text{kJ}", |
| "gt_answer": "348.7 kJ", |
| "correct": false |
| }, |
| { |
| "index": 817, |
| "pred_answer": "-10.2\\ \\text{kJ}", |
| "gt_answer": "-498.3 kJ", |
| "correct": false |
| }, |
| { |
| "index": 818, |
| "pred_answer": "11580\\ \\text{J}", |
| "gt_answer": "-319.85 kJ", |
| "correct": false |
| }, |
| { |
| "index": 819, |
| "pred_answer": "0.15\\ \\text{J}", |
| "gt_answer": "-8.92 \\mu\\text{J}", |
| "correct": false |
| }, |
| { |
| "index": 820, |
| "pred_answer": "125\\ \\text{mN/m}", |
| "gt_answer": "101.9 N/m", |
| "correct": false |
| }, |
| { |
| "index": 821, |
| "pred_answer": "235000\\ \\text{J}", |
| "gt_answer": "-7421 kJ", |
| "correct": false |
| }, |
| { |
| "index": 822, |
| "pred_answer": "379000\\ \\text{J}", |
| "gt_answer": "744 kJ", |
| "correct": false |
| }, |
| { |
| "index": 824, |
| "pred_answer": "554000\\ \\text{J}", |
| "gt_answer": "129.9 kJ", |
| "correct": false |
| }, |
| { |
| "index": 825, |
| "pred_answer": "2100\\ \\text{J}", |
| "gt_answer": "5536 kJ", |
| "correct": false |
| }, |
| { |
| "index": 826, |
| "pred_answer": "343000\\ \\text{J}", |
| "gt_answer": "330 kJ", |
| "correct": false |
| }, |
| { |
| "index": 827, |
| "pred_answer": "38.4\\ \\text{kJ}", |
| "gt_answer": "26758 kJ", |
| "correct": false |
| }, |
| { |
| "index": 828, |
| "pred_answer": "-194.8\\ \\text{kJ}", |
| "gt_answer": "359.8 kJ", |
| "correct": false |
| }, |
| { |
| "index": 829, |
| "pred_answer": "146^\\circ\\text{C}", |
| "gt_answer": "161.75 \\circ\\text{C}", |
| "correct": false |
| }, |
| { |
| "index": 830, |
| "pred_answer": "12.5\\ \\text{kJ}", |
| "gt_answer": "77.73 kJ", |
| "correct": false |
| }, |
| { |
| "index": 831, |
| "pred_answer": "-1.356\\ \\text{kJ}", |
| "gt_answer": "-2068.5 kJ", |
| "correct": false |
| }, |
| { |
| "index": 832, |
| "pred_answer": "Q = 2.45\\times 10^5\\ \\text{J}", |
| "gt_answer": "-135.6 kJ", |
| "correct": false |
| }, |
| { |
| "index": 833, |
| "pred_answer": "3.63\\times 10^{4}\\ \\text{J}", |
| "gt_answer": "2080 kJ", |
| "correct": false |
| }, |
| { |
| "index": 840, |
| "pred_answer": "5.5\\ \\text{m/s}", |
| "gt_answer": "581.8 m/s", |
| "correct": false |
| }, |
| { |
| "index": 845, |
| "pred_answer": "268^\\circ\\text{C}", |
| "gt_answer": "45.8\\circ\\text{C}", |
| "correct": false |
| }, |
| { |
| "index": 846, |
| "pred_answer": "107.5\\ \\text{kJ/kg}", |
| "gt_answer": " 1400.5 kJ", |
| "correct": false |
| }, |
| { |
| "index": 850, |
| "pred_answer": "128\\ \\text{kW}", |
| "gt_answer": " 2463 kW", |
| "correct": false |
| }, |
| { |
| "index": 851, |
| "pred_answer": "184000\\ \\text{W}", |
| "gt_answer": " 7.4 kW", |
| "correct": false |
| }, |
| { |
| "index": 852, |
| "pred_answer": "28500000\\ \\text{W}", |
| "gt_answer": "18.804 MW", |
| "correct": false |
| }, |
| { |
| "index": 853, |
| "pred_answer": "-25.23\\ \\text{kW}", |
| "gt_answer": "17 MW", |
| "correct": false |
| }, |
| { |
| "index": 857, |
| "pred_answer": "0.158\\ \\text{m}^3/\\text{s}", |
| "gt_answer": "3 m^3/s", |
| "correct": false |
| }, |
| { |
| "index": 859, |
| "pred_answer": "125\\ \\text{kW}", |
| "gt_answer": "193.18 kW", |
| "correct": false |
| }, |
| { |
| "index": 862, |
| "pred_answer": "38.5\\ \\text{m/s}", |
| "gt_answer": "753 m/s", |
| "correct": false |
| }, |
| { |
| "index": 864, |
| "pred_answer": "164.6^\\circ\\text{C}", |
| "gt_answer": "410.5 K", |
| "correct": false |
| }, |
| { |
| "index": 865, |
| "pred_answer": "1440\\ \\text{kW}", |
| "gt_answer": "41.04 MJ", |
| "correct": false |
| }, |
| { |
| "index": 867, |
| "pred_answer": "39.1^\\circ\\text{C}", |
| "gt_answer": "692.3 K", |
| "correct": false |
| }, |
| { |
| "index": 870, |
| "pred_answer": "17000000\\ \\text{J}", |
| "gt_answer": "202629 kJ", |
| "correct": false |
| }, |
| { |
| "index": 873, |
| "pred_answer": "1.13\\times 10^{3}\\ \\text{kJ/h}", |
| "gt_answer": "538450 kJ", |
| "correct": false |
| }, |
| { |
| "index": 875, |
| "pred_answer": "50\\%", |
| "gt_answer": "56.3 %", |
| "correct": false |
| }, |
| { |
| "index": 876, |
| "pred_answer": "-6.67", |
| "gt_answer": "0.687", |
| "correct": false |
| }, |
| { |
| "index": 877, |
| "pred_answer": "7.17\\ \\text{MW}", |
| "gt_answer": "1.09 MW", |
| "correct": false |
| }, |
| { |
| "index": 879, |
| "pred_answer": "2.34\\ \\text{kJ}", |
| "gt_answer": "60.1 kJ", |
| "correct": false |
| }, |
| { |
| "index": 882, |
| "pred_answer": "41500000000\\ \\text{J}", |
| "gt_answer": "81946 kJ", |
| "correct": false |
| }, |
| { |
| "index": 886, |
| "pred_answer": "139000\\ \\text{J}", |
| "gt_answer": "1244 kJ", |
| "correct": false |
| }, |
| { |
| "index": 890, |
| "pred_answer": "0.0195\\ \\text{kW/K}", |
| "gt_answer": "0.0607 kJ/K", |
| "correct": false |
| }, |
| { |
| "index": 891, |
| "pred_answer": "0.0000283\\ \\text{kW/K}", |
| "gt_answer": "0.273 kJ/K", |
| "correct": false |
| }, |
| { |
| "index": 894, |
| "pred_answer": "0.0844\\ \\text{kJ/K}", |
| "gt_answer": "0.2947 kJ/K", |
| "correct": false |
| }, |
| { |
| "index": 896, |
| "pred_answer": "0.00165\\ \\text{kW/K}", |
| "gt_answer": "3.9 WJ/K", |
| "correct": false |
| }, |
| { |
| "index": 898, |
| "pred_answer": "-0.0136\\ \\text{kW/K}", |
| "gt_answer": "1.722 kJ/K", |
| "correct": false |
| }, |
| { |
| "index": 899, |
| "pred_answer": "346\\ \\text{J}", |
| "gt_answer": "25.2 kJ", |
| "correct": false |
| }, |
| { |
| "index": 900, |
| "pred_answer": null, |
| "gt_answer": "93.6 kPa", |
| "correct": false |
| }, |
| { |
| "index": 901, |
| "pred_answer": "1000\\ \\text{W}", |
| "gt_answer": "-2.74 kW", |
| "correct": false |
| }, |
| { |
| "index": 903, |
| "pred_answer": "0\\ \\text{kJ/kg}", |
| "gt_answer": "788.6 kJ/kg", |
| "correct": false |
| }, |
| { |
| "index": 905, |
| "pred_answer": "650^\\circ\\text{C}", |
| "gt_answer": "744.4 K", |
| "correct": false |
| }, |
| { |
| "index": 906, |
| "pred_answer": "3590000\\ \\text{Pa}", |
| "gt_answer": "245 kPa", |
| "correct": false |
| }, |
| { |
| "index": 907, |
| "pred_answer": "1.08\\times 10^{6}\\ \\text{W}", |
| "gt_answer": "-121.6 kW", |
| "correct": false |
| }, |
| { |
| "index": 908, |
| "pred_answer": "0.435", |
| "gt_answer": "0.428", |
| "correct": false |
| }, |
| { |
| "index": 909, |
| "pred_answer": "44.2\\ \\text{m/s}", |
| "gt_answer": "42.4 m/s", |
| "correct": false |
| }, |
| { |
| "index": 911, |
| "pred_answer": "1500\\ \\text{kPa}", |
| "gt_answer": "106 kPa", |
| "correct": false |
| }, |
| { |
| "index": 917, |
| "pred_answer": "0.704", |
| "gt_answer": "-0.1669 ", |
| "correct": false |
| }, |
| { |
| "index": 918, |
| "pred_answer": "0.00584\\ \\text{kW/K}", |
| "gt_answer": "0.8097 kJ/K s ", |
| "correct": false |
| }, |
| { |
| "index": 919, |
| "pred_answer": "4.184\\ \\text{kW/K}", |
| "gt_answer": "0.0379 kW/K", |
| "correct": false |
| }, |
| { |
| "index": 920, |
| "pred_answer": "0.0475\\ \\text{kW/K}", |
| "gt_answer": "15.14 kJ/K s ", |
| "correct": false |
| }, |
| { |
| "index": 921, |
| "pred_answer": "1.0\\ \\text{kW}", |
| "gt_answer": "50 kW ", |
| "correct": false |
| }, |
| { |
| "index": 923, |
| "pred_answer": "0.00565\\ \\text{kJ/K}", |
| "gt_answer": "0.0182 kW/K ", |
| "correct": false |
| }, |
| { |
| "index": 926, |
| "pred_answer": "3.98\\ \\text{kJ/K}", |
| "gt_answer": "0.21 kJ/K ", |
| "correct": false |
| }, |
| { |
| "index": 932, |
| "pred_answer": "58.1\\ \\text{kW}", |
| "gt_answer": "1200 kJ/kg ", |
| "correct": false |
| }, |
| { |
| "index": 933, |
| "pred_answer": "5.94\\ \\text{kW}", |
| "gt_answer": "12.45 W ", |
| "correct": false |
| }, |
| { |
| "index": 934, |
| "pred_answer": "0.0833\\%", |
| "gt_answer": "0.67 ", |
| "correct": false |
| }, |
| { |
| "index": 935, |
| "pred_answer": "\\frac{1}{3}", |
| "gt_answer": "5.7 \\% ", |
| "correct": false |
| }, |
| { |
| "index": 936, |
| "pred_answer": "10.8\\ \\text{kW/K}", |
| "gt_answer": "279 kJ ", |
| "correct": false |
| }, |
| { |
| "index": 937, |
| "pred_answer": "P_0", |
| "gt_answer": "125.4 kPa ", |
| "correct": false |
| }, |
| { |
| "index": 938, |
| "pred_answer": "3.6\\ \\text{m}", |
| "gt_answer": "0.8 m ", |
| "correct": false |
| }, |
| { |
| "index": 939, |
| "pred_answer": "4.0\\ \\text{m/s}", |
| "gt_answer": "10 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 940, |
| "pred_answer": "20\\ \\text{m}", |
| "gt_answer": "2.34 m ", |
| "correct": false |
| }, |
| { |
| "index": 941, |
| "pred_answer": "0\\ \\text{m/s}", |
| "gt_answer": "-19 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 943, |
| "pred_answer": "18300000000000", |
| "gt_answer": "5 ", |
| "correct": false |
| }, |
| { |
| "index": 944, |
| "pred_answer": "1.80\\ \\text{s}", |
| "gt_answer": "4 s", |
| "correct": false |
| }, |
| { |
| "index": 947, |
| "pred_answer": "11.01\\ \\text{GHz}", |
| "gt_answer": "10.5 Hz", |
| "correct": false |
| }, |
| { |
| "index": 948, |
| "pred_answer": "10^8\\ \\text{Hz}", |
| "gt_answer": "12.1 kHz", |
| "correct": false |
| }, |
| { |
| "index": 949, |
| "pred_answer": "40\\text{ cm}", |
| "gt_answer": "3 m", |
| "correct": false |
| }, |
| { |
| "index": 953, |
| "pred_answer": "0.10\\ \\text{mm}", |
| "gt_answer": "0.24 mm", |
| "correct": false |
| }, |
| { |
| "index": 956, |
| "pred_answer": "72\\ \\text{m}", |
| "gt_answer": "167 cm", |
| "correct": false |
| }, |
| { |
| "index": 957, |
| "pred_answer": "40000000\\ \\text{nm}", |
| "gt_answer": "500 nm", |
| "correct": false |
| }, |
| { |
| "index": 959, |
| "pred_answer": "0.000189\\ \\text{nm}", |
| "gt_answer": "670 nm", |
| "correct": false |
| }, |
| { |
| "index": 961, |
| "pred_answer": "3930", |
| "gt_answer": "3646 ", |
| "correct": false |
| }, |
| { |
| "index": 962, |
| "pred_answer": "10\\ \\text{m}", |
| "gt_answer": "20.8 cm ", |
| "correct": false |
| }, |
| { |
| "index": 963, |
| "pred_answer": "6.5\\times 10^{5}\\ \\text{m/s}", |
| "gt_answer": " 27500 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 964, |
| "pred_answer": "14.4^\\circ", |
| "gt_answer": "10 \\circ", |
| "correct": false |
| }, |
| { |
| "index": 965, |
| "pred_answer": "16300\\ \\text{mm}", |
| "gt_answer": "7.2 m", |
| "correct": false |
| }, |
| { |
| "index": 966, |
| "pred_answer": "56^\\circ", |
| "gt_answer": "55 \\circ", |
| "correct": false |
| }, |
| { |
| "index": 969, |
| "pred_answer": "1.8^\\circ", |
| "gt_answer": "62.1 \\circ", |
| "correct": false |
| }, |
| { |
| "index": 970, |
| "pred_answer": "19.6^\\circ", |
| "gt_answer": "33.7 \\circ", |
| "correct": false |
| }, |
| { |
| "index": 972, |
| "pred_answer": "1.50", |
| "gt_answer": "1.1 ", |
| "correct": false |
| }, |
| { |
| "index": 973, |
| "pred_answer": "0^\\circ", |
| "gt_answer": "51.9 \\circ", |
| "correct": false |
| }, |
| { |
| "index": 975, |
| "pred_answer": "1.60", |
| "gt_answer": "1.35 ", |
| "correct": false |
| }, |
| { |
| "index": 977, |
| "pred_answer": "3.0\\ \\text{mm}", |
| "gt_answer": "0.725 m", |
| "correct": false |
| }, |
| { |
| "index": 980, |
| "pred_answer": "2.00\\text{ cm}", |
| "gt_answer": "487 nm ", |
| "correct": false |
| }, |
| { |
| "index": 981, |
| "pred_answer": "5", |
| "gt_answer": "50 ", |
| "correct": false |
| }, |
| { |
| "index": 986, |
| "pred_answer": "0.99999999999999999999999999999999\\,\\mathrm{c}", |
| "gt_answer": "0.93 c ", |
| "correct": false |
| }, |
| { |
| "index": 987, |
| "pred_answer": "7.0\\ \\text{m/s}", |
| "gt_answer": "0.7 c ", |
| "correct": false |
| }, |
| { |
| "index": 988, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "40.2 \\circ ", |
| "correct": false |
| }, |
| { |
| "index": 991, |
| "pred_answer": "2.0\\ \\text{kHz}", |
| "gt_answer": "10 Hz ", |
| "correct": false |
| }, |
| { |
| "index": 996, |
| "pred_answer": "1.00\\ \\text{Hz}", |
| "gt_answer": "5 Hz ", |
| "correct": false |
| }, |
| { |
| "index": 999, |
| "pred_answer": "4.44\\ \\text{s}", |
| "gt_answer": " 2 mm", |
| "correct": false |
| }, |
| { |
| "index": 1000, |
| "pred_answer": "0.094\\ \\text{m/s}", |
| "gt_answer": " 1 cm/s", |
| "correct": false |
| }, |
| { |
| "index": 1001, |
| "pred_answer": "1250\\ \\text{Hz}", |
| "gt_answer": " 17.36 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1003, |
| "pred_answer": "5000\\ \\text{Hz}", |
| "gt_answer": " 163.4 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1004, |
| "pred_answer": "7.5\\ \\text{ms}", |
| "gt_answer": " 0.02 s", |
| "correct": false |
| }, |
| { |
| "index": 1006, |
| "pred_answer": "30\\ \\text{Hz}", |
| "gt_answer": " 37.5 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1008, |
| "pred_answer": "\\frac{4}{3}", |
| "gt_answer": " 3 ", |
| "correct": false |
| }, |
| { |
| "index": 1009, |
| "pred_answer": "1500\\ \\text{Hz}", |
| "gt_answer": " 0.5f ", |
| "correct": false |
| }, |
| { |
| "index": 1010, |
| "pred_answer": "1000000\\ \\text{Hz}", |
| "gt_answer": " 40 kHz ", |
| "correct": false |
| }, |
| { |
| "index": 1011, |
| "pred_answer": "307\\ \\text{Hz}", |
| "gt_answer": " 525.5 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1013, |
| "pred_answer": "3.3\\ \\text{Hz}", |
| "gt_answer": " 60.7 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1014, |
| "pred_answer": "6\\ \\text{Hz}", |
| "gt_answer": " 0 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1015, |
| "pred_answer": "484\\ \\text{Hz}", |
| "gt_answer": " 403.33 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1016, |
| "pred_answer": "0.028\\ \\text{m}", |
| "gt_answer": " 0.875 m", |
| "correct": false |
| }, |
| { |
| "index": 1017, |
| "pred_answer": "0.625\\ \\text{m}", |
| "gt_answer": " 320 m", |
| "correct": false |
| }, |
| { |
| "index": 1018, |
| "pred_answer": "3.35\\ \\text{m}", |
| "gt_answer": " 0.9375 m", |
| "correct": false |
| }, |
| { |
| "index": 1019, |
| "pred_answer": "700\\ \\text{Hz}", |
| "gt_answer": " 100 kHz", |
| "correct": false |
| }, |
| { |
| "index": 1021, |
| "pred_answer": "687.5\\ \\text{N}", |
| "gt_answer": " 11.56 N", |
| "correct": false |
| }, |
| { |
| "index": 1022, |
| "pred_answer": "0.20\\ \\text{m}", |
| "gt_answer": " 7.5 m", |
| "correct": false |
| }, |
| { |
| "index": 1023, |
| "pred_answer": "2.0\\ \\text{Hz}\\ \\text{and}\\ 3.0\\ \\text{Hz}", |
| "gt_answer": " 100 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1026, |
| "pred_answer": "2", |
| "gt_answer": " 1", |
| "correct": false |
| }, |
| { |
| "index": 1027, |
| "pred_answer": "4.4\\times 10^{-12}\\ \\text{W}", |
| "gt_answer": " 68.2 W", |
| "correct": false |
| }, |
| { |
| "index": 1030, |
| "pred_answer": "37^\\circ", |
| "gt_answer": " 30 \\circ", |
| "correct": false |
| }, |
| { |
| "index": 1032, |
| "pred_answer": null, |
| "gt_answer": " 2\\pi \\sqrt{\\frac{m}{k_1 + k_2}}", |
| "correct": false |
| }, |
| { |
| "index": 1037, |
| "pred_answer": "2.35\\ \\text{Hz}", |
| "gt_answer": " \\frac{1}{2\\pi} \\sqrt{\\frac{mgL + kh^2}{mL^2}}", |
| "correct": false |
| }, |
| { |
| "index": 1039, |
| "pred_answer": "0.209\\ \\text{s}", |
| "gt_answer": " 2\\pi \\sqrt{\\frac{l}{2\\mu g}}", |
| "correct": false |
| }, |
| { |
| "index": 1041, |
| "pred_answer": null, |
| "gt_answer": " 2\\pi \\sqrt{\\frac{3(R-r)}{2g}} ", |
| "correct": false |
| }, |
| { |
| "index": 1045, |
| "pred_answer": "0", |
| "gt_answer": " \\frac{\\ell}{6} (\\sqrt{2} + 1) ", |
| "correct": false |
| }, |
| { |
| "index": 1046, |
| "pred_answer": "1.67\\ \\text{s}", |
| "gt_answer": " 2\\pi \\sqrt{\\frac{M + m}{k}} ", |
| "correct": false |
| }, |
| { |
| "index": 1048, |
| "pred_answer": "0.06\\ \\text{m}", |
| "gt_answer": "0.14 m", |
| "correct": false |
| }, |
| { |
| "index": 1049, |
| "pred_answer": "0.5\\ \\text{J}", |
| "gt_answer": "0.04 J", |
| "correct": false |
| }, |
| { |
| "index": 1050, |
| "pred_answer": "1.25\\ \\text{s}", |
| "gt_answer": "\\frac{T_1*T_2}{T}", |
| "correct": false |
| }, |
| { |
| "index": 1052, |
| "pred_answer": "200\\ \\text{N/m}", |
| "gt_answer": " \\frac{20k}{9} ", |
| "correct": false |
| }, |
| { |
| "index": 1053, |
| "pred_answer": "0.249\\ \\text{m}", |
| "gt_answer": "4.8 cm", |
| "correct": false |
| }, |
| { |
| "index": 1055, |
| "pred_answer": "0.20\\ \\text{Hz}", |
| "gt_answer": "3.85 s", |
| "correct": false |
| }, |
| { |
| "index": 1056, |
| "pred_answer": "1.095\\ \\text{m}", |
| "gt_answer": "2 cm", |
| "correct": false |
| }, |
| { |
| "index": 1059, |
| "pred_answer": null, |
| "gt_answer": " \\pi \\sqrt{\\frac{m}{k}} ", |
| "correct": false |
| }, |
| { |
| "index": 1060, |
| "pred_answer": null, |
| "gt_answer": " 2\\pi \\sqrt{\\frac{\\sqrt{10}*a}{3*g}} ", |
| "correct": false |
| }, |
| { |
| "index": 1061, |
| "pred_answer": "\\sqrt{2}T", |
| "gt_answer": "2T ", |
| "correct": false |
| }, |
| { |
| "index": 1065, |
| "pred_answer": "2060\\ \\text{Hz}", |
| "gt_answer": "1200 Hz ", |
| "correct": false |
| }, |
| { |
| "index": 1067, |
| "pred_answer": "0.05\\ \\text{m}", |
| "gt_answer": "0.04 m ", |
| "correct": false |
| }, |
| { |
| "index": 1068, |
| "pred_answer": "0.157\\ \\text{m}", |
| "gt_answer": "0.1 m ", |
| "correct": false |
| }, |
| { |
| "index": 1070, |
| "pred_answer": "0.082\\ \\text{m/s}", |
| "gt_answer": "0.1 m ", |
| "correct": false |
| }, |
| { |
| "index": 1071, |
| "pred_answer": "2\\pi\\omega", |
| "gt_answer": "0.083 s ", |
| "correct": false |
| }, |
| { |
| "index": 1072, |
| "pred_answer": "0.15\\ \\text{m}", |
| "gt_answer": "2.55 m ", |
| "correct": false |
| }, |
| { |
| "index": 1073, |
| "pred_answer": "0\\ \\text{m}", |
| "gt_answer": "0 m ", |
| "correct": false |
| }, |
| { |
| "index": 1075, |
| "pred_answer": "10^{-7}\\ \\text{m}", |
| "gt_answer": "0.6 m ", |
| "correct": false |
| }, |
| { |
| "index": 1079, |
| "pred_answer": "40\\ \\text{m/s}", |
| "gt_answer": "10 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 1080, |
| "pred_answer": "0\\ \\text{m/s}", |
| "gt_answer": "0 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 1082, |
| "pred_answer": "6\\ \\text{m}", |
| "gt_answer": "1.2 m ", |
| "correct": false |
| }, |
| { |
| "index": 1083, |
| "pred_answer": "1.00\\ \\text{s}", |
| "gt_answer": "6 s ", |
| "correct": false |
| }, |
| { |
| "index": 1084, |
| "pred_answer": "16\\ \\text{cm}", |
| "gt_answer": "0.08 m ", |
| "correct": false |
| }, |
| { |
| "index": 1085, |
| "pred_answer": "0\\text{ cm}", |
| "gt_answer": "0.08 m ", |
| "correct": false |
| }, |
| { |
| "index": 1086, |
| "pred_answer": "4\\ \\text{m}", |
| "gt_answer": "6 m ", |
| "correct": false |
| }, |
| { |
| "index": 1087, |
| "pred_answer": "3\\ \\text{m}", |
| "gt_answer": "2.5 m ", |
| "correct": false |
| }, |
| { |
| "index": 1089, |
| "pred_answer": "2.0\\ \\text{m}", |
| "gt_answer": "4 m ", |
| "correct": false |
| }, |
| { |
| "index": 1092, |
| "pred_answer": "6\\ \\text{m/s}", |
| "gt_answer": "10 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 1094, |
| "pred_answer": "0.0267\\ \\text{s}", |
| "gt_answer": "0.1 s ", |
| "correct": false |
| }, |
| { |
| "index": 1095, |
| "pred_answer": "2\\ \\text{m/s}", |
| "gt_answer": "1 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 1097, |
| "pred_answer": "L\\cos(\\omega t+\\phi)", |
| "gt_answer": "\\( x = R \\sin(\\omega t + \\frac{\\pi}{2}) \\) ", |
| "correct": false |
| }, |
| { |
| "index": 1098, |
| "pred_answer": "0.28\\ \\text{m}", |
| "gt_answer": " \\frac{4\\mu mg}{k} ", |
| "correct": false |
| }, |
| { |
| "index": 1100, |
| "pred_answer": "0.1\\ \\text{m}", |
| "gt_answer": "2 m ", |
| "correct": false |
| }, |
| { |
| "index": 1101, |
| "pred_answer": "1.5\\ \\text{m}", |
| "gt_answer": "4 m ", |
| "correct": false |
| }, |
| { |
| "index": 1102, |
| "pred_answer": null, |
| "gt_answer": "T/2 ", |
| "correct": false |
| }, |
| { |
| "index": 1104, |
| "pred_answer": "0.5\\ \\text{m/s}", |
| "gt_answer": "0.2 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 1105, |
| "pred_answer": "7.5\\ \\text{m}", |
| "gt_answer": "1.2 m/s ", |
| "correct": false |
| }, |
| { |
| "index": 1107, |
| "pred_answer": "654\\ \\text{Hz}", |
| "gt_answer": "580 Hz ", |
| "correct": false |
| }, |
| { |
| "index": 1108, |
| "pred_answer": "400\\ \\text{Hz}", |
| "gt_answer": "370 Hz ", |
| "correct": false |
| }, |
| { |
| "index": 1109, |
| "pred_answer": "8.2\\times 10^{7}", |
| "gt_answer": "0.0000000822N", |
| "correct": false |
| }, |
| { |
| "index": 1110, |
| "pred_answer": "0.0000000000487\\ \\text{N}", |
| "gt_answer": "0.0000000126N.", |
| "correct": false |
| }, |
| { |
| "index": 1112, |
| "pred_answer": "0.0100\\ \\text{m}", |
| "gt_answer": "-0.00000273m", |
| "correct": false |
| }, |
| { |
| "index": 1114, |
| "pred_answer": "-\\hat{\\jmath}", |
| "gt_answer": "0.0000000173N, at 32.4^\\circ above the horizontal (toward the midpoint between the two electrons)", |
| "correct": false |
| }, |
| { |
| "index": 1116, |
| "pred_answer": "6000\\ \\text{N/C downward}", |
| "gt_answer": "33900 N/C, to the left", |
| "correct": false |
| }, |
| { |
| "index": 1117, |
| "pred_answer": "-4.0\\times 10^{-13}\\ \\text{C}", |
| "gt_answer": "0.0000000617C, -0.0000000617C", |
| "correct": false |
| }, |
| { |
| "index": 1118, |
| "pred_answer": "\\frac{L\\sin\\theta}{q}", |
| "gt_answer": "2960N/C", |
| "correct": false |
| }, |
| { |
| "index": 1119, |
| "pred_answer": "1.7\\times 10^4\\ \\text{C/kg}", |
| "gt_answer": "2180C/kg", |
| "correct": false |
| }, |
| { |
| "index": 1121, |
| "pred_answer": "E_x = -\\frac{kQ}{x^2},\\quad E_y = \\frac{kQ}{x^2}", |
| "gt_answer": "E_x = \\frac{Q}{4\\pi\\varepsilon_0 a x \\sqrt{x^2 + a^2}}, \\quadE_y = -\\frac{Q}{4\\pi\\varepsilon_0 a} \\left( \\frac{1}{x} - \\frac{1}{\\sqrt{x^2 + a^2}} \night)", |
| "correct": false |
| }, |
| { |
| "index": 1123, |
| "pred_answer": "1800\\ \\text{N/C}", |
| "gt_answer": "62500N/C, 225^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 1125, |
| "pred_answer": "0.000000129\\ \\text{C}", |
| "gt_answer": "5.0nC", |
| "correct": false |
| }, |
| { |
| "index": 1127, |
| "pred_answer": "2.81\\ \\mu\\text{C}", |
| "gt_answer": "0.843µC}", |
| "correct": false |
| }, |
| { |
| "index": 1130, |
| "pred_answer": "0.0084\\ \\text{mm/N}", |
| "gt_answer": "0.000199 \\text{C/m}^3", |
| "correct": false |
| }, |
| { |
| "index": 1131, |
| "pred_answer": "0.00000282\\ \\text{N·m}^2/\\text{C}", |
| "gt_answer": "7.39\\text{N} \\cdot \\text{m}^2/\\text{C}", |
| "correct": false |
| }, |
| { |
| "index": 1133, |
| "pred_answer": "625\\ \\text{V}", |
| "gt_answer": "47.8V", |
| "correct": false |
| }, |
| { |
| "index": 1134, |
| "pred_answer": "10000\\ \\text{V}", |
| "gt_answer": "1157V", |
| "correct": false |
| }, |
| { |
| "index": 1135, |
| "pred_answer": "0.30\\ \\mu\\text{C}", |
| "gt_answer": "0.0000000000303C", |
| "correct": false |
| }, |
| { |
| "index": 1138, |
| "pred_answer": "0.0032\\ \\text{m/s}", |
| "gt_answer": "15.5m/s", |
| "correct": false |
| }, |
| { |
| "index": 1139, |
| "pred_answer": "6.3\\times 10^{-14}\\ \\text{C}", |
| "gt_answer": "0.000000000000006C", |
| "correct": false |
| }, |
| { |
| "index": 1140, |
| "pred_answer": "72.0\\ \\text{nF}", |
| "gt_answer": "19.3nF", |
| "correct": false |
| }, |
| { |
| "index": 1141, |
| "pred_answer": "4.8\\,\\mu\\mathrm{F/cm}^2", |
| "gt_answer": "1.18\\mu\\text{F}/ \\text{cm}^2", |
| "correct": false |
| }, |
| { |
| "index": 1142, |
| "pred_answer": "1.43\\ \\text{pF}", |
| "gt_answer": "62.5 pF", |
| "correct": false |
| }, |
| { |
| "index": 1143, |
| "pred_answer": "2.41", |
| "gt_answer": "1.24, 1.48, 1.71", |
| "correct": false |
| }, |
| { |
| "index": 1145, |
| "pred_answer": "0.500\\ \\text{mm}", |
| "gt_answer": "4.12cm", |
| "correct": false |
| }, |
| { |
| "index": 1146, |
| "pred_answer": "\\frac{(K-1)\\varepsilon_0 V^2 L}{2D}\\,dx", |
| "gt_answer": "(K - 1) \\varepsilon_0 \\frac{V^2 L}{2D} \\ dx", |
| "correct": false |
| }, |
| { |
| "index": 1147, |
| "pred_answer": "1.80\\times 10^{-3}\\ \\mathrm{S/m}", |
| "gt_answer": "1.60 ppt", |
| "correct": false |
| }, |
| { |
| "index": 1150, |
| "pred_answer": "5.0\\ \\Omega", |
| "gt_answer": "8.00Ω", |
| "correct": false |
| }, |
| { |
| "index": 1151, |
| "pred_answer": "16.0\\ \\Omega", |
| "gt_answer": "7.5Ω", |
| "correct": false |
| }, |
| { |
| "index": 1153, |
| "pred_answer": "9.93\\text{ V}", |
| "gt_answer": "398V", |
| "correct": false |
| }, |
| { |
| "index": 1155, |
| "pred_answer": "200\\ \\text{min}", |
| "gt_answer": "1010s", |
| "correct": false |
| }, |
| { |
| "index": 1159, |
| "pred_answer": "35\\text{ V}", |
| "gt_answer": "46.1V", |
| "correct": false |
| }, |
| { |
| "index": 1161, |
| "pred_answer": "0.500\\ \\text{A}", |
| "gt_answer": "13.6A", |
| "correct": false |
| }, |
| { |
| "index": 1162, |
| "pred_answer": "194\\ \\Omega", |
| "gt_answer": "12.1Ω", |
| "correct": false |
| }, |
| { |
| "index": 1163, |
| "pred_answer": "0.68\\ \\text{W}", |
| "gt_answer": "72W", |
| "correct": false |
| }, |
| { |
| "index": 1164, |
| "pred_answer": "0.0036\\ \\text{g/s}", |
| "gt_answer": "0.00619g/s", |
| "correct": false |
| }, |
| { |
| "index": 1170, |
| "pred_answer": "1.00\\ \\text{s}", |
| "gt_answer": "595pJ", |
| "correct": false |
| }, |
| { |
| "index": 1172, |
| "pred_answer": null, |
| "gt_answer": "200μC", |
| "correct": false |
| }, |
| { |
| "index": 1174, |
| "pred_answer": "1.32\\ \\text{s}", |
| "gt_answer": "\\frac{4RC}{5}(\\ln 7 + 4 \\ln 2)", |
| "correct": false |
| }, |
| { |
| "index": 1175, |
| "pred_answer": "\\frac{5}{3}\\,R", |
| "gt_answer": "\\frac{5R}{6}", |
| "correct": false |
| }, |
| { |
| "index": 1176, |
| "pred_answer": "0", |
| "gt_answer": "0", |
| "correct": true |
| }, |
| { |
| "index": 1177, |
| "pred_answer": "1.04\\,\\mu\\text{s}", |
| "gt_answer": "0.000000111\\,\\text{s}", |
| "correct": false |
| }, |
| { |
| "index": 1178, |
| "pred_answer": "0.15\\ \\text{T}", |
| "gt_answer": "0.00167\\,\\text{T}", |
| "correct": false |
| }, |
| { |
| "index": 1180, |
| "pred_answer": "0.13\\ \\text{N}", |
| "gt_answer": "0.724N, at an angle of \\( \theta = 63.4^\\circ \\) below the horizontal and to the right", |
| "correct": false |
| }, |
| { |
| "index": 1181, |
| "pred_answer": "5.58\\ \\text{W}", |
| "gt_answer": "362W", |
| "correct": false |
| }, |
| { |
| "index": 1184, |
| "pred_answer": "1\\ \\text{kg}", |
| "gt_answer": "0.83N", |
| "correct": false |
| }, |
| { |
| "index": 1189, |
| "pred_answer": "10.0\\ \\text{A}", |
| "gt_answer": "2.26A", |
| "correct": false |
| }, |
| { |
| "index": 1190, |
| "pred_answer": "0", |
| "gt_answer": "-IB_0L\\hat{j}", |
| "correct": false |
| }, |
| { |
| "index": 1192, |
| "pred_answer": "1.14\\ \\text{A/m}^2", |
| "gt_answer": "\\sigma > \\frac{1}{2}\\left(1 + \\frac{\\pi}{2}\night)", |
| "correct": false |
| }, |
| { |
| "index": 1193, |
| "pred_answer": "0.000000218\\ \\text{kg}", |
| "gt_answer": "0\\,\\text{kg}", |
| "correct": false |
| }, |
| { |
| "index": 1196, |
| "pred_answer": "\\frac{2E}{B}", |
| "gt_answer": "\\frac{2E}{B}", |
| "correct": true |
| }, |
| { |
| "index": 1198, |
| "pred_answer": "B_P = 6.0\\times 10^{-5}\\ \\text{T}", |
| "gt_answer": "0.000000264\\,\\text{T}", |
| "correct": false |
| }, |
| { |
| "index": 1200, |
| "pred_answer": "9.43\\times 10^{-7}\\,I\\ \\text{T}", |
| "gt_answer": "\\( 0.00000219\\,\\text{T} \\) at \\( 46.8^\\circ \\) from \\( x \\) toward \\( z \\)", |
| "correct": false |
| }, |
| { |
| "index": 1203, |
| "pred_answer": "1.10\\ \\text{A}", |
| "gt_answer": "23.2A", |
| "correct": false |
| }, |
| { |
| "index": 1204, |
| "pred_answer": "0.00000251\\ \\text{T}", |
| "gt_answer": "4.19μT, into the page", |
| "correct": false |
| }, |
| { |
| "index": 1207, |
| "pred_answer": "\\frac{\\mu_0\\omega Q}{2\\pi R^2}\\frac{3\\delta(x)-1}{R^2}", |
| "gt_answer": "\\frac{\\mu_0}{2\\pi} \\cdot \\frac{Q\\omega}{\\sqrt{W^2 + 4R^2}} \\hat{i}", |
| "correct": false |
| }, |
| { |
| "index": 1208, |
| "pred_answer": null, |
| "gt_answer": "\\frac{Q}{2M}", |
| "correct": false |
| }, |
| { |
| "index": 1209, |
| "pred_answer": "0.400\\ \\text{m}", |
| "gt_answer": "\\frac{1}{2g} \\left( \\frac{\\mu_0 Q_0^2}{4 \\pi \\lambda RC d} \\right)^2", |
| "correct": false |
| }, |
| { |
| "index": 1210, |
| "pred_answer": "450\\ \\text{T}", |
| "gt_answer": "1.32T", |
| "correct": false |
| }, |
| { |
| "index": 1212, |
| "pred_answer": "0\\ \\text{mA}", |
| "gt_answer": "1.33A", |
| "correct": false |
| }, |
| { |
| "index": 1214, |
| "pred_answer": "2.5\\ \\text{m/s}", |
| "gt_answer": "14m/s", |
| "correct": false |
| }, |
| { |
| "index": 1216, |
| "pred_answer": "0.451\\ \\text{mA}", |
| "gt_answer": "365mA", |
| "correct": false |
| }, |
| { |
| "index": 1217, |
| "pred_answer": "1.60\\ \\text{m}", |
| "gt_answer": "5.13cm", |
| "correct": false |
| }, |
| { |
| "index": 1220, |
| "pred_answer": "0.0395\\ \\text{A}", |
| "gt_answer": "4.73mA", |
| "correct": false |
| }, |
| { |
| "index": 1221, |
| "pred_answer": "\\text{counterclockwise}", |
| "gt_answer": "\\frac{{\\mu_0 \\varepsilon_0 \\eta b^2 a^2}}{{2R}}", |
| "correct": false |
| }, |
| { |
| "index": 1224, |
| "pred_answer": "10.0\\ \\text{V}", |
| "gt_answer": "9.0V", |
| "correct": false |
| }, |
| { |
| "index": 1225, |
| "pred_answer": "1.5\\,\\mu\\text{C}", |
| "gt_answer": "0.350mC", |
| "correct": false |
| }, |
| { |
| "index": 1228, |
| "pred_answer": "2.48\\,\\mu\\mathrm{H}", |
| "gt_answer": "6.67Ω", |
| "correct": false |
| }, |
| { |
| "index": 1229, |
| "pred_answer": "1.0\\ \\text{s}", |
| "gt_answer": "0.22s", |
| "correct": false |
| }, |
| { |
| "index": 1230, |
| "pred_answer": "1.27\\times 10^{-3}\\ \\text{N}", |
| "gt_answer": "0.0187N", |
| "correct": false |
| }, |
| { |
| "index": 1231, |
| "pred_answer": "0.0015\\ \\text{s}", |
| "gt_answer": "0.0000000034\\, \\text{s}", |
| "correct": false |
| }, |
| { |
| "index": 1232, |
| "pred_answer": "\\vec E \\approx 1.1\\times 10^{12}\\,\\text{N/C}", |
| "gt_answer": "(4900\\, \\text{N/C})\\hat{\\mathbf{i}}", |
| "correct": false |
| }, |
| { |
| "index": 1240, |
| "pred_answer": "10000\\ \\text{N/C}", |
| "gt_answer": "\\frac{1}{2\\pi\\epsilon_0} \\frac{\\lambda}{r}", |
| "correct": false |
| }, |
| { |
| "index": 1241, |
| "pred_answer": "\\frac{\\sigma}{2\\pi\\varepsilon_0 r}", |
| "gt_answer": "\\frac{\\sigma}{2\\epsilon_0}", |
| "correct": false |
| }, |
| { |
| "index": 1242, |
| "pred_answer": "0\\ \\text{V/m}", |
| "gt_answer": "\\frac{\\sigma}{\\epsilon_0}", |
| "correct": false |
| }, |
| { |
| "index": 1243, |
| "pred_answer": "-11.3\\ \\text{V}", |
| "gt_answer": "-900V", |
| "correct": false |
| }, |
| { |
| "index": 1249, |
| "pred_answer": "3.12\\ \\text{pF}", |
| "gt_answer": "\\frac{4\\pi\\epsilon_0 r_a r_b}{r_b - r_a}", |
| "correct": false |
| }, |
| { |
| "index": 1251, |
| "pred_answer": "0.00576\\ \\text{J}", |
| "gt_answer": "0.0384J", |
| "correct": false |
| }, |
| { |
| "index": 1252, |
| "pred_answer": "0.00225\\ \\text{J}", |
| "gt_answer": "0.000797 , \\text{J}", |
| "correct": false |
| }, |
| { |
| "index": 1256, |
| "pred_answer": "B=0.016\\ \\text{T},\\quad \\text{direction of }\\vec A:\\text{ so that }\\vec A\\times \\vec B=\\vec B.", |
| "gt_answer": "6.0T", |
| "correct": false |
| }, |
| { |
| "index": 1257, |
| "pred_answer": "0.000000000000024\\ \\text{N}", |
| "gt_answer": "2IRB\\hat{j}", |
| "correct": false |
| }, |
| { |
| "index": 1260, |
| "pred_answer": "0.000048\\ \\text{A}", |
| "gt_answer": "0.048mA", |
| "correct": false |
| }, |
| { |
| "index": 1263, |
| "pred_answer": "1.0\\times 10^{-5}\\ \\text{V}", |
| "gt_answer": "\\frac{1}{2} \\omega BR^2", |
| "correct": false |
| }, |
| { |
| "index": 1265, |
| "pred_answer": "0.020\\ \\text{H}", |
| "gt_answer": "40μH", |
| "correct": false |
| }, |
| { |
| "index": 1266, |
| "pred_answer": "13.8\\ \\text{Gy}", |
| "gt_answer": "13000000000 \\, \\text{years}", |
| "correct": false |
| }, |
| { |
| "index": 1267, |
| "pred_answer": "Y \\approx 10^6\\,\\text{J}", |
| "gt_answer": "8.65 megatons of TNT", |
| "correct": false |
| }, |
| { |
| "index": 1273, |
| "pred_answer": "10\\ \\text{eV}", |
| "gt_answer": "18T", |
| "correct": false |
| }, |
| { |
| "index": 1274, |
| "pred_answer": "2.08\\ \\text{eV}", |
| "gt_answer": "10.0μm", |
| "correct": false |
| }, |
| { |
| "index": 1278, |
| "pred_answer": "1", |
| "gt_answer": "0.0014 \\", |
| "correct": false |
| }, |
| { |
| "index": 1279, |
| "pred_answer": "6.38\\ \\text{mJ}", |
| "gt_answer": "\\frac{n^2 h^2}{8 \\pi^2 m d^2}", |
| "correct": false |
| }, |
| { |
| "index": 1280, |
| "pred_answer": "1.0\\ \\text{eV}", |
| "gt_answer": "7.00eV", |
| "correct": false |
| }, |
| { |
| "index": 1281, |
| "pred_answer": "E_3", |
| "gt_answer": "109eV", |
| "correct": false |
| }, |
| { |
| "index": 1282, |
| "pred_answer": "10^{-7}\\ \\text{pm}", |
| "gt_answer": "350pm", |
| "correct": false |
| }, |
| { |
| "index": 1284, |
| "pred_answer": "0.25\\ \\text{km/s}", |
| "gt_answer": "0.5c", |
| "correct": false |
| }, |
| { |
| "index": 1285, |
| "pred_answer": "0.70\\ \\text{km/s}", |
| "gt_answer": "0.858c", |
| "correct": false |
| }, |
| { |
| "index": 1287, |
| "pred_answer": "1.0\\ \\text{m}", |
| "gt_answer": "0.79m", |
| "correct": false |
| }, |
| { |
| "index": 1288, |
| "pred_answer": null, |
| "gt_answer": "\tau_0 \\sqrt{\\frac{c+v}{c-v}}", |
| "correct": false |
| }, |
| { |
| "index": 1291, |
| "pred_answer": "4600\\ \\text{km/s}", |
| "gt_answer": "7000000\\,\\text{m/s}", |
| "correct": false |
| }, |
| { |
| "index": 1292, |
| "pred_answer": "0.8\\,c", |
| "gt_answer": "-c", |
| "correct": false |
| }, |
| { |
| "index": 1295, |
| "pred_answer": "78^\\circ", |
| "gt_answer": "37.8^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 1296, |
| "pred_answer": "0.284\\ \\text{nm}", |
| "gt_answer": "0.570nm", |
| "correct": false |
| }, |
| { |
| "index": 1298, |
| "pred_answer": "1.36\\ \\text{rad}", |
| "gt_answer": "79.0^\\circ", |
| "correct": false |
| }, |
| { |
| "index": 1300, |
| "pred_answer": "0.18\\ \\text{mm}", |
| "gt_answer": "2.33μm", |
| "correct": false |
| }, |
| { |
| "index": 1302, |
| "pred_answer": "4.05\\,\\mu\\text{m}", |
| "gt_answer": "594nm", |
| "correct": false |
| }, |
| { |
| "index": 1305, |
| "pred_answer": "0.26\\,\\lambda", |
| "gt_answer": "2.90λ", |
| "correct": false |
| }, |
| { |
| "index": 1308, |
| "pred_answer": "1.18\\ \\text{rad}", |
| "gt_answer": "5.80λ", |
| "correct": false |
| }, |
| { |
| "index": 1310, |
| "pred_answer": "S_{12}=\\frac{F-A}{F-G},\\qquad\nS_{21}=\\frac{G-A}{G-F}", |
| "gt_answer": "\\frac{1}{|M_{22}|^2}", |
| "correct": false |
| }, |
| { |
| "index": 1313, |
| "pred_answer": null, |
| "gt_answer": "3k_B \\left( \\frac{\\Theta_E}{T} \night)^2 \\frac{e^{\\Theta_E/T}}{(e^{\\Theta_E/T} - 1)^2}", |
| "correct": false |
| }, |
| { |
| "index": 1315, |
| "pred_answer": null, |
| "gt_answer": "-\\frac{3}{4} J \\hbar^2, degeneracy = 4", |
| "correct": false |
| }, |
| { |
| "index": 1316, |
| "pred_answer": "-0.02\\ \\text{J}", |
| "gt_answer": "60J", |
| "correct": false |
| }, |
| { |
| "index": 1326, |
| "pred_answer": "-900\\ \\text{J}", |
| "gt_answer": "-91 J", |
| "correct": false |
| }, |
| { |
| "index": 1328, |
| "pred_answer": "450\\ \\text{J}", |
| "gt_answer": "-1.01 kJ", |
| "correct": false |
| }, |
| { |
| "index": 1331, |
| "pred_answer": "1600\\ \\text{atm}\\cdot\\text{cm}^3", |
| "gt_answer": "40 J", |
| "correct": false |
| }, |
| { |
| "index": 1334, |
| "pred_answer": "0.35\\%", |
| "gt_answer": "0.088", |
| "correct": false |
| }, |
| { |
| "index": 1340, |
| "pred_answer": "152000\\ \\text{W}", |
| "gt_answer": "13 W", |
| "correct": false |
| }, |
| { |
| "index": 1341, |
| "pred_answer": "93.5\\%", |
| "gt_answer": "0.0901", |
| "correct": false |
| }, |
| { |
| "index": 1342, |
| "pred_answer": "0.415", |
| "gt_answer": "0.32", |
| "correct": false |
| }, |
| { |
| "index": 1343, |
| "pred_answer": "50\\%", |
| "gt_answer": "0.17", |
| "correct": false |
| }, |
| { |
| "index": 1356, |
| "pred_answer": "200\\ \\text{m/s}", |
| "gt_answer": "400 m/s", |
| "correct": false |
| }, |
| { |
| "index": 1357, |
| "pred_answer": "0.44\\ \\text{m}", |
| "gt_answer": "18 cm", |
| "correct": false |
| }, |
| { |
| "index": 1358, |
| "pred_answer": "0.036\\ \\text{Hz}", |
| "gt_answer": "13 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1359, |
| "pred_answer": "0.004\\ \\text{kg/m}", |
| "gt_answer": "$\\mu_0 \\frac{9}{4}$", |
| "correct": false |
| }, |
| { |
| "index": 1362, |
| "pred_answer": "43\\ \\text{Hz}", |
| "gt_answer": "1.6 kHz", |
| "correct": false |
| }, |
| { |
| "index": 1364, |
| "pred_answer": "0.1\\ \\text{ns}", |
| "gt_answer": "250 ns", |
| "correct": false |
| }, |
| { |
| "index": 1365, |
| "pred_answer": "125850\\ \\text{Pa}", |
| "gt_answer": "113.2 kPa", |
| "correct": false |
| }, |
| { |
| "index": 1367, |
| "pred_answer": null, |
| "gt_answer": "P_0 + (H - h)\\rho g", |
| "correct": false |
| }, |
| { |
| "index": 1370, |
| "pred_answer": "2.0\\ \\text{MPa}", |
| "gt_answer": "139.9 kPa", |
| "correct": false |
| }, |
| { |
| "index": 1373, |
| "pred_answer": "0.00101\\ \\text{m}^3/\\text{s}", |
| "gt_answer": "0.02526 \\, \\text{m}^3/\\text{min}", |
| "correct": false |
| }, |
| { |
| "index": 1376, |
| "pred_answer": "0.80\\ \\text{MPa}", |
| "gt_answer": "217 psia", |
| "correct": false |
| }, |
| { |
| "index": 1379, |
| "pred_answer": "0\\ \\text{J}", |
| "gt_answer": "877.8 kJ", |
| "correct": false |
| }, |
| { |
| "index": 1380, |
| "pred_answer": "-138\\ \\text{kJ}", |
| "gt_answer": "587 kJ", |
| "correct": false |
| }, |
| { |
| "index": 1382, |
| "pred_answer": "-42588\\ \\text{J}", |
| "gt_answer": "-318.72 kJ", |
| "correct": false |
| }, |
| { |
| "index": 1384, |
| "pred_answer": "15605^\\circ\\text{C}", |
| "gt_answer": "80 \\, ^{\\circ}\\text{C}", |
| "correct": false |
| }, |
| { |
| "index": 1386, |
| "pred_answer": "101000\\ \\text{Pa}", |
| "gt_answer": "613 kPa", |
| "correct": false |
| }, |
| { |
| "index": 1391, |
| "pred_answer": "1474400\\ \\text{J}", |
| "gt_answer": "25961 kJ", |
| "correct": false |
| }, |
| { |
| "index": 1392, |
| "pred_answer": "15.5\\ \\text{kJ}", |
| "gt_answer": "725.0 kJ", |
| "correct": false |
| }, |
| { |
| "index": 1395, |
| "pred_answer": "16820000\\ \\text{W}", |
| "gt_answer": "1489.6 kW", |
| "correct": false |
| }, |
| { |
| "index": 1396, |
| "pred_answer": "0.334", |
| "gt_answer": "0.366", |
| "correct": false |
| }, |
| { |
| "index": 1397, |
| "pred_answer": "23.4\\%", |
| "gt_answer": "0.033", |
| "correct": false |
| }, |
| { |
| "index": 1398, |
| "pred_answer": "5.19\\ \\text{kW}", |
| "gt_answer": "15.24 kW", |
| "correct": false |
| }, |
| { |
| "index": 1399, |
| "pred_answer": "60^{\\circ}\\text{C}", |
| "gt_answer": "62.5°C", |
| "correct": false |
| }, |
| { |
| "index": 1400, |
| "pred_answer": "8.29\\ \\text{MW}", |
| "gt_answer": "26182 kW", |
| "correct": false |
| }, |
| { |
| "index": 1401, |
| "pred_answer": "0.368", |
| "gt_answer": "0.729", |
| "correct": false |
| }, |
| { |
| "index": 1402, |
| "pred_answer": "0.45", |
| "gt_answer": "0.34", |
| "correct": false |
| }, |
| { |
| "index": 1403, |
| "pred_answer": "2.43\\ \\text{m}", |
| "gt_answer": "50.009 m", |
| "correct": false |
| }, |
| { |
| "index": 1405, |
| "pred_answer": "0.417", |
| "gt_answer": "0.687", |
| "correct": false |
| }, |
| { |
| "index": 1409, |
| "pred_answer": "1382\\ \\text{m/s}", |
| "gt_answer": "1012 m/s", |
| "correct": false |
| }, |
| { |
| "index": 1410, |
| "pred_answer": "398\\ \\text{kW}", |
| "gt_answer": "32.8 kW", |
| "correct": false |
| }, |
| { |
| "index": 1413, |
| "pred_answer": "668^\\circ\\text{C}", |
| "gt_answer": "320.8 K", |
| "correct": false |
| }, |
| { |
| "index": 1415, |
| "pred_answer": "1.74\\ \\text{kW/K}", |
| "gt_answer": "3.64 kW/K", |
| "correct": false |
| }, |
| { |
| "index": 1416, |
| "pred_answer": null, |
| "gt_answer": "1.01 kW/K", |
| "correct": false |
| }, |
| { |
| "index": 1417, |
| "pred_answer": "0.45\\ \\text{kW·K}", |
| "gt_answer": "5.3 k/J", |
| "correct": false |
| }, |
| { |
| "index": 1419, |
| "pred_answer": "142.2\\ \\text{kJ/min}", |
| "gt_answer": "8847 kW", |
| "correct": false |
| }, |
| { |
| "index": 1422, |
| "pred_answer": "2.85\\ \\text{kW}", |
| "gt_answer": "1.36 kW", |
| "correct": false |
| }, |
| { |
| "index": 1425, |
| "pred_answer": "105.3\\ \\text{kJ}", |
| "gt_answer": "1.165 kW", |
| "correct": false |
| }, |
| { |
| "index": 1427, |
| "pred_answer": "0.948", |
| "gt_answer": "0.012175 kg water/kg", |
| "correct": false |
| }, |
| { |
| "index": 1429, |
| "pred_answer": "10\\ \\text{MPa}", |
| "gt_answer": "141 kPa", |
| "correct": false |
| }, |
| { |
| "index": 1433, |
| "pred_answer": null, |
| "gt_answer": "366 kW", |
| "correct": false |
| }, |
| { |
| "index": 1436, |
| "pred_answer": "0\\ \\text{kg}", |
| "gt_answer": "A: ", |
| "correct": false |
| }, |
| { |
| "index": 1438, |
| "pred_answer": "0.70", |
| "gt_answer": "1.34", |
| "correct": false |
| }, |
| { |
| "index": 1440, |
| "pred_answer": "42000\\ \\text{W}", |
| "gt_answer": "1.06 kW", |
| "correct": false |
| }, |
| { |
| "index": 1441, |
| "pred_answer": "2250\\ \\text{K}", |
| "gt_answer": "4991 K", |
| "correct": false |
| }, |
| { |
| "index": 1442, |
| "pred_answer": "2488\\ \\text{K}", |
| "gt_answer": "1480 K", |
| "correct": false |
| }, |
| { |
| "index": 1444, |
| "pred_answer": "11300000\\ \\text{W}", |
| "gt_answer": "-83.27 kW", |
| "correct": false |
| }, |
| { |
| "index": 1447, |
| "pred_answer": "197.8\\ \\text{C}", |
| "gt_answer": "433.4 ∘C", |
| "correct": false |
| }, |
| { |
| "index": 1450, |
| "pred_answer": "443\\ \\text{m/s}", |
| "gt_answer": "36.2 m/s", |
| "correct": false |
| }, |
| { |
| "index": 1457, |
| "pred_answer": "950\\ \\text{nm}", |
| "gt_answer": "95.2 nm", |
| "correct": false |
| }, |
| { |
| "index": 1458, |
| "pred_answer": "6\\ \\text{cm}", |
| "gt_answer": "12 cm", |
| "correct": false |
| }, |
| { |
| "index": 1459, |
| "pred_answer": "4.0\\ \\text{m}", |
| "gt_answer": "0.90 m", |
| "correct": false |
| }, |
| { |
| "index": 1460, |
| "pred_answer": "53.7^\\circ", |
| "gt_answer": "48.6°", |
| "correct": false |
| }, |
| { |
| "index": 1461, |
| "pred_answer": "35.3^\\circ", |
| "gt_answer": "13.9°", |
| "correct": false |
| }, |
| { |
| "index": 1462, |
| "pred_answer": "\\theta_3 \\text{ increases}", |
| "gt_answer": "22.0°", |
| "correct": false |
| }, |
| { |
| "index": 1463, |
| "pred_answer": "\\frac{\\Phi_B}{A}", |
| "gt_answer": "\\( 0.0145 \\, \\mathrm{A} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1464, |
| "pred_answer": "0.0000133\\ \\mathrm{T}", |
| "gt_answer": "\\( 0.0000267 \\, \\mathrm{T} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1465, |
| "pred_answer": "0.0000116\\ \\text{m}", |
| "gt_answer": "0.210 m", |
| "correct": false |
| }, |
| { |
| "index": 1468, |
| "pred_answer": "34.0\\ \\text{W}", |
| "gt_answer": "200 W", |
| "correct": false |
| }, |
| { |
| "index": 1469, |
| "pred_answer": "4.95\\,\\mu\\text{F}", |
| "gt_answer": "\\( \\frac{2 \\varepsilon_0 A}{d} \\cdot \\frac{\\kappa_1 \\kappa_2}{\\kappa_1 + \\kappa_2} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1470, |
| "pred_answer": "18\\ \\text{V}", |
| "gt_answer": "2.4 V", |
| "correct": false |
| }, |
| { |
| "index": 1474, |
| "pred_answer": "400\\ \\text{V/m}", |
| "gt_answer": "\\( 836000 \\, \\mathrm{N/C} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1478, |
| "pred_answer": "59\\ \\text{Hz}", |
| "gt_answer": "1.3 kHz", |
| "correct": false |
| }, |
| { |
| "index": 1479, |
| "pred_answer": "1.71\\ \\text{s}", |
| "gt_answer": "0.079 s", |
| "correct": false |
| }, |
| { |
| "index": 1480, |
| "pred_answer": "-5.4\\ \\text{J}", |
| "gt_answer": "\\( -85000 \\, \\mathrm{J} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1481, |
| "pred_answer": "12000\\ \\text{K}", |
| "gt_answer": "\\( 1300 \\, \\mathrm{K} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1482, |
| "pred_answer": "12.5^\\circ\\text{C}", |
| "gt_answer": "\\( 6.7^{\\circ}\\mathrm{C} \\)", |
| "correct": false |
| }, |
| { |
| "index": 1484, |
| "pred_answer": "1\\ \\text{s}", |
| "gt_answer": "+11.0 s", |
| "correct": false |
| }, |
| { |
| "index": 1487, |
| "pred_answer": "0.022\\ \\text{mm}", |
| "gt_answer": "5.0 μm", |
| "correct": false |
| }, |
| { |
| "index": 1488, |
| "pred_answer": "20\\ \\text{nm}", |
| "gt_answer": "99.6nm", |
| "correct": false |
| }, |
| { |
| "index": 1490, |
| "pred_answer": "1.20\\ \\text{m}", |
| "gt_answer": "4.0 mm", |
| "correct": false |
| }, |
| { |
| "index": 1492, |
| "pred_answer": "34.3^\\circ", |
| "gt_answer": "58.75°", |
| "correct": false |
| }, |
| { |
| "index": 1493, |
| "pred_answer": "0.30\\ \\mu_0 \\left(1 - 0.5\\frac{R}{L}\\right)", |
| "gt_answer": "2.3 mH", |
| "correct": false |
| }, |
| { |
| "index": 1494, |
| "pred_answer": "0.00011\\ \\text{V}", |
| "gt_answer": "5.2 V", |
| "correct": false |
| }, |
| { |
| "index": 1495, |
| "pred_answer": "10\\ \\text{V}", |
| "gt_answer": "14 V", |
| "correct": false |
| }, |
| { |
| "index": 1497, |
| "pred_answer": "\\text{into the page}", |
| "gt_answer": "0.016\\ \\mathrm{T}", |
| "correct": false |
| }, |
| { |
| "index": 1501, |
| "pred_answer": "2.00\\ \\text{V}", |
| "gt_answer": "3.8 V", |
| "correct": false |
| }, |
| { |
| "index": 1503, |
| "pred_answer": "0.00000000000001358\\ \\text{J}", |
| "gt_answer": "24.6 MeV", |
| "correct": false |
| }, |
| { |
| "index": 1504, |
| "pred_answer": "5.4\\times 10^{-10}\\ \\mathrm{J}", |
| "gt_answer": "-17 mJ", |
| "correct": false |
| }, |
| { |
| "index": 1506, |
| "pred_answer": "2\\pi aE", |
| "gt_answer": "0", |
| "correct": false |
| }, |
| { |
| "index": 1508, |
| "pred_answer": "0\\ \\text{W}", |
| "gt_answer": "-0.48 W", |
| "correct": false |
| }, |
| { |
| "index": 1511, |
| "pred_answer": "4.57\\times10^{-15}\\ \\text{N·m}", |
| "gt_answer": "\\frac{ehB}{8\\pi m}", |
| "correct": false |
| }, |
| { |
| "index": 1512, |
| "pred_answer": "0.2\\ \\text{m}", |
| "gt_answer": "4.0 m", |
| "correct": false |
| }, |
| { |
| "index": 1513, |
| "pred_answer": "0.01\\ \\text{mm}", |
| "gt_answer": "D + \\frac{2.44\\,Lh}{D \\sqrt{3MkT}}", |
| "correct": false |
| }, |
| { |
| "index": 1514, |
| "pred_answer": "1.0\\times 10^{-12}\\ \\text{A}", |
| "gt_answer": "0.096 µA", |
| "correct": false |
| }, |
| { |
| "index": 1516, |
| "pred_answer": "10\\ \\text{m}", |
| "gt_answer": "f \\theta", |
| "correct": false |
| }, |
| { |
| "index": 1520, |
| "pred_answer": "10\\ \\text{cm}", |
| "gt_answer": "25 cm", |
| "correct": false |
| }, |
| { |
| "index": 1522, |
| "pred_answer": "\\frac{dh}{h+d}", |
| "gt_answer": "h + \\frac{2d}{n} \\right", |
| "correct": false |
| }, |
| { |
| "index": 1524, |
| "pred_answer": "90^\\circ-\\theta", |
| "gt_answer": "180^\\circ - 2\\theta", |
| "correct": false |
| }, |
| { |
| "index": 1526, |
| "pred_answer": "f", |
| "gt_answer": "\\frac{R - h}{\\mu}", |
| "correct": false |
| }, |
| { |
| "index": 1530, |
| "pred_answer": "2.8\\times 10^{-11}\\,c", |
| "gt_answer": "0.6427 c", |
| "correct": false |
| }, |
| { |
| "index": 1531, |
| "pred_answer": "19.47^\\circ", |
| "gt_answer": "19.2∘", |
| "correct": false |
| }, |
| { |
| "index": 1533, |
| "pred_answer": "3.66\\ \\text{m}", |
| "gt_answer": "3/4d", |
| "correct": false |
| }, |
| { |
| "index": 1537, |
| "pred_answer": "7000\\ \\text{cm}^{-1}", |
| "gt_answer": "6700 slits/cm", |
| "correct": false |
| }, |
| { |
| "index": 1540, |
| "pred_answer": "100^\\circ", |
| "gt_answer": "100∘", |
| "correct": false |
| }, |
| { |
| "index": 1541, |
| "pred_answer": "31.7^\\circ", |
| "gt_answer": "23.3∘", |
| "correct": false |
| }, |
| { |
| "index": 1544, |
| "pred_answer": "30^\\circ", |
| "gt_answer": "39.9°", |
| "correct": false |
| }, |
| { |
| "index": 1546, |
| "pred_answer": "35.3^\\circ", |
| "gt_answer": "19.2°", |
| "correct": false |
| }, |
| { |
| "index": 1547, |
| "pred_answer": "0.30", |
| "gt_answer": "-2.0", |
| "correct": false |
| }, |
| { |
| "index": 1549, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "60°", |
| "correct": false |
| }, |
| { |
| "index": 1552, |
| "pred_answer": "414\\ \\text{m/s}", |
| "gt_answer": "2 \\( 1 + \\frac{m_2}{m_1} \\) v_0", |
| "correct": false |
| }, |
| { |
| "index": 1554, |
| "pred_answer": "BP", |
| "gt_answer": "167 cm", |
| "correct": false |
| }, |
| { |
| "index": 1559, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "56.3°", |
| "correct": false |
| }, |
| { |
| "index": 1561, |
| "pred_answer": "1.414", |
| "gt_answer": "\\frac{\\sqrt{5}}{2}", |
| "correct": false |
| }, |
| { |
| "index": 1565, |
| "pred_answer": "0.5", |
| "gt_answer": "2/3", |
| "correct": false |
| }, |
| { |
| "index": 1567, |
| "pred_answer": "10\\,\\text{D}", |
| "gt_answer": "2.5 D", |
| "correct": false |
| }, |
| { |
| "index": 1568, |
| "pred_answer": "0.5", |
| "gt_answer": "-1/2", |
| "correct": false |
| }, |
| { |
| "index": 1569, |
| "pred_answer": "20\\ \\text{cm}", |
| "gt_answer": "\\frac{R}{2(\\mu n + \\mu - 1)}", |
| "correct": false |
| }, |
| { |
| "index": 1570, |
| "pred_answer": "41.8^\\circ", |
| "gt_answer": "\\sin^{-1}(\\tan i)", |
| "correct": false |
| }, |
| { |
| "index": 1571, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "90°", |
| "correct": false |
| }, |
| { |
| "index": 1573, |
| "pred_answer": "90^\\circ", |
| "gt_answer": "30°", |
| "correct": false |
| }, |
| { |
| "index": 1574, |
| "pred_answer": "2\\ \\text{m}", |
| "gt_answer": "6.6 cm", |
| "correct": false |
| }, |
| { |
| "index": 1575, |
| "pred_answer": "4.00\\ \\text{cm}", |
| "gt_answer": "2.4 cm", |
| "correct": false |
| }, |
| { |
| "index": 1576, |
| "pred_answer": "0.010\\ \\text{m}", |
| "gt_answer": "0.22 mm", |
| "correct": false |
| }, |
| { |
| "index": 1578, |
| "pred_answer": "59.0^\\circ", |
| "gt_answer": "\\sin^{-1} \\left( \\sqrt{ \\left( \frac{n_2}{n_1} \\right)^2 - 1 } \\right)", |
| "correct": false |
| }, |
| { |
| "index": 1579, |
| "pred_answer": "3.6^\\circ", |
| "gt_answer": "157.2°", |
| "correct": false |
| }, |
| { |
| "index": 1582, |
| "pred_answer": "1.0\\ \\text{m}", |
| "gt_answer": "10 cm", |
| "correct": false |
| }, |
| { |
| "index": 1583, |
| "pred_answer": "2.5\\ \\text{cm}", |
| "gt_answer": "20 cm", |
| "correct": false |
| }, |
| { |
| "index": 1589, |
| "pred_answer": "34.3\\text{ cm}", |
| "gt_answer": "26.65 cm", |
| "correct": false |
| }, |
| { |
| "index": 1590, |
| "pred_answer": "h", |
| "gt_answer": "15 cm", |
| "correct": false |
| }, |
| { |
| "index": 1591, |
| "pred_answer": "0.000000275\\ \\text{m}", |
| "gt_answer": "94.83nm", |
| "correct": false |
| }, |
| { |
| "index": 1592, |
| "pred_answer": "0.5\\,\\lambda", |
| "gt_answer": "0.12 m", |
| "correct": false |
| }, |
| { |
| "index": 1593, |
| "pred_answer": null, |
| "gt_answer": "\\pm D \\tan\\left\\{ \\cos^{-1}\\left( \\frac{7}{8} \\right) \night\\}", |
| "correct": false |
| }, |
| { |
| "index": 1595, |
| "pred_answer": "0.05\\ \\text{mm}", |
| "gt_answer": "500 nm", |
| "correct": false |
| }, |
| { |
| "index": 1599, |
| "pred_answer": "0.24\\,\\mu\\text{m}", |
| "gt_answer": "2000\\,\\text{\\AA}", |
| "correct": false |
| }, |
| { |
| "index": 1600, |
| "pred_answer": "0.00000563\\ \\text{m}", |
| "gt_answer": "7.8 μm", |
| "correct": false |
| }, |
| { |
| "index": 1601, |
| "pred_answer": "0.0032\\ \\text{T}", |
| "gt_answer": "0.0000568\\,\\text{T}", |
| "correct": false |
| }, |
| { |
| "index": 1602, |
| "pred_answer": "150\\,\\Omega", |
| "gt_answer": "185000\\,\\Omega", |
| "correct": false |
| }, |
| { |
| "index": 1606, |
| "pred_answer": "0\\ \\text{mm}", |
| "gt_answer": "0.00167\\,\\text{mm}", |
| "correct": false |
| }, |
| { |
| "index": 1614, |
| "pred_answer": "I(\\theta)\\propto \\frac{1}{\\beta^4}\\left(1-\\frac{\\beta^2}{L^2}\\right)\\left(1-\\frac{\\beta^2}{l^2}\\right)", |
| "gt_answer": "\\left( \\frac{1}{\\lambda z_1} \night)^2 \\left[ L^2 \\, \\text{sinc} \\left( \\frac{Lx}{\\lambda z_1} \\right) \\text{sinc} \\left( \\frac{Ly}{\\lambda z_1} \\right) - l^2 \\, \text{sinc} \\left( \\frac{lx}{\\lambda z_1} \\right) \\text{sinc} \\left( \\frac{ly}{\\lambda z_1} \\right) \\right]^2", |
| "correct": false |
| }, |
| { |
| "index": 1617, |
| "pred_answer": "11.7\\ \\text{h}", |
| "gt_answer": "$(16000 \\text{s})\\sqrt{1 - 10^{-12}}$", |
| "correct": false |
| }, |
| { |
| "index": 1618, |
| "pred_answer": "399\\ \\text{m}", |
| "gt_answer": "56.4 m", |
| "correct": false |
| }, |
| { |
| "index": 1619, |
| "pred_answer": "0.34c", |
| "gt_answer": "0.98 c", |
| "correct": false |
| }, |
| { |
| "index": 1620, |
| "pred_answer": "0.0000000000216\\ \\text{J}", |
| "gt_answer": "67.4 MeV", |
| "correct": false |
| }, |
| { |
| "index": 1621, |
| "pred_answer": "3\\ \\text{J·s}", |
| "gt_answer": "$0 \\text{ J} \\cdot \\text{s}$", |
| "correct": false |
| }, |
| { |
| "index": 1622, |
| "pred_answer": "18\\ \\text{eV}", |
| "gt_answer": "20 eV", |
| "correct": false |
| }, |
| { |
| "index": 1623, |
| "pred_answer": "97.3\\ \\text{nm}", |
| "gt_answer": "378 nm", |
| "correct": false |
| }, |
| { |
| "index": 1628, |
| "pred_answer": "12.24\\ \\text{m}", |
| "gt_answer": "2500/3 m", |
| "correct": false |
| }, |
| { |
| "index": 1629, |
| "pred_answer": "12\\text{ m}", |
| "gt_answer": "329.8 m", |
| "correct": false |
| }, |
| { |
| "index": 1632, |
| "pred_answer": "2.0\\ \\text{s}", |
| "gt_answer": "$2\\sqrt{\\frac{L}{g}}$", |
| "correct": false |
| }, |
| { |
| "index": 1633, |
| "pred_answer": "\\sqrt{2}A", |
| "gt_answer": "0.05 m", |
| "correct": false |
| }, |
| { |
| "index": 1635, |
| "pred_answer": "4\\ \\text{m}", |
| "gt_answer": "3 m", |
| "correct": false |
| }, |
| { |
| "index": 1638, |
| "pred_answer": null, |
| "gt_answer": "70.71 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1641, |
| "pred_answer": "1400\\ \\text{N}", |
| "gt_answer": "$1.5 \\,\\mathrm{kg \\cdot wt}$", |
| "correct": false |
| }, |
| { |
| "index": 1642, |
| "pred_answer": "51\\ \\text{Hz}", |
| "gt_answer": "0.6 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1643, |
| "pred_answer": "2.52\\ \\text{Hz}", |
| "gt_answer": "6 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1644, |
| "pred_answer": "200\\ \\text{Hz}", |
| "gt_answer": "1350 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1645, |
| "pred_answer": "122\\text{ m}", |
| "gt_answer": "320 m", |
| "correct": false |
| }, |
| { |
| "index": 1646, |
| "pred_answer": "918\\ \\text{Hz}", |
| "gt_answer": "442 Hz", |
| "correct": false |
| }, |
| { |
| "index": 1650, |
| "pred_answer": "3.3\\ \\text{eV}", |
| "gt_answer": "$h\\nu_c$", |
| "correct": false |
| }, |
| { |
| "index": 1652, |
| "pred_answer": "2.5\\ \\text{eV}", |
| "gt_answer": "12.09 eV", |
| "correct": false |
| }, |
| { |
| "index": 1653, |
| "pred_answer": "0.0000000000000000000014\\ \\mathrm{kg\\cdot m/s}", |
| "gt_answer": "$\\frac{6}{7}mv$", |
| "correct": false |
| }, |
| { |
| "index": 1655, |
| "pred_answer": "m", |
| "gt_answer": "ek", |
| "correct": false |
| }, |
| { |
| "index": 1657, |
| "pred_answer": "4", |
| "gt_answer": "2", |
| "correct": false |
| }, |
| { |
| "index": 1658, |
| "pred_answer": "15.56\\ \\text{eV}", |
| "gt_answer": "0.45 eV", |
| "correct": false |
| }, |
| { |
| "index": 1660, |
| "pred_answer": "0.0000003\\ \\text{s}", |
| "gt_answer": "15.6\\ \\mu\\text{s}$", |
| "correct": false |
| }, |
| { |
| "index": 1661, |
| "pred_answer": "25\\ \\text{min}", |
| "gt_answer": "$16000 \\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 1663, |
| "pred_answer": "1.01\\times 10^{-27}\\ \\text{kg·m/s}", |
| "gt_answer": "$16299999999999998$ photons/s", |
| "correct": false |
| }, |
| { |
| "index": 1664, |
| "pred_answer": "0.000000000000000000002\\ \\text{J}", |
| "gt_answer": "1.25 eV", |
| "correct": false |
| }, |
| { |
| "index": 1665, |
| "pred_answer": "6.75\\times 10^{-14}\\ \\text{eV}", |
| "gt_answer": "$0 \\mathrm{J} \\cdot \\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 1666, |
| "pred_answer": "0.00156\\ \\text{J}", |
| "gt_answer": "2.40 eV", |
| "correct": false |
| }, |
| { |
| "index": 1667, |
| "pred_answer": "2.46\\times 10^{-11}\\ \\text{eV}", |
| "gt_answer": "2.46 eV", |
| "correct": false |
| }, |
| { |
| "index": 1668, |
| "pred_answer": "1.20\\times 10^{20}\\ \\text{photons/s}", |
| "gt_answer": "$225999999999999967232$ photons/s", |
| "correct": false |
| }, |
| { |
| "index": 1669, |
| "pred_answer": "3400000\\ \\text{m/s}", |
| "gt_answer": "$249000 \\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 1670, |
| "pred_answer": "2.25\\ \\text{eV}", |
| "gt_answer": "2.14 eV", |
| "correct": false |
| }, |
| { |
| "index": 1671, |
| "pred_answer": "0\\ \\text{m/s}", |
| "gt_answer": "$1220000\\ \\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 1672, |
| "pred_answer": "143.1^\\circ", |
| "gt_answer": "118°", |
| "correct": false |
| }, |
| { |
| "index": 1673, |
| "pred_answer": "0.108\\ \\text{nm}", |
| "gt_answer": "$0.000000000000026\\ \\mathrm{m}$", |
| "correct": false |
| }, |
| { |
| "index": 1674, |
| "pred_answer": "0.135\\ \\text{mJ}", |
| "gt_answer": "$0.00507\\ \\mathrm{J}$", |
| "correct": false |
| }, |
| { |
| "index": 1675, |
| "pred_answer": "196\\ \\text{pm}", |
| "gt_answer": "$0\\ \\mathrm{kg\\cdot m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 1676, |
| "pred_answer": "0.000000000000000305\\ \\text{kg m/s}", |
| "gt_answer": "-59.4°", |
| "correct": false |
| }, |
| { |
| "index": 1677, |
| "pred_answer": "0.016\\ \\text{eV}", |
| "gt_answer": "319 eV", |
| "correct": false |
| }, |
| { |
| "index": 1679, |
| "pred_answer": "500\\ \\text{nm}", |
| "gt_answer": "500 nm", |
| "correct": false |
| }, |
| { |
| "index": 1682, |
| "pred_answer": "0.200\\ \\text{mm}", |
| "gt_answer": "0.488 nm", |
| "correct": false |
| }, |
| { |
| "index": 1684, |
| "pred_answer": "169000\\ \\text{m}", |
| "gt_answer": "$0.000000000000055\\ \\mathrm{m}$", |
| "correct": false |
| }, |
| { |
| "index": 1687, |
| "pred_answer": "0.333\\ \\text{m}", |
| "gt_answer": "0.58", |
| "correct": false |
| }, |
| { |
| "index": 1689, |
| "pred_answer": "155\\ \\text{nm}", |
| "gt_answer": "130 nm", |
| "correct": false |
| }, |
| { |
| "index": 1690, |
| "pred_answer": "13.1\\ \\text{eV}", |
| "gt_answer": "0.90 eV", |
| "correct": false |
| }, |
| { |
| "index": 1695, |
| "pred_answer": "3.43^\\circ", |
| "gt_answer": "20.9°", |
| "correct": false |
| }, |
| { |
| "index": 1696, |
| "pred_answer": "11.4\\ \\text{eV}", |
| "gt_answer": "4.6 eV", |
| "correct": false |
| }, |
| { |
| "index": 1700, |
| "pred_answer": "0.000165\\ \\text{T}", |
| "gt_answer": "46T", |
| "correct": false |
| }, |
| { |
| "index": 1701, |
| "pred_answer": "1000\\ \\text{mV}", |
| "gt_answer": "7.74V", |
| "correct": false |
| }, |
| { |
| "index": 1702, |
| "pred_answer": "L = 375\\ \\text{mH},\\ R = 2.5\\ \\Omega", |
| "gt_answer": "32Ω", |
| "correct": false |
| }, |
| { |
| "index": 1703, |
| "pred_answer": "19\\ \\text{mH}", |
| "gt_answer": "20.0Ω", |
| "correct": false |
| }, |
| { |
| "index": 1707, |
| "pred_answer": "1.0\\ \\text{A}", |
| "gt_answer": "19.4A", |
| "correct": false |
| }, |
| { |
| "index": 1708, |
| "pred_answer": "2.0\\times 10^{8}\\ \\mathrm{m/s}", |
| "gt_answer": "300000000 \\, \text{m/s}", |
| "correct": false |
| }, |
| { |
| "index": 1710, |
| "pred_answer": "82.7^\\circ", |
| "gt_answer": "82°", |
| "correct": false |
| }, |
| { |
| "index": 1712, |
| "pred_answer": "0", |
| "gt_answer": "I = 0", |
| "correct": false |
| }, |
| { |
| "index": 1714, |
| "pred_answer": "1.33", |
| "gt_answer": "1.3", |
| "correct": false |
| }, |
| { |
| "index": 1716, |
| "pred_answer": "10^\\circ", |
| "gt_answer": " 90°", |
| "correct": false |
| }, |
| { |
| "index": 1717, |
| "pred_answer": "34.5^\\circ", |
| "gt_answer": "12.1°", |
| "correct": false |
| }, |
| { |
| "index": 1718, |
| "pred_answer": "50^\\circ", |
| "gt_answer": "39.1°", |
| "correct": false |
| }, |
| { |
| "index": 1719, |
| "pred_answer": "1.13", |
| "gt_answer": "1.35", |
| "correct": false |
| }, |
| { |
| "index": 1720, |
| "pred_answer": "13.5^\\circ", |
| "gt_answer": "0.23°", |
| "correct": false |
| }, |
| { |
| "index": 1721, |
| "pred_answer": "0.00664\\ \\text{m}", |
| "gt_answer": "1.62cm", |
| "correct": false |
| }, |
| { |
| "index": 1724, |
| "pred_answer": "17\\ \\text{W/m}^2\\ \\text{and}\\ 25\\ \\text{W/m}^2", |
| "gt_answer": "20W/m^2", |
| "correct": false |
| }, |
| { |
| "index": 1725, |
| "pred_answer": "3.9\\ \\text{mm}", |
| "gt_answer": "68.9mm", |
| "correct": false |
| }, |
| { |
| "index": 1726, |
| "pred_answer": "0.051\\ \\text{m}", |
| "gt_answer": "2.07cm", |
| "correct": false |
| }, |
| { |
| "index": 1727, |
| "pred_answer": "1.70", |
| "gt_answer": "59.1", |
| "correct": false |
| }, |
| { |
| "index": 1728, |
| "pred_answer": "-10\\ \\text{cm}", |
| "gt_answer": "18.0cm", |
| "correct": false |
| }, |
| { |
| "index": 1729, |
| "pred_answer": "d_o", |
| "gt_answer": "24.1cm", |
| "correct": false |
| }, |
| { |
| "index": 1730, |
| "pred_answer": "2.5\\ \\text{cm}", |
| "gt_answer": "-15.0cm", |
| "correct": false |
| }, |
| { |
| "index": 1733, |
| "pred_answer": "\\frac{a}{2}", |
| "gt_answer": "f = 1/4a", |
| "correct": false |
| }, |
| { |
| "index": 1734, |
| "pred_answer": "45.0\\ \\text{cm}", |
| "gt_answer": "17.1cm", |
| "correct": false |
| }, |
| { |
| "index": 1738, |
| "pred_answer": "0.667\\ \\text{mm}", |
| "gt_answer": "620nm", |
| "correct": false |
| }, |
| { |
| "index": 1742, |
| "pred_answer": "0.056\\ \\text{arcsec}", |
| "gt_answer": "$19400000000000$ km", |
| "correct": false |
| }, |
| { |
| "index": 1745, |
| "pred_answer": null, |
| "gt_answer": "$210000000$ m/s", |
| "correct": false |
| }, |
| { |
| "index": 1746, |
| "pred_answer": "1.3\\ \\text{T}", |
| "gt_answer": "$\\mathbf{B}_\\gamma$", |
| "correct": false |
| }, |
| { |
| "index": 1747, |
| "pred_answer": "0.0001\\ \\text{m}^2", |
| "gt_answer": "cLT", |
| "correct": false |
| }, |
| { |
| "index": 1750, |
| "pred_answer": "1.3\\ \\text{MeV}", |
| "gt_answer": " 10.0MeV", |
| "correct": false |
| }, |
| { |
| "index": 1751, |
| "pred_answer": "0.018\\ \\text{A}", |
| "gt_answer": "91.1A", |
| "correct": false |
| }, |
| { |
| "index": 1752, |
| "pred_answer": "1.96\\times 10^{15}", |
| "gt_answer": "0.014", |
| "correct": false |
| }, |
| { |
| "index": 1754, |
| "pred_answer": "0", |
| "gt_answer": "$Ce^{\\kappa x} + De^{-\\kappa x}$", |
| "correct": false |
| }, |
| { |
| "index": 1756, |
| "pred_answer": "1.30\\ \\text{m}", |
| "gt_answer": "1.01m", |
| "correct": false |
| }, |
| { |
| "index": 1757, |
| "pred_answer": null, |
| "gt_answer": "$h_{oil} = \\frac{\\rho_{water}}{\\rho_{oil}} h_{water}$", |
| "correct": false |
| }, |
| { |
| "index": 1758, |
| "pred_answer": "4.90\\ \\text{N}", |
| "gt_answer": "147N", |
| "correct": false |
| }, |
| { |
| "index": 1759, |
| "pred_answer": "0.000523\\ \\text{m}^3/\\text{s}", |
| "gt_answer": "0.47L/s", |
| "correct": false |
| }, |
| { |
| "index": 1760, |
| "pred_answer": null, |
| "gt_answer": "$\\sqrt{2 \\left( \\frac{p_0 - p_{atm}}{\\rho} \\right) + 2gh}$", |
| "correct": false |
| }, |
| { |
| "index": 1762, |
| "pred_answer": "1350000000000000000\\ \\text{N}", |
| "gt_answer": "$187000000000000014579400704 \\, \\text{N}$", |
| "correct": false |
| }, |
| { |
| "index": 1763, |
| "pred_answer": null, |
| "gt_answer": "7910m/s", |
| "correct": false |
| }, |
| { |
| "index": 1764, |
| "pred_answer": "76\\ \\text{years}", |
| "gt_answer": "75.3y", |
| "correct": false |
| }, |
| { |
| "index": 1765, |
| "pred_answer": "F_g = \\frac{4}{3}\\pi G\\rho R_E^3\\frac{m}{r^2}", |
| "gt_answer": "$F_g = \\frac{G m_E m}{R_E^3} r$", |
| "correct": false |
| }, |
| { |
| "index": 1767, |
| "pred_answer": null, |
| "gt_answer": "$2\\pi \\sqrt{\\frac{M + m}{k}}$", |
| "correct": false |
| }, |
| { |
| "index": 1769, |
| "pred_answer": "104\\ \\text{m/s}", |
| "gt_answer": "88.5m/s", |
| "correct": false |
| }, |
| { |
| "index": 1776, |
| "pred_answer": "0\\ \\text{Hz}", |
| "gt_answer": "274Hz", |
| "correct": false |
| }, |
| { |
| "index": 1777, |
| "pred_answer": "1097\\ \\text{Hz}", |
| "gt_answer": "277Hz", |
| "correct": false |
| }, |
| { |
| "index": 1779, |
| "pred_answer": "23.3\\ \\text{s}", |
| "gt_answer": "20.5s", |
| "correct": false |
| }, |
| { |
| "index": 1781, |
| "pred_answer": "1660\\ \\text{J/s}", |
| "gt_answer": "32.4J/s", |
| "correct": false |
| }, |
| { |
| "index": 1782, |
| "pred_answer": "2080\\ \\text{W}", |
| "gt_answer": "15.9W", |
| "correct": false |
| }, |
| { |
| "index": 1783, |
| "pred_answer": "0.64\\ \\text{W}", |
| "gt_answer": "97.1W", |
| "correct": false |
| }, |
| { |
| "index": 1784, |
| "pred_answer": "847^\\circ\\text{C}", |
| "gt_answer": "450°C", |
| "correct": false |
| }, |
| { |
| "index": 1785, |
| "pred_answer": "11.8\\ \\text{J}", |
| "gt_answer": "500J", |
| "correct": false |
| }, |
| { |
| "index": 1786, |
| "pred_answer": "140\\ \\text{kJ}", |
| "gt_answer": "600J", |
| "correct": false |
| }, |
| { |
| "index": 1788, |
| "pred_answer": "0.188\\ \\text{kg}", |
| "gt_answer": "0.20g", |
| "correct": false |
| }, |
| { |
| "index": 1789, |
| "pred_answer": "1180\\ \\text{J}", |
| "gt_answer": "30%", |
| "correct": false |
| }, |
| { |
| "index": 1795, |
| "pred_answer": "2\\ \\text{s}", |
| "gt_answer": "$x = 40 \\mathrm{m}$", |
| "correct": false |
| }, |
| { |
| "index": 1796, |
| "pred_answer": "1619\\ \\text{m}", |
| "gt_answer": "12000m", |
| "correct": false |
| }, |
| { |
| "index": 1797, |
| "pred_answer": "\\frac{L^2}{a_F^2}", |
| "gt_answer": "6.9yards", |
| "correct": false |
| }, |
| { |
| "index": 1798, |
| "pred_answer": "1.98\\ \\text{s}", |
| "gt_answer": "4.52s", |
| "correct": false |
| }, |
| { |
| "index": 1801, |
| "pred_answer": "8\\ \\text{m/s}", |
| "gt_answer": "34m/s", |
| "correct": false |
| }, |
| { |
| "index": 1802, |
| "pred_answer": "1840\\ \\text{m}", |
| "gt_answer": "5300m", |
| "correct": false |
| }, |
| { |
| "index": 1805, |
| "pred_answer": "|\\vec v|=3.0\\ \\text{m/s},\\quad \\theta=-90^\\circ", |
| "gt_answer": "$(7.2\\,\\mathrm{m/s},\\,34^{\\circ}\\,\\mathrm{above\\ the\\ negative\\ x-axis})$", |
| "correct": false |
| }, |
| { |
| "index": 1806, |
| "pred_answer": "(-6.43\\ \\text{m/s})\\,\\hat{i}+(7.66\\ \\text{m/s})\\,\\hat{j}", |
| "gt_answer": "$(-7.66\\hat{\\imath} + 6.43\\hat{\\jmath})\\,\\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 1809, |
| "pred_answer": "2.7\\ \\text{m}", |
| "gt_answer": "4.5m", |
| "correct": false |
| }, |
| { |
| "index": 1810, |
| "pred_answer": "0.44^\\circ", |
| "gt_answer": "56°", |
| "correct": false |
| }, |
| { |
| "index": 1813, |
| "pred_answer": "3.04\\ \\text{km}", |
| "gt_answer": "1.54km", |
| "correct": false |
| }, |
| { |
| "index": 1814, |
| "pred_answer": "6.0\\ \\text{m}", |
| "gt_answer": "1.0m", |
| "correct": false |
| }, |
| { |
| "index": 1817, |
| "pred_answer": "0.167\\ \\mathrm{m/s^2}", |
| "gt_answer": "$3.9\\,\\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 1823, |
| "pred_answer": "0\\ \\text{m}", |
| "gt_answer": "17m", |
| "correct": false |
| }, |
| { |
| "index": 1826, |
| "pred_answer": "15\\ \\text{m/s}", |
| "gt_answer": "14m/s", |
| "correct": false |
| }, |
| { |
| "index": 1827, |
| "pred_answer": "117\\ \\text{rpm}", |
| "gt_answer": "135rpm", |
| "correct": false |
| }, |
| { |
| "index": 1833, |
| "pred_answer": "1.67\\ \\text{m/s}", |
| "gt_answer": "1.7m/s", |
| "correct": false |
| }, |
| { |
| "index": 1835, |
| "pred_answer": "12.3\\ \\text{m/s},\\ 34.3^\\circ", |
| "gt_answer": "15m/s", |
| "correct": false |
| }, |
| { |
| "index": 1839, |
| "pred_answer": "9.9\\ \\text{m/s}", |
| "gt_answer": "10m/s", |
| "correct": false |
| }, |
| { |
| "index": 1840, |
| "pred_answer": "10.0\\ \\text{m/s}", |
| "gt_answer": "320m/s", |
| "correct": false |
| }, |
| { |
| "index": 1841, |
| "pred_answer": "0.30", |
| "gt_answer": "4.7s", |
| "correct": false |
| }, |
| { |
| "index": 1842, |
| "pred_answer": "3.18\\ \\text{m/s}", |
| "gt_answer": "3.2m/s", |
| "correct": false |
| }, |
| { |
| "index": 1845, |
| "pred_answer": "32.3^\\circ", |
| "gt_answer": "$19^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 1847, |
| "pred_answer": "99\\ \\text{m/s}", |
| "gt_answer": "130m/s", |
| "correct": false |
| }, |
| { |
| "index": 1848, |
| "pred_answer": "14\\ \\text{m/s}", |
| "gt_answer": "26m/s", |
| "correct": false |
| }, |
| { |
| "index": 1849, |
| "pred_answer": "22.2\\ \\text{m/s}", |
| "gt_answer": "13m/s", |
| "correct": false |
| }, |
| { |
| "index": 1852, |
| "pred_answer": "1.22\\ \\text{m/s}", |
| "gt_answer": "1.68m/s", |
| "correct": false |
| }, |
| { |
| "index": 1853, |
| "pred_answer": "0.0040\\ \\mathrm{m/s^2}", |
| "gt_answer": "$4.8\\,\\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 1855, |
| "pred_answer": "2.2\\ \\text{m/s}", |
| "gt_answer": "5.4m/s", |
| "correct": false |
| }, |
| { |
| "index": 1858, |
| "pred_answer": "1.6\\ \\text{N}\\cdot\\text{m}", |
| "gt_answer": "3920N", |
| "correct": false |
| }, |
| { |
| "index": 1860, |
| "pred_answer": "0.25\\ \\text{s}", |
| "gt_answer": "4.6s", |
| "correct": false |
| }, |
| { |
| "index": 1861, |
| "pred_answer": "15\\ \\text{rad/s}^2", |
| "gt_answer": "$400\\,\\mathrm{rad/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 1864, |
| "pred_answer": "525000\\ \\text{m/s}", |
| "gt_answer": "$613000\\,\\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 1868, |
| "pred_answer": "42\\ \\text{rad/s}", |
| "gt_answer": "100rpm", |
| "correct": false |
| }, |
| { |
| "index": 1870, |
| "pred_answer": "52500\\ \\text{m/s}", |
| "gt_answer": "11200m/s", |
| "correct": false |
| }, |
| { |
| "index": 1873, |
| "pred_answer": "0.1\\ \\text{s},\\ 1.9\\ \\text{s}", |
| "gt_answer": "0.51s", |
| "correct": false |
| }, |
| { |
| "index": 1877, |
| "pred_answer": "101300\\ \\text{Pa}", |
| "gt_answer": "1.06atm", |
| "correct": false |
| }, |
| { |
| "index": 1879, |
| "pred_answer": "0.992\\ \\text{kg/m}^3", |
| "gt_answer": "$1260\\,\\mathrm{kg/m^3}$", |
| "correct": false |
| }, |
| { |
| "index": 1880, |
| "pred_answer": "12.5\\ \\text{kPa}", |
| "gt_answer": "4.6kPa", |
| "correct": false |
| }, |
| { |
| "index": 1881, |
| "pred_answer": "9800\\ \\text{Pa}", |
| "gt_answer": "1.5atm", |
| "correct": false |
| }, |
| { |
| "index": 1885, |
| "pred_answer": "0.031\\ \\text{kW}", |
| "gt_answer": "360W", |
| "correct": false |
| }, |
| { |
| "index": 1886, |
| "pred_answer": "0.500", |
| "gt_answer": "15%", |
| "correct": false |
| }, |
| { |
| "index": 1889, |
| "pred_answer": "4.62\\ \\text{MeV}", |
| "gt_answer": "5.4MeV", |
| "correct": false |
| }, |
| { |
| "index": 1890, |
| "pred_answer": "0.048\\ \\text{mSv}", |
| "gt_answer": "0.45mSv", |
| "correct": false |
| }, |
| { |
| "index": 1893, |
| "pred_answer": "1.00\\ \\text{m}", |
| "gt_answer": "0.65m", |
| "correct": false |
| }, |
| { |
| "index": 1894, |
| "pred_answer": "0.000000000105\\ \\text{m}", |
| "gt_answer": "0.30nm", |
| "correct": false |
| }, |
| { |
| "index": 1896, |
| "pred_answer": "1.8^\\circ", |
| "gt_answer": "$98^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 1897, |
| "pred_answer": "0.013\\,\\mu\\text{m}", |
| "gt_answer": "100nm", |
| "correct": false |
| }, |
| { |
| "index": 1898, |
| "pred_answer": "1.84~\\mu\\text{m}", |
| "gt_answer": "99.6nm", |
| "correct": false |
| }, |
| { |
| "index": 1901, |
| "pred_answer": "0.45", |
| "gt_answer": "$14 \\times x$", |
| "correct": false |
| }, |
| { |
| "index": 1902, |
| "pred_answer": "0.000139\\ \\text{arcsec}", |
| "gt_answer": "$0.00016\\,\\mathrm{rad}$", |
| "correct": false |
| }, |
| { |
| "index": 1904, |
| "pred_answer": "0.883", |
| "gt_answer": "-0.50", |
| "correct": false |
| }, |
| { |
| "index": 1908, |
| "pred_answer": "32.3^\\circ", |
| "gt_answer": "60.0°", |
| "correct": false |
| }, |
| { |
| "index": 1909, |
| "pred_answer": "1", |
| "gt_answer": "+0.44", |
| "correct": false |
| }, |
| { |
| "index": 1910, |
| "pred_answer": "-0.126", |
| "gt_answer": "+3.00", |
| "correct": false |
| }, |
| { |
| "index": 1912, |
| "pred_answer": "105^\\circ", |
| "gt_answer": "75°", |
| "correct": false |
| }, |
| { |
| "index": 1916, |
| "pred_answer": "27.4^\\circ", |
| "gt_answer": "$56.2^{\\circ}\\,\\mathrm{from\\ the\\ normal}$", |
| "correct": false |
| }, |
| { |
| "index": 1922, |
| "pred_answer": "1.52", |
| "gt_answer": "1.004328", |
| "correct": false |
| }, |
| { |
| "index": 1925, |
| "pred_answer": "6.0\\times 10^{5}\\ \\mathrm{J/mol}", |
| "gt_answer": "980J/mol", |
| "correct": false |
| }, |
| { |
| "index": 1929, |
| "pred_answer": "700\\,^\\circ\\text{C}", |
| "gt_answer": "170°C", |
| "correct": false |
| }, |
| { |
| "index": 1936, |
| "pred_answer": "3370\\ \\text{J}", |
| "gt_answer": "480J", |
| "correct": false |
| }, |
| { |
| "index": 1937, |
| "pred_answer": "1", |
| "gt_answer": "74%", |
| "correct": false |
| }, |
| { |
| "index": 1938, |
| "pred_answer": "-25\\ \\text{J}", |
| "gt_answer": "16J", |
| "correct": false |
| }, |
| { |
| "index": 1939, |
| "pred_answer": "2400\\ \\text{J}", |
| "gt_answer": "3830J", |
| "correct": false |
| }, |
| { |
| "index": 1941, |
| "pred_answer": "3.1\\ \\text{Hz}", |
| "gt_answer": "13Hz", |
| "correct": false |
| }, |
| { |
| "index": 1942, |
| "pred_answer": "62.5\\ \\text{ms}", |
| "gt_answer": "0.14s", |
| "correct": false |
| }, |
| { |
| "index": 1943, |
| "pred_answer": "460\\ \\text{m/s}", |
| "gt_answer": "312.6m/s", |
| "correct": false |
| }, |
| { |
| "index": 1945, |
| "pred_answer": "0.10\\ \\text{kg}", |
| "gt_answer": "1.2kg", |
| "correct": false |
| }, |
| { |
| "index": 1949, |
| "pred_answer": "\\lambda_m=\\frac{2L}{m}", |
| "gt_answer": "$\\lambda = \\frac{4\\ell}{2n - 1},\\; n = 1, 2, 3, \\dots$", |
| "correct": false |
| }, |
| { |
| "index": 1950, |
| "pred_answer": "1.8\\ \\text{m}", |
| "gt_answer": "0.44m", |
| "correct": false |
| }, |
| { |
| "index": 1954, |
| "pred_answer": "160\\ \\text{Hz}", |
| "gt_answer": "500Hz", |
| "correct": false |
| }, |
| { |
| "index": 1959, |
| "pred_answer": "37500\\ \\text{mm}", |
| "gt_answer": "4.2cm", |
| "correct": false |
| }, |
| { |
| "index": 1960, |
| "pred_answer": "0.30\\ \\text{m}", |
| "gt_answer": "0.429m", |
| "correct": false |
| }, |
| { |
| "index": 1961, |
| "pred_answer": "31.4^\\circ", |
| "gt_answer": "36°", |
| "correct": false |
| }, |
| { |
| "index": 1962, |
| "pred_answer": "-14000\\ \\text{m}", |
| "gt_answer": "16km", |
| "correct": false |
| }, |
| { |
| "index": 1964, |
| "pred_answer": "108\\ \\text{Hz}", |
| "gt_answer": "635Hz", |
| "correct": false |
| }, |
| { |
| "index": 1965, |
| "pred_answer": "182\\ \\text{Hz}", |
| "gt_answer": "50Hz", |
| "correct": false |
| }, |
| { |
| "index": 1966, |
| "pred_answer": "0.50\\ \\text{s}", |
| "gt_answer": "0.628s", |
| "correct": false |
| }, |
| { |
| "index": 1967, |
| "pred_answer": "1.00\\ \\text{J}", |
| "gt_answer": "0.125 J", |
| "correct": false |
| }, |
| { |
| "index": 1968, |
| "pred_answer": "11.8\\%", |
| "gt_answer": "4.08%", |
| "correct": false |
| }, |
| { |
| "index": 1969, |
| "pred_answer": "5.0\\times 10^{-11}\\ \\text{N·m}^2", |
| "gt_answer": "$0.000316\\,\\mathrm{N\\cdot m/rad}$", |
| "correct": false |
| }, |
| { |
| "index": 1973, |
| "pred_answer": "11\\ \\text{rad/s}", |
| "gt_answer": "$7.75\\,\\mathrm{s^{-1}}$", |
| "correct": false |
| }, |
| { |
| "index": 1974, |
| "pred_answer": null, |
| "gt_answer": "$\\frac{1}{2\\pi L} \\sqrt{gL + \\frac{kh^2}{M}}$", |
| "correct": false |
| }, |
| { |
| "index": 1978, |
| "pred_answer": "0.100\\ \\text{s}", |
| "gt_answer": "$2\\pi \\sqrt{\\frac{M + m/3}{k}}$", |
| "correct": false |
| }, |
| { |
| "index": 1980, |
| "pred_answer": "3", |
| "gt_answer": "3", |
| "correct": true |
| }, |
| { |
| "index": 1981, |
| "pred_answer": "a_{y,\\max}=\\mu v^2\\left(\\frac{2\\pi}{\\lambda}\\right)^2 A", |
| "gt_answer": "$118\\,\\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 1982, |
| "pred_answer": "0.53\\ \\text{m/s}", |
| "gt_answer": "19.6 m/s", |
| "correct": false |
| }, |
| { |
| "index": 1983, |
| "pred_answer": "0.244\\ \\text{kg}", |
| "gt_answer": "3.89 kg", |
| "correct": false |
| }, |
| { |
| "index": 1985, |
| "pred_answer": "T=\\frac{mg(1+\\mu)}{2(1-\\mu)(1+\\mu)}", |
| "gt_answer": "$T = \\alpha v_0^2$", |
| "correct": false |
| }, |
| { |
| "index": 1991, |
| "pred_answer": "0.000000000000018\\ \\text{m}", |
| "gt_answer": "0.00485 \\mathrm{nm}", |
| "correct": false |
| }, |
| { |
| "index": 1992, |
| "pred_answer": "225^\\circ\\text{C}", |
| "gt_answer": "5200 K", |
| "correct": false |
| }, |
| { |
| "index": 1994, |
| "pred_answer": "5^\\circ", |
| "gt_answer": "55°", |
| "correct": false |
| }, |
| { |
| "index": 1996, |
| "pred_answer": "3.00\\ \\text{cm}", |
| "gt_answer": "1.48 cm", |
| "correct": false |
| }, |
| { |
| "index": 2000, |
| "pred_answer": "B", |
| "gt_answer": "point B", |
| "correct": false |
| }, |
| { |
| "index": 2002, |
| "pred_answer": "0.000000016\\ \\text{s}", |
| "gt_answer": "$$0.000000000106\\ \\text{s}$$", |
| "correct": false |
| }, |
| { |
| "index": 2003, |
| "pred_answer": "39.0^\\circ", |
| "gt_answer": "22.3°", |
| "correct": false |
| }, |
| { |
| "index": 2007, |
| "pred_answer": "0.007^\\circ", |
| "gt_answer": "4.5°", |
| "correct": false |
| }, |
| { |
| "index": 2008, |
| "pred_answer": "60.0^\\circ", |
| "gt_answer": "27.5°", |
| "correct": false |
| }, |
| { |
| "index": 2009, |
| "pred_answer": "0.18\\ \\text{m}", |
| "gt_answer": "4.54 m", |
| "correct": false |
| }, |
| { |
| "index": 2010, |
| "pred_answer": "490\\ \\text{mrad}", |
| "gt_answer": "67.3°", |
| "correct": false |
| }, |
| { |
| "index": 2011, |
| "pred_answer": "0.55\\ \\text{m}", |
| "gt_answer": "1.65 m", |
| "correct": false |
| }, |
| { |
| "index": 2012, |
| "pred_answer": "1.41", |
| "gt_answer": "1.44", |
| "correct": false |
| }, |
| { |
| "index": 2013, |
| "pred_answer": "\\frac{d}{2\\pi}", |
| "gt_answer": "350\\,\\mu\\mathrm{m}", |
| "correct": false |
| }, |
| { |
| "index": 2014, |
| "pred_answer": "34.3^\\circ", |
| "gt_answer": "8.0°", |
| "correct": false |
| }, |
| { |
| "index": 2016, |
| "pred_answer": "58.0^\\circ", |
| "gt_answer": "38.7°", |
| "correct": false |
| }, |
| { |
| "index": 2018, |
| "pred_answer": "30^\\circ", |
| "gt_answer": "15.9°", |
| "correct": false |
| }, |
| { |
| "index": 2020, |
| "pred_answer": "0.83\\ \\text{cm}", |
| "gt_answer": "12 cm", |
| "correct": false |
| }, |
| { |
| "index": 2021, |
| "pred_answer": "10.0\\text{ cm}", |
| "gt_answer": "12.6 cm", |
| "correct": false |
| }, |
| { |
| "index": 2022, |
| "pred_answer": "2.00", |
| "gt_answer": "+1", |
| "correct": false |
| }, |
| { |
| "index": 2023, |
| "pred_answer": "3.2\\ \\text{m}", |
| "gt_answer": "$9.00$ cm inside the wall of the bowl", |
| "correct": false |
| }, |
| { |
| "index": 2024, |
| "pred_answer": "10.0\\ \\text{cm}", |
| "gt_answer": "5.68 cm", |
| "correct": false |
| }, |
| { |
| "index": 2025, |
| "pred_answer": "0.32", |
| "gt_answer": "-5.91", |
| "correct": false |
| }, |
| { |
| "index": 2028, |
| "pred_answer": "15\\ \\text{cm}", |
| "gt_answer": "21.3 cm", |
| "correct": false |
| }, |
| { |
| "index": 2029, |
| "pred_answer": "q=\\frac{fp}{p-f}", |
| "gt_answer": "$32.0$ cm to the right of the second surface", |
| "correct": false |
| }, |
| { |
| "index": 2030, |
| "pred_answer": "1.50", |
| "gt_answer": "1.99", |
| "correct": false |
| }, |
| { |
| "index": 2035, |
| "pred_answer": "40\\ \\text{m}", |
| "gt_answer": "148 m", |
| "correct": false |
| }, |
| { |
| "index": 2037, |
| "pred_answer": "10.0\\ \\text{W/m}^2", |
| "gt_answer": "6.89 units", |
| "correct": false |
| }, |
| { |
| "index": 2040, |
| "pred_answer": "60\\,\\text{mm}", |
| "gt_answer": "$0.00723$ m", |
| "correct": false |
| }, |
| { |
| "index": 2041, |
| "pred_answer": "1.67", |
| "gt_answer": "6.08", |
| "correct": false |
| }, |
| { |
| "index": 2044, |
| "pred_answer": "24\\ \\text{N/m}", |
| "gt_answer": "49.3 N/m", |
| "correct": false |
| }, |
| { |
| "index": 2046, |
| "pred_answer": "0.0000000261\\ \\text{N}", |
| "gt_answer": "0.438 N", |
| "correct": false |
| }, |
| { |
| "index": 2047, |
| "pred_answer": "1.0\\ \\text{C}", |
| "gt_answer": "$16.7 \\mu$C", |
| "correct": false |
| }, |
| { |
| "index": 2048, |
| "pred_answer": "0.100\\,\\mu\\text{C}", |
| "gt_answer": "7.2 nC", |
| "correct": false |
| }, |
| { |
| "index": 2049, |
| "pred_answer": "mg(\\sin\\theta+\\cos\\theta)", |
| "gt_answer": "mg \\sin \\theta / |Q|", |
| "correct": false |
| }, |
| { |
| "index": 2050, |
| "pred_answer": "1.4\\ \\text{N}", |
| "gt_answer": "0.075~\\mathrm{N}", |
| "correct": false |
| }, |
| { |
| "index": 2051, |
| "pred_answer": "\\frac{3k|q|}{r^2}", |
| "gt_answer": "0", |
| "correct": false |
| }, |
| { |
| "index": 2055, |
| "pred_answer": "1.4\\ \\text{s}", |
| "gt_answer": "0.307 s", |
| "correct": false |
| }, |
| { |
| "index": 2057, |
| "pred_answer": "4.35\\ \\mu\\text{C}", |
| "gt_answer": "$1.98 \\mu$C", |
| "correct": false |
| }, |
| { |
| "index": 2058, |
| "pred_answer": "37.7~\\text{pm}", |
| "gt_answer": "$0.000000000000027$ m", |
| "correct": false |
| }, |
| { |
| "index": 2063, |
| "pred_answer": "\\frac{14}{9}I", |
| "gt_answer": "\\( \\frac{2I}{3} \\)", |
| "correct": false |
| }, |
| { |
| "index": 2064, |
| "pred_answer": "40\\,\\Omega", |
| "gt_answer": "\\( \\frac{2I}{3} \\)", |
| "correct": false |
| }, |
| { |
| "index": 2067, |
| "pred_answer": "10.5\\text{ A}", |
| "gt_answer": "3.0 A", |
| "correct": false |
| }, |
| { |
| "index": 2068, |
| "pred_answer": "+9.00\\ \\text{V}", |
| "gt_answer": "-1.82 V", |
| "correct": false |
| }, |
| { |
| "index": 2069, |
| "pred_answer": "44.6\\ \\text{V}", |
| "gt_answer": "200 V", |
| "correct": false |
| }, |
| { |
| "index": 2070, |
| "pred_answer": "0.28\\text{ W}", |
| "gt_answer": "0.50 W", |
| "correct": false |
| }, |
| { |
| "index": 2071, |
| "pred_answer": "550\\ \\text{mA}", |
| "gt_answer": "2.69 mA", |
| "correct": false |
| }, |
| { |
| "index": 2072, |
| "pred_answer": "9.90\\ \\text{V}", |
| "gt_answer": "0.20 A", |
| "correct": false |
| }, |
| { |
| "index": 2073, |
| "pred_answer": "3.30\\ \\text{A}", |
| "gt_answer": "3.30 A", |
| "correct": false |
| }, |
| { |
| "index": 2078, |
| "pred_answer": "0.055\\ \\text{T}", |
| "gt_answer": "0.26 T", |
| "correct": false |
| }, |
| { |
| "index": 2080, |
| "pred_answer": "0.0001\\ \\text{T}", |
| "gt_answer": "0.59 T", |
| "correct": false |
| }, |
| { |
| "index": 2081, |
| "pred_answer": "2.66^\\circ", |
| "gt_answer": "8.90°", |
| "correct": false |
| }, |
| { |
| "index": 2083, |
| "pred_answer": "0.020\\ \\text{m}", |
| "gt_answer": "1.54 cm", |
| "correct": false |
| }, |
| { |
| "index": 2085, |
| "pred_answer": "11\\ \\text{N/m}", |
| "gt_answer": "1250\\,\\mathrm{N/m}", |
| "correct": false |
| }, |
| { |
| "index": 2087, |
| "pred_answer": "1800\\ \\text{N/m}", |
| "gt_answer": "2940\\,\\mathrm{N/m}", |
| "correct": false |
| }, |
| { |
| "index": 2090, |
| "pred_answer": "0.271\\ \\text{kg·m}^2", |
| "gt_answer": "0.0166\\,\\mathrm{kg\\cdot m^2", |
| "correct": false |
| }, |
| { |
| "index": 2092, |
| "pred_answer": "1.05\\ \\text{m}", |
| "gt_answer": "0.990 m", |
| "correct": false |
| }, |
| { |
| "index": 2095, |
| "pred_answer": "\\ell^2 B", |
| "gt_answer": "0.0031\\, \\mathrm{T \\cdot m^2}", |
| "correct": false |
| }, |
| { |
| "index": 2097, |
| "pred_answer": "0.5\\ \\text{V}", |
| "gt_answer": "0.0000000627\\, \\mathrm{V}", |
| "correct": false |
| }, |
| { |
| "index": 2103, |
| "pred_answer": "0.0000128\\ \\text{s}", |
| "gt_answer": "8.00 s", |
| "correct": false |
| }, |
| { |
| "index": 2104, |
| "pred_answer": "0.0000066\\ \\text{T/s}", |
| "gt_answer": "62.2 mT/s", |
| "correct": false |
| }, |
| { |
| "index": 2105, |
| "pred_answer": "4.3\\ \\text{A}", |
| "gt_answer": "51.9 mA", |
| "correct": false |
| }, |
| { |
| "index": 2111, |
| "pred_answer": "0.0108\\ \\text{N}", |
| "gt_answer": "10.8 N", |
| "correct": false |
| }, |
| { |
| "index": 2112, |
| "pred_answer": "N I \\ell^2 B", |
| "gt_answer": "\\frac{N^2 B^2 \\ell^2 v}{R}", |
| "correct": false |
| }, |
| { |
| "index": 2114, |
| "pred_answer": "3.8\\ \\text{W}", |
| "gt_answer": "6.76 W", |
| "correct": false |
| }, |
| { |
| "index": 2115, |
| "pred_answer": "3270\\ \\text{rad/s}", |
| "gt_answer": "942 rad/s", |
| "correct": false |
| }, |
| { |
| "index": 2116, |
| "pred_answer": "5000\\ \\text{V}", |
| "gt_answer": "1.88 V", |
| "correct": false |
| }, |
| { |
| "index": 2118, |
| "pred_answer": "29950\\ \\text{Hz}", |
| "gt_answer": "3.60 kHz", |
| "correct": false |
| }, |
| { |
| "index": 2119, |
| "pred_answer": "345000\\ \\text{W}", |
| "gt_answer": "0.000000000000017\\,\\mathrm{W}", |
| "correct": false |
| }, |
| { |
| "index": 2120, |
| "pred_answer": "0.305\\ \\text{N}", |
| "gt_answer": "0.813 N", |
| "correct": false |
| }, |
| { |
| "index": 2124, |
| "pred_answer": "-4.80\\times 10^{-17}\\ \\text{J}", |
| "gt_answer": "0 J", |
| "correct": false |
| }, |
| { |
| "index": 2126, |
| "pred_answer": "18", |
| "gt_answer": "4", |
| "correct": false |
| }, |
| { |
| "index": 2127, |
| "pred_answer": "16.8\\ \\Omega", |
| "gt_answer": "25\\,\\Omega", |
| "correct": false |
| }, |
| { |
| "index": 2130, |
| "pred_answer": "15.0\\ \\Omega", |
| "gt_answer": "3.5\\,\\Omega", |
| "correct": false |
| }, |
| { |
| "index": 2131, |
| "pred_answer": "V = 8.0\\ \\text{V}", |
| "gt_answer": "1.80 V", |
| "correct": false |
| }, |
| { |
| "index": 2133, |
| "pred_answer": "0.000000000001\\ \\text{N}", |
| "gt_answer": "0.00000000013\\,\\mathrm{N}", |
| "correct": false |
| }, |
| { |
| "index": 2135, |
| "pred_answer": "1.00\\ \\text{N}", |
| "gt_answer": "0 N", |
| "correct": false |
| }, |
| { |
| "index": 2138, |
| "pred_answer": "0.43\\ \\text{N}", |
| "gt_answer": "0.49 N", |
| "correct": false |
| }, |
| { |
| "index": 2139, |
| "pred_answer": "1.98\\ \\text{mA}", |
| "gt_answer": "14 A", |
| "correct": false |
| }, |
| { |
| "index": 2140, |
| "pred_answer": "0.000138\\ \\text{N·m}", |
| "gt_answer": "170\\,\\mathrm{N\\cdot m}", |
| "correct": false |
| }, |
| { |
| "index": 2143, |
| "pred_answer": "-0.39\\ \\text{A}", |
| "gt_answer": "9.4 A", |
| "correct": false |
| }, |
| { |
| "index": 2147, |
| "pred_answer": "0.0015\\,\\text{Wb}", |
| "gt_answer": "-0.094 Wb", |
| "correct": false |
| }, |
| { |
| "index": 2150, |
| "pred_answer": "50000\\ \\mathrm{rad/s}", |
| "gt_answer": "2100 rad/s", |
| "correct": false |
| }, |
| { |
| "index": 2152, |
| "pred_answer": "4\\,\\mu\\text{N}", |
| "gt_answer": "0.050 V", |
| "correct": false |
| }, |
| { |
| "index": 2154, |
| "pred_answer": "0.0675\\ \\text{Hz}", |
| "gt_answer": "615900000000000\\,\\mathrm{Hz}", |
| "correct": false |
| }, |
| { |
| "index": 2156, |
| "pred_answer": "25^\\circ", |
| "gt_answer": "5600 W", |
| "correct": false |
| }, |
| { |
| "index": 2157, |
| "pred_answer": "2.12\\times 10^{7}\\ \\text{J}", |
| "gt_answer": "374 J", |
| "correct": false |
| }, |
| { |
| "index": 2158, |
| "pred_answer": "0.84\\ \\text{s}", |
| "gt_answer": "1.40 s", |
| "correct": false |
| }, |
| { |
| "index": 2161, |
| "pred_answer": "\\frac{1}{2}", |
| "gt_answer": "5", |
| "correct": false |
| }, |
| { |
| "index": 2162, |
| "pred_answer": "\\frac{x}{v}", |
| "gt_answer": "56.3 s", |
| "correct": false |
| }, |
| { |
| "index": 2163, |
| "pred_answer": "3.0\\ \\text{cm}", |
| "gt_answer": "0.454 m", |
| "correct": false |
| }, |
| { |
| "index": 2164, |
| "pred_answer": "1220\\ \\text{m}", |
| "gt_answer": "800 m", |
| "correct": false |
| }, |
| { |
| "index": 2166, |
| "pred_answer": "1.5\\ \\text{m}", |
| "gt_answer": "0.855 m", |
| "correct": false |
| }, |
| { |
| "index": 2167, |
| "pred_answer": "4.9\\ \\text{Hz}", |
| "gt_answer": "211\\,\\mathrm{Hz}", |
| "correct": false |
| }, |
| { |
| "index": 2169, |
| "pred_answer": "3.01\\ \\text{dB}", |
| "gt_answer": "69.6 dB", |
| "correct": false |
| }, |
| { |
| "index": 2171, |
| "pred_answer": "1.9\\ \\text{m}", |
| "gt_answer": "7.8 m", |
| "correct": false |
| }, |
| { |
| "index": 2173, |
| "pred_answer": "g=0.16", |
| "gt_answer": "1", |
| "correct": false |
| }, |
| { |
| "index": 2174, |
| "pred_answer": "530000\\ \\text{nm}", |
| "gt_answer": "2.59mm", |
| "correct": false |
| }, |
| { |
| "index": 2175, |
| "pred_answer": "3.75\\ \\text{mA}", |
| "gt_answer": "0.006A", |
| "correct": false |
| }, |
| { |
| "index": 2180, |
| "pred_answer": "82.47\\ \\text{m}", |
| "gt_answer": "12.7m", |
| "correct": false |
| }, |
| { |
| "index": 2184, |
| "pred_answer": "0.9\\ \\text{m}", |
| "gt_answer": "15", |
| "correct": false |
| }, |
| { |
| "index": 2185, |
| "pred_answer": "43.0\\ \\text{m}", |
| "gt_answer": "55m", |
| "correct": false |
| }, |
| { |
| "index": 2186, |
| "pred_answer": "7.5\\ \\text{m/s}", |
| "gt_answer": "30m/s", |
| "correct": false |
| }, |
| { |
| "index": 2187, |
| "pred_answer": "-44.1\\ \\text{m}", |
| "gt_answer": "-44m", |
| "correct": false |
| }, |
| { |
| "index": 2188, |
| "pred_answer": "-9.80\\ \\text{m/s}^2", |
| "gt_answer": "-9.80 \\ \\mathrm{m/s}^2$", |
| "correct": false |
| }, |
| { |
| "index": 2189, |
| "pred_answer": "2.83\\ \\text{m}", |
| "gt_answer": "2.4m", |
| "correct": false |
| }, |
| { |
| "index": 2192, |
| "pred_answer": "260\\ \\text{km/h}", |
| "gt_answer": "$260 \\ \\mathrm{km/h}$", |
| "correct": false |
| }, |
| { |
| "index": 2193, |
| "pred_answer": null, |
| "gt_answer": "0.58$w$", |
| "correct": false |
| }, |
| { |
| "index": 2194, |
| "pred_answer": "mg\\cos\\alpha", |
| "gt_answer": "$w \\sin \\alpha$", |
| "correct": false |
| }, |
| { |
| "index": 2198, |
| "pred_answer": "5.54\\ \\text{m/s}^2", |
| "gt_answer": "$g \\sin \\alpha$", |
| "correct": false |
| }, |
| { |
| "index": 2199, |
| "pred_answer": "0\\ \\text{N}", |
| "gt_answer": "3N", |
| "correct": false |
| }, |
| { |
| "index": 2201, |
| "pred_answer": "0.30", |
| "gt_answer": "0.40", |
| "correct": false |
| }, |
| { |
| "index": 2202, |
| "pred_answer": "130\\ \\text{N}", |
| "gt_answer": "406N", |
| "correct": false |
| }, |
| { |
| "index": 2205, |
| "pred_answer": "14.5\\ \\text{m/s}", |
| "gt_answer": "$\\sqrt{\\mu_{\\textrm{s}} g R}$", |
| "correct": false |
| }, |
| { |
| "index": 2206, |
| "pred_answer": "100000000\\ \\text{J}", |
| "gt_answer": "10kJ", |
| "correct": false |
| }, |
| { |
| "index": 2207, |
| "pred_answer": "34000\\ \\text{N}", |
| "gt_answer": "79,000N", |
| "correct": false |
| }, |
| { |
| "index": 2208, |
| "pred_answer": "0.12\\ \\text{J}", |
| "gt_answer": "3.0J", |
| "correct": false |
| }, |
| { |
| "index": 2211, |
| "pred_answer": "101\\ \\text{W}", |
| "gt_answer": "241W", |
| "correct": false |
| }, |
| { |
| "index": 2213, |
| "pred_answer": "8100\\ \\text{N}", |
| "gt_answer": "735N", |
| "correct": false |
| }, |
| { |
| "index": 2215, |
| "pred_answer": "0.28\\ \\text{m/s}", |
| "gt_answer": "$-0.30 \\, \\textrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2216, |
| "pred_answer": "2000\\ \\text{N/m}", |
| "gt_answer": "$10600 \\, \\textrm{N/m}$", |
| "correct": false |
| }, |
| { |
| "index": 2217, |
| "pred_answer": "784\\ \\text{J}", |
| "gt_answer": "78J", |
| "correct": false |
| }, |
| { |
| "index": 2220, |
| "pred_answer": "900\\ \\text{N}", |
| "gt_answer": "850N", |
| "correct": false |
| }, |
| { |
| "index": 2221, |
| "pred_answer": "0.375\\ \\text{J}", |
| "gt_answer": "0.375J", |
| "correct": false |
| }, |
| { |
| "index": 2222, |
| "pred_answer": "-0.40\\ \\text{m/s}", |
| "gt_answer": "$-0.40 \\, \\textrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2223, |
| "pred_answer": "10.0\\ \\text{m/s}", |
| "gt_answer": "$2.1 \\, \\textrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2225, |
| "pred_answer": "1.67\\ \\text{m/s}", |
| "gt_answer": "$8.3 \\, \\textrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2226, |
| "pred_answer": "4.00\\ \\text{m/s}", |
| "gt_answer": "$4.47 \\, \\textrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2228, |
| "pred_answer": "10.8\\ \\text{m/s}^2", |
| "gt_answer": "$89.4 \\, \\mathrm{m/s}^2$", |
| "correct": false |
| }, |
| { |
| "index": 2230, |
| "pred_answer": "0.25\\ \\text{J}", |
| "gt_answer": "0.46J", |
| "correct": false |
| }, |
| { |
| "index": 2231, |
| "pred_answer": "10\\ \\text{m/s}", |
| "gt_answer": "$1.2 \\, \\textrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2232, |
| "pred_answer": "226\\ \\text{N}\\cdot\\text{m}", |
| "gt_answer": "$680 \\, \\mathrm{N} \\cdot \\mathrm{m}$", |
| "correct": false |
| }, |
| { |
| "index": 2233, |
| "pred_answer": "1.8\\ \\text{m/s}", |
| "gt_answer": "$\\sqrt{\\frac{4}{3}gh}$", |
| "correct": false |
| }, |
| { |
| "index": 2234, |
| "pred_answer": "0.0033\\ \\text{N}", |
| "gt_answer": "$\\frac{2}{7}Mg \\sin \\beta$", |
| "correct": false |
| }, |
| { |
| "index": 2235, |
| "pred_answer": "7.9\\ \\text{rad/s}", |
| "gt_answer": "$2.5 \\, \\textrm{rev/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2236, |
| "pred_answer": "3.33\\ \\text{rad/s}", |
| "gt_answer": "$\\frac{I_A\\omega_A + I_B\\omega_B}{I_A + I_B}$", |
| "correct": false |
| }, |
| { |
| "index": 2237, |
| "pred_answer": "400\\ \\text{rad/s}", |
| "gt_answer": "$0.4 \\, \\textrm{rad/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2239, |
| "pred_answer": "10.4\\ \\text{nm}", |
| "gt_answer": "632.9930nm", |
| "correct": false |
| }, |
| { |
| "index": 2240, |
| "pred_answer": "2I_0", |
| "gt_answer": "$0.95I_0$", |
| "correct": false |
| }, |
| { |
| "index": 2242, |
| "pred_answer": "0.22\\ \\text{mm}", |
| "gt_answer": "15.8mm", |
| "correct": false |
| }, |
| { |
| "index": 2244, |
| "pred_answer": "1.000104", |
| "gt_answer": "1.00034", |
| "correct": false |
| }, |
| { |
| "index": 2245, |
| "pred_answer": "2.00\\ \\text{m}", |
| "gt_answer": "3.75m", |
| "correct": false |
| }, |
| { |
| "index": 2248, |
| "pred_answer": "4.5\\ \\text{m}", |
| "gt_answer": "6.8m", |
| "correct": false |
| }, |
| { |
| "index": 2250, |
| "pred_answer": "1.3\\text{ cm}", |
| "gt_answer": "1.3cm", |
| "correct": false |
| }, |
| { |
| "index": 2251, |
| "pred_answer": "-3.00", |
| "gt_answer": "3.0", |
| "correct": false |
| }, |
| { |
| "index": 2252, |
| "pred_answer": "-0.5", |
| "gt_answer": "0.33", |
| "correct": false |
| }, |
| { |
| "index": 2253, |
| "pred_answer": "16\\text{ mm}", |
| "gt_answer": "3.8mm", |
| "correct": false |
| }, |
| { |
| "index": 2257, |
| "pred_answer": "2.0\\times 10^{-4}\\ \\text{N}", |
| "gt_answer": "$0.00062\\;N$", |
| "correct": false |
| }, |
| { |
| "index": 2259, |
| "pred_answer": "E_x=\\frac{k}{x^2+d^2}\\left[q_1\\cos\\theta-q_2\\frac{x^2}{d^2}-q_3\\sin\\theta\\right]", |
| "gt_answer": "$\\frac{q}{4\\pi\\epsilon_0} \\left[ \\frac{1}{x^2} + \\frac{2x}{(x^2 + d^2)^{3/2}} \\right] \\hat{i}$", |
| "correct": false |
| }, |
| { |
| "index": 2261, |
| "pred_answer": null, |
| "gt_answer": "$\\frac{1}{4\\pi\\epsilon_0} \\frac{zQ}{(z^2 + R^2)^{3/2}}$", |
| "correct": false |
| }, |
| { |
| "index": 2262, |
| "pred_answer": "10^{-9}\\ \\text{C/m}^2", |
| "gt_answer": "$0.000089\\;C/m^2$", |
| "correct": false |
| }, |
| { |
| "index": 2265, |
| "pred_answer": "500000\\ \\text{rad/s}^2", |
| "gt_answer": "$5.0\\;rad/s^2$", |
| "correct": false |
| }, |
| { |
| "index": 2266, |
| "pred_answer": "2.6\\times 10^{-25}\\ \\text{N}", |
| "gt_answer": "$0.000000000000018\\;N$", |
| "correct": false |
| }, |
| { |
| "index": 2267, |
| "pred_answer": "-3.0\\ \\mu\\mathrm{C}", |
| "gt_answer": "$-0.0000000000099\\;C$", |
| "correct": false |
| }, |
| { |
| "index": 2268, |
| "pred_answer": "122000\\ \\text{N}\\cdot\\text{m}^2/\\text{C}", |
| "gt_answer": "$\\frac{2\\pi L R^3}{r_0^2} E_0$", |
| "correct": false |
| }, |
| { |
| "index": 2269, |
| "pred_answer": "\\frac{3Q}{4\\pi\\varepsilon_0 R^3}\\,r", |
| "gt_answer": "$\\frac{1}{4\\pi\\epsilon_0} \\frac{Q}{R^3} r$", |
| "correct": false |
| }, |
| { |
| "index": 2270, |
| "pred_answer": "\\frac{\\eta}{\\varepsilon_0 L}", |
| "gt_answer": "$\\frac{\\eta}{2\\epsilon_0}$", |
| "correct": false |
| }, |
| { |
| "index": 2271, |
| "pred_answer": null, |
| "gt_answer": "$\\frac{\\rho_0 a}{2\\epsilon_0}$", |
| "correct": false |
| }, |
| { |
| "index": 2272, |
| "pred_answer": "14800000\\ \\text{m/s}", |
| "gt_answer": "$18600000\\;m/s$", |
| "correct": false |
| }, |
| { |
| "index": 2279, |
| "pred_answer": "34.6\\%", |
| "gt_answer": "87%", |
| "correct": false |
| }, |
| { |
| "index": 2280, |
| "pred_answer": "0.0101\\ \\text{J}", |
| "gt_answer": "0.21 J", |
| "correct": false |
| }, |
| { |
| "index": 2282, |
| "pred_answer": "4\\text{ A}", |
| "gt_answer": "0.80 A", |
| "correct": false |
| }, |
| { |
| "index": 2284, |
| "pred_answer": "4.0\\times 10^{-10}\\ \\text{N}", |
| "gt_answer": "$0\\;N$", |
| "correct": false |
| }, |
| { |
| "index": 2290, |
| "pred_answer": "0.0050\\ \\text{N}", |
| "gt_answer": "$0.005\\;N$", |
| "correct": false |
| }, |
| { |
| "index": 2291, |
| "pred_answer": "0.02\\ \\text{Wb}", |
| "gt_answer": "$0.0002\\;Wb$", |
| "correct": false |
| }, |
| { |
| "index": 2292, |
| "pred_answer": "0.00006\\ \\text{Wb}", |
| "gt_answer": "$0.0000000055\\;Wb$", |
| "correct": false |
| }, |
| { |
| "index": 2293, |
| "pred_answer": "5.0\\ \\text{A}", |
| "gt_answer": "$5.7\\;\\mu A$", |
| "correct": false |
| }, |
| { |
| "index": 2295, |
| "pred_answer": "12.6\\ \\text{m}^{\\circ}\\text{C}/\\text{min}", |
| "gt_answer": "$200\\;^\\circ C / min$", |
| "correct": false |
| }, |
| { |
| "index": 2296, |
| "pred_answer": "5100000000\\ \\text{T}", |
| "gt_answer": "$0.000005\\;T$", |
| "correct": false |
| }, |
| { |
| "index": 2297, |
| "pred_answer": "0\\ \\text{s}", |
| "gt_answer": "$-1.33\\;\\mu s$", |
| "correct": false |
| }, |
| { |
| "index": 2300, |
| "pred_answer": "1.016\\ \\text{eV}", |
| "gt_answer": "$13.1\\;MeV$", |
| "correct": false |
| }, |
| { |
| "index": 2301, |
| "pred_answer": "121.6\\ \\text{nm}", |
| "gt_answer": "434 nm", |
| "correct": false |
| }, |
| { |
| "index": 2303, |
| "pred_answer": "45^\\circ", |
| "gt_answer": "$16.3^\\circ$", |
| "correct": false |
| }, |
| { |
| "index": 2304, |
| "pred_answer": "104000000000000\\ \\text{V/m}", |
| "gt_answer": "0.99998 T", |
| "correct": false |
| }, |
| { |
| "index": 2305, |
| "pred_answer": "1\\ \\text{T}", |
| "gt_answer": "-6 T", |
| "correct": false |
| }, |
| { |
| "index": 2307, |
| "pred_answer": "200000\\ \\text{V/m},\\ \\text{directed opposite } \\vec v", |
| "gt_answer": "$200000\\;V/m$", |
| "correct": false |
| }, |
| { |
| "index": 2311, |
| "pred_answer": "20\\ \\Omega", |
| "gt_answer": "$20\\;\\Omega$", |
| "correct": false |
| }, |
| { |
| "index": 2312, |
| "pred_answer": "100\\ \\text{V}", |
| "gt_answer": "8.0 V", |
| "correct": false |
| }, |
| { |
| "index": 2313, |
| "pred_answer": "3680\\ \\mu\\text{Hz}", |
| "gt_answer": "$8.1\\;kHz$", |
| "correct": false |
| }, |
| { |
| "index": 2317, |
| "pred_answer": "625000000000000\\ \\text{photons/s}", |
| "gt_answer": "$62500000000000$", |
| "correct": false |
| }, |
| { |
| "index": 2318, |
| "pred_answer": "4\\ \\text{m/s}", |
| "gt_answer": "200 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2322, |
| "pred_answer": "0.60", |
| "gt_answer": "0.80", |
| "correct": false |
| }, |
| { |
| "index": 2323, |
| "pred_answer": "1", |
| "gt_answer": "0.25", |
| "correct": false |
| }, |
| { |
| "index": 2327, |
| "pred_answer": "\\frac{c^2}{6}", |
| "gt_answer": "0.125", |
| "correct": false |
| }, |
| { |
| "index": 2328, |
| "pred_answer": "2\\text{ cm}", |
| "gt_answer": "0 cm", |
| "correct": false |
| }, |
| { |
| "index": 2329, |
| "pred_answer": "0.1\\,\\mu\\text{J}", |
| "gt_answer": "$0$ $m$", |
| "correct": false |
| }, |
| { |
| "index": 2332, |
| "pred_answer": "1.0\\ \\text{eV}", |
| "gt_answer": "1.3 eV", |
| "correct": false |
| }, |
| { |
| "index": 2333, |
| "pred_answer": "[5.38\\times 10^{-19}\\ \\mathrm{J},\\ 1.09\\times 10^{-19}\\ \\mathrm{J},\\ 1.63\\times 10^{-19}\\ \\mathrm{J},\\ 2.27\\times 10^{-19}\\ \\mathrm{J}]", |
| "gt_answer": "0.0634 eV", |
| "correct": false |
| }, |
| { |
| "index": 2335, |
| "pred_answer": "0.69", |
| "gt_answer": "$0$", |
| "correct": false |
| }, |
| { |
| "index": 2338, |
| "pred_answer": "1.0\\ \\text{s}", |
| "gt_answer": "10 s", |
| "correct": false |
| }, |
| { |
| "index": 2339, |
| "pred_answer": "23.1\\ \\text{m/s}", |
| "gt_answer": "2.5 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2342, |
| "pred_answer": "0.128\\ \\text{s}", |
| "gt_answer": "$D_{23} / v_p$", |
| "correct": false |
| }, |
| { |
| "index": 2344, |
| "pred_answer": "35.3^\\circ", |
| "gt_answer": "$90^\\circ$", |
| "correct": false |
| }, |
| { |
| "index": 2347, |
| "pred_answer": "52.9\\ \\text{m/s}", |
| "gt_answer": "0.0083 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2348, |
| "pred_answer": "21.6\\ \\text{m}", |
| "gt_answer": "897 m", |
| "correct": false |
| }, |
| { |
| "index": 2351, |
| "pred_answer": "32.6^\\circ", |
| "gt_answer": "$40.4^\\circ$", |
| "correct": false |
| }, |
| { |
| "index": 2352, |
| "pred_answer": "55.4^\\circ", |
| "gt_answer": "$55.5^\\circ$", |
| "correct": false |
| }, |
| { |
| "index": 2361, |
| "pred_answer": "13.0\\ \\text{m/s}", |
| "gt_answer": "23 ft/s", |
| "correct": false |
| }, |
| { |
| "index": 2364, |
| "pred_answer": "0\\ \\text{m/s}", |
| "gt_answer": "$9.80\\ m/s^2$", |
| "correct": false |
| }, |
| { |
| "index": 2365, |
| "pred_answer": "2600\\ \\text{m/s}^2", |
| "gt_answer": "$0.88\\ m/s^2$", |
| "correct": false |
| }, |
| { |
| "index": 2366, |
| "pred_answer": "397\\ \\text{N}", |
| "gt_answer": "241 N", |
| "correct": false |
| }, |
| { |
| "index": 2367, |
| "pred_answer": "1.7\\ \\text{kg}", |
| "gt_answer": "4.0 kg", |
| "correct": false |
| }, |
| { |
| "index": 2369, |
| "pred_answer": "34\\ \\text{N}", |
| "gt_answer": "$1130\\\\ N$", |
| "correct": false |
| }, |
| { |
| "index": 2371, |
| "pred_answer": "2F", |
| "gt_answer": "4.92 N", |
| "correct": false |
| }, |
| { |
| "index": 2374, |
| "pred_answer": "3.5\\ \\text{Hz}", |
| "gt_answer": "54 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2377, |
| "pred_answer": "0.40\\ \\text{m}", |
| "gt_answer": "4.0 m", |
| "correct": false |
| }, |
| { |
| "index": 2378, |
| "pred_answer": "0.38\\ \\text{Hz}", |
| "gt_answer": "18.2 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2387, |
| "pred_answer": null, |
| "gt_answer": "0.16 m", |
| "correct": false |
| }, |
| { |
| "index": 2388, |
| "pred_answer": "10\\ \\text{ms}", |
| "gt_answer": "2.1 s", |
| "correct": false |
| }, |
| { |
| "index": 2390, |
| "pred_answer": null, |
| "gt_answer": "0.0653 s", |
| "correct": false |
| }, |
| { |
| "index": 2392, |
| "pred_answer": "0.00101\\ \\mathrm{N\\cdot m^2}", |
| "gt_answer": "$18.5\\ N \\cdot m/rad$", |
| "correct": false |
| }, |
| { |
| "index": 2393, |
| "pred_answer": "0", |
| "gt_answer": "0.050 m", |
| "correct": false |
| }, |
| { |
| "index": 2394, |
| "pred_answer": null, |
| "gt_answer": "$\\sqrt{k/m}. $", |
| "correct": false |
| }, |
| { |
| "index": 2396, |
| "pred_answer": "0.218\\ \\text{m}", |
| "gt_answer": "1.53 m", |
| "correct": false |
| }, |
| { |
| "index": 2403, |
| "pred_answer": "0.296\\ \\text{m}", |
| "gt_answer": "2.00 cm", |
| "correct": false |
| }, |
| { |
| "index": 2406, |
| "pred_answer": "0.50\\ \\text{s}", |
| "gt_answer": "8.3 s", |
| "correct": false |
| }, |
| { |
| "index": 2409, |
| "pred_answer": "0.5\\ \\text{m}", |
| "gt_answer": "0.0127 m", |
| "correct": false |
| }, |
| { |
| "index": 2410, |
| "pred_answer": "\\pi", |
| "gt_answer": "-0.64 rad", |
| "correct": false |
| }, |
| { |
| "index": 2411, |
| "pred_answer": "4.3\\ \\text{rad/s}", |
| "gt_answer": "$240$ rad/s", |
| "correct": false |
| }, |
| { |
| "index": 2413, |
| "pred_answer": "0.06\\ \\text{s}", |
| "gt_answer": "0.033 s", |
| "correct": false |
| }, |
| { |
| "index": 2414, |
| "pred_answer": "11\\ \\text{m/s}", |
| "gt_answer": "22.1 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2417, |
| "pred_answer": "15.5\\ \\text{Hz}", |
| "gt_answer": "241 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2418, |
| "pred_answer": "0\\ \\text{cm/s}", |
| "gt_answer": "-0.13 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2420, |
| "pred_answer": "0.036\\ \\text{kg}", |
| "gt_answer": "0.846 kg", |
| "correct": false |
| }, |
| { |
| "index": 2422, |
| "pred_answer": "\\frac{\\pi}{2}", |
| "gt_answer": "2.8 rad", |
| "correct": false |
| }, |
| { |
| "index": 2425, |
| "pred_answer": "15.7\\ \\text{rad/s}", |
| "gt_answer": "754 rad/s", |
| "correct": false |
| }, |
| { |
| "index": 2426, |
| "pred_answer": "1.8\\ \\text{mm}", |
| "gt_answer": "$0.01$ m", |
| "correct": false |
| }, |
| { |
| "index": 2427, |
| "pred_answer": "5\\ \\text{cm/s}", |
| "gt_answer": "3.2 cm", |
| "correct": false |
| }, |
| { |
| "index": 2431, |
| "pred_answer": "1.57\\ \\text{rad m}^{-1}", |
| "gt_answer": "9.2 rad/m", |
| "correct": false |
| }, |
| { |
| "index": 2433, |
| "pred_answer": "1.43", |
| "gt_answer": "1.5", |
| "correct": false |
| }, |
| { |
| "index": 2434, |
| "pred_answer": "4", |
| "gt_answer": "14", |
| "correct": false |
| }, |
| { |
| "index": 2441, |
| "pred_answer": "1143\\ \\text{Hz}", |
| "gt_answer": "$1045$ Hz", |
| "correct": false |
| }, |
| { |
| "index": 2444, |
| "pred_answer": "0.031\\,\\lambda", |
| "gt_answer": "$0.25 \\lambda$", |
| "correct": false |
| }, |
| { |
| "index": 2447, |
| "pred_answer": "\\frac{1}{15}", |
| "gt_answer": "2", |
| "correct": false |
| }, |
| { |
| "index": 2450, |
| "pred_answer": "825\\ \\text{m/s}", |
| "gt_answer": "821 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2453, |
| "pred_answer": "3.15\\ \\mathrm{m/s^2}", |
| "gt_answer": "$21.0 \\, \\mathrm{m/s}^2$", |
| "correct": false |
| }, |
| { |
| "index": 2454, |
| "pred_answer": "0.450\\ \\text{m}", |
| "gt_answer": "0.191 m", |
| "correct": false |
| }, |
| { |
| "index": 2457, |
| "pred_answer": "102\\ \\text{kg}", |
| "gt_answer": "23 kg", |
| "correct": false |
| }, |
| { |
| "index": 2459, |
| "pred_answer": "T = \\frac{m_1 g\\sin\\theta\\, m_2}{m_1+m_2}", |
| "gt_answer": "20.8 N", |
| "correct": false |
| }, |
| { |
| "index": 2461, |
| "pred_answer": "10\\ \\text{N}", |
| "gt_answer": "120 N", |
| "correct": false |
| }, |
| { |
| "index": 2463, |
| "pred_answer": "4.1\\ \\text{kN}", |
| "gt_answer": "$18000 \\mathrm{ N}$", |
| "correct": false |
| }, |
| { |
| "index": 2467, |
| "pred_answer": "16.4^\\circ", |
| "gt_answer": "$17.2^\\circ$", |
| "correct": false |
| }, |
| { |
| "index": 2473, |
| "pred_answer": "5.0\\text{ N}", |
| "gt_answer": "3.1 N", |
| "correct": false |
| }, |
| { |
| "index": 2475, |
| "pred_answer": "2.04\\ \\text{m/s}^2", |
| "gt_answer": "$2.17 \\ \\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2482, |
| "pred_answer": "0.18", |
| "gt_answer": "0.37", |
| "correct": false |
| }, |
| { |
| "index": 2483, |
| "pred_answer": "45.5\\ \\text{N}", |
| "gt_answer": "100 N", |
| "correct": false |
| }, |
| { |
| "index": 2485, |
| "pred_answer": "\\vec a = \\frac{m}{\\mu_k g\\cos\\theta}g\\left(\\sin\\theta-\\mu_k\\cos\\theta\\right)\\hat i", |
| "gt_answer": "$-1.0\\,\\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2486, |
| "pred_answer": "1.8\\ \\text{m/s}^2", |
| "gt_answer": "$2.3\\,\\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2487, |
| "pred_answer": "216\\ \\text{N}", |
| "gt_answer": "74 N", |
| "correct": false |
| }, |
| { |
| "index": 2490, |
| "pred_answer": "1250\\ \\text{N}", |
| "gt_answer": "1372 N", |
| "correct": false |
| }, |
| { |
| "index": 2491, |
| "pred_answer": "414\\ \\text{m}", |
| "gt_answer": "2151 m", |
| "correct": false |
| }, |
| { |
| "index": 2492, |
| "pred_answer": "0.0000003\\ \\text{N}", |
| "gt_answer": "2600 N", |
| "correct": false |
| }, |
| { |
| "index": 2493, |
| "pred_answer": null, |
| "gt_answer": "1.81 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2494, |
| "pred_answer": "5260\\ \\text{N}", |
| "gt_answer": "8008 N", |
| "correct": false |
| }, |
| { |
| "index": 2496, |
| "pred_answer": "0.51\\ \\text{m/s}^2", |
| "gt_answer": "$3.62 \\frac{\\mathrm{m}}{\\mathrm{s}^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2501, |
| "pred_answer": "g(\\sin\\theta-\\mu_k\\cos\\theta)", |
| "gt_answer": "$g(\\sin\\theta - \\sqrt{2}\\mu_k \\cos\\theta)$", |
| "correct": false |
| }, |
| { |
| "index": 2508, |
| "pred_answer": "\\frac{\\pi}{2}", |
| "gt_answer": "$55^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 2509, |
| "pred_answer": "11.8\\ \\text{N}", |
| "gt_answer": "9.4 N", |
| "correct": false |
| }, |
| { |
| "index": 2511, |
| "pred_answer": null, |
| "gt_answer": "$\\tan^{-1} \\mu_s$", |
| "correct": false |
| }, |
| { |
| "index": 2513, |
| "pred_answer": "16.0\\ \\text{J}", |
| "gt_answer": "15.3 J", |
| "correct": false |
| }, |
| { |
| "index": 2514, |
| "pred_answer": "50\\ \\text{J}", |
| "gt_answer": "+1.50 J", |
| "correct": false |
| }, |
| { |
| "index": 2515, |
| "pred_answer": "4.7\\ \\text{J}", |
| "gt_answer": "25 J", |
| "correct": false |
| }, |
| { |
| "index": 2516, |
| "pred_answer": "3.5\\ \\text{J}", |
| "gt_answer": "4.41 J", |
| "correct": false |
| }, |
| { |
| "index": 2517, |
| "pred_answer": "0\\ \\text{m/s}", |
| "gt_answer": "0.935 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2518, |
| "pred_answer": "1500\\ \\text{N}", |
| "gt_answer": "2.45 N", |
| "correct": false |
| }, |
| { |
| "index": 2520, |
| "pred_answer": "3.0\\ \\text{m/s}", |
| "gt_answer": "1.10 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2523, |
| "pred_answer": "-25\\ \\text{J}", |
| "gt_answer": "-3.9 J", |
| "correct": false |
| }, |
| { |
| "index": 2526, |
| "pred_answer": "mgh", |
| "gt_answer": "$340000\\,\\mathrm{J}$", |
| "correct": false |
| }, |
| { |
| "index": 2527, |
| "pred_answer": "-2.15\\ \\text{J}", |
| "gt_answer": "-167 J", |
| "correct": false |
| }, |
| { |
| "index": 2528, |
| "pred_answer": "0\\ \\text{J}", |
| "gt_answer": "0 J", |
| "correct": false |
| }, |
| { |
| "index": 2532, |
| "pred_answer": "1.6\\ \\text{m}", |
| "gt_answer": "66.5 m", |
| "correct": false |
| }, |
| { |
| "index": 2533, |
| "pred_answer": "18.0\\ \\text{J}", |
| "gt_answer": "62.7 J", |
| "correct": false |
| }, |
| { |
| "index": 2535, |
| "pred_answer": "\\sqrt{2g(1+h)}", |
| "gt_answer": "2.42 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2536, |
| "pred_answer": "0.14\\ \\text{m}", |
| "gt_answer": "0.10 m", |
| "correct": false |
| }, |
| { |
| "index": 2538, |
| "pred_answer": "4.47\\ \\text{cm/s}", |
| "gt_answer": "0.055 m", |
| "correct": false |
| }, |
| { |
| "index": 2539, |
| "pred_answer": "2.63\\ \\text{m/s}", |
| "gt_answer": "1.69 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2540, |
| "pred_answer": "0.32\\ \\text{m}", |
| "gt_answer": "0.21 m", |
| "correct": false |
| }, |
| { |
| "index": 2542, |
| "pred_answer": "550\\ \\text{J}", |
| "gt_answer": "0.001 J", |
| "correct": false |
| }, |
| { |
| "index": 2544, |
| "pred_answer": "0.5\\ \\text{m}", |
| "gt_answer": "9.2 m", |
| "correct": false |
| }, |
| { |
| "index": 2547, |
| "pred_answer": "3.7\\times 10^{10}\\ \\text{K/s}", |
| "gt_answer": "0.217 K/s", |
| "correct": false |
| }, |
| { |
| "index": 2549, |
| "pred_answer": "2.5\\ \\text{J/(g·K)}", |
| "gt_answer": "$2.3\\,\\mathrm{\\frac{kJ}{kg\\cdot{}^{\\circ}C}}$", |
| "correct": false |
| }, |
| { |
| "index": 2550, |
| "pred_answer": "0.22\\ \\text{kJ/(kg}\\cdot\\text{K)}", |
| "gt_answer": "$400\\,\\mathrm{J/(kg\\cdot K)}$", |
| "correct": false |
| }, |
| { |
| "index": 2551, |
| "pred_answer": "1.0\\ \\text{kg}", |
| "gt_answer": "0.13 kg", |
| "correct": false |
| }, |
| { |
| "index": 2552, |
| "pred_answer": "0.027\\ \\text{kg}", |
| "gt_answer": "$0.00871\\,\\mathrm{kg}$", |
| "correct": false |
| }, |
| { |
| "index": 2556, |
| "pred_answer": "-8\\ \\text{cal}", |
| "gt_answer": "40 cal", |
| "correct": false |
| }, |
| { |
| "index": 2563, |
| "pred_answer": "1.4\\ \\text{W}", |
| "gt_answer": "0.208 W", |
| "correct": false |
| }, |
| { |
| "index": 2564, |
| "pred_answer": null, |
| "gt_answer": "$-4.2\\,{}^{\\circ}\\mathrm{C}$", |
| "correct": false |
| }, |
| { |
| "index": 2566, |
| "pred_answer": "0.74\\ \\text{J/(g·°C)}", |
| "gt_answer": "$450\\,\\mathrm{J/(kg\\cdot K)}$", |
| "correct": false |
| }, |
| { |
| "index": 2568, |
| "pred_answer": "0\\ \\text{J}", |
| "gt_answer": "310 J", |
| "correct": false |
| }, |
| { |
| "index": 2569, |
| "pred_answer": "26\\ \\text{W}", |
| "gt_answer": "(16.7A)W", |
| "correct": false |
| }, |
| { |
| "index": 2571, |
| "pred_answer": "22.4\\ \\text{J}", |
| "gt_answer": "$11 p_iV_i$", |
| "correct": false |
| }, |
| { |
| "index": 2572, |
| "pred_answer": "1460\\ \\text{J}", |
| "gt_answer": "-45 J", |
| "correct": false |
| }, |
| { |
| "index": 2574, |
| "pred_answer": "4.00", |
| "gt_answer": "1.5", |
| "correct": false |
| }, |
| { |
| "index": 2575, |
| "pred_answer": "46\\ \\text{m}^2", |
| "gt_answer": "$0.00797\\,\\mathrm{m^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2577, |
| "pred_answer": "300\\ \\text{K}", |
| "gt_answer": "360 K", |
| "correct": false |
| }, |
| { |
| "index": 2578, |
| "pred_answer": null, |
| "gt_answer": "$200000\\,\\mathrm{Pa}$", |
| "correct": false |
| }, |
| { |
| "index": 2579, |
| "pred_answer": "\\frac{2}{3}", |
| "gt_answer": "0.33", |
| "correct": false |
| }, |
| { |
| "index": 2580, |
| "pred_answer": "3100\\ \\text{m/s}", |
| "gt_answer": "490 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2582, |
| "pred_answer": "19\\ \\text{J}", |
| "gt_answer": "-15 J", |
| "correct": false |
| }, |
| { |
| "index": 2583, |
| "pred_answer": "3.00\\ \\text{atm}", |
| "gt_answer": "$202000\\,\\mathrm{Pa}$", |
| "correct": false |
| }, |
| { |
| "index": 2587, |
| "pred_answer": "2\\ \\text{J/(kg·K)}", |
| "gt_answer": "$450\\,\\mathrm{J/(kg\\cdot K)}$", |
| "correct": false |
| }, |
| { |
| "index": 2588, |
| "pred_answer": "10", |
| "gt_answer": "3.5 mol", |
| "correct": false |
| }, |
| { |
| "index": 2589, |
| "pred_answer": "0", |
| "gt_answer": "3.0", |
| "correct": false |
| }, |
| { |
| "index": 2591, |
| "pred_answer": "10.0\\ \\text{J}", |
| "gt_answer": "9.5 kJ", |
| "correct": false |
| }, |
| { |
| "index": 2592, |
| "pred_answer": "450\\ \\text{J}", |
| "gt_answer": "14.8 kJ", |
| "correct": false |
| }, |
| { |
| "index": 2593, |
| "pred_answer": "39\\ \\text{kJ}", |
| "gt_answer": "1692 J", |
| "correct": false |
| }, |
| { |
| "index": 2594, |
| "pred_answer": "-0.52\\ \\text{kJ}", |
| "gt_answer": "918 J", |
| "correct": false |
| }, |
| { |
| "index": 2595, |
| "pred_answer": "\\frac{V_0}{p_0}", |
| "gt_answer": "75%", |
| "correct": false |
| }, |
| { |
| "index": 2596, |
| "pred_answer": "3.00", |
| "gt_answer": "1.98", |
| "correct": false |
| }, |
| { |
| "index": 2600, |
| "pred_answer": "11000\\ \\text{J}", |
| "gt_answer": "75 J", |
| "correct": false |
| }, |
| { |
| "index": 2601, |
| "pred_answer": "2.64\\ \\text{s}", |
| "gt_answer": "39 s", |
| "correct": false |
| }, |
| { |
| "index": 2602, |
| "pred_answer": "0.119\\ \\text{m}", |
| "gt_answer": "3.3 cm", |
| "correct": false |
| }, |
| { |
| "index": 2605, |
| "pred_answer": "-157000\\ \\text{J}", |
| "gt_answer": "8830 J", |
| "correct": false |
| }, |
| { |
| "index": 2607, |
| "pred_answer": "0.8\\ \\mathrm{m/s}^2", |
| "gt_answer": "$164\\,\\mathrm{m/s^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2608, |
| "pred_answer": "1", |
| "gt_answer": "44.7", |
| "correct": false |
| }, |
| { |
| "index": 2609, |
| "pred_answer": "0.36\\ \\text{N}", |
| "gt_answer": "0.17 N", |
| "correct": false |
| }, |
| { |
| "index": 2612, |
| "pred_answer": "1.50", |
| "gt_answer": "1.29", |
| "correct": false |
| }, |
| { |
| "index": 2614, |
| "pred_answer": "1.5\\ \\text{s}", |
| "gt_answer": "7.1 s", |
| "correct": false |
| }, |
| { |
| "index": 2615, |
| "pred_answer": "5.45\\ \\text{ns}", |
| "gt_answer": "0.05 ms", |
| "correct": false |
| }, |
| { |
| "index": 2616, |
| "pred_answer": "20\\ \\text{m/s}", |
| "gt_answer": "1.8 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2618, |
| "pred_answer": "2560000\\ \\text{Pa}", |
| "gt_answer": "$46000000\\,\\mathrm{N/m^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2621, |
| "pred_answer": "+130.0^\\circ\\mathrm{B}", |
| "gt_answer": "$105.4^{\\circ}\\mathrm{B}$", |
| "correct": false |
| }, |
| { |
| "index": 2625, |
| "pred_answer": "284\\ \\text{N}", |
| "gt_answer": "996 N", |
| "correct": false |
| }, |
| { |
| "index": 2627, |
| "pred_answer": "3.32\\ \\text{m}", |
| "gt_answer": "$0.0014\\,\\mathrm{m}$", |
| "correct": false |
| }, |
| { |
| "index": 2628, |
| "pred_answer": "10", |
| "gt_answer": "0.25", |
| "correct": false |
| }, |
| { |
| "index": 2631, |
| "pred_answer": "1600\\ \\text{W/m}^2", |
| "gt_answer": "$6580\\,\\mathrm{J/(s\\cdot m^2)}$", |
| "correct": false |
| }, |
| { |
| "index": 2632, |
| "pred_answer": "0.125", |
| "gt_answer": "0.74", |
| "correct": false |
| }, |
| { |
| "index": 2634, |
| "pred_answer": "1", |
| "gt_answer": "1.27", |
| "correct": false |
| }, |
| { |
| "index": 2636, |
| "pred_answer": "1.4\\,\\mu\\text{g}", |
| "gt_answer": "$0.000000003\\,\\mathrm{kg}$", |
| "correct": false |
| }, |
| { |
| "index": 2641, |
| "pred_answer": "+20.0\\ \\text{J}", |
| "gt_answer": "+3700 J", |
| "correct": false |
| }, |
| { |
| "index": 2642, |
| "pred_answer": "20\\ \\text{J}", |
| "gt_answer": "+180 J", |
| "correct": false |
| }, |
| { |
| "index": 2643, |
| "pred_answer": "-1.62\\ \\text{J/K}", |
| "gt_answer": "1.6 J/K", |
| "correct": false |
| }, |
| { |
| "index": 2644, |
| "pred_answer": "680\\ \\text{J}", |
| "gt_answer": "680 J", |
| "correct": false |
| }, |
| { |
| "index": 2645, |
| "pred_answer": "1000\\ \\text{K}", |
| "gt_answer": "449 K", |
| "correct": false |
| }, |
| { |
| "index": 2646, |
| "pred_answer": "235\\ \\text{K}", |
| "gt_answer": "323 K", |
| "correct": false |
| }, |
| { |
| "index": 2647, |
| "pred_answer": "64.0\\ \\text{J}", |
| "gt_answer": "2100 J", |
| "correct": false |
| }, |
| { |
| "index": 2650, |
| "pred_answer": "0.00376\\ \\text{W/m}^2", |
| "gt_answer": "$0.00001\\,\\mathrm{W/m^2}$", |
| "correct": false |
| }, |
| { |
| "index": 2651, |
| "pred_answer": "4.36\\ \\text{m/s}", |
| "gt_answer": "9.66 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2654, |
| "pred_answer": "3.0\\ \\text{m/s}", |
| "gt_answer": "14 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2656, |
| "pred_answer": "1.30\\ \\text{kg}", |
| "gt_answer": "14.3 kg", |
| "correct": false |
| }, |
| { |
| "index": 2666, |
| "pred_answer": "10.0\\ \\text{cm}", |
| "gt_answer": "0.628 m", |
| "correct": false |
| }, |
| { |
| "index": 2667, |
| "pred_answer": "34.5\\ \\text{cm}", |
| "gt_answer": "0.656 m", |
| "correct": false |
| }, |
| { |
| "index": 2670, |
| "pred_answer": "262\\ \\text{Hz}", |
| "gt_answer": "270 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2672, |
| "pred_answer": "36\\ \\text{Hz}", |
| "gt_answer": "1.7 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2676, |
| "pred_answer": "0.36\\ \\text{Hz}", |
| "gt_answer": "13 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2677, |
| "pred_answer": "0.0523\\ \\text{m}", |
| "gt_answer": "0.0249 m", |
| "correct": false |
| }, |
| { |
| "index": 2678, |
| "pred_answer": "100\\ \\text{Hz}", |
| "gt_answer": "45.0 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2680, |
| "pred_answer": "4280\\ \\text{m/s}", |
| "gt_answer": "$497700.0000000001\\,\\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2681, |
| "pred_answer": null, |
| "gt_answer": "$13600000000000000000000$", |
| "correct": false |
| }, |
| { |
| "index": 2683, |
| "pred_answer": "v + u", |
| "gt_answer": "20 km/h", |
| "correct": false |
| }, |
| { |
| "index": 2688, |
| "pred_answer": "0.20\\ \\text{m}", |
| "gt_answer": "4.43 m", |
| "correct": false |
| }, |
| { |
| "index": 2691, |
| "pred_answer": "4200000\\ \\text{m/s}", |
| "gt_answer": "1300 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2696, |
| "pred_answer": "0\\ \\text{Hz}", |
| "gt_answer": "274 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2697, |
| "pred_answer": "350\\ \\text{Hz}", |
| "gt_answer": "277 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2698, |
| "pred_answer": "0.300\\ \\text{m}", |
| "gt_answer": "45.0 cm", |
| "correct": false |
| }, |
| { |
| "index": 2699, |
| "pred_answer": "2.14\\ \\text{m}", |
| "gt_answer": "0.237 m", |
| "correct": false |
| }, |
| { |
| "index": 2700, |
| "pred_answer": "35\\ \\text{Hz}", |
| "gt_answer": "410 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2701, |
| "pred_answer": "34300\\ \\text{Hz}", |
| "gt_answer": "3.6 kHz", |
| "correct": false |
| }, |
| { |
| "index": 2703, |
| "pred_answer": "31.7^\\circ", |
| "gt_answer": "$39.4^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 2706, |
| "pred_answer": "2.00\\ \\text{m}", |
| "gt_answer": "1.71 m", |
| "correct": false |
| }, |
| { |
| "index": 2707, |
| "pred_answer": "0.616", |
| "gt_answer": "2.34", |
| "correct": false |
| }, |
| { |
| "index": 2708, |
| "pred_answer": "48.8^\\circ", |
| "gt_answer": "$28.7^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 2709, |
| "pred_answer": "31.5^\\circ", |
| "gt_answer": "$54.3^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 2710, |
| "pred_answer": "78.4^\\circ", |
| "gt_answer": "$9.43^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 2712, |
| "pred_answer": "0\\ \\text{W/m}^2", |
| "gt_answer": "0", |
| "correct": false |
| }, |
| { |
| "index": 2713, |
| "pred_answer": "37.3^\\circ", |
| "gt_answer": "$71.6^{\\circ}$", |
| "correct": false |
| }, |
| { |
| "index": 2716, |
| "pred_answer": "1.13", |
| "gt_answer": "1.12", |
| "correct": false |
| }, |
| { |
| "index": 2717, |
| "pred_answer": "2300\\ \\text{Hz}", |
| "gt_answer": "f", |
| "correct": false |
| }, |
| { |
| "index": 2718, |
| "pred_answer": "0.01\\ \\text{m}", |
| "gt_answer": "$0.009\\,\\mathrm{kg/m^3}$", |
| "correct": false |
| }, |
| { |
| "index": 2719, |
| "pred_answer": "16500000\\ \\text{ps}", |
| "gt_answer": "3.85 s", |
| "correct": false |
| }, |
| { |
| "index": 2720, |
| "pred_answer": "92\\%", |
| "gt_answer": "49 %", |
| "correct": false |
| }, |
| { |
| "index": 2724, |
| "pred_answer": "0.0636\\ \\text{J}", |
| "gt_answer": "$\\frac{\\pi S \\rho \\omega^2 a^2}{4k}$", |
| "correct": false |
| }, |
| { |
| "index": 2725, |
| "pred_answer": "\\pi^2 \\mu f l^2", |
| "gt_answer": "$E = \\frac{a_0^2 \\pi^2 T}{l}$", |
| "correct": false |
| }, |
| { |
| "index": 2726, |
| "pred_answer": "1.5f_0", |
| "gt_answer": "$\\frac{f}{\\sqrt{1 + \\frac{2at_0}{c}}}$", |
| "correct": false |
| }, |
| { |
| "index": 2728, |
| "pred_answer": "7.5\\text{ cm}", |
| "gt_answer": "4.95 mm", |
| "correct": false |
| }, |
| { |
| "index": 2729, |
| "pred_answer": "250\\ \\text{Hz}", |
| "gt_answer": "163.4 Hz", |
| "correct": false |
| }, |
| { |
| "index": 2733, |
| "pred_answer": "0.001\\ \\text{J}", |
| "gt_answer": "$\\frac{\\pi^2 a^2 T}{4l}$", |
| "correct": false |
| }, |
| { |
| "index": 2737, |
| "pred_answer": "0.10\\ \\text{s}", |
| "gt_answer": "0.14 s", |
| "correct": false |
| }, |
| { |
| "index": 2739, |
| "pred_answer": "4.97\\ \\text{s}", |
| "gt_answer": "4 s", |
| "correct": false |
| }, |
| { |
| "index": 2740, |
| "pred_answer": null, |
| "gt_answer": "E_1", |
| "correct": false |
| }, |
| { |
| "index": 2744, |
| "pred_answer": "18.0\\ \\text{m/s}", |
| "gt_answer": "$\\frac{50}{3}\\,\\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2745, |
| "pred_answer": "0.0942\\ \\text{m}", |
| "gt_answer": "2 m", |
| "correct": false |
| }, |
| { |
| "index": 2747, |
| "pred_answer": "0.16\\ \\mathrm{m/s}", |
| "gt_answer": "0 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2748, |
| "pred_answer": "50\\,\\text{cm}", |
| "gt_answer": "$0.3 + 0.2 \\sin\\left[ \\frac{10\\pi}{3}(t - 0.2) - \\frac{\\pi}{6} \\right]$", |
| "correct": false |
| }, |
| { |
| "index": 2751, |
| "pred_answer": "0.83\\ \\text{m/s}", |
| "gt_answer": "10 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2753, |
| "pred_answer": "1.2\\ \\text{m}", |
| "gt_answer": "20 m", |
| "correct": false |
| }, |
| { |
| "index": 2754, |
| "pred_answer": "1.5\\ \\text{m}", |
| "gt_answer": "1.2 m", |
| "correct": false |
| }, |
| { |
| "index": 2756, |
| "pred_answer": "50\\ \\text{cm/s}", |
| "gt_answer": "0.5 m/s", |
| "correct": false |
| }, |
| { |
| "index": 2757, |
| "pred_answer": "+4.0\\ \\text{cm}", |
| "gt_answer": "-2.0 cm", |
| "correct": false |
| }, |
| { |
| "index": 2759, |
| "pred_answer": "2\\ \\text{m/s}", |
| "gt_answer": "$\\frac{8a}{T}$", |
| "correct": false |
| }, |
| { |
| "index": 2761, |
| "pred_answer": "0.1\\ \\text{N}", |
| "gt_answer": "$\\frac{F_1 - F_2}{2 \\rho S g}$", |
| "correct": false |
| }, |
| { |
| "index": 2762, |
| "pred_answer": "0.0067\\ \\text{s}", |
| "gt_answer": "448 y", |
| "correct": false |
| }, |
| { |
| "index": 2764, |
| "pred_answer": "1.13\\ \\text{min}", |
| "gt_answer": "0.425 y", |
| "correct": false |
| }, |
| { |
| "index": 2766, |
| "pred_answer": "6480000\\ \\text{km}", |
| "gt_answer": "2684 y", |
| "correct": false |
| }, |
| { |
| "index": 2767, |
| "pred_answer": "0.042\\ \\mu\\text{s}", |
| "gt_answer": "1.487", |
| "correct": false |
| }, |
| { |
| "index": 2769, |
| "pred_answer": "7.09", |
| "gt_answer": "3.705 y", |
| "correct": false |
| }, |
| { |
| "index": 2772, |
| "pred_answer": "96900\\ \\text{s}", |
| "gt_answer": "$0.0000258\\,\\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2773, |
| "pred_answer": "5:27\\ \\text{pm}", |
| "gt_answer": "$0.0000008\\,\\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2775, |
| "pred_answer": "428\\ \\mu\\text{s}", |
| "gt_answer": "$0.0000012\\,\\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2776, |
| "pred_answer": "1.05\\ \\text{ly}", |
| "gt_answer": "4.00 y", |
| "correct": false |
| }, |
| { |
| "index": 2778, |
| "pred_answer": "190\\ \\text{GHz}", |
| "gt_answer": "22.9 MHz", |
| "correct": false |
| }, |
| { |
| "index": 2779, |
| "pred_answer": "6000\\ \\text{m/s}", |
| "gt_answer": "$1200000\\,\\mathrm{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2782, |
| "pred_answer": "120\\ \\text{km}", |
| "gt_answer": "110 km", |
| "correct": false |
| }, |
| { |
| "index": 2784, |
| "pred_answer": "9.08\\,\\mu\\text{m}", |
| "gt_answer": "0.222 cm", |
| "correct": false |
| }, |
| { |
| "index": 2785, |
| "pred_answer": "11100000000000000000000000000\\ \\text{kg/s}", |
| "gt_answer": "18 smu/y", |
| "correct": false |
| }, |
| { |
| "index": 2786, |
| "pred_answer": "-2219\\ \\text{MeV}", |
| "gt_answer": "2.08 MeV", |
| "correct": false |
| }, |
| { |
| "index": 2787, |
| "pred_answer": "2.1\\times 10^{-6}", |
| "gt_answer": "$0.00000000000221$", |
| "correct": false |
| }, |
| { |
| "index": 2788, |
| "pred_answer": "0\\ \\text{km/h}", |
| "gt_answer": "$54000\\,\\mathrm{km/h}$", |
| "correct": false |
| }, |
| { |
| "index": 2792, |
| "pred_answer": "0.065\\ \\text{mm}", |
| "gt_answer": "$0.000000000000224\\,\\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2794, |
| "pred_answer": "0.0000001\\ \\text{ns}", |
| "gt_answer": "$0.00000138\\,\\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2795, |
| "pred_answer": "10^{-29}\\ \\mathrm{kg}", |
| "gt_answer": "$0\\,\\mathrm{kg}$", |
| "correct": false |
| }, |
| { |
| "index": 2796, |
| "pred_answer": "100\\ \\text{bpm}", |
| "gt_answer": "65.4/min", |
| "correct": false |
| }, |
| { |
| "index": 2797, |
| "pred_answer": "\\lambda", |
| "gt_answer": "415 nm", |
| "correct": false |
| }, |
| { |
| "index": 2798, |
| "pred_answer": "0.0036\\ \\text{s}", |
| "gt_answer": "$0.000000000672\\,\\mathrm{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2799, |
| "pred_answer": "0.0000000000000329\\ \\text{fm}", |
| "gt_answer": "11 nm", |
| "correct": false |
| }, |
| { |
| "index": 2800, |
| "pred_answer": "1.1\\times 10^{14}\\ \\mathrm{kg/m^3}", |
| "gt_answer": "$200000000000000000\\,\\mathrm{kg/m^3}$", |
| "correct": false |
| }, |
| { |
| "index": 2803, |
| "pred_answer": "184\\ \\text{g}", |
| "gt_answer": "18.9 g", |
| "correct": false |
| }, |
| { |
| "index": 2804, |
| "pred_answer": "250\\ \\text{N}", |
| "gt_answer": "1.24 N", |
| "correct": false |
| }, |
| { |
| "index": 2805, |
| "pred_answer": "3.2\\ \\text{km}", |
| "gt_answer": "7.8 km", |
| "correct": false |
| }, |
| { |
| "index": 2807, |
| "pred_answer": "4500\\ \\text{N}\\cdot\\text{m}", |
| "gt_answer": "22.3 N \\cdot m", |
| "correct": false |
| }, |
| { |
| "index": 2809, |
| "pred_answer": "1.0\\times 10^{-10}\\ \\text{N}", |
| "gt_answer": "0.000000000427 N", |
| "correct": false |
| }, |
| { |
| "index": 2811, |
| "pred_answer": "354000\\ \\text{N/C}", |
| "gt_answer": "10400000 N/C", |
| "correct": false |
| }, |
| { |
| "index": 2812, |
| "pred_answer": "-129000\\ \\text{N}\\cdot\\text{m}^2/\\text{C}", |
| "gt_answer": "680000 N \\cdot m^2 / C", |
| "correct": false |
| }, |
| { |
| "index": 2816, |
| "pred_answer": "2.00\\ \\mu\\text{C}", |
| "gt_answer": "$0.00000614$ C", |
| "correct": false |
| }, |
| { |
| "index": 2817, |
| "pred_answer": "4.00\\ \\text{cm}", |
| "gt_answer": "$-3.33\\ \\text{diopters}$", |
| "correct": false |
| }, |
| { |
| "index": 2821, |
| "pred_answer": "-20\\text{ cm}", |
| "gt_answer": "$33 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2824, |
| "pred_answer": "5.76\\ \\text{mJ}", |
| "gt_answer": "$0.058 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2825, |
| "pred_answer": "0.000001\\ \\text{J}", |
| "gt_answer": "$0.038 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2826, |
| "pred_answer": "1.00\\ \\text{pF}", |
| "gt_answer": "$531 \\text{ pF}$", |
| "correct": false |
| }, |
| { |
| "index": 2827, |
| "pred_answer": "0.00000000000000000125\\ \\text{J}", |
| "gt_answer": "$0.00000234$ J", |
| "correct": false |
| }, |
| { |
| "index": 2830, |
| "pred_answer": "1260\\ \\text{kV}", |
| "gt_answer": "$-737 \\text{ V}$", |
| "correct": false |
| }, |
| { |
| "index": 2831, |
| "pred_answer": "1.0\\ \\text{m}", |
| "gt_answer": "$98 \\text{ mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2835, |
| "pred_answer": "1.0\\ \\mu\\text{C}", |
| "gt_answer": "$0.00008$ C", |
| "correct": false |
| }, |
| { |
| "index": 2836, |
| "pred_answer": "40\\ \\text{cm}", |
| "gt_answer": "$4.43 \\text{ m}$", |
| "correct": false |
| }, |
| { |
| "index": 2837, |
| "pred_answer": "9.0\\text{ cm}", |
| "gt_answer": "$14.2 \\text{ cm}$, $3.8 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2838, |
| "pred_answer": "Q_1 = 2.57\\,\\mu\\text{C},\\; Q_2 = 4.29\\,\\mu\\text{C},\\; Q_3 = 5.15\\,\\mu\\text{C}", |
| "gt_answer": "$30.9 \\ \\mu \\text{C}$, $51.5 \\ \\mu \\text{C}$, $82.3 \\ \\mu \\text{C}$", |
| "correct": false |
| }, |
| { |
| "index": 2839, |
| "pred_answer": "-30\\ \\text{cm}", |
| "gt_answer": "$-6.2 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2840, |
| "pred_answer": "3.92\\ \\mu\\text{F}", |
| "gt_answer": "$3.47 \\ \\mu \\text{F}$", |
| "correct": false |
| }, |
| { |
| "index": 2844, |
| "pred_answer": "28.3\\text{ cm}", |
| "gt_answer": "$-3.0 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2845, |
| "pred_answer": "10\\ \\text{cm}", |
| "gt_answer": "$18.0 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2846, |
| "pred_answer": "2700\\ \\text{nC}", |
| "gt_answer": "$2.4 \\ \\mu \\text{C}$", |
| "correct": false |
| }, |
| { |
| "index": 2847, |
| "pred_answer": "-10\\ \\text{cm}", |
| "gt_answer": "$24.0 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2848, |
| "pred_answer": "-3.3\\ \\text{cm}", |
| "gt_answer": "$-6.0 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2849, |
| "pred_answer": "25\\ \\text{V}", |
| "gt_answer": "$220 \\text{ V}$", |
| "correct": false |
| }, |
| { |
| "index": 2851, |
| "pred_answer": "1050\\ \\text{V/m}", |
| "gt_answer": "$1130000$ V/m", |
| "correct": false |
| }, |
| { |
| "index": 2853, |
| "pred_answer": "\\frac{C_1}{2} + C_2", |
| "gt_answer": "$2.3 \\ \\mu \\text{F}$", |
| "correct": false |
| }, |
| { |
| "index": 2854, |
| "pred_answer": "0.00000687\\ \\text{J}", |
| "gt_answer": "$0.0000000046$ J", |
| "correct": false |
| }, |
| { |
| "index": 2855, |
| "pred_answer": "0.26\\ \\Omega", |
| "gt_answer": "$0.26 \\ \\Omega$", |
| "correct": false |
| }, |
| { |
| "index": 2856, |
| "pred_answer": "5.88\\ \\text{mΩ}", |
| "gt_answer": "$0.006 \\ \\Omega$", |
| "correct": false |
| }, |
| { |
| "index": 2860, |
| "pred_answer": "8.0\\ \\Omega", |
| "gt_answer": "$9.0 \\ \\Omega$", |
| "correct": false |
| }, |
| { |
| "index": 2863, |
| "pred_answer": "400\\,\\Omega", |
| "gt_answer": "$150 \\ \\Omega$", |
| "correct": false |
| }, |
| { |
| "index": 2866, |
| "pred_answer": null, |
| "gt_answer": "$1.80 \\ \\Omega$", |
| "correct": false |
| }, |
| { |
| "index": 2867, |
| "pred_answer": "28.8\\ \\text{W}", |
| "gt_answer": "$20.0 \\text{ W}$", |
| "correct": false |
| }, |
| { |
| "index": 2868, |
| "pred_answer": "100\\ \\text{N}", |
| "gt_answer": "$-17000$ N", |
| "correct": false |
| }, |
| { |
| "index": 2870, |
| "pred_answer": "0.0032\\text{ kg}", |
| "gt_answer": "$3.1 \\text{ kg}$", |
| "correct": false |
| }, |
| { |
| "index": 2871, |
| "pred_answer": "10800\\ \\text{W}", |
| "gt_answer": "$15.9 \\text{ W}$", |
| "correct": false |
| }, |
| { |
| "index": 2873, |
| "pred_answer": "27.9^\\circ\\text{C}", |
| "gt_answer": "$29.6 \\ ^{\\circ}\\text{C}$", |
| "correct": false |
| }, |
| { |
| "index": 2874, |
| "pred_answer": null, |
| "gt_answer": "$5.82 \\text{ g}$", |
| "correct": false |
| }, |
| { |
| "index": 2875, |
| "pred_answer": "1.5\\ \\text{cm}", |
| "gt_answer": "$8.0 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2877, |
| "pred_answer": "-525\\ \\text{K}", |
| "gt_answer": "$510 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2878, |
| "pred_answer": "2040000\\ \\text{Pa}", |
| "gt_answer": "$613 \\ ^{\\circ}\\text{C}$", |
| "correct": false |
| }, |
| { |
| "index": 2879, |
| "pred_answer": "1500\\ \\text{J}", |
| "gt_answer": "$0 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2881, |
| "pred_answer": "500\\ \\text{J}", |
| "gt_answer": "$1330 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2882, |
| "pred_answer": "36\\ \\text{atm·L}", |
| "gt_answer": "$1200 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2888, |
| "pred_answer": "5500\\ \\text{J}", |
| "gt_answer": "$8000 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2889, |
| "pred_answer": "17.6\\ \\text{J}", |
| "gt_answer": "$2230 \\text{ J}$", |
| "correct": false |
| }, |
| { |
| "index": 2890, |
| "pred_answer": "280\\ \\text{K}", |
| "gt_answer": "$665 \\text{ K}$", |
| "correct": false |
| }, |
| { |
| "index": 2893, |
| "pred_answer": "4\\ \\text{cm}", |
| "gt_answer": "$6.38 \\text{ mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2897, |
| "pred_answer": "0.50\\ \\text{L}", |
| "gt_answer": "$0.80 \\text{ L}$", |
| "correct": false |
| }, |
| { |
| "index": 2898, |
| "pred_answer": "1.0\\times 10^5\\ \\text{Pa}", |
| "gt_answer": "$800000 \\text{ Pa}$", |
| "correct": false |
| }, |
| { |
| "index": 2900, |
| "pred_answer": "0.0455\\ \\text{kg/s}", |
| "gt_answer": "$5.0 \\text{ g/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2901, |
| "pred_answer": "1.15\\ \\text{J/K}", |
| "gt_answer": "$5.76 \\text{ J/K}$", |
| "correct": false |
| }, |
| { |
| "index": 2908, |
| "pred_answer": "-1", |
| "gt_answer": "$-1$", |
| "correct": false |
| }, |
| { |
| "index": 2909, |
| "pred_answer": "-\\infty", |
| "gt_answer": "$\\pm \\infty$", |
| "correct": false |
| }, |
| { |
| "index": 2910, |
| "pred_answer": "-2.00\\ \\text{cm}", |
| "gt_answer": "$2$", |
| "correct": false |
| }, |
| { |
| "index": 2911, |
| "pred_answer": "2.15", |
| "gt_answer": "$-0.929$", |
| "correct": false |
| }, |
| { |
| "index": 2913, |
| "pred_answer": "1.05\\ \\text{m}", |
| "gt_answer": "$-1.50 \\text{ m}$", |
| "correct": false |
| }, |
| { |
| "index": 2914, |
| "pred_answer": "-10\\ \\text{cm}", |
| "gt_answer": "$-7.7 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2915, |
| "pred_answer": "-0.27\\ \\text{m}", |
| "gt_answer": "$7.5 \\text{ mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2918, |
| "pred_answer": "-2h_o", |
| "gt_answer": "$1.20 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2920, |
| "pred_answer": "6.60\\text{ mm}", |
| "gt_answer": "$0.944 \\text{ mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2921, |
| "pred_answer": "R \\approx 15\\ \\text{cm},\\quad f \\approx 7.5\\ \\text{cm}", |
| "gt_answer": "$5.00 \\text{ cm}$", |
| "correct": false |
| }, |
| { |
| "index": 2922, |
| "pred_answer": "-0.07", |
| "gt_answer": "$1.33$", |
| "correct": false |
| }, |
| { |
| "index": 2935, |
| "pred_answer": "1", |
| "gt_answer": "$2.17$", |
| "correct": false |
| }, |
| { |
| "index": 2937, |
| "pred_answer": "1.97\\ \\text{mm}", |
| "gt_answer": "$0.233\\ \\text{mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2939, |
| "pred_answer": "200\\ \\text{nm}", |
| "gt_answer": "$0.833\\ \\text{mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2943, |
| "pred_answer": "15^\\circ", |
| "gt_answer": "$0.000409\\ \\text{rad}$", |
| "correct": false |
| }, |
| { |
| "index": 2945, |
| "pred_answer": "4.2\\ \\text{mm}", |
| "gt_answer": "$10.9\\ \\text{mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2946, |
| "pred_answer": "1.0\\ \\text{mm}", |
| "gt_answer": "$5.4\\ \\text{mm}$", |
| "correct": false |
| }, |
| { |
| "index": 2947, |
| "pred_answer": "450\\ \\text{nm}", |
| "gt_answer": "$635\\ \\text{nm}$", |
| "correct": false |
| }, |
| { |
| "index": 2948, |
| "pred_answer": "0.0375\\ \\text{eV}", |
| "gt_answer": "$0.0375\\ \\text{eV},\\ 0.75\\ \\text{eV}$", |
| "correct": false |
| }, |
| { |
| "index": 2951, |
| "pred_answer": "\\infty\\ \\text{nm}", |
| "gt_answer": "$0.557\\ \\text{pm}$", |
| "correct": false |
| }, |
| { |
| "index": 2952, |
| "pred_answer": "2.4\\times 10^{7}\\ \\text{m/s}", |
| "gt_answer": "$11299999.9999999981\\ \\text{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2953, |
| "pred_answer": null, |
| "gt_answer": "$0.00657\\ \\text{u}$", |
| "correct": false |
| }, |
| { |
| "index": 2954, |
| "pred_answer": "0.0038\\ \\text{ms}", |
| "gt_answer": "$0.301\\ \\text{ms}$", |
| "correct": false |
| }, |
| { |
| "index": 2955, |
| "pred_answer": "2.29\\ \\text{s}", |
| "gt_answer": "$2.27\\ \\text{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2956, |
| "pred_answer": "1.12\\ \\text{minutes}", |
| "gt_answer": "$0.80\\ \\text{s}$", |
| "correct": false |
| }, |
| { |
| "index": 2957, |
| "pred_answer": "0.99999999999999999999999999999999999999999999999999", |
| "gt_answer": "$0.998\\ c$", |
| "correct": false |
| }, |
| { |
| "index": 2958, |
| "pred_answer": "1.732\\,c", |
| "gt_answer": "$0.867\\ c$", |
| "correct": false |
| }, |
| { |
| "index": 2959, |
| "pred_answer": "1.58\\ \\text{m}", |
| "gt_answer": "$1.57\\ \\text{m}$", |
| "correct": false |
| }, |
| { |
| "index": 2960, |
| "pred_answer": "3.00\\ \\text{m/s}", |
| "gt_answer": "$0.952\\ c$", |
| "correct": false |
| }, |
| { |
| "index": 2961, |
| "pred_answer": "83.33\\ \\text{m}", |
| "gt_answer": "$233\\ \\text{m}$", |
| "correct": false |
| }, |
| { |
| "index": 2963, |
| "pred_answer": "55.0\\ \\text{km}", |
| "gt_answer": "$9.17\\ \\text{km}$", |
| "correct": false |
| }, |
| { |
| "index": 2964, |
| "pred_answer": "0.920\\,c", |
| "gt_answer": "$0.837\\ c$", |
| "correct": false |
| }, |
| { |
| "index": 2965, |
| "pred_answer": "-0.700\\,c", |
| "gt_answer": "$-0.385\\ c$", |
| "correct": false |
| }, |
| { |
| "index": 2966, |
| "pred_answer": "6.1\\times 10^{6}\\ \\text{m/s}", |
| "gt_answer": "$0.229\\ c$", |
| "correct": false |
| }, |
| { |
| "index": 2968, |
| "pred_answer": "0.0045\\ \\text{J}", |
| "gt_answer": "$1880\\ \\text{MeV}$", |
| "correct": false |
| }, |
| { |
| "index": 2970, |
| "pred_answer": "13.3\\text{ years}", |
| "gt_answer": "$24.7\\ \\text{yr}$", |
| "correct": false |
| }, |
| { |
| "index": 2971, |
| "pred_answer": "0.000000020\\ \\text{m}", |
| "gt_answer": "$3.65\\ \\text{m}$", |
| "correct": false |
| }, |
| { |
| "index": 2973, |
| "pred_answer": "4500000000000\\ \\text{J}", |
| "gt_answer": "$72000000000000\\ \\text{J}$", |
| "correct": false |
| }, |
| { |
| "index": 2974, |
| "pred_answer": "10.3\\ \\text{km/s}", |
| "gt_answer": "$513000000\\ \\text{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2975, |
| "pred_answer": "0.0028\\ \\text{eV}", |
| "gt_answer": "$0.168\\ \\text{MeV}$", |
| "correct": false |
| }, |
| { |
| "index": 2976, |
| "pred_answer": "3.03\\ \\text{eV}", |
| "gt_answer": "$2.14\\ \\text{eV}$", |
| "correct": false |
| }, |
| { |
| "index": 2979, |
| "pred_answer": "4.0\\ \\text{V}", |
| "gt_answer": "$1.22\\ \\text{eV}$", |
| "correct": false |
| }, |
| { |
| "index": 2980, |
| "pred_answer": "3.50\\ \\text{eV}", |
| "gt_answer": "$0.27\\ \\text{eV}$", |
| "correct": false |
| }, |
| { |
| "index": 2981, |
| "pred_answer": "611\\ \\text{nm}", |
| "gt_answer": "$434\\ \\text{nm}$", |
| "correct": false |
| }, |
| { |
| "index": 2986, |
| "pred_answer": "49.6\\ \\text{nm}", |
| "gt_answer": "$0.245\\ \\text{nm}$", |
| "correct": false |
| }, |
| { |
| "index": 2988, |
| "pred_answer": "28.2\\ \\text{eV}", |
| "gt_answer": "$0.9\\ \\text{eV}$", |
| "correct": false |
| }, |
| { |
| "index": 2990, |
| "pred_answer": "6.89\\ \\text{eV}", |
| "gt_answer": "$183\\ \\text{eV}$", |
| "correct": false |
| }, |
| { |
| "index": 2994, |
| "pred_answer": "1840\\ \\text{N}", |
| "gt_answer": "$79{,}000\\ \\text{N}$", |
| "correct": false |
| }, |
| { |
| "index": 2995, |
| "pred_answer": "-3.75\\ \\text{J}", |
| "gt_answer": "$3.0\\ \\text{J}$", |
| "correct": false |
| }, |
| { |
| "index": 2996, |
| "pred_answer": "20.4\\ \\text{m}", |
| "gt_answer": "$20.4\\ \\text{m}$", |
| "correct": false |
| }, |
| { |
| "index": 2997, |
| "pred_answer": "10.8\\ \\text{m/s}", |
| "gt_answer": "$7.67\\ \\text{m/s}$", |
| "correct": false |
| }, |
| { |
| "index": 2998, |
| "pred_answer": "14000\\ \\text{N/m}", |
| "gt_answer": "$27300\\ \\text{N/m}$", |
| "correct": false |
| } |
| ] |
