[
  {
    "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
  },
  {
    "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}",
    "gt_answer": "\\( 2.51 \\text{year} \\)",
    "correct": false
  },
  {
    "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
  }
]