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| "markdown": "## ู ุจุฑููุฉ\nุชุฌุจ ุนููู ุงูุฒููุงุฉ ูู ู ุงูู - ููุฎุฑุฌูุง ุงูููู - ููุฌุจ ุนููู ุงูุญุฌู ูุงูุนุจุงุฏุงุช. ูู ููุง: ูุตุญู ุฅูุฑุงุฑู\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n\\iint_{D} \\beta^2 = \\sigma^2 \\, dx \\, dy\n## ู ูุงุญุธุฉ\nุจุงูุนููุจุงุช. ุงูุจุฏูููุฉ ูุงูู ุงูููุฉ. ูู ููุง: ุชุตุญู ูุตุงูุงู ุจุงูููุฑูุจ ู ู ุงูุซููุซ. ูู ููุง: ุฅูู ุงูุตูุจู ุฅุฐุง ููุชูู ู ุชุนู ูุฏุงู ูุงูุฏูููุฉ ุนูู ุนุงููุชูุ ูุฃูู ุนู ุฏ ุงูุตูุจู\n\\int_{1}^{M} \\sin(t) \\, dt = \\lambda^2 + C", | |
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| "header": null, | |
| "footer": null, | |
| "dimensions": { | |
| "dpi": 96, | |
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| "confidence_scores": { | |
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| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 0 | |
| }, | |
| { | |
| "text": "ู ุจุฑููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "ุชุฌุจ", | |
| "confidence": 1.0, | |
| "start_index": 10 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 14 | |
| }, | |
| { | |
| "text": "ุงูุฒููุงุฉ", | |
| "confidence": 1.0, | |
| "start_index": 19 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 27 | |
| }, | |
| { | |
| "text": "ู ุงูู", | |
| "confidence": 1.0, | |
| "start_index": 30 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 35 | |
| }, | |
| { | |
| "text": "ููุฎุฑุฌูุง", | |
| "confidence": 1.0, | |
| "start_index": 37 | |
| }, | |
| { | |
| "text": "ุงูููู", | |
| "confidence": 1.0, | |
| "start_index": 45 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 51 | |
| }, | |
| { | |
| "text": "ููุฌุจ", | |
| "confidence": 1.0, | |
| "start_index": 53 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 58 | |
| }, | |
| { | |
| "text": "ุงูุญุฌู", | |
| "confidence": 1.0, | |
| "start_index": 63 | |
| }, | |
| { | |
| "text": "ูุงูุนุจุงุฏุงุช.", | |
| "confidence": 1.0, | |
| "start_index": 69 | |
| }, | |
| { | |
| "text": "ูู ููุง:", | |
| "confidence": 1.0, | |
| "start_index": 80 | |
| }, | |
| { | |
| "text": "ูุตุญู", | |
| "confidence": 1.0, | |
| "start_index": 87 | |
| }, | |
| { | |
| "text": "ุฅูุฑุงุฑู", | |
| "confidence": 1.0, | |
| "start_index": 92 | |
| }, | |
| { | |
| "text": "P(A|B)", | |
| "confidence": 1.0, | |
| "start_index": 99 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\frac{P(A", | |
| "confidence": 1.0, | |
| "start_index": 108 | |
| }, | |
| { | |
| "text": "\\cap", | |
| "confidence": 1.0, | |
| "start_index": 118 | |
| }, | |
| { | |
| "text": "B)}{P(B)}", | |
| "confidence": 1.0, | |
| "start_index": 123 | |
| }, | |
| { | |
| "text": "\\iint_{D}", | |
| "confidence": 1.0, | |
| "start_index": 133 | |
| }, | |
| { | |
| "text": "\\beta^2", | |
| "confidence": 1.0, | |
| "start_index": 143 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 151 | |
| }, | |
| { | |
| "text": "\\sigma^2", | |
| "confidence": 1.0, | |
| "start_index": 153 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 162 | |
| }, | |
| { | |
| "text": "dx", | |
| "confidence": 1.0, | |
| "start_index": 165 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 168 | |
| }, | |
| { | |
| "text": "dy", | |
| "confidence": 1.0, | |
| "start_index": 171 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 174 | |
| }, | |
| { | |
| "text": "ู ูุงุญุธุฉ", | |
| "confidence": 1.0, | |
| "start_index": 177 | |
| }, | |
| { | |
| "text": "ุจุงูุนููุจุงุช.", | |
| "confidence": 1.0, | |
| "start_index": 184 | |
| }, | |
| { | |
| "text": "ุงูุจุฏูููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 195 | |
| }, | |
| { | |
| "text": "ูุงูู ุงูููุฉ.", | |
| "confidence": 1.0, | |
| "start_index": 204 | |
| }, | |
| { | |
| "text": "ูู ููุง:", | |
| "confidence": 1.0, | |
| "start_index": 215 | |
| }, | |
| { | |
| "text": "ุชุตุญู", | |
| "confidence": 1.0, | |
| "start_index": 222 | |
| }, | |
| { | |
| "text": "ูุตุงูุงู", | |
| "confidence": 1.0, | |
| "start_index": 227 | |
| }, | |
| { | |
| "text": "ุจุงูููุฑูุจ", | |
| "confidence": 1.0, | |
| "start_index": 234 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 243 | |
| }, | |
| { | |
| "text": "ุงูุซููุซ.", | |
| "confidence": 1.0, | |
| "start_index": 246 | |
| }, | |
| { | |
| "text": "ูู ููุง:", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฅูู", | |
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| "start_index": 261 | |
| }, | |
| { | |
| "text": "ุงูุตูุจู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฅุฐุง", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ููุชูู", | |
| "confidence": 1.0, | |
| "start_index": 276 | |
| }, | |
| { | |
| "text": "ู ุชุนู ูุฏุงู", | |
| "confidence": 1.0, | |
| "start_index": 282 | |
| }, | |
| { | |
| "text": "ูุงูุฏูููุฉ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 300 | |
| }, | |
| { | |
| "text": "ุนุงููุชูุ", | |
| "confidence": 1.0, | |
| "start_index": 304 | |
| }, | |
| { | |
| "text": "ูุฃูู", | |
| "confidence": 1.0, | |
| "start_index": 312 | |
| }, | |
| { | |
| "text": "ุนู ุฏ", | |
| "confidence": 1.0, | |
| "start_index": 317 | |
| }, | |
| { | |
| "text": "ุงูุตูุจู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\int_{1}^{M}", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\sin(t)", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 349 | |
| }, | |
| { | |
| "text": "dt", | |
| "confidence": 1.0, | |
| "start_index": 352 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 355 | |
| }, | |
| { | |
| "text": "\\lambda^2", | |
| "confidence": 1.0, | |
| "start_index": 357 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
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| { | |
| "text": "C", | |
| "confidence": 1.0, | |
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| "content": "ุชุฌุจ ุนููู ุงูุฒููุงุฉ ูู ู ุงูู - ููุฎุฑุฌูุง ุงูููู - ููุฌุจ ุนููู ุงูุญุฌู ูุงูุนุจุงุฏุงุช. ูู ููุง: ูุตุญู ุฅูุฑุงุฑู", | |
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| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
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| "content": "ุจุงูุนููุจุงุช. ุงูุจุฏูููุฉ ูุงูู ุงูููุฉ. ูู ููุง: ุชุตุญู ูุตุงูุงู ุจุงูููุฑูุจ ู ู ุงูุซููุซ. ูู ููุง: ุฅูู ุงูุตูุจู ุฅุฐุง ููุชูู ู ุชุนู ูุฏุงู ูุงูุฏูููุฉ ุนูู ุนุงููุชูุ ูุฃูู ุนู ุฏ ุงูุตูุจู", | |
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| "content": "\\int_{1}^{M} \\sin(t) \\, dt = \\lambda^2 + C", | |
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