{"id":15,"date":"2023-08-06T21:48:18","date_gmt":"2023-08-06T21:48:18","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%8a%a0%e6%9d%83%e5%b9%b3%e5%9d%87\/"},"modified":"2023-08-06T21:48:18","modified_gmt":"2023-08-06T21:48:18","slug":"%e5%8a%a0%e6%9d%83%e5%b9%b3%e5%9d%87","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%8a%a0%e6%9d%83%e5%b9%b3%e5%9d%87\/","title":{"rendered":"\u52a0\u6743\u5e73\u5747"},"content":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u52a0\u6743\u5e73\u5747\u503c\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5173\u4e8e\u6211\u4eec\u5982\u4f55\u627e\u5230\u52a0\u6743\u5e73\u5747\u503c\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\u3002\u800c\u4e14\uff0c\u66f4\u91cd\u8981\u7684\u662f\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u6700\u540e\u7684\u8ba1\u7b97\u5668\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u96c6\u7684\u52a0\u6743\u5e73\u5747\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-media-ponderada\"><\/span>\u52a0\u6743\u5e73\u5747\u503c\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u52a0\u6743\u5e73\u5747\u503c\u662f\u63cf\u8ff0\u6027\u7edf\u8ba1\u4e2d\u5fc3\u6027\u7684\u5ea6\u91cf\u3002<strong>\u8ba1\u7b97\u52a0\u6743\u5e73\u5747\u503c\u65f6\uff0c<\/strong>\u5fc5\u987b\u9996\u5148\u5c06\u6bcf\u4e2a\u7edf\u8ba1\u6570\u636e\u4e58\u4ee5\u5176\u6743\u91cd\uff08\u6216\u6743\u91cd\uff09\uff0c\u7136\u540e\u5c06\u6240\u6709\u4e58\u79ef\u76f8\u52a0\uff0c\u6700\u540e\u5c06\u52a0\u6743\u603b\u548c\u9664\u4ee5\u6240\u6709\u6743\u91cd\u4e4b\u548c\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u52a0\u6743\u5e73\u5747\u7684\u516c\u5f0f\u5982\u4e0b\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyenne-ponderee.png\" alt=\"\u52a0\u6743\u5e73\u5747\" class=\"wp-image-208\" width=\"298\" height=\"298\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5176\u4e2d x <sub>i<\/sub>\u4ee3\u8868\u6bcf\u4e2a\u6570\u636e\u6837\u672c\uff0cw <sub>i<\/sub>\u4ee3\u8868\u76f8\u5e94\u7684\u6743\u91cd\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4e00\u6761\u6570\u636e\u7684\u6743\u91cd\u8d8a\u5927\uff0c\u5728\u52a0\u6743\u5e73\u5747\u503c\u7684\u8ba1\u7b97\u4e2d\u5c31\u8d8a\u91cd\u8981\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u67d0\u6761\u6570\u636e\u7684\u6743\u91cd\u8d8a\u9ad8\uff0c\u5bf9\u52a0\u6743\u5e73\u5747\u7684\u7ed3\u679c\u5f71\u54cd\u5c31\u8d8a\u5927\u3002<\/p>\n<p>\u52a0\u6743\u5e73\u5747\u503c\u5bf9\u4e8e\u8ba1\u7b97\u6210\u7ee9\u7279\u522b\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u60a8\u4ee5\u4e0d\u540c\u7684\u91cd\u8981\u6027\u8bc4\u4f30\u8bfe\u7a0b\u671f\u95f4\u8fdb\u884c\u7684\u7ec3\u4e60\u6216\u8003\u8bd5\u3002\u52a0\u6743\u5e73\u5747\u6570\u8fd8\u7528\u4e8e\u8ba1\u7b97CPI\uff08\u6d88\u8d39\u8005\u4ef7\u683c\u6307\u6570\uff09\uff0c\u8fd9\u662f\u8861\u91cf\u4eba\u53e3\u4ef7\u683c\u7684\u6307\u6807\u3002<\/p>\n<p>\u9664\u52a0\u6743\u5e73\u5747\u5916\uff0c\u8fd8\u6709\u51e0\u4f55\u5e73\u5747\u3001\u7b97\u672f\u5e73\u5747\u3001\u5e73\u65b9\u5e73\u5747\u3001\u8c03\u548c\u5e73\u5747\u7b49\u5176\u4ed6\u7c7b\u578b\u7684\u5e73\u5747\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-media-ponderada\"><\/span>\u5982\u4f55\u8ba1\u7b97\u52a0\u6743\u5e73\u5747\u503c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97\u52a0\u6743\u5e73\u5747\u503c\uff0c\u5fc5\u987b\u9075\u5faa\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u6bcf\u4e2a\u7edf\u8ba1\u6570\u636e\u4e58\u4ee5\u76f8\u5e94\u7684\u6743\u91cd\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u4e0a\u4e00\u6b65\u4e2d\u8ba1\u7b97\u51fa\u7684\u6240\u6709\u4e58\u79ef\u76f8\u52a0\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u4e0a\u9762\u7684\u52a0\u6743\u603b\u548c\u9664\u4ee5\u6240\u6709\u6743\u91cd\u7684\u603b\u548c\u3002<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u6240\u5f97\u7ed3\u679c\u4e3a\u7edf\u8ba1\u6837\u672c\u7684\u52a0\u6743\u5e73\u5747\u503c\u3002<\/span><\/li>\n<\/ol>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u96c6\u7684\u52a0\u6743\u5e73\u5747\u503c\u3002<\/u> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-media-ponderada\"><\/span>\u52a0\u6743\u5e73\u5747\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u52a0\u6743\u5e73\u5747\u503c\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u73b0\u5728\u5c06\u89e3\u51b3\u4e00\u4e2a\u7ec3\u4e60\uff0c\u4ee5\u5145\u5206\u7406\u89e3\u5982\u4f55\u4ece\u4e00\u7ec4\u6570\u636e\u83b7\u5f97\u52a0\u6743\u5e73\u5747\u503c\u3002<\/p>\n<ul>\n<li>\u4e00\u540d\u9ad8\u4e2d\u4e00\u5e74\u7ea7\u5b66\u751f\u5728\u6570\u5b66\u79d1\u76ee\u4e2d\u83b7\u5f97\u4ee5\u4e0b\u6210\u7ee9\uff1a\u90e8\u5206\u8003\u8bd5 7 \u5206\uff08\u5360 30%\uff09\u3001\u5c0f\u7ec4\u4f5c\u4e1a 9 \u5206\uff08\u5360 20%\uff09\u3001\u8bfe\u5802\u7ec3\u4e60\uff08\u5e26\u6743\u91cd\uff096 \u5206\u671f\u672b\u8003\u8bd5\u5f97\u5206\u4e3a 10%\uff0c\u671f\u672b\u8003\u8bd5\u5f97\u5206\u4e3a 8 \u5206\uff0c\u6743\u91cd\u4e3a 40%\u3002\u60a8\u8be5\u79d1\u76ee\u7684\u6700\u7ec8\u6210\u7ee9\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u8981\u786e\u5b9a\u5b66\u751f\u7684\u5206\u6570\uff0c\u60a8\u5fc5\u987b\u4f7f\u7528\u9648\u8ff0\u7ed9\u51fa\u7684\u503c\u627e\u5230\u52a0\u6743\u5e73\u5747\u503c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5e94\u7528\u52a0\u6743\u5e73\u5747\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a9466480b1fa1efeed0d79cb707b6531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_p}=\\cfrac{\\sum_{i=1}^N x_i\\cdot w_i}{\\sum_{i=1}^N w_i}=\\cfrac{x_1\\cdot w_1+x_2\\cdot w_2+x_3\\cdot w_3+x_4\\cdot w_4+x_5\\cdot w_5}{w_1+w_2+w_3+w_4+w_5}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"505\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u6bcf\u4e2a\u4ea4\u4ed8\u6210\u679c\u7684\u5f97\u5206\u662f\u7edf\u8ba1\u503c\uff0c\u5176\u767e\u5206\u6bd4\u5bf9\u5e94\u4e8e\u8be5\u503c\u7684\u6743\u91cd\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6570\u503c\u548c\u6743\u91cd\u4ee3\u5165\u516c\u5f0f\u4e2d\uff0c\u8fdb\u884c\u52a0\u6743\u5e73\u5747\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b4c40861b8f18a1c3c1b03ebb30ee6cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_p}=\\cfrac{7\\cdot 0,30+9\\cdot 0,20+6\\cdot 0,10+8\\cdot 0,40}{0,30+0,20+0,10+0,40}=7,7\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"382\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8be5\u5b66\u751f\u7684\u6700\u7ec8\u6570\u5b66\u6210\u7ee9\u5c06\u4e3a 7.7\uff0c\u56e0\u4e3a\u8fd9\u662f\u6839\u636e\u52a0\u6743\u5e73\u5747\u503c\u83b7\u5f97\u7684\u7ed3\u679c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-media-ponderada\"><\/span>\u52a0\u6743\u5e73\u5747\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c06\u4efb\u4f55\u7edf\u8ba1\u6837\u672c\u7684\u6570\u636e\u53ca\u5176\u5404\u81ea\u7684\u6743\u91cd\u8f93\u5165\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u4ee5\u8ba1\u7b97\u5176\u52a0\u6743\u5e73\u5747\u503c\u3002<\/p>\n<p>\u5728\u7b2c\u4e00\u4e2a\u6846\u4e2d\u8f93\u5165\u7edf\u8ba1\u6570\u636e\uff0c\u5728\u7b2c\u4e8c\u4e2a\u6846\u4e2d\u8f93\u5165\u5404\u81ea\u7684\u6743\u91cd\u3002\u60a8\u5fc5\u987b\u6309\u7167\u4e0e\u6570\u636e\u76f8\u540c\u7684\u987a\u5e8f\u5e76\u4ee5\u5341\u8fdb\u5236\u683c\u5f0f\u5199\u5165\u6743\u91cd\u3002\u6240\u6709\u6570\u5b57\u5fc5\u987b\u7528\u7a7a\u683c\u5206\u9694\uff0c\u5e76\u4f7f\u7528\u53e5\u70b9\u4f5c\u4e3a\u5c0f\u6570\u70b9\u5206\u9694\u7b26\u8f93\u5165\u3002 <\/p>\n<form action=\"\" method=\"post\"><textarea name=\"datos\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"7 9 6 8  ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><textarea name=\"pesos\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"0.3 0.2 0.1 0.4 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin-top:0px; margin-bottom: 20px\" type=\"submit\" name=\"submit\" value=\"\u8ba1\u7b97\u52a0\u6743\u5e73\u5747\u503c\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pesos-normalizados\"><\/span>\u6807\u51c6\u5316\u91cd\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u5728\u52a0\u6743\u5e73\u5747\u503c\u4e2d\uff0c\u6743\u91cd\u662f\u8d4b\u4e88\u6bcf\u6761\u6570\u636e\u4ee5\u8d4b\u4e88\u5176\u6216\u591a\u6216\u5c11\u91cd\u8981\u6027\u7684\u503c\u3002\u56e0\u6b64\uff0c\u5982\u679c\u4fe1\u606f\u975e\u5e38\u91cd\u8981\uff0c\u5b83\u7684\u6743\u91cd\u5c31\u4f1a\u975e\u5e38\u9ad8\uff0c\u4f46\u5982\u679c\u4fe1\u606f\u76f8\u5173\u6027\u4e0d\u662f\u5f88\u9ad8\uff0c\u5b83\u7684\u6743\u91cd\u5c31\u4f1a\u975e\u5e38\u4f4e\u3002<\/p>\n<p>\u5f52\u4e00\u5316\u6743\u91cd\u662f\u4e00\u79cd\u52a0\u6743\u65b9\u6cd5\uff0c\u7528\u4e8e\u65e0\u9700\u8fdb\u884c\u4efb\u4f55\u9664\u6cd5\u5373\u53ef\u83b7\u5f97\u52a0\u6743\u5e73\u5747\u503c\u3002<\/p>\n<p><strong>\u5f52\u4e00\u5316\u6743\u91cd<\/strong>\u662f\u6570\u636e\u9879\u7684\u6743\u91cd\u9664\u4ee5\u6240\u6709\u6743\u91cd\u7684\u603b\u548c\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d545c9a224969ca7ee8da985ed5426f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"w_i'=\\cfrac{w_i}{\\sum_{k=1}^N w_k}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"113\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6240\u6709\u5f52\u4e00\u5316\u6743\u91cd\u7684\u603b\u548c\u7b49\u4e8e 1\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-14d524eea7b0540e622012049655ad5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sum_{i=1}^N w_i'=1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"95\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8981<strong>\u4f7f\u7528\u5f52\u4e00\u5316\u6743\u91cd \u8ba1\u7b97\u52a0\u6743\u5e73\u5747\u503c<\/strong>\uff0c\u53ea\u9700\u5c06\u6bcf\u4e2a\u6570\u636e\u9879\u4e58\u4ee5\u5176\u5f52\u4e00\u5316\u6743\u91cd\u5373\u53ef\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a8e6993f8f1fa47fd17c0c41a12e2225_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\overline{x_p}=\\sum_{i=1}^N x_i\\cdot w_i'=x_1\\cdot w_1'+x_2\\cdot w_2'+\\dots+x_N\\cdot w_N'\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"389\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u7edf\u8ba1\u6837\u672c\uff0c\u5176\u6570\u636e\u4e3a 24, 35, 17, 41\uff0c\u5176\u6743\u91cd\u5206\u522b\u4e3a 4, 9, 6, 3\u3002\u4e3a\u4e86\u6c42\u51fa\u8be5\u6570\u636e\u96c6\u7684\u52a0\u6743\u5e73\u5747\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u9996\u5148\u901a\u8fc7\u9664\u4ee5\u8ba1\u7b97\u5f52\u4e00\u5316\u6743\u91cd\u6bcf\u4e2a\u6743\u91cd\u9664\u4ee5\u6240\u6709\u6743\u91cd\u4e4b\u548c\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-17 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bbc85021f85f056a412eadd17dc4160d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{4+9+6+3}=0,18\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"159\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-59beb55972c66498c98541ae8c0af159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{9}{4+9+6+3}=0,41\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"158\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<div class=\"wp-block-columns is-layout-flex wp-container-20 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-14674547f258f18c769accef0fc19cad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{4+9+6+3}=0,27\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"159\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6920b49ca998ba629b2339049c936f0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3}{4+9+6+3}=0,14\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"159\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u73b0\u5728\u53ea\u9700\u5c06\u6bcf\u4e2a\u6570\u636e\u4e58\u4ee5\u5176\u5f52\u4e00\u5316\u6743\u91cd\uff0c\u7ed3\u679c\u5c31\u662f\u52a0\u6743\u5e73\u5747\u503c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9c372bf9b3176312c86c1f57024ebdd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_p}=24\\cdot 0,18+35\\cdot 0,41+17\\cdot 0,27+41\\cdot 0,14=28,91\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"433\" 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