20230110 afternoon
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parent
158fc7bbc8
commit
537c3f15aa
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@ -19,7 +19,7 @@
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"source": [
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"import os,re,json\n",
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"\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n",
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"problems = \"30552\"\n",
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"problems = \"30526,10916,10917\"\n",
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"\n",
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"def generate_number_set(string,dict):\n",
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" string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
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@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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@ -11,7 +11,7 @@
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"0"
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]
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},
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"execution_count": 27,
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -21,7 +21,7 @@
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"\n",
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"\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n",
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"keywords_dict_table = [\n",
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" {\"usages\":[r\"2023届高三02班\"],\"usages2\":[r\"202209\",r\"20221[012]\"],\"usages3\":[r\"0\\.[678][\\d]{2}\"],\"usages_not\":[r\"2023届高三02班[^\\n]*0\\.[0-59][\\d]{2}\"]}\n",
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" {\"content\":[\"花粉热\",r\"散点图分析[\\S\\s]*?m\",\"发动机\",\"彩色显像\"]}\n",
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"]\n",
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"\"\"\"---关键字设置完毕---\"\"\"\n",
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"# 示例： keywords_dict_table = [\n",
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@ -31,6 +31,13 @@
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"# {\"tags\":[\"第三单元\"],\"content\":[\"f\\(\",\"y=\",\"函数\"],\"usages\":[r\"0\\.9\",r\"0\\.8[3-9]\"],\"usages_not\":[r\"0\\.[0-7]\",r\"0\\.8[0-2]\"],\"usages1\":[\"2023届\"]},\n",
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"# {\"tags\":[\"第五单元\"],\"usages\":[r\"0\\.9\"],\"usages_not\":[r\"0\\.[0-7]\",r\"0\\.8[0-2]\"],\"usages1\":[\"2023届\"]}\n",
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"# ]\n",
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"# 实例3: \n",
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"# keywords_dict_table = [\n",
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"# {\"usages\":[r\"2023届高三02班\"],\"usages2\":[r\"202209\",r\"20221[012]\"],\"usages3\":[r\"0\\.[678][\\d]{2}\"],\"usages_not\":[r\"2023届高三02班[^\\n]*0\\.[0-59][\\d]{2}\"]}\n",
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" \n",
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"# ]\n",
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"\n",
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"\n",
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"\"\"\"---设置输出文件名---\"\"\"\n",
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"filename = \"文本文件/题号筛选.txt\"\n",
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"\"\"\"---文件名设置完毕---\"\"\"\n",
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@ -89,7 +96,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "mathdept",
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"display_name": "Python 3.9.15 ('pythontest')",
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"language": "python",
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"name": "python3"
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},
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@ -108,7 +115,7 @@
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
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"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
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}
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}
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},
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@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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@ -11,7 +11,7 @@
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"text": [
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"首个空闲id: 12760 , 直至 020000\n",
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"首个空闲id: 21441 , 直至 030000\n",
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"首个空闲id: 31158 , 直至 999999\n"
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"首个空闲id: 31201 , 直至 999999\n"
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]
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}
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],
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@ -2,20 +2,16 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"题号: 031158 , 字段: tags 中已添加数据: 第八单元\n",
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"题号: 031159 , 字段: tags 中已添加数据: 第八单元\n",
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"题号: 031160 , 字段: tags 中已添加数据: 第八单元\n",
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"题号: 031161 , 字段: tags 中已添加数据: 第八单元\n",
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"题号: 031162 , 字段: tags 中已添加数据: 第八单元\n",
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"题号: 031163 , 字段: tags 中已添加数据: 第八单元\n",
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"题号: 031164 , 字段: tags 中已添加数据: 第八单元\n"
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"题号: 031201 , 字段: tags 中已添加数据: 第九单元\n",
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"题号: 031202 , 字段: tags 中已添加数据: 第九单元\n",
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"题号: 031203 , 字段: tags 中已添加数据: 第九单元\n"
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]
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}
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],
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@ -1,22 +1,15 @@
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tags
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31158
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第八单元
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031201
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第九单元
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31159
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第八单元
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31160
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第八单元
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031202
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第九单元
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31161
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第八单元
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31162
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第八单元
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031203
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第九单元
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31163
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第八单元
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31164
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第八单元
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@ -1 +1 @@
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000023,000035,000060,000069,000087,000092,000141,000182,000230,000233,000312,000322,000360,000413,000474,000540,000655,000704,000749,000778,000795,000863,000884,000908,000939,001049,001050,001069,001072,001074,001231,001239,001242,001244,001262,001308,001309,001316,001324,001325,001328,001340,001351,001352,001353,001631,001643,001667,001668,001677,001726,001803,001853,001894,002004,002010,002017,002088,002273,002369,002372,002417,002424,002429,002434,002662,002750,002773,002775,002778,002785,002790,002791,002794,002838,002863,002871,002878,002884,002888,002893,002894,002895,002898,002905,002911,002914,002918,002966,002994,003138,003253,003281,003309,003312,003322,003337,003400,003421,003431,003567,003585,003648,003747,003777,003781,003828,003884,003959,003985,004008,004243,004409,004448,004463,004636,005016,005236,005239,005463,005508,005569,005621,005650,005720,005851,006468,006968,007911,007939,007941,007950,008392,008811,008912,008956,009200,009333,009349,009488,009490,009511,009517,009744,009858,009860,009887,009912,010060,010114,010178,010196,010453,010470,010523,010540,010631,010721,010947,011057,011078,011100,011993,012004,012015,030030,030096,030160,030202,030215,030253,030262,030280,030291,030322,030337,030398,030427,030438,030441,030462,030468,030478
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010015,031179,031182,031188,031196
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@ -2,21 +2,21 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"#修改起始id,出处,文件名\n",
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"starting_id = 31158\n",
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"starting_id = 31201\n",
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"origin = \"自拟题目\"\n",
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"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\prostat.tex\"\n",
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"editor = \"20230109\\t王伟叶\"\n",
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"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目8.tex\"\n",
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"editor = \"20230110\\t王伟叶\"\n",
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"indexed = False\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -2,16 +2,16 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"开始编译教师版本pdf文件: 临时文件/题库_教师用_20230108.tex\n",
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"开始编译教师版本pdf文件: 临时文件/概率统计测验预选_教师用_20230110.tex\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/题库_学生用_20230108.tex\n",
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"开始编译学生版本pdf文件: 临时文件/概率统计测验预选_学生用_20230110.tex\n",
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"0\n"
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]
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}
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"\"\"\"---设置题目列表---\"\"\"\n",
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"#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
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"problems = r\"\"\"\n",
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"031158,031159,031160,031161,031162,031163,031164,031201,031202,031203,031179,031188,031196\n",
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"\n",
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"\"\"\"\n",
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"\"\"\"---设置题目列表结束---\"\"\"\n",
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"\n",
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"\"\"\"---设置文件名---\"\"\"\n",
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"#目录和文件的分隔务必用/\n",
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"filename = \"临时文件/题库\"\n",
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"filename = \"临时文件/概率统计测验预选\"\n",
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"\"\"\"---设置文件名结束---\"\"\"\n",
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"\n",
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"\n",
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],
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"metadata": {
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"kernelspec": {
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"display_name": "mathdept",
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"display_name": "Python 3.8.15 ('mathdept')",
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"language": "python",
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"name": "python3"
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},
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@ -187,12 +188,12 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.15"
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"version": "3.8.15"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
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"hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2"
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}
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}
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},
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@ -1,71 +0,0 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [],
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"source": [
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"import os,re,json\n",
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"with open(r\"../题库0.3/problems.json\",\"r\",encoding = \"utf8\") as f:\n",
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" jsondata = f.read()\n",
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"pro_dict = json.loads(jsondata)\n",
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"id = input(\"输入题目id:\")\n",
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"id = id.zfill(6)\n",
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"content = pro_dict[id][\"content\"]\n",
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"\n",
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"with open(r\"模板文件/题目编辑.tex\",\"r\",encoding = \"utf8\") as f:\n",
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" template_data = f.read()\n",
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"\n",
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"output_data = template_data.replace(\"待替换\",content)\n",
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"with open(r\"临时文件/toedit.tex\",\"w\",encoding = \"utf8\") as f:\n",
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" f.write(output_data)\n",
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"\n",
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"os.system(\"code 临时文件/toedit.tex\")\n",
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"cont = input(\"继续请按回车\")\n",
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"with open(r\"临时文件/toedit.tex\",\"r\",encoding = \"utf8\") as f:\n",
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" edited_data = f.read()\n",
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"new_content = re.findall(r\"\\\\begin{document}([\\s\\S]*?)\\\\end{document}\",edited_data)[0].strip()\n",
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"pro_dict[id][\"content\"] = new_content\n",
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"\n",
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"jsondata_new=json.dumps(pro_dict,indent = 4,ensure_ascii=False)\n",
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"with open(r\"../题库0.3/problems.json\",\"w\",encoding = \"utf8\") as f:\n",
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" f.write(jsondata_new)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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},
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"010916": {
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"id": "010916",
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"content": "为了解大学校园附近餐馆的月营业收入(单位: 千元)和该店周围的大学生人数(单位: 千人)之间的关系, 抽取了$10$所大学附近餐馆的有关数据, 如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n学生人数$x$/千人 & $2$ & $6$ & $8$ & $8$ & $12$ & $16$ & $20$ & $20$ & $22$ & $26$ \\\\ \\hline\n月营业收入$y$/千元 & $58$ & $105$ & $88$ & $118$ & $117$ & $137$ & $157$ & $169$ & $149$ & $202$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 根据以上数据, 建立月营业收入$y$与该店周围的大学生人数$x$的回归方程;\n(2) 已知某餐馆周围的大学生人数为$10000$人, 试对该店月营业收入作出预测.",
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"content": "为了解大学校园附近餐馆的月营业收入(单位: 千元)和该店周围的大学生人数(单位: 千人)之间的关系, 抽取了$10$所大学附近餐馆的有关数据, 如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n学生人数$x$/千人 & $2$ & $6$ & $8$ & $8$ & $12$ & $16$ & $20$ & $20$ & $22$ & $26$ \\\\ \\hline\n月营业收入$y$/千元 & $58$ & $105$ & $88$ & $118$ & $117$ & $137$ & $157$ & $169$ & $149$ & $202$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 根据以上数据, 建立月营业收入$y$与该店周围的大学生人数$x$的回归方程;\\\\\n(2) 已知某餐馆周围的大学生人数为$10000$人, 试对该店月营业收入作出预测.",
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"objs": [],
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"tags": [
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"第九单元"
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},
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"010917": {
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"id": "010917",
|
||||
"content": "某运动生理学家在一项健身活动中选择了$19$位参与者, 以他们的皮下脂肪厚度来估计身体的脂肪含量, 其中脂肪含量以占体重(单位: $\\text{kg}$)的百分比表示. 得到脂肪含量和体重的数据如下表所示. 其中, 参与者$1-10$为男性, $11-19$为女性.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ & 参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ \\\\ \\hline\n$1$ & $89$ & $28$ & $2$ & $88$ & $27$ \\\\ \\hline\n$3$ & $66$ & $24$ & $4$ & $59$ & $23$ \\\\ \\hline\n$5$ & $93$ & $29$ & $6$ & $73$ & $25$ \\\\ \\hline\n$7$ & $82$ & $29$ & $8$ & $77$ & $25$ \\\\ \\hline\n$9$ & $100$ & $30$ & $10$ & $67$ & $23$ \\\\ \\hline\n$11$ & $57$ & $29$ & $12$ & $68$ & $32$ \\\\ \\hline\n$13$ & $69$ & $35$ & $14$ & $59$ & $31$ \\\\ \\hline\n$15$ & $62$ & $29$ & $16$ & $59$ & $26$ \\\\ \\hline\n$17$ & $56$ & $28$ & $18$ & $66$ & $33$ \\\\ \\hline\n$19$ & $72$ & $33$ & / & / & / \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 分别建立男性和女性体重与脂肪含量的回归方程;\\\\\n(2) 男性和女性合在一起所构成的样本的回归方程为$y=0.021x+26.88$, 其斜率与\n(1)中所计算的斜率有差异吗? 能否对这种差异进行解释?\n(3) 计算下列情况下体重与脂肪含量的相关系数: \\textcircled{1} 男性; \\textcircled{2} 女性; \\textcircled{3} 男女合计. 这些值与(2)中所反映的信息是否一致?",
|
||||
"content": "某运动生理学家在一项健身活动中选择了$19$位参与者, 以他们的皮下脂肪厚度来估计身体的脂肪含量, 其中脂肪含量以占体重(单位: $\\text{kg}$)的百分比表示. 得到脂肪含量和体重的数据如下表所示. 其中, 参与者$1-10$为男性, $11-19$为女性.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ & 参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ \\\\ \\hline\n$1$ & $89$ & $28$ & $2$ & $88$ & $27$ \\\\ \\hline\n$3$ & $66$ & $24$ & $4$ & $59$ & $23$ \\\\ \\hline\n$5$ & $93$ & $29$ & $6$ & $73$ & $25$ \\\\ \\hline\n$7$ & $82$ & $29$ & $8$ & $77$ & $25$ \\\\ \\hline\n$9$ & $100$ & $30$ & $10$ & $67$ & $23$ \\\\ \\hline\n$11$ & $57$ & $29$ & $12$ & $68$ & $32$ \\\\ \\hline\n$13$ & $69$ & $35$ & $14$ & $59$ & $31$ \\\\ \\hline\n$15$ & $62$ & $29$ & $16$ & $59$ & $26$ \\\\ \\hline\n$17$ & $56$ & $28$ & $18$ & $66$ & $33$ \\\\ \\hline\n$19$ & $72$ & $33$ & / & / & / \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 分别建立男性和女性体重与脂肪含量的回归方程;\\\\\n(2) 男性和女性合在一起所构成的样本的回归方程为$y=0.021x+26.88$, 其斜率与(1)中所计算的斜率有差异吗? 能否对这种差异进行解释?\\\\\n(3) 计算下列情况下体重与脂肪含量的相关系数: \\textcircled{1} 男性; \\textcircled{2} 女性; \\textcircled{3} 男女合计. 这些值与(2)中所反映的信息是否一致?",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
|
|
@ -360478,7 +360478,7 @@
|
|||
},
|
||||
"030526": {
|
||||
"id": "030526",
|
||||
"content": "对下面两组数据\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline $x$ & 1 & 2 & 3 & 4 & 10 & 10 \\\\\n\\hline $y$ & 1 & 3 & 3 & 5 & 1 & 11 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n计算相关系数, 大概在$0.5$左右. 通过观察散点图, 发现对这两组大部分数据来说, 变量$x$与$y$有很强的线性相关关系, 是什么因素导致相关系数只存$0.5$左右?",
|
||||
"content": "对下面两组数据\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline $x$ & 1 & 2 & 3 & 4 & 10 & 10 \\\\\n\\hline $y$ & 1 & 3 & 3 & 5 & 1 & 11 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n计算相关系数, 大概在$0.5$左右. 通过观察散点图, 发现对这两组大部分数据来说, 变量$x$与$y$有很强的线性相关关系, 是什么因素导致相关系数只有$0.5$左右?",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
|
|
@ -373895,5 +373895,824 @@
|
|||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031165": {
|
||||
"id": "031165",
|
||||
"content": "试举几例具有相关关系的变量.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031166": {
|
||||
"id": "031166",
|
||||
"content": "判断下列两个变量之间是否具有相关关系:\\\\\n(1) 家庭月用电量与月平均气温;\\\\\n(2) 一天中的最高气温与最低气温;\\\\\n(3) 某企业生产的一种商品的销量与其广告费用;\\\\\n(4) 谷物的价格与牛肉的价格;\\\\\n(5) 在公式$L W=12$中的$L$与$W$.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031167": {
|
||||
"id": "031167",
|
||||
"content": "与同学一起测量脚长与身高, 并用适当方式探究它们之间是否具有相关关系.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031168": {
|
||||
"id": "031168",
|
||||
"content": "下列几对变量, 哪些有明显的正相关、明显的负相关、接近于$0$的相关系数?\n(1) 广告费与销售额;\\\\\n(2) 施肥量与粮食产量;\\\\\n(3) 汽车车速与司机的年龄;\\\\\n(4) 人的体重与身高.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031169": {
|
||||
"id": "031169",
|
||||
"content": "充气不足或过于膨胀会增加轮胎磨损, 并减少行驶里程. 对一种新型轮胎在不同压力下的行驶里程进行测试, 数据如下表:\n\\begin{center}\n\\begin{tabular}{|c|c||c|c|}\n\\hline 压力$x /(\\text{lb} / \\text{in}^2)$& 里程$y / 10^3 \\text{~km}$& 压力$x /(\\text{lb} / \\text{in}^2)$& 里程$y / 10^3 \\text{~km}$\\\\\n\\hline 30 &$29.5$& 33 &$37.6$\\\\\n\\hline 30 &$30.2$& 34 &$37.7$\\\\\n\\hline 31 &$32.1$& 34 &$36.1$\\\\\n\\hline 31 &$34.5$& 35 &$33.6$\\\\\n\\hline 32 &$36.3$& 35 &$34.2$\\\\\n\\hline 32 &$35.0$& 36 &$26.8$\\\\\n\\hline 33 &$38.2$& 36 &$27.4$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求出相关系数;\\\\\n(3) 将散点图与相关系数进行比照分析, 并作出适当解释.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031170": {
|
||||
"id": "031170",
|
||||
"content": "统计表明, 世界各国人均拥有电视机的数量与人均寿命有着较高的正相关的相关系数. 这是否说明: 国家的人均寿命与人均拥有电视机的多少有关? 运送一大批电视机到某人均寿命低的国家是否能延长该国人的寿命?",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031171": {
|
||||
"id": "031171",
|
||||
"content": "为了探讨学生的物理成绩$y$与数学成绩$x$之间的关系, 从某批学生中随机抽取$10$名学生的成绩$(x_i, y_i)$($i=1,2, \\cdots, 10)$, 并已计算出$\\displaystyle\\sum_{i=1}^{10} x_i=758$, $\\displaystyle\\sum_{i=1}^{10} x_i^2=58732$, $\\displaystyle\\sum_{i=1}^{10} y_i=774$, $\\displaystyle\\sum_{i=1}^{10} x_i y_i=59686$. 试求:\\\\\n(1) 物理成绩$y$关于数学成绩$x$的线性回归方程;\\\\\n(2) 当数学成绩为$92$分时, 物理成绩$y$的线性回归估计值.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031172": {
|
||||
"id": "031172",
|
||||
"content": "某种产品的广告费支出$x$与销售额$y$之间有如下对应数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline$x / 10^6$元 & 2 & 4 & 5 & 6 & 8 \\\\\n\\hline$y / 10^6$元 & 30 & 40 & 60 & 50 & 70 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求出线性回归方程.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031173": {
|
||||
"id": "031173",
|
||||
"content": "每立方米混凝土的水泥用量$x$(单位:$\\text{kg}$) 与$28$天后混凝土的抗压强度$y$(单位:$\\text{kg} / \\text{cm}^2)$之间有如下对应数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline$x / \\text{kg}$& 150 & 160 & 170 & 180 & 190 & 200 \\\\\n\\hline$y /(\\text{kg} / \\text{cm}^2)$&$56.9$&$58.3$&$61.1$&$64.6$&$68.1$&$71.3$\\\\\n\\hline \\hline$x / \\text{kg}$& 210 & 220 & 230 & 240 & 250 & 260 \\\\\n\\hline$y /(\\text{kg} / \\text{cm}^2)$&$74.1$&$77.4$&$80.2$&$82.6$&$86.4$&$89.7$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求出线性回归方程.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031174": {
|
||||
"id": "031174",
|
||||
"content": "某小吃店的日盈利$y$(单位: 百元) 与当天平均气温$x$(单位:${ }^{\\circ} \\text{C}$) 之间有如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline$x /{}^{\\circ} \\text{C}$&$-2$&$-1$& 0 & 1 & 2 \\\\\n\\hline$y /$百元 & 5 & 4 & 2 & 2 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n甲、乙、丙$3$位同学对上述数据进行了分析, 发现$y$与$x$之间具有线性相关关系, 他们通过计算分别得到$3$个线性回归方程: \\textcircled{1} $\\hat{y}=-x+2.8$;\n\\textcircled{2} $\\hat{y}=-x+3$; \\textcircled{3} $\\hat{y}=-1.2 x+2.6$. 其中正确的是\\blank{50}. (填序号)",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031175": {
|
||||
"id": "031175",
|
||||
"content": "二手车车龄与其价格之间是正相关, 还是负相关? 为什么? (古董车除外)",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031176": {
|
||||
"id": "031176",
|
||||
"content": "车重与其每千米耗油量之间的相关系数是正还是负? 为什么?",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031177": {
|
||||
"id": "031177",
|
||||
"content": "某工厂在某年里每月产品的总成本$y$(单位: 万元) 与月产量$x$(单位: 万件)之间有如下一组数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline$x /$万件 &$1.08$&$1.12$&$1.19$&$1.28$&$1.36$&$1.48$&$1.59$&$1.68$&$1.80$&$1.87$&$1.98$&$2.07$\\\\\n\\hline$y /$万元 &$2.25$&$2.37$&$2.40$&$2.55$&$2.64$&$2.75$&$2.92$&$3.03$&$3.14$&$3.26$&$3.36$&$3.50$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求相关系数;\\\\\n(3) 求线性回归方程.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"031178": {
|
||||
"id": "031178",
|
||||
"content": "某研究所研究耕种深度$x$(单位: $\\text{cm}$) 与水稻每公顷产量$y$(单位: $\\text{t}$)的关系, 所得数据资料如下表, 试求每公顷水稻产量与耕种深度的相关系数和线性回归方程.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 耕种深度$x / \\text{cm}$& 8 & 10 & 12 & 14 & 16 & 18 \\\\\n\\hline 每公顷产量$y / \\text{t}$&$6.0$&$7.5$&$7.8$&$9.2$&$10.8$&$12.0$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"031179": {
|
||||
"id": "031179",
|
||||
"content": "为了解发动机的动力$x$(单位: $\\text{PH}$) 与排气温度$y$(单位:${ }^{\\circ} \\text{C}$) 之间的关系, 某部门进行相关试验, 得到如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c||c|c|}\n\\hline$x / \\text{PH}$&$y /{ }^{\\circ} \\text{C}$&$x / \\text{PH}$&$y /{ }^{\\circ} \\text{C}$\\\\\n\\hline 4300 & 960 & 4010 & 907 \\\\\n\\hline 4650 & 900 & 3810 & 843 \\\\\n\\hline 3200 & 807 & 4500 & 927 \\\\\n\\hline 3150 & 755 & 3008 & 688 \\\\\n\\hline 4950 & 993 & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 求相关系数;\\\\\n(2) 求线性回归方程;\\\\\n(3) 估计当$x=3100$时对应$y$的值.",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"031180": {
|
||||
"id": "031180",
|
||||
"content": "为测定湖中水的清洁程度, 将一有刻度线的玻璃片放人水中直至完全看不见刻度线, 此时它与水表面的距离称为``Secchi 深度''. 为了测量湖水被水藻污染的程度, 科学家要确定水中叶绿素的总浓度. 在某一湖中, 从四月至九月每周四中午都测量 Secchi 深度和叶绿素的总浓度. 这两个变量间是正相关还是负相关? 简要说明理由.",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
"edit": [
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
},
|
||||
"031181": {
|
||||
"id": "031181",
|
||||
"content": "对下面这组数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline$x$& 1 & 2 & 3 & 4 & 10 & 10 \\\\\n\\hline$y$& 1 & 3 & 3 & 5 & 1 & 11 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n计算相关系数, 大概在$0.5$左右. 对这组数据大部分点来说, $x$与$y$之间有很强的线性相关关系. 是什么因素导致相关系数只有$0.5$左右?",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
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|
||||
},
|
||||
"031182": {
|
||||
"id": "031182",
|
||||
"content": "在彩色显像中, 根据以往的经验, 形成染料的光学密度$y$与析出银的光学密度$x$之间存在关系式$y=a \\mathrm{e}^{-\\frac{b}{x}}$($b>0$). 现对$y$与$x$同时做$10$次观测, 获得$10$对数据如下表, 试根据表中数据, 求出$a$与$b$的估计值.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline 编号 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\n\\hline$x$&$0.05$&$0.06$&$0.07$&$0.10$&$0.14$&$0.20$&$0.25$&$0.31$&$0.38$&$0.43$\\\\\n\\hline$y$&$0.10$&$0.14$&$0.23$&$0.37$&$0.59$&$0.79$&$1.00$&$1.12$&$1.19$&$1.25$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
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|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
},
|
||||
"031183": {
|
||||
"id": "031183",
|
||||
"content": "下表是研究某品种小麦的施肥量与小麦产量之间关系时所获得的数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\n\\hline 亩施肥量$x / \\text{kg}$& 0 &$2.5$& 5 &$7.5$& 10 &$12.5$& 15 &$17.5$& 20 \\\\\n\\hline 亩产量$y / \\text{kg}$& 76 & 150 &$202.5$&$273.5$&$326.5$& 396 & 436 & 420 & 390 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n可以求得$y$与$x$的线性相关系数约为$0.9375, y$与$x$具有很强的线性相关关系. 不过, 从下面的散点图可以看出, 当施肥量超过$15 \\text{kg}$时, 小麦产量在下降, 这与经验判断一致 : 过量施肥会降低农作物产量.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {1/100,2/200,3/300,4/400,5/500}\n{\\draw [dashed,gray] (5,\\i) -- (0,\\i) node [left] {$\\j$};};\n\\foreach \\i/\\j in {1/5,2/10,3/15,4/20,5/25}\n{\\draw [dashed,gray] (\\i,5) -- (\\i,0) node [below] {$\\j$};};\n\\foreach \\i/\\j in {0/0.76,0.5/1.5,1/2.025,1.5/2.735,2/3.265,2.5/3.96,3/4.36,3.5/4.2,4/3.9}\n{\\filldraw (\\i,\\j) circle (0.03);};\n\\end{tikzpicture}\n\\end{center}\n(1) 施肥量在怎样的范围内, 线性回归模型的拟合效果比较好?\\\\\n(2) 感兴趣的同学可以查阅相关资料, 尝试用二次函数模型进行拟合, 并与线性回归模型比较, 看哪种模型更加符合本题中的现实问题.",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
},
|
||||
"031184": {
|
||||
"id": "031184",
|
||||
"content": "某桑场为了解职工发生皮炎是否与采桑有关, 对其工作人员进行了一次调查, 结果如下表. 问: 发生皮炎是否与采桑有关?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 采桑 & 不采桑 & 合计 \\\\\n\\hline 患皮炎 & 18 & 12 & 30 \\\\\n\\hline 末患皮炎 & 4 & 78 & 82 \\\\\n\\hline 合计 & 22 & 90 & 112 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
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|
||||
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|
||||
"第九单元"
|
||||
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|
||||
"genre": "",
|
||||
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|
||||
"solution": "",
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"031185": {
|
||||
"id": "031185",
|
||||
"content": "为了鉴定新疫苗的效力, 将$60$只豚鼠随机地分为两组, 在其中一组接种疫苗后, 两组都注射了病源菌, 其结果列于下表. 问: 能否有$90 \\%$的把握认为新疫苗有效?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 发病 & 没发病 & 合计 \\\\\n\\hline 接种 & 3 & 27 & 30 \\\\\n\\hline 没接种 & 17 & 13 & 30 \\\\\n\\hline 合计 & 20 & 40 & 60 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
"20230110\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031186": {
|
||||
"id": "031186",
|
||||
"content": "某医疗研究机构为了解打鼾与患心脏病的关系, 进行了一次抽样调查, 得到如下数据. 问: 打鼾与患心脏病是否有关?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 患心脏病 & 未患心脏病 & 合计 \\\\\n\\hline 每一晚都打鼾 & 30 & 224 & 254 \\\\\n\\hline 不打鼾 & 24 & 1355 & 1379 \\\\\n\\hline 合计 & 54 & 1579 & 1633 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
},
|
||||
"031187": {
|
||||
"id": "031187",
|
||||
"content": "为了解小麦种子是否灭菌与小麦发生黑穗病的关系, 经试验观察, 得到如下数据. 根据这组数据, 能否认为发生黑穗病与种子是否灭菌有关?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 种子灭菌 & 种子末灭菌 & 合计 \\\\\n\\hline 有黑穗病 & 26 & 184 & 210 \\\\\n\\hline 无黑穗病 & 50 & 200 & 250 \\\\\n\\hline 合计 & 76 & 384 & 460 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
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|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
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|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
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|
||||
},
|
||||
"031188": {
|
||||
"id": "031188",
|
||||
"content": "下表所示的是关于$11$岁儿童患花粉热与湿疹情况的调查数据. 若按$95 \\%$的可靠性的要求, 则对$11$岁儿童能否做出花粉热与湿疹有关的结论?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 患花粉热 & 末患花粉热 & 合计 \\\\\n\\hline 患湿疹 & 141 & 420 & 561 \\\\\n\\hline 末患湿疹 & 928 & 13525 & 14453 \\\\\n\\hline 合计 & 1069 & 13945 & 15014 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
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|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031189": {
|
||||
"id": "031189",
|
||||
"content": "一个随机抽取的样本包括$110$位女士和$90$位男士, 女士中约有$9 \\%$是左利手, 男士中约有$11 \\%$是左利手. 基于这些数据, 你认为在样本所代表的总体中, 左利手与性别有关吗? 为什么?",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031190": {
|
||||
"id": "031190",
|
||||
"content": "``使用动物做医学实验是正确的, 这样做能够挽救人的生命''. 某机构调查了 1152 位成年人对这种说法的态度, 以下是调查对象回答情况的列联表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline 回答情况 & 男性 & 女性 \\\\\n\\hline 同意 & 346 & 306 \\\\\n\\hline 不置可否 & 87 & 139 \\\\\n\\hline 不同意 & 83 & 191 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 用适当的方式描述男性与女性对该问题态度的差异 (比例、图或文字均可).\\\\\n(2) 你能用独立性检验的思想方法研究``男性与女性对该问题态度的差异''吗? 如果希望解决这个问题, 请在独立研究的基础上, 查阅相关资料, 给出你的结论.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
"20230110\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031191": {
|
||||
"id": "031191",
|
||||
"content": "如果$x, y$之间的一组数据如下表所示, 那么回归直线必过的一个定点坐标是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x$& 0 & 1 & 2 & 3 \\\\\n\\hline$y$& 1 & 2 & 5 & 8 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
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|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031192": {
|
||||
"id": "031192",
|
||||
"content": "下表中的数据是关于青年观众的性别与是否喜欢戏剧的调查数据, 那么女性青年观众喜欢戏剧的频率与男性青年观众喜欢戏剧的频率的比值是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 不喜欢戏剧 & 喜欢戏剧 & 合计 \\\\\n\\hline 男性青年观众 & 40 & 10 & 50 \\\\\n\\hline 女性青年观众 & 40 & 60 & 100 \\\\\n\\hline 合计 & 80 & 70 & 150 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
"20230110\t王伟叶"
|
||||
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|
||||
"same": [],
|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031193": {
|
||||
"id": "031193",
|
||||
"content": "某单位通过对数据的统计与分析得知, 日用电量$y$(单位:$\\text{kW} \\cdot \\text{h}$) 与当天平均气温$x$(单位:${ }^{\\circ} \\text{C}$) 之间线性相关, 且线性回归方程为$\\hat{y}=-2 x+60$. 据此可以预测, 当平均气温为$-4^{\\circ} \\text{C}$时, 日用电量的度数约为\\blank{50}.",
|
||||
"objs": [],
|
||||
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|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
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|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031194": {
|
||||
"id": "031194",
|
||||
"content": "已知变量$y$与$x$线性相关, 若$\\overline {x}=5$, $\\overline {y}=50$, 且$y$与$x$的线性回归直线的斜率为$6.5$, 则线性回归方程是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
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|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031195": {
|
||||
"id": "031195",
|
||||
"content": "为了考察某种药物预防疾病的效果, 进行动物试验后得到如下数据. 经过计算得$\\chi^2 \\approx 6.979$, 根据$\\chi^2$临界值表, 可以认为该种药物对预防疾病有效果的把握为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 患病 & 末患病 & 合计 \\\\\n\\hline 服用药 & 10 & 46 & 56 \\\\\n\\hline 末服用药 & 22 & 32 & 54 \\\\\n\\hline 合计 & 32 & 78 & 110 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031196": {
|
||||
"id": "031196",
|
||||
"content": "已知$x$, $y$的取值如下表所示, 从散点图分析可知$y$与$x$线性相关, 如果线性回归方程为$\\hat{y}=0.95 x+2.6$, 那么表格中的数据$m$的值为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x$& 0 & 1 & 3 & 4 \\\\\n\\hline$y$&$2.2$&$4.3$&$4.8$&$m$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031197": {
|
||||
"id": "031197",
|
||||
"content": "某中学对$50$名学生的学习兴趣和主动预习情况进行了长期的调查, 得到的统计数据如下表所示. 试运用独立性检验的思想方法判断: 是否有$99 \\%$以上的把握认为, 学生的学习兴趣与主动预习有关.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 主动预习 & 不太主动预习 & 合计 \\\\\n\\hline 学习兴趣高 & 18 & 7 & 25 \\\\\n\\hline 学习兴趣一般 & 6 & 19 & 25 \\\\\n\\hline 合计 & 24 & 26 & 50 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031198": {
|
||||
"id": "031198",
|
||||
"content": "为了对某班考试成绩进行分析, 现从全班同学中随机抽取$8$位, 他们的数学、物理成绩如下表所示. 根据表中数据分析: 变量$x$与$y$是否具有线性相关关系.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline 学生编号 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\\\n\\hline 数学分数$x$& 60 & 65 & 70 & 75 & 80 & 85 & 90 & 95 \\\\\n\\hline 物理分数$y$& 72 & 77 & 80 & 85 & 88 & 90 & 93 & 95 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031199": {
|
||||
"id": "031199",
|
||||
"content": "某兴趣小组欲研究昼夜温差大小与患感冒人数多少之间的关系, 他们分别到气象局与某医院抄录了$1-6$月份每月$10$日的昼夜温差情况与因患感冒而就诊的人数, 得到如下资料:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 日期 & 1 月 10 日 & 2 月 10 日 & 3 月 10 日 & 4 月 10 日 & 5 月 10 日 & 6 月 10 日 \\\\\n\\hline 昼夜温差$x /{ }^{\\circ} \\text{C}$& 10 & 11 & 13 & 12 & 8 & 6 \\\\\n\\hline 就诊人数$y$& 22 & 25 & 29 & 26 & 16 & 12 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n该兴趣小组确定的研究方案是: 先从这$6$组数据中选取$2$组, 用剩下的$4$组数据求线性回归方程, 再用被选取的$2$组数据进行检验.\\\\\n(1) 若选取的是$1$月与$6$月的两组数据, 请根据$2-5$月份的数据, 求出$y$关于$x$的线性回归方程$\\hat{y}=\\hat{b} x+\\hat{a}$;\\\\\n(2) 若由线性回归方程得到的估计数据与所选出的检验数据的误差均不超过$2$人, 则认为得到的线性回归方程是理想的. 问: 该小组所得线性回归方程是否理想?",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031200": {
|
||||
"id": "031200",
|
||||
"content": "下表提供了某厂进行技术改造后生产产品过程中记录的产量$x$(单位:$\\text{t})$与相应的生产能耗$y$(单位:$\\text{t}$标准煤)的几组对应数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x / \\text{t}$& 3 & 4 & 5 & 6 \\\\\n\\hline$y / \\text{t}$标准煤 &$2.5$& 3 & 4 &$4.5$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 请画出表中数据的散点图, 并求出$y$关于$x$的线性回归方程$\\hat{y}=\\hat{b} x+\\hat{a}$;\\\\\n(2) 已知该厂技术改造前$100 \\text{t}$产品的生产能耗为$90 \\text{t}$标准煤, 试根据(1)中求出的线性回归方程, 预测该厂技术改造后$100 \\text{t}$产品的生产能耗比技术改造前降低了多少$\\text{t}$标准煤.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "苏教版教材习题",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031201": {
|
||||
"id": "031201",
|
||||
"content": "设$x_i$($i=1,2,3,\\cdots,100$)和$y_i$($i=1,2,\\cdots,100$)是两组两两不同的数据, 以$x_i$为解释变量, $y_i$为反应变量计算可得相关系数$r_1$, 拟合直线的斜率为$\\hat{a}_1$; 以$y_i$为解释变量, $x_i$为反应变量计算可得相关系数$r_2$, 拟合直线的斜率为$\\hat{a}_2$. 则关于$r_1,r_2,\\hat{a}_1,\\hat{a}_2$的以下两个结论: \\textcircled{1} $r_1$一定与$r_2$相等; \\textcircled {2} $\\hat{a}_1\\cdot \\hat{a}_2$一定等于$1$, 它们的真假情况为\\bracket{20}.\n\\fourch{\\textcircled{1}和\\textcircled{2}都为真}{\\textcircled{1}和\\textcircled{2}都为假}{\\textcircled{1}为真, \\textcircled{2}为假}{\\textcircled{1}为假, \\textcircled{2}为真}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031202": {
|
||||
"id": "031202",
|
||||
"content": "若一组成对数据$x_i$($i=1,2,\\cdots,n$)与$y_i$($i=1,2,\\cdots,n$)的相关系数为$0.4$, 则$x_i$($i=1,2,\\cdots,n$)与$-y_i+0.1$($i=1,2,\\cdots,n$)的相关系数为\\bracket{20}.\n\\fourch{$0.5$}{$0.4$}{$-0.3$}{$-0.4$}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"031203": {
|
||||
"id": "031203",
|
||||
"content": "为了判断甲、乙两种药物对某疾病的疗效是否有显著差异, 在两个地区分别进行了采样, 所得的列联表如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nA地区 & 治愈 & 未治愈 & 合计 \\\\ \\hline\n药物甲 & $a$ & $b$ & $a+b$ \\\\ \\hline\n药物乙 & $c$ & $d$ & $c+d$ \\\\ \\hline\n合计 & $a+c$ & $b+d$ & $a+b+c+d$\\\\ \\hline\n\\end{tabular}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nB地区 & 治愈 & 未治愈 & 合计 \\\\ \\hline\n药物甲 & $3a$ & $3b$ & $3a+3b$ \\\\ \\hline\n药物乙 & $3c$ & $3d$ & $3c+3d$ \\\\ \\hline\n合计 & $3a+3c$ & $3b+3d$ & $3a+3b+3c+3d$\\\\ \\hline\n\\end{tabular}\n\\end{center}\n巧合的是, B地区每一类型的人数恰好是A地区的$3$倍. 规定显著性水平为$p=0.05$, 则以下两个论断:\\\\\n\\textcircled{1} 如果A地区的数据支持两种药物的疗效有显著差异, 那么B地区的数据一定支持两种药物的疗效有显著差异;\\\\\n\\textcircled{2} 如果A地区的数据支持两种药物的疗效无显著差异, 那么B地区的数据一定支持两种药物的疗效无显著差异. 正确与否的情况为\\bracket{20}.\n\\fourch{\\textcircled{1}和\\textcircled{2}都正确}{\\textcircled{1}和\\textcircled{2}都错误}{\\textcircled{1}正确, \\textcircled{2}错误}{\\textcircled{1}错误, \\textcircled{2}正确}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第九单元"
|
||||
],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20230110\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
}
|
||||
}
|
||||
Reference in New Issue