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收录高二寒假作业4

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工具v2/文本文件/新题收录列表.txt
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@ -328,3 +328,6 @@
20240204-121033 高二寒假作业3(9-18题)
003570,024450:024457
20240204-131518 高二寒假作业4
024458:024475

449
题库0.3/Problems.json
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@ -21138,7 +21138,9 @@
"20220624\t朱敏慧, 王伟叶"
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@ -662509,6 +662534,390 @@
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"024458": {
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"content": "将一个各面均涂有油漆的正方体, 锯成 1000 个同样大小的小正方体, 若将这些小正方体均匀地搅拌在一起, 然后从中任取一个小正方体, 则恰好是一个具有两面漆的正方体的概率是\\bracket{20}.\n\\fourch{$\\dfrac{12}{125}$}{$\\dfrac{3}{25}$}{$\\dfrac{1}{10}$}{$\\dfrac{1}{12}$}",
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"024459": {
"id": "024459",
"content": "若 $x_1$、$x_2$、$x_3$、$\\cdots$、$x_{314}$ 的标准差为 $2$, 那么 $3(x_1+5)$、$3(x_2+5)$、$\\cdots$、$3(x_{314}+5)$ 的标准差为\\bracket{20}.\n\\fourch{$18$}{$14$}{$6$}{$3$}",
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"024460": {
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"content": "投掷一枚骰子, 下列事件中是对立事件的是\\bracket{20}.\n\\twoch{向上的点数是 1 与向上的点数是 5}{向上的点数小于 3 与向上的点数大于 3}{向上的点数是奇数与向上的点数是偶数}{向上的点数大于 3 与向上的点数小于 5}",
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"024461": {
"id": "024461",
"content": "高三年级有11名同学参加男子百米竞赛, 预赛成绩各不相同, 要取前 6 名参加决赛, 小明同学已经知道了自己的成绩, 为了判断自己是否能进入决赛, 他还需要知道11名同学成绩的\\bracket{20}.\n\\fourch{平均数}{众数}{中位数}{方差}",
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"content": "把 $10$ 本书随意地放在书架上, 则其中指定的 $3$ 本书放在一起的概率为\\blank{50}.",
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"content": "将一颗质地均匀的骰子(一种各个面上分别标有 $1,2,3,4,5,6$ 个点的正方体玩具)先后抛掷 $2$ 次, 则出现向上的点数之和小于 $10$ 的概率是\\blank{50}.",
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"content": "某甲、乙两人练习跳绳, 每人练习 $10$ 组, 每组不间断跳绳计数的茎叶图如图, 则下面结论中所有正确的序号是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{cccccc|c|ccccc}\n\\multicolumn{6}{c|}{甲} & &\\multicolumn{5}{c}{乙}\\\\\n\\hline\n&&&&&8&0&9\\\\\n&&&&3&2&1&1&3&4&8&9\\\\\n7&6&5&4&2&0&2&0&1&1&3\\\\\n&&&&&7&3\n\\end{tabular}\n\\end{center}\n\\textcircled{1} 甲比乙的极差大;\\\\\n\\textcircled{2} 乙的中位数是 $18$;\\\\\n\\textcircled{3} 甲的平均数比乙的大;\\\\\n\\textcircled{4} 乙的众数是 $21$.",
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"content": "已知一个样本 $1,3,4,a,7$, 它的平均值是 $4$, 则这个样本的方差是\\blank{50}.",
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"024466": {
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"content": "袋中装有标号为 $1,2,3,4$ 的四只球, 四人从中各取一只球, 其中甲不取 $1$ 号球, 乙不取 $2$ 号球, 丙不取 $3$ 号球, 丁不取 $4$ 号球的概率为\\blank{50}.",
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"024467": {
"id": "024467",
"content": "甲、乙、丙三人 100 米跑的成绩 (互不影响) 合格的概率分别为 $\\dfrac{2}{5}$、$\\dfrac{3}{4}$、$\\dfrac{1}{3}$, 若对这三人进行一次 100 米跑检测, 则三人都合格的概率是\\blank{50}(结果用最简分数表示).",
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"024468": {
"id": "024468",
"content": "若投掷 3 枚硬币, 则恰有二枚正面朝上的概率为\\blank{50}.",
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"024469": {
"id": "024469",
"content": "随机投掷一枚均匀的硬币两次, 则两次都正面朝上的概率为\\blank{50}.",
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"024470": {
"id": "024470",
"content": "某骰子为正方体, 六面分别印上 $1$、$2$、$3$、$4$、$5$、$6$ 的数字, 掷一次骰子出现``6''朝上的概率为\\blank{50}.",
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"024471": {
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"content": "设五个数值 $31,37,33, a, 35$ 的平均数是 34 , 则这组数据的方差是\\blank{50}.",
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"content": "若同时掷两颗骰子, 则出现两颗骰子的点数之和大于 $9$ 的概率为\\blank{50}.",
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"024473": {
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"content": "已知某社区的家庭年收入(单位: 万元)的频率分布直方图如图所示, 同一组中的数据用该组区间的中点值做代表, 则该社区内家庭的平均年收入的估计值是\\blank{50}万元.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.6, yscale = 10]\n\\draw [->] (3,0) -- (3.3,0) -- (3.4,0.02) -- (3.6,-0.02) -- (3.7,0) -- (11,0) node [below right] {收入/万元};\n\\draw [->] (3,0) -- (3,0.32) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (3,0) node [below left] {$O$};\n\\foreach \\i/\\j in {4/0.2,5/0.2,6/0.2,7/0.26,8/0.07,9/0.07}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (1,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {8/0.07,7/0.26,4/0.2}\n{\\draw [dashed] (\\i,\\j) -- (3,\\j) node [left] {$\\k$};};\n\\draw (10,0) node [below] {$10$};\n\\end{tikzpicture}\n\\end{center}",
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"024474": {
"id": "024474",
"content": "已知 10 件产品中有 2 件次品,\\\\\n(1) 任意取出 4 件产品检验, 求其中恰有 1 件次品的概率;\\\\\n(2) 为了保证使 2 件次品全部检验出的概率在 0.6 以上, 至少应抽取几件产品作检验?",
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"024475": {
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"content": "某教师为了了解本校高三学生一模考试的数学成绩情况, 将所教两个班级的数学成绩 (单位: 分)绘制成如图所示的茎叶图.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲班 & & 乙班\\\\ \\hline\n& 8 & 8 \\\\\n9 \\ 9 \\ 8 \\ 7 \\ 6 \\ 5 \\ 5 \\ 4 \\ 3 \\ 1 \\ 1 \\ 0 & 9 & 0 \\ 1 \\ 1 \\ 2 \\ 2 \\ 2 \\ 2 \\ 4 \\ 6 \\ 7 \\ 8 \\ 8 \\ 9 \\\\\n9 \\ 8 \\ 8 \\ 7 \\ 7 \\ 6 \\ 5 \\ 5 \\ 4 \\ 3 \\ 3 \\ 3 \\ 3 \\ 0 & 10 & 0 \\ 1 \\ 1 \\ 1 \\ 1 \\ 2 \\ 2 \\ 5 \\ 6 \\ 6 \\ 7 \\ 9 \\ 9 \\\\\n9 \\ 7 \\ 5 \\ 5 \\ 5 \\ 2 \\ 2 \\ 1 \\ 0 & 11 & 0 \\ 3 \\ 4 \\ 5 \\ 5 \\ 6 \\ 7 \\ 9 \\\\\n9 \\ 8 \\ 6 \\ 5 \\ 3 \\ 3 \\ 1 \\ 0 \\ 0 & 12 & 0 \\ 1 \\ 2 \\ 2 \\ 3 \\ 3 \\ 5 \\ 8 \\ 9 \\\\\n6 \\ 2 \\ 1 \\ 1 & 13 & 0 \\ 1 \\ 8 \\\\\n6 \\ 0 & 14 & 3\n\\end{tabular}\n\\end{center}\n(1) 分别求出甲、乙两个班级数学成绩的中位数、众数;\\\\\n(2) 若规定成绩不小于 115 分为优秀, 分别求出两个班级数学成绩的优秀率.",
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"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
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