1 . 已知椭圆
的左、右焦点分别为
为坐标原点,直线
与
交于
两点,点
在第一象限,点
在第四象限且满足直线
与直线
的斜率之积为
.当
垂直于
轴时,
.
(1)求
的方程;
(2)若点
为
的左顶点且满足
,直线
与
交于
,直线
与
交于
.
①证明:
为定值;
②证明:四边形
的面积是
面积的2倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4baaf1a6c7794dc95ba89c9e2820c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dd2505b79dc4bad657e97c6bfd6c9c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742ff39a10a7fc9deb693abb7fe26680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
②证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d89641052a363c69069bc2d747eebf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2 . 在推动电子制造业高质量发展的大环境下,某企业统筹各类资源,进行了积极的改革探索.下表是该企业每月生产的一种核心产品的产量
(件)与相应的生产总成本
(万元)的四组对照数据.
企业研究人员建立了
与
的两种回归模型,利用计算机算得近似结果如下:
经验回归方程①:
;经验回归方程②:
.
其中经验回归方程①的残差图如图所示(残差
观测值
预测值):
关于
的回归方程,并说明理由;
(2)从该企业在过去几年生产的该产品中随机抽取100件,优等品有60件,合格品有40件.每件优等品利润为20万元,每件合格品利润为15万元.若视频率为概率,该企业某月计划生产12件该产品,记优等品件数为
,总利润为
.
(ⅰ)求
与
的关系式,并求
和
;
(ⅱ)记该月的成本利润率
,在(1)中选择的经验回归方程下,求
的估计值.(结果保留2位小数)
附:成本利润率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9331944645ed52340897b03c4ca4e387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![]() | 5 | 7 | 9 | 11 |
![]() | 200 | 298 | 431 | 609 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
经验回归方程①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d911ec5ea8316c34058601b248687b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb39cb146fbd0b7a1efc1bbaee3517f.png)
其中经验回归方程①的残差图如图所示(残差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![]() | 5 | 7 | 9 | 11 |
![]() | 200 | 298 | 431 | 609 |
![]() |
(2)从该企业在过去几年生产的该产品中随机抽取100件,优等品有60件,合格品有40件.每件优等品利润为20万元,每件合格品利润为15万元.若视频率为概率,该企业某月计划生产12件该产品,记优等品件数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0919cf56a1b743189a019551b2d5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0bd6753e573bfbe6742d08ef6dfe83.png)
(ⅱ)记该月的成本利润率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
附:成本利润率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2db54470411f1dcb192c4a57ce13d34.png)
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3 . 已知数列
满足:
,定义:
表示整数
除以4的余数与整数
除以4的余数相同,例:
.设
,其中
,数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f37c41b3d37ebff1242f840b5fe0c0.png)
______ ;满足
的
最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bd1701942436577888033dddab56db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770e90a2561b0d1d2b29a3b79826ce3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f6d0719b5ca93d2c769cb1dfde76a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41483f8495363a91ed69f7ca4eb82e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f37c41b3d37ebff1242f840b5fe0c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb38963c8058ddefb44934c83ab6c86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 某校“五一田径运动会”上,共有12名同学参加100米、400米、1500米三个项目,其中有8人参加“100米比赛”,有7人参加“400米比赛”,有5人参加“1500米比赛”,“100米和400米”都参加的有4人,“100米和1500米”都参加的有3人,“400米和1500米”都参加的有3人,则下列说法正确的是( )
A.三项比赛都参加的有2人 | B.只参加100米比赛的有3人 |
C.只参加400米比赛的有3人 | D.只参加1500米比赛的有1人 |
您最近一年使用:0次
解题方法
5 . 某项活动在周一至周五举行五天,现在需要安排甲、乙、丙、丁四位负责人值班,每个人至少值班一天,每天仅需一人值班,已知甲不能值第一天和最后一天,乙要值班两天且这两天必须相邻,则不同安排方法的种数为( )
A.24 | B.10 | C.16 | D.12 |
您最近一年使用:0次
6 . 设集合
是一个非空数集,对任意
,定义
,称
为集合
的一个度量,称集合
为一个对于度量
而言的度量空间,该度量空间记为
.
定义1:若
是度量空间
上的一个函数,且存在
,使得对任意
,均有:
,则称
是度量空间
上的一个“压缩函数”.
定义2:记无穷数列
为
,若
是度量空间
上的数列,且对任意正实数
,都存在一个正整数
,使得对任意正整数
,均有
,则称
是度量空间
上的一个“基本数列”.
(1)设
,证明:
是度量空间
上的一个“压缩函数”;
(2)已知
是度量空间
上的一个压缩函数,且
,定义
,
,证明:
为度量空间
上的一个“基本数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a1f35848a78a4f00c21500e2610e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
定义1:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974cd5eed14d5002f6155dced3e62432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034e4d52bd5ae47074a93c0647f67399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f1ada25dccde00dfff2525360188a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
定义2:记无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da889327e4b9a31336a88e6da53334d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859cf5bf57a50d2da19c0bb926ce9c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e61e145e5a49ebbe72c3b9ba1f7cdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6f5c5649285cbabda20a452db04f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8557a6d85a35cd171e43087afd1b0576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c95a62ca5cb2f440792632ec36595b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd6ebf0a370d321e89a8f9921041a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae4c872929a492d8bcd9e649f190a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8671bcd155dd76d76d83573c6f20e930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6961967d7e48061a9cbb14f597e73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae4c872929a492d8bcd9e649f190a66.png)
您最近一年使用:0次
名校
解题方法
7 . 某社区有甲、乙两队社区服务小组,其中甲队有3位男士、2位女士,乙队有2位男士、3位女士.现从甲队中随机抽取一人派往乙队,分别以事件
和
表示从甲队中随机抽取一人抽到的是男士和女士;以事件B表示从乙队(甲队已经抽取一人派往乙队)中随机抽取一人抽到的是男士,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-16更新
|
1161次组卷
|
2卷引用:河北省沧州市部分示范性高中2024届高三下学期三模数学试题
名校
解题方法
8 . 给定一个
元函数组:
,若对任意正整数
,均有
,则把
称作该函数组的“初始函数”.已知
是函数组
,
的“初始函数”,且
.
(1)求函数
的单调区间;
(2)设
,记
,数列
的前
项和为
.
是三个互不相等的正整数,若
,求
除以4的余数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1e172d9471217f913ef909703c72fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbd8ffa3e98548a4b258f9571ed3ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca56bb7e4c2761cfc543d002f6b6db70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104b081cfbc9120b476831c79a749c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f2f9bcca1436fd46b52426b3380b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f2f9bcca1436fd46b52426b3380b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639ba36dbe7ac0e206ec7506bfb5f3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5cd4f2248ed2c605408692ffe300b6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eac268e854f1d13a101ec88af5afd2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c517ff84243df1cd32c27c56afcfcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d44ddab6e0c60119be69985ae7fa65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d9c8c661360ed5865ce5bc91f3fcad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
您最近一年使用:0次
名校
解题方法
9 . 三等分角是古希腊几何尺规作图的三大问题之一,如今数学上已经证明三等分任意角是尺规作图不可能问题,如果不局限于尺规,三等分任意角是可能的.下面是数学家帕普斯给出的一种三等分角的方法:已知角
的顶点为
,在
的两边上截取
,连接
,在线段
上取一点
,使得
,记
的中点为
,以
为中心,
为顶点作离心率为2的双曲线
,以
为圆心,
为半径作圆,与双曲线
左支交于点
(射线
在
内部),则
.在上述作法中,以
为原点,直线
为
轴建立如图所示的平面直角坐标系,若
,点
在
轴的上方.
的方程;
(2)若过点
且与
轴垂直的直线交
轴于点
,点
到直线
的距离为
.
证明:①
为定值;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a998a7d4d980e848ee050b706480ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75eb52879657138c23304b1634c73f7c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d566a90ab70e7133f0f110143a4f06ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422fd5f0bdef76f7f05c6f803dddc982.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d566a90ab70e7133f0f110143a4f06ae.png)
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10 . 中国共产党第二十次全国代表大会于2022年10月16日在北京开幕,各地报起了一股学习党史风潮,某市为了促进市民学习党史,举办了党史知识竞赛活动,通过随机抽样,得到了1000人的竞赛成绩(满分100分)数据,统计结果如下表所示:
(1)求上表数据中的平均值(同一区间中的数据用该区间的中点值为代表);
(2)根据样本估计总体的方法,用频率代替概率,从该学校中随机抽取3位同学参加党史知识竞赛,记他们之中不低于60分的人数为
,求
的分布列及数学期望.
成绩区间 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
频数 | 20 | 180 | 200 | 280 | 220 | 80 | 20 |
(2)根据样本估计总体的方法,用频率代替概率,从该学校中随机抽取3位同学参加党史知识竞赛,记他们之中不低于60分的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次