名校
解题方法
1 . 噪声污染已经成为影响人们身体健康和生活质量的严重问题,为了了解强度
(单位:分贝)与声音能量
(单位:
)之间的关系,将测量得到的声音强度
和声音能量
数据作了初步处理,得到下面的散点图及一些统计量的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/57d4f63f-a56e-4f0b-8202-62999b1b975c.png?resizew=220)
表中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dc83a0e5f8c817f4fbdcd540121c99.png)
(1)根据表中数据,求声音强度
关于声音能量
的回归方程
;
(2)当声音强度大于60分贝时属于噪音,会产生噪声污染,城市中某点
共受到两个声源的影响,这两个声源的声音能量分别是
和
,且
.已知点
的声音能量等于声音能量
与
之和.请根据(1)中的回归方程,判断
点是否受到噪声污染的干扰,并说明理由.
附:对于一组数据
,其回归直线
的斜率和截距的最小二乘估计分别为:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7ff182bb0783379a6edeb77421e878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2451fdae3c590a4099e9ad91e5edea9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1be5cf97131db38f911856b5e55c3ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/57d4f63f-a56e-4f0b-8202-62999b1b975c.png?resizew=220)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | 45.7 | -11.5 | ![]() | 0.51 | ![]() | 5.1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44933ef0fbe19cf89199b06a56a01aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dc83a0e5f8c817f4fbdcd540121c99.png)
(1)根据表中数据,求声音强度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c237e0e8a5586daad0d0bf77d29fa2b0.png)
(2)当声音强度大于60分贝时属于噪音,会产生噪声污染,城市中某点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea7ad079543f47fdbf23639650fa521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b09f36db58b939b0418a7d22a57ded4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9ebbe62bcb439fe0b829c0f41318e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78cecd81e5d4977692c22dff7dc64f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3906000a1cb2ddf14657f645a21305.png)
您最近一年使用:0次
名校
2 . 某手机企业为确定下一年度投入某种产品的研发费用,统计了近
年投入的年研发费用
千万元与年销售量
千万件的数据,得到散点图1,对数据作出如下处理:令
,
,得到相关统计量的值如图2:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/0a4ef51d-f437-4fe9-b533-9c8559eb6e2b.png?resizew=275)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/a8884aef-be9a-41c0-b874-5f6f989d8474.png?resizew=218)
(1)利用散点图判断
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7c4f1ac6cc57f6c5084479badd1f71.png)
哪一个更适合作为年研发费用
和年销售量
的回归类型(不必说明理由),并根据数据,求出
与
的回归方程;
(2)已知企业年利润
千万元与
的关系式为
(其中
为自然对数的底数),根据(1)的结果,要使得该企业下一年的年利润最大,预计下一年应投入多少研发费用?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90229c4f76db5de308cf8d5fc382099b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c26fa1e573812fab6a173a4eb0ed38.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/0a4ef51d-f437-4fe9-b533-9c8559eb6e2b.png?resizew=275)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/a8884aef-be9a-41c0-b874-5f6f989d8474.png?resizew=218)
(1)利用散点图判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7c4f1ac6cc57f6c5084479badd1f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cd959016b2050b1ccda23cda482eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知企业年利润
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f66d3a55ac5924f52fefff6c450b267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
您最近一年使用:0次
2020-04-14更新
|
920次组卷
|
6卷引用:福建省莆田第二十四中学2019-2020学年高二下学期返校测试数学(文)试题
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