某大学为调查来自南方和北方的同龄大学生的身高差异,从2011级的年龄在18~19岁之间的大学生中随机抽取了来自南方和北方的大学生各10名,测量他们的身高,量出的身高如下:(单位:cm)
南方:158,170,166,169,180,175,171,176,162,163;
北方:183,173,169,163,179,171,157,175,178,166;
(1)根据抽测结果,画出茎叶图,并根据你画的茎叶图,对来自南方和北方的大学生的身高作比较,写出两个统计结论;
(2)若将样本频率视为总体的概率,现从来自南方的大学生中随机抽取3名同学,其中身高不低于平均身高的同学的人数为X,求X的分布列和数学期望EX.
考点分析:
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已知函数
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,x∈R.
(1)求函数f(x)的最大值和最小正周期;
(2)设△ABC的内角A,B,C的对边分别a,b,c,且c=3,f(C)=0,若sin(A+C)=2sinA,求a,b的值.
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对于下列命题:
①在△ABC中,若sin2A=sin2B,则△ABC为等腰三角形;
②已知a,b,c是△ABC的三边长,若a=2,b=5,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100003398019021/SYS201311031000033980190014_ST/0.png)
,则△ABC有两组解;
③设
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,
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,
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,则a>b>c;
④将函数
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图象向左平移
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个单位,得到函数
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图象.
其中正确命题的序号是
.
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函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100003398019021/SYS201311031000033980190013_ST/0.png)
的导函数y=f'(x)的部分图象如图所示:图象与y轴交点
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100003398019021/SYS201311031000033980190013_ST/1.png)
,与x轴正半轴的交点为A、C,B为图象的最低点,则函数y=f'(x)在点C处的切线方程为
.
注:(f[g(x)])′=f′[g(x)]•g′(x)
查看答案
已知圆C:x
2+y
2-4x=0,l过点P(3,0)的直线,则l与C的位置关系是
(填“相交”、“相切”、“相离”或“三种位置关系均有可能”).
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设x,y∈R,向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100003398019021/SYS201311031000033980190011_ST/0.png)
=(x,1),
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=(1,y),
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=(2,-4)且
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⊥
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,
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∥
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,则|
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+
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|=
.
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