(1)0×9=0
(2)√81=9
(3)cot(45º)=tan(45º)=1
(4)log 2=0.3010; log 3=0.4771; 1<=a<10
2^30=a×10^k => 2^30/a=10^k
log(10)^k=log(2*^30/a)
k=30*log(2)-log(a)
=30*0.3010-log(1~10)
=9.03-(0~1)
=9.03~8.03
(5)某次模擬考,自然組數學一科,第二類組學生Nx=200人,平均成績Xbar=71分.標
準差為Sx=4分,第三類組學生N2=100人,平均成績Ybar=77分,標準差為Sy=5分,兩
類組學生300人之標準差為(四捨五入)?
Xbar=ΣX/200 => ΣX=200*Xbar=200*71=14200
Ybar=ΣY/100 => ΣY=100*Ybar=100*77=7700
Wbar=Σ(X+Y)/300=(14200+7700)/300=73
Vx=ΣX^2/200-Xbar^2=16
=> ΣX^2=200(Vx+Xbar^2)=200*(16+71^2)=1,011,400
Vy=ΣY^2/100-Ybar^2=25
=> ΣY^2=100(Vy+Ybar^2)=100*(25+77^2)=595,400
V=Σ(X^2+Y^2)/300-Wbar^2
=(1011400+595400)/300-73^2
=5356-5329
=27
S=√27=3√3=5.196........ans
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