2022英语周报九6答案

21.解:(1)记A4表示第i道题答对,其中i=1,2,3,4由题意得A1A2A3A4 A1A2A3A4表示得30分的事件(2分)P(AArAA AlAzAsAs)=P(AAaA) P(A1A2A3A4)=P(A,)P(A2)P(A3)P(A) P(A,)P(A2)P(A3)P(A4)=0.7×0.6×0.2×0.9 0.70.4X0.8×0.9=0.2772.(5分)(2)X的取值为0,10,20,30,40,50(6分)P(X=0)=0.3×0.4=0.12;P(X=10)=0.7×0.4×0.2 0.3×0.6×0.2×0.1=0.0596;P(X=20)=0.7×0.6×0.2×0.1 0.7×0.4×0.8×0.1 0.3×0.6×0.8×0.1 0.3×0.6×0.2×0.9=0.0776;P(X=30)=0.2772;P(X=40)=0.7×0.6×0.8×0.1 0.3×0.6×0.8×0.9=0.1632;P(X=50)=0.7×0.6×0.8×0.9=0.3024.(10分)故E(X)=0×0.12 10×0.0596 20×0.0776 30×0.2772 40×0.1632 50×0.3024=32.112.(12分)

18.解:(1)由已知及正弦定理sin a sinc a sin即a2=b2 c2 bc(2分所以 A-b2 c2-a2又A∈(0°,180°),所以A=120°(5分)2△ABC的面积S=1smA-2如=(6分)2b 3c≥2√6bc=12,当且仅当2b=3c时等号成立解得b=3,c=2.(8分)在△ABC中,由余弦定理得a2=b2 c2-2bccos120°=32 22-2×3×2故a=√19(9分)在△ABC中,由正弦定理nC=n120得sC=在△ACM中,由正弦定理AM=b,得AM=bcsin 120sin C6c 6sin60°sin60°a(12分)

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