ricardorendon100

03.07.2019 • 

Mathematics

Based on a survey, assume that 48% of consumers are comfortable having drones deliver their purchases. suppose we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with the drones. what is wrong with using the multiplication rule to find the probability of getting two consumers comfortable with drones followed by two consumers not comfortable, as in this calculation: left parenthesis 0.48 right parenthesis left parenthesis 0.48 right parenthesisleft parenthesis 0.52 right parenthesis left parenthesis 0.52 right parenthesisequals0.0623?

Ответ:

wakandafoodyoup9ioz4

17.07.2021

Mathematics

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sin(α+β)=sinαcosβ+cosαsinβ,

and the double angle formula of cosine:

cos(2α)=cos2α−sin2α=2cos2α−1=1−2sin2α

then:

sin(3x)=sin(2x+x)=sin(2x)cosx+cos(2x)sinx=

=(2sinxcosx)⋅cosx+(1−2sin2x)sinx=

=2sinxcos2x+sinx−2sin3x=

=2sinx(1−sin2x)+sinx−2sin3x=

=2sinx−2sin3x+sinx−2sin3x=

=3sinx−4sin3x.

cos3x
=cos(x+2x)
=cosxcos2x−sinxsin2x using cos(A+B)=cosAcosB-sinAsinB
=cosx(2cos^2x−1)−sinx(2sinxcosx) using cos2A=2cos^2A-1 and sin2A=2sinAcosA
=2cos^3x−cosx−2sin^2xcosx 
=2cos^3x−cosx−2(1−cos^2x)cosx  using sin^2x+cos^2x=1
=2cos^3x−cosx−2(cosx−cos3^x) [open the brackets]
=2cos^3x−cosx−2cosx+2cos^3x
=4cos^3x−3cosx [collect terms]

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