N=400
sample proportion >= .475 => n>=.475N=190
mean response rate of population, p=0.5
Problem satisfies criteria for binomial distribution, where
P(x>=190)=sum P(x=i), i=190 to 400
This can be obtained from binomial distribution tables, calculators, or software as
P(x>=190)=1-P(x<190)=1-0.14685=0.85315
Alternatively, normal approximation can be used.
mean=Np=400*.5=200
variance=Npq=400(.5)(1-.5)=100
standard deviation=sqrt(variance)=sqrt(100)=10
Calculate P(X>=190)=1-P(X<190)
X with continuity correction = 189.5
Z=(X-mean)/standard deviation=(189.5-200)/10=-1.05
P(z<Z)=P(z<-1.05)=0.14686 (from normal probability tables)
hence
P(X>=190)=1-P(X<190)=1-P(z<-1.05)=1-0.14686=0.85314 (approximately)
almost same as the exact binomial solution.
Answer:
cos(60) cos(-20) - sin(60) sin(-20) = cos (40)
Step-by-step explanation:
Using the trigonometric identity rule:
Given that:
cos(60) cos(-20) - sin(60) sin(-20)
Let A = 60 and B = -20
then;
Using identity rule:
Therefore, the following as a function of a single angle is cos (40)
X - y = 2400/6 = 400 where x = speed of plane and y = speed of wind.
x + y = 2400/5 = 480 - flying with the wind
adding the 2 equations
2x = 880
x = 440
Speed of the plane with no wind = 440 mph
7x+2y=9xy-1=8xy
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