Answer:
p= 43.96
a= 153.86
Step-by-step explanation:
The perimeter is the same as saying the circumference and the formula for circumference is C= 2(pi)r
The area formula is A= (pi)r^2
The picture shows the diameter being 7. If you divide it in half it will give you the radius
My calculation go off pi as 3.14.
The first one is 0.97 the second one is 6
Answer:
= - 5n - 2
Step-by-step explanation:
There is a common difference between consecutive terms, that is
- 12 - (- 7) = - 17 - (- 12) = - 5
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 7 and d = - 5, then
= - 7 - 5(n - 1) = - 7 - 5n + 5 = - 5n - 2
Probability of success (showing up) = 1-0.05=0.95 is constant and known.
Trials are Bernoulli (show or no show).
Trials are independent and random (assumed from context)
Number of trials is known, n=160.
All being satisfied, we can then model with binomial distribution, where
P(x)=C(n,x)p^x*(1-p)^(n-x)
where C(n,x)=n!/(x!(n-x)!)
Here we look for
P(X<=155)=P(X=0)+P(X=1)+P(X=2)+...+P(X=155)
=0.9061461 (using technology, or add up 156 values calculated, or read from binomial distribution table).
Alternatively, the normal approximation can be used, when n is large.
mean=np=160*0.95=152
standard deviation=sqrt(np(1-p))=2.75681
Apply continuity correction, x=155.5
Z=(155.5-152)/2.75681=1.26958
P(z<=Z)=0.89788 (read from normal distribution tables)
Error=(0.89788-0.9061461)*100%=-0.83%
The approximation is considered good considering p=0.95 is quite skewed, but compensated by n>>50.