The formula of the present value of annuity due:
![PV=C*[\frac{1-(1+i)^{-n}}{i}]*(1+i)](https://tex.z-dn.net/?f=PV%3DC%2A%5B%5Cfrac%7B1-%281%2Bi%29%5E%7B-n%7D%7D%7Bi%7D%5D%2A%281%2Bi%29)
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is:
![PV=3000*[\frac{1-(1+0.12)^{-6}}{0.12}]*(1+0.12)=3000*[\frac{1-0.5066}{0.12}]*1.12=](https://tex.z-dn.net/?f=PV%3D3000%2A%5B%5Cfrac%7B1-%281%2B0.12%29%5E%7B-6%7D%7D%7B0.12%7D%5D%2A%281%2B0.12%29%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D)
![=3000*[\frac{1-0.5066}{0.12}]*1.12=3000*4.1114*1.12=13814.32](https://tex.z-dn.net/?f=%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D3000%2A4.1114%2A1.12%3D13814.32)
Answer:
Step-by-step explanation:
Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit.
a) P(X = n) = q(n-1)p, where q = 1 - p.
From the information given, probability if success, p = 12.6/100 = 0.126
b) for n = 3, the probability value from the geometric probability distribution calculator is
P(n = 3) = 0.096
For n = 5, the probability value from the geometric probability distribution calculator is
P(n = 5) = 0.074
For n = 12, the probability value from the geometric probability distribution calculator is
P(n = 12) = 0.8
c) For n ≥ 5, the probability value from the geometric probability distribution calculator is
P(n ≥ 5) = 0.58
d) the expected number of apples that must be examined to find the first one with bitter pit is the mean.
Mean = 1/p
Mean = 1/0.126 = 7.9
Approximately 8 apples
Answer:
a or b but i think a
Step-by-step explanation:
