Answer:
5
Step-by-step explanation:
It is best to make a table for this one
Hour | Cells
0 | 1
1 | 2
2 | 4
3 | 8
4 | 16
5 | 32
6 | 64
7 | 128
After 7 hours, there are 128 cells. To find this, you multiply the starting amount by two each hour.
Answer:
The probability is 0.68
Step-by-step explanation:
We are going to use conditional probability to solve this problem.
We define the following events :
A : '' Alex replaced the starter''
B : ''Alex replaced the battery''
M : ''The engine works''
NM : ''The engine doesn't work''
Given two events A and B, we define the conditional probability:
![P(A/B) =\frac{P(A,B)}{P(B)} \\P(B)> 0](https://tex.z-dn.net/?f=P%28A%2FB%29%20%3D%5Cfrac%7BP%28A%2CB%29%7D%7BP%28B%29%7D%20%5C%5CP%28B%29%3E%200)
![P(B/A)=\frac{P(B,A)}{P(A)} \\P(A)> 0](https://tex.z-dn.net/?f=P%28B%2FA%29%3D%5Cfrac%7BP%28B%2CA%29%7D%7BP%28A%29%7D%20%5C%5CP%28A%29%3E%200)
Where P(A,B) = P(B,A) = P(A∩B) = P(B∩A)
In our problem :
![P(M/B)=0.7\\P(M/A)=0.2\\P(B)=0.85\\](https://tex.z-dn.net/?f=P%28M%2FB%29%3D0.7%5C%5CP%28M%2FA%29%3D0.2%5C%5CP%28B%29%3D0.85%5C%5C)
Alex replaced the battery or either the starter ⇒
![P(A)=1-P(B)=1-0.85=0.15\\P(A)=0.15](https://tex.z-dn.net/?f=P%28A%29%3D1-P%28B%29%3D1-0.85%3D0.15%5C%5CP%28A%29%3D0.15)
We need to find ![P(B/NM)=\frac{P(B,NM)}{P(NM)}](https://tex.z-dn.net/?f=P%28B%2FNM%29%3D%5Cfrac%7BP%28B%2CNM%29%7D%7BP%28NM%29%7D)
We write :
![P(M/B)=\frac{P(M,B)}{P(B)} \\0.7=\frac{P(M,B)}{0.85}\\ P(M,B)=0.595](https://tex.z-dn.net/?f=P%28M%2FB%29%3D%5Cfrac%7BP%28M%2CB%29%7D%7BP%28B%29%7D%20%5C%5C0.7%3D%5Cfrac%7BP%28M%2CB%29%7D%7B0.85%7D%5C%5C%20P%28M%2CB%29%3D0.595)
![P(M/A)=\frac{P(M,A)}{P(A)} \\0.2=\frac{P(M,A)}{0.15} \\P(M,A)=0.03](https://tex.z-dn.net/?f=P%28M%2FA%29%3D%5Cfrac%7BP%28M%2CA%29%7D%7BP%28A%29%7D%20%5C%5C0.2%3D%5Cfrac%7BP%28M%2CA%29%7D%7B0.15%7D%20%5C%5CP%28M%2CA%29%3D0.03)
P(M) = [P(M∩B) ∪ P(M∩A)]
P(M) = P(M∩B) + P(M∩A) - P[(M∩B)∩(M∩A)]
But P[(M∩B)∩(M∩A)] = 0 because he replaced the battery or either the starter
P(M) = P(M∩B) + P(M∩A)
P(M)=0.595+0.03
P(M)=0.625
P(NM)= 1-P(M)=1-0.625=0.375
P(NM)= 0.375
P(NM/B) = 1-P(M/B)=1-0.7=0.3
P(NM/B) = 0.3
![P(NM/B)=0.3=\frac{P(NM,B)}{P(B)}=\frac{P(NM,B)}{0.85} \\P(NM,B)=0.255](https://tex.z-dn.net/?f=P%28NM%2FB%29%3D0.3%3D%5Cfrac%7BP%28NM%2CB%29%7D%7BP%28B%29%7D%3D%5Cfrac%7BP%28NM%2CB%29%7D%7B0.85%7D%20%5C%5CP%28NM%2CB%29%3D0.255)
![P(B/NM)=\frac{P(NM,B)}{P(NM)} =\frac{0.255}{0.375} =0.68](https://tex.z-dn.net/?f=P%28B%2FNM%29%3D%5Cfrac%7BP%28NM%2CB%29%7D%7BP%28NM%29%7D%20%3D%5Cfrac%7B0.255%7D%7B0.375%7D%20%3D0.68)
Answer:
I think the answer will be 16 pieces
Step-by-step explanation:
16 x 3/4 will equal 12