Answer:
the answer would be a
Step-by-step explanation:
Answer: ![1-(\frac{364}{365})^n](https://tex.z-dn.net/?f=1-%28%5Cfrac%7B364%7D%7B365%7D%29%5En)
Step-by-step explanation:
Binomial probability formula :-
, where P(x) is the probability of getting success in x trials, n is the total number of trials and p is the probability of getting success in each trial.
We assume that the total number of days in a particular year are 365.
Then , the probability for each employee to have birthday on a certain day :
![p=\dfrac{1}{365}](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B1%7D%7B365%7D)
Given : The number of employee in the company = n
Then, the probability there is at least one day in a year when nobody has a birthday is given by :-
![P(x\geq1)=1-P(x](https://tex.z-dn.net/?f=P%28x%5Cgeq1%29%3D1-P%28x%3C1%29%5C%5C%5C%5C1-P%280%29%5C%5C%5C%5C%3D1-%28%5EnC_0%28%5Cfrac%7B1%7D%7B365%7D%29%5E0%281-%5Cfrac%7B1%7D%7B365%7D%29%5En%29%5C%5C%5C%5C%3D1-%281%29%28%5Cfrac%7B364%7D%7B365%7D%29%5En%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5B%5Ctext%7Bsince%7D%5C%20%5EnC_0%3D1%5D%5C%5C%5C%5C%3D1-%28%5Cfrac%7B364%7D%7B365%7D%29%5En)
Hence, the probability there is at least one day in a year when nobody has a birthday =![1-(\frac{364}{365})^n](https://tex.z-dn.net/?f=1-%28%5Cfrac%7B364%7D%7B365%7D%29%5En)
Answer:
Option D.
![A =96\pi\ cm^2](https://tex.z-dn.net/?f=A%20%3D96%5Cpi%5C%20cm%5E2)
Step-by-step explanation:
The area of the circular bases is:
![A_c = 2\pi(a) ^ 2](https://tex.z-dn.net/?f=A_c%20%3D%202%5Cpi%28a%29%20%5E%202)
Where
is the radius of the circle
Then
![A = 2\pi(4) ^ 2](https://tex.z-dn.net/?f=A%20%3D%202%5Cpi%284%29%20%5E%202)
![A = 32\pi\ cm^2](https://tex.z-dn.net/?f=A%20%3D%2032%5Cpi%5C%20cm%5E2)
The area of the rectangle is:
![A_r=b * 2\pi r](https://tex.z-dn.net/?f=A_r%3Db%20%2A%202%5Cpi%20r)
Where
![b=8\ cm](https://tex.z-dn.net/?f=b%3D8%5C%20cm)
b is the width of the rectangle and
is the length
Then the area of the rectangle is:
![A_r=8 * 2\pi (4)](https://tex.z-dn.net/?f=A_r%3D8%20%2A%202%5Cpi%20%284%29)
![A_r=64\pi\ cm^2](https://tex.z-dn.net/?f=A_r%3D64%5Cpi%5C%20cm%5E2)
Finally the total area is:
![A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\](https://tex.z-dn.net/?f=A%20%3D%20A_c%20%2B%20A_r%5C%5C%5C%5CA%20%3D%2032%5Cpi%5C%20cm%5E2%20%2B%2064%5Cpi%5C%20cm%5E2%5C%5C%5C%5C)
![A =96\pi\ cm^2](https://tex.z-dn.net/?f=A%20%3D96%5Cpi%5C%20cm%5E2)
Answer:
Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.
Step-by-step explanation:
comment how it helps
X = -4 + e to the sixth power