Answer:
Angle 1 is 105°
Angle 2 is 75°
Step-by-step explanation:
Angle 2 is the same angle as angle 6 which is 75°
Angle 1 can be found by subtracting 75° (angle 2) from 180° which is the angle of a straight line. Which equals 105°.
Hope this helps! :)
Answer:
sabah al khair
Step-by-step explanation:
Answer:
32.33% probability of having at least 3 erros in an hour.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
The mean number of errors is 2 per hour.
This means that ![\mu = 2](https://tex.z-dn.net/?f=%5Cmu%20%3D%202)
(a) What is the probability of having at least 3 errors in an hour?
Either you have 2 or less errors in an hour, or we have at least 3 errors. The sum of the probabilities of these events is decimal 1. So
![P(X \leq 2) + P(X \geq 3) = 1](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%2B%20P%28X%20%5Cgeq%203%29%20%3D%201)
We want ![P(X \geq 3)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%203%29)
So
![P(X \geq 3) = 1 - P(X \leq 2)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%203%29%20%3D%201%20-%20P%28X%20%5Cleq%202%29)
In which
![P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29)
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-2}*(2)^{0}}{(0)!} = 0.1353](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-2%7D%2A%282%29%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.1353)
![P(X = 1) = \frac{e^{-2}*(2)^{1}}{(1)!} = 0.2707](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-2%7D%2A%282%29%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.2707)
![P(X = 2) = \frac{e^{-2}*(2)^{2}}{(2)!} = 0.2707](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-2%7D%2A%282%29%5E%7B2%7D%7D%7B%282%29%21%7D%20%3D%200.2707)
![P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1353 + 0.2707 + 0.2707 = 0.6767](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%3D%200.1353%20%2B%200.2707%20%2B%200.2707%20%3D%200.6767)
![P(X \geq 3) = 1 - P(X \leq 2) = 1 - 0.6767 = 0.3233](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%203%29%20%3D%201%20-%20P%28X%20%5Cleq%202%29%20%3D%201%20-%200.6767%20%3D%200.3233)
32.33% probability of having at least 3 erros in an hour.