Answer:
3
Step-by-step explanation:
Answer:
There could be many but one of them is
(m+5)(m-9)=0....
Answer:
9/5
Step-by-step explanation:
solve the original equation for x
-4× + 3 = 1x +(-6)
-1x
-5x + 3 = -6
-3
-5x = -9
/-5
x = 9/5
CHECK
-4(9/5) + 3 = 1(9/5) +(-6)
-21/5 = -21/5
Answer:
1.76% probability that in one hour more than 5 clients arrive
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 arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per hour.
This means that ![\mu = 2](https://tex.z-dn.net/?f=%5Cmu%20%3D%202)
What is the probability that in one hour more than 5 clients arrive
Either 5 or less clients arrive, or more than 5 do. The sum of the probabilities of these events is decimal 1. So
![P(X \leq 5) + P(X > 5) = 1](https://tex.z-dn.net/?f=P%28X%20%5Cleq%205%29%20%2B%20P%28X%20%3E%205%29%20%3D%201)
We want P(X > 5). So
![P(X > 5) = 1 - P(X \leq 5)](https://tex.z-dn.net/?f=P%28X%20%3E%205%29%20%3D%201%20-%20P%28X%20%5Cleq%205%29)
In which
![P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%205%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%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%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%2A2%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%2A2%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%2A2%5E%7B2%7D%7D%7B%282%29%21%7D%20%3D%200.2707)
![P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20%5Cfrac%7Be%5E%7B-2%7D%2A2%5E%7B3%7D%7D%7B%283%29%21%7D%20%3D%200.1804)
![P(X = 4) = \frac{e^{-2}*2^{4}}{(4)!} = 0.0902](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20%5Cfrac%7Be%5E%7B-2%7D%2A2%5E%7B4%7D%7D%7B%284%29%21%7D%20%3D%200.0902)
![P(X = 5) = \frac{e^{-2}*2^{5}}{(5)!} = 0.0361](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20%5Cfrac%7Be%5E%7B-2%7D%2A2%5E%7B5%7D%7D%7B%285%29%21%7D%20%3D%200.0361)
![P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.1353 + 0.2702 + 0.2702 + 0.1804 + 0.0902 + 0.0361 = 0.9824](https://tex.z-dn.net/?f=P%28X%20%5Cleq%205%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%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%29%20%3D%200.1353%20%2B%200.2702%20%2B%200.2702%20%2B%200.1804%20%2B%200.0902%20%2B%200.0361%20%3D%200.9824)
![P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9824 = 0.0176](https://tex.z-dn.net/?f=P%28X%20%3E%205%29%20%3D%201%20-%20P%28X%20%5Cleq%205%29%20%3D%201%20-%200.9824%20%3D%200.0176)
1.76% probability that in one hour more than 5 clients arrive
Answer:
congruent, alternate exterior
Step-by-step explanation:
For the first question, the angles are congruent (they are not complementary because they dont add p to 90 degrees, and they are not supplementary because they dont add up to 180 degrees so they must be congrunet)
For the second- they are alternate exterior (i know that they are on the outisde so they are exterior)