Answer:
0.8743 = 87.43% probability that more than one accident occurs per year
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 interval.
Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year.
This means that ![\mu = 3.1](https://tex.z-dn.net/?f=%5Cmu%20%3D%203.1)
What is the probability that more than one accident occurs per year?
This is:
![P(X > 1) = 1 - P(X \leq 1)](https://tex.z-dn.net/?f=P%28X%20%3E%201%29%20%3D%201%20-%20P%28X%20%5Cleq%201%29)
In which
![P(X \leq 1) = P(X = 0) + P(X = 1)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%201%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29)
Then
![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^{-3.6}*(3.6)^{0}}{(0)!} = 0.0273](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-3.6%7D%2A%283.6%29%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.0273)
![P(X = 1) = \frac{e^{-3.6}*(3.6)^{1}}{(1)!} = 0.0984](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-3.6%7D%2A%283.6%29%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.0984)
![P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0273 + 0.0984 = 0.1257](https://tex.z-dn.net/?f=P%28X%20%5Cleq%201%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%3D%200.0273%20%2B%200.0984%20%3D%200.1257)
![P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1257 = 0.8743](https://tex.z-dn.net/?f=P%28X%20%3E%201%29%20%3D%201%20-%20P%28X%20%5Cleq%201%29%20%3D%201%20-%200.1257%20%3D%200.8743)
0.8743 = 87.43% probability that more than one accident occurs per year
Answer:
x≈6.4
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }24900
a=starting value = 24900
r=\text{rate = }6.75\% = 0.0675
r=rate = 6.75%=0.0675
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.0675=0.9325
b=1−r=1−0.0675=0.9325
\text{Write Exponential Function:}
Write Exponential Function:
y=24900(0.9325)^x
y=24900(0.9325)
x
Put it all together
\text{Plug in y-value:}
Plug in y-value:
15900=24900(0.9325)^x
15900=24900(0.9325)
x
\frac{15900}{24900}=\frac{24900(0.9325)^x}{24900}
24900
15900
=
24900
24900(0.9325)
x
Divide both sides by 24900
0.638554=0.9325^x
0.638554=0.9325
x
\log 0.638554=\log 0.9325^x
log0.638554=log0.9325
x
Take the log of both sides
\log 0.638554=x\log 0.9325
log0.638554=xlog0.9325
use power rule to bring x to the front
\frac{\log 0.638554}{\log 0.9325}=\frac{x\log 0.9325}{\log 0.9325}
log0.9325
log0.638554
=
log0.9325
xlog0.9325
Divide both sides by log(0.9325)
6.418279=x
6.418279=x
Answer: $16.60
Step-by-step explanation:
5.80+ 3.60= 9.40+ 3.60= 13.00+ 3.60= 16.60
So after 4 weeks he earned $16.60
A = 7
B = 14
For A:
(7(sqrt)2)sin(45) = 7
7/sin(30) = 14
Answer:
Step-by-step explanation:
It represents 7.