See picture below. Being that you did not provide possible answers, I don't know what answer you can choose from.
9514 1404 393
Answer:
4² = 16
Step-by-step explanation:
The applicable rule of exponents is ...
1/a^-b = a^b
So, ...
![\dfrac{1}{4^{-2}}=\boxed{4^2 = 16}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%5E%7B-2%7D%7D%3D%5Cboxed%7B4%5E2%20%3D%2016%7D)
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<em>Additional comment</em>
If you were to evaluate this using the Order of Operations, you would evaluate the exponent first:
1/4^-2 = 1/(1/16)
Then, you would do the division.
1/(1/16) = 16
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We sometimes find it convenient to manipulate exponential terms to the form with the smallest positive exponents before we begin the evaluation.
Answer:
64.65% probability of at least one injury commuting to work in the next 20 years
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%0A)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Each day:
Bikes to work with probability 0.4.
If he bikes to work, 0.1 injuries per year.
Walks to work with probability 0.6.
If he walks to work, 0.02 injuries per year.
20 years.
So
![\mu = 20*(0.4*0.1 + 0.6*0.02) = 1.04](https://tex.z-dn.net/?f=%5Cmu%20%3D%2020%2A%280.4%2A0.1%20%2B%200.6%2A0.02%29%20%3D%201.04)
Either he suffers no injuries, or he suffer at least one injury. The sum of the probabilities of these events is decimal 1. So
![P(X = 0) + P(X \geq 1) = 1](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%2B%20P%28X%20%5Cgeq%201%29%20%3D%201)
We want
. Then
![P(X \geq 1) = 1 - P(X = 0)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29)
In which
![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%0A)
![P(X = 0) = \frac{e^{-1.04}*1.04^{0}}{(0)!} = 0.3535 ](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-1.04%7D%2A1.04%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.3535%0A)
![P(X \geq 1) = 1 - P(X = 0) = 1 - 0.3535 = 0.6465](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29%20%3D%201%20-%200.3535%20%3D%200.6465)
64.65% probability of at least one injury commuting to work in the next 20 years
Answer:
btw we cant see the image sorry
Step-by-step explanation: