Answer:
2.24
Step-by-step explanation:
The probability formula using a Poisson distribution is:
![P(k\ events) = \frac{\lambda^{k}e^{-\lambda}}{k!} \\\lambda\ is\ the\ average\ number\ of\ events\ per\ interval \\e\ is\ euler's\ number \\k\ is\ the\ number\ of\ events\ you\ want\ to\ calculate](https://tex.z-dn.net/?f=P%28k%5C%20events%29%20%3D%20%5Cfrac%7B%5Clambda%5E%7Bk%7De%5E%7B-%5Clambda%7D%7D%7Bk%21%7D%20%5C%5C%5Clambda%5C%20is%5C%20the%5C%20average%5C%20number%5C%20of%5C%20events%5C%20per%5C%20interval%20%5C%5Ce%5C%20is%5C%20euler%27s%5C%20number%20%5C%5Ck%5C%20is%5C%20the%5C%20number%5C%20of%5C%20events%5C%20you%5C%20want%5C%20to%5C%20calculate)
λ = 90 / 18 = 5 average goals per interval (interval = a game)
So if for example you were interested in the probability of making 2 goals in a game
k = 2
![P(k = 2) = \frac{5^{2}e^{-5}}{2!} = 0.084](https://tex.z-dn.net/?f=P%28k%20%3D%202%29%20%3D%20%5Cfrac%7B5%5E%7B2%7De%5E%7B-5%7D%7D%7B2%21%7D%20%3D%200.084)
This was just an example,
The standard deviation is ![\sqrt{\lambda}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Clambda%7D)
![\sigma = \sqrt{\lambda} \\\sigma = \sqrt{5} \\\sigma = 2.24](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Clambda%7D%20%5C%5C%5Csigma%20%3D%20%5Csqrt%7B5%7D%20%5C%5C%5Csigma%20%3D%202.24)
5:6
The fraction 85/102 goes to 5/6 so it is 5:6 or 5/6...
Answer:
Required logarithmic function is :
![f\left(x\right)=\log_3\left(x\right)](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D%5Clog_3%5Cleft%28x%5Cright%29)
Step-by-step explanation:
We have been fiven that table for the logarithmic function is:
x f(x)
9 2
27 3
81 4
which can be rewritten as:
x f(x)
3^2 2
3^3 3
3^4 4
Which are basically powers of 3
So we can use logarithmic function as
![\log_3\left(9\right)=\log_3\left(3^2\right)=2\log_3\left(3\right)=2(1)=2](https://tex.z-dn.net/?f=%5Clog_3%5Cleft%289%5Cright%29%3D%5Clog_3%5Cleft%283%5E2%5Cright%29%3D2%5Clog_3%5Cleft%283%5Cright%29%3D2%281%29%3D2)
Hence required logarithmic function is :
![f\left(x\right)=\log_3\left(x\right)](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D%5Clog_3%5Cleft%28x%5Cright%29)
Answer:
4.71
Step-by-step explanation:
Area of shaded sector formula: r2(data)(pi)/360
Substitute the info into the formula
(60)(pi)/360
9(60)=540
540/360(pi)=4.71
Hope this helps! :)