<em>The answer to your question would be 54</em>
<em />
<em>Work Shown:</em>
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<em>5-2(5-27+5</em>
<em>Calculate with parenthesis (5-27): -22</em>
<em>5-2(-22)+5</em>
<em>Multiply and divide (left to right) 2(-22): -44</em>
<em>5-(-44)+5</em>
<em>Add and subtract (left to right) 5-(-44)+5</em>
<em>54</em>
Answer:
We want to find:
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D)
Here we can use Stirling's approximation, which says that for large values of n, we get:

Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7B%5Csqrt%7B2%2A%5Cpi%2An%7D%20%2A%28%5Cfrac%7Bn%7D%7Be%7D%20%29%5En%7D%20%7D%7Bn%7D%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bn%7D%7Be%2An%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D)
Now we can just simplify this, so we get:
![\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Be%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D%20%5C%5C)
And we can rewrite it as:

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:

Answer:
144 hope it helps
Step-by-step explanation:
Answer:
an event with no possible outcomes
Step-by-step explanation:
because there is only one posible thing that can happen
Answer:
<u>1/20 of the patrons at Joe's restaurant are expected to be male and out of town.</u>
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Proportion of patrons that are male at Joe's restaurant = 1/4
Proportion of patrons that are from out of town at Joe's restaurant = 1/5
2. What proportion would you expect to be male and out of town?
For finding the proportion of the patrons, that would be male and that would be from out of town, we do this calculation:
Proportion of patrons that are male at Joe's restaurant * Proportion of patrons that are from out of town at Joe's restaurant
<u>1/4 * 1/5 = 1/20 </u>
<u>It means that 1/20 of the patrons at Joe's restaurant are expected to be male and out of town.</u>