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In order to find the average you have to add up all the data values and then find the sum of the data values.

So on average he ran about 82.5 miles.
<h2>
Hello!</h2>
The answer is:
The second option,
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
<h2>
Why?</h2>
Discarding each given option in order to find the correct one, we have:
<h2>
First option,</h2>
![\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%7D%5Csqrt%5Bm%5D%7By%7D%3D%5Csqrt%5B2m%5D%7Bxy%7D)
The statement is false, the correct form of the statement (according to the property of roots) is:
![\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%7D%5Csqrt%5Bm%5D%7By%7D%3D%5Csqrt%5Bm%5D%7Bxy%7D)
<h2>
Second option,</h2>
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
The statement is true, we can prove it by using the following properties of exponents:

![\sqrt[n]{x^{m} }=x^{\frac{m}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%20%7D%3Dx%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%20%7D)
We are given the expression:
![(\sqrt[m]{x^{a} } )^{b}](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D)
So, applying the properties, we have:
![(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%28x%5E%7B%5Cfrac%7Ba%7D%7Bm%7D%7D%29%5E%7Bb%7D%3Dx%5E%7B%5Cfrac%7Bab%7D%7Bm%7D%7D%5C%5C%5C%5Cx%5E%7B%5Cfrac%7Bab%7D%7Bm%7D%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
Hence,
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
<h2>
Third option,</h2>
![a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}](https://tex.z-dn.net/?f=a%5Csqrt%5Bn%5D%7Bx%7D%2Bb%5Csqrt%5Bn%5D%7Bx%7D%3Dab%5Csqrt%5Bn%5D%7Bx%7D)
The statement is false, the correct form of the statement (according to the property of roots) is:
![a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}](https://tex.z-dn.net/?f=a%5Csqrt%5Bn%5D%7Bx%7D%2Bb%5Csqrt%5Bn%5D%7Bx%7D%3D%28a%2Bb%29%5Csqrt%5Bn%5D%7Bx%7D)
<h2>
Fourth option,</h2>
![\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5Bm%5D%7Bx%7D%20%7D%7B%5Csqrt%5Bm%5D%7By%7D%7D%3Dm%5Csqrt%7Bxy%7D)
The statement is false, the correct form of the statement (according to the property of roots) is:
![\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5Bm%5D%7Bx%7D%20%7D%7B%5Csqrt%5Bm%5D%7By%7D%7D%3D%5Csqrt%5Bm%5D%7B%5Cfrac%7Bx%7D%7By%7D%20%7D)
Hence, the answer is, the statement that is true is the second statement:
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
Have a nice day!
Answer:

Step-by-step explanation:
Use the inverse cosine function.



Answer:
The 6 people would each get 5lb. of beans. 5 lies between 4 and 6.
Step-by-step explanation:
To get the answer to this problem, all you have to do is divide the total pounds of beans by how many people there are. 30 ÷ 6= 5, so each person would get 5 pounds. Since 5 comes between 4 & 6, you can use that as your answer.