Answer:
![x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D%2Fx%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2%7D)
Step-by-step explanation:
Given

Required
Rewrite in simplest radical form
Using laws of indices:

This implies that

Solve Exponents


Simplify exponent to lowest fraction

Using laws of indices:
![a^{\frac{m}{n}} = \sqrt[n]{a^m}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%5Em%7D)
This implies that
![x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D%2Fx%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2%7D)
This is as far as the expression can be simplified
0.35 cups/hour
To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:
12 cups/34 hours= 0.35 cups/hour
According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.
Hope this helps!!
Answer:
.
Step-by-step explanation:
We have been given that a lumber yard has a scrap sheet of plywood that is 23 3/4 inches by 41 1/5 inches long.
Since plywood is in shape of rectangle, so to find the area of plywood we will multiply the length of plywood by its width.


Let us convert our mixed fractions into improper fractions.


Upon cancelling out greatest common factors we will get,

Now let us convert our answer into mixed fraction.
Therefore, the area of plywood is
.
Answer:
A baseline score of 99% needs to be set.
Step-by-step explanation:
Since this is an example of a classification problem (the classes being whether somebody has been infected with a new virus or not), the ideal score to achieve in such a case is 100%. Hence, a baseline score of 99% should be set in order to get to 100% by outperforming it.
Answer:
Mean is 3.05
Standard deviation is 1.69.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they are foreign, or they are not. This means that we can solve this problem using concepts of the binomial probability distribution.
Binomial probability distribution
The probability of x sucesses on n repeated trials, with p probability.
In this problem, we have a sample of 50 students, so
. The proportion of all UNC students that are foreign students is 0.061, so
.
The mean is given by the following formula:

The standard deviation is given by the following formula:
