Answer:
= 6, 9
Step-by-step explanation:
To find the midpoint , we use the formula
midpoint = (x1+x1)/2, (y1+y2)/2
= (2+10)/2, (6+12)/2
= 12/2, 18/2
= 6, 9
By definition, we have

So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:
Suppose that 
In this case, the absolute value doesn't do anything: the equation is

We are supposing
, so we can accept this solution.
Now, suppose that
. Now the sign of the expression is flipped by the absolute value, and the equation becomes

Again, the solution is coherent with the assumption, so we can accept this value as well.
<h3>
Answer: Choice B</h3>
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Explanation:
The rule we use is
![\Large a^{m/n} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m](https://tex.z-dn.net/?f=%5CLarge%20a%5E%7Bm%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%5Em%7D%20%3D%20%5Cleft%28%5Csqrt%5Bn%5D%7Ba%7D%5Cright%29%5Em)
where 'a' is the base, m stays in the role of the exponent, and n plays the role of the root index (eg: n = 3 is a cube root, n = 4 is a fourth root, and so on).
So for instance,
![\Large 2^{3/4} = \sqrt[4]{2^3} = \left(\sqrt[4]{2}\right)^3](https://tex.z-dn.net/?f=%5CLarge%202%5E%7B3%2F4%7D%20%3D%20%5Csqrt%5B4%5D%7B2%5E3%7D%20%3D%20%5Cleft%28%5Csqrt%5B4%5D%7B2%7D%5Cright%29%5E3)
or in this case,
![\Large t^{5/8} = \sqrt[8]{t^5} = \left(\sqrt[8]{t}\right)^5](https://tex.z-dn.net/?f=%5CLarge%20t%5E%7B5%2F8%7D%20%3D%20%5Csqrt%5B8%5D%7Bt%5E5%7D%20%3D%20%5Cleft%28%5Csqrt%5B8%5D%7Bt%7D%5Cright%29%5E5)
Answer:
Option B:


Classification:
The hypothesis test is Two-tailed.
Step-by-step explanation:
The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months.
This means that the null hypothesis is that the mean is of 22.1 months, that is:

A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.
At the alternate hypothesis, we test if this mean is different of 22.1, that is:

Which means that the answer is given by option b).
Which of the following is the correct classification of the hypothesis test?
We test if the mean is different from a value, which means that the hypothesis test is Two-tailed.
BRO I am to we just can’t do maths