Answer:

Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The t distribution or Student’s t-distribution is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
Data given
Confidence =0.99 or 99%
represent the significance level
n =16 represent the sample size
We don't know the population deviation 
Solution for the problem
For this case since we don't know the population deviation and our sample size is <30 we can't use the normal distribution. We neeed to use on this case the t distribution, first we need to calculate the degrees of freedom given by:

We know that
so then
and we can find on the t distribution with 15 degrees of freedom a value that accumulates 0.005 of the area on the left tail. We can use the following excel code to find it:
"=T.INV(0.005;15)" and we got
on this case since the distribution is symmetric we know that the other critical value is 
Answer: a = -3
Explanations:
The given equation is:

This can be re-written as:

Collect like terms:

Cross multiply:

To verify if the solution is correct, substitute a = -3 into the question given. If the Right Hand Side equals the Left Hand Side, then the solution is correct.

Since the Left Hand Side = Right Hand Side = 7, the solution a = -3 is correct
Answer:
5.5 segments
Step-by-step explanation:
I am not sure if you meant 11/12 and 1/6 but here's how I solved it.
11/12 ÷ 1/6
11/12*6/1=
66/12 Simplify
5 6/12=5.5
Answer:
81
Step-by-step explanation:
perfect-square trinomial form: a² +2ab +b²
a = x
2ab = 18x = 2 * x * 9
c = 9*9 = 81