Answer:
x = 40
Step-by-step explanation:
Here's a fun fact, all of those angles actually add up to 360 degrees!
How do we know this? Well if you were to draw a small arc between each of the lines, you would see that the arc would end up making a circle. And remember, circles have 360 degrees!
Now we can do some basic algebra. Add up all the angles and set that equal to 360.
(2x) + (x) + (3x + 20) + (2x+20) = 360.
8x + 40 = 360
8x = 320
x = 40
Hope this helped!
Answer:
g(6) = 71
f(11) = 62
Step-by-step explanation:
Let's solve g(6) first
Plug 6 into x
g(6) = 2(6)^2 - 1
g(6) = 2(36) - 1
g(6) = 72 - 1
g(6) = 71
Now let's solve f(11)
f(11) = 5(11) + 7
f(11) = 55 + 7
f(11) = 62
<em>Thus, out answers are 71 and 62 respectively</em>
12 for the first one, 6*4=24 24 divided by 2
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 