Answer:
a) The formula is given by mean 
the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.
b) 
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean 
is given by:
Part a
The formula is given by mean the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.
Part b
The confidence interval for the mean is given by the following formula:
Answer:
Step-by-step explanation:
Use the Pythagorean Theorem:
![\displaystyle a^2 + b^2 = c^2 \\ \\ 9,7^2 + b^2 = 13,3^2; \sqrt{82,8} = \sqrt{b^2} \\ \\ \frac{3\sqrt{230}}{5}\:[or\:9,0994505329...] = b](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%20%5C%5C%20%5C%5C%209%2C7%5E2%20%2B%20b%5E2%20%3D%2013%2C3%5E2%3B%20%5Csqrt%7B82%2C8%7D%20%3D%20%5Csqrt%7Bb%5E2%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B3%5Csqrt%7B230%7D%7D%7B5%7D%5C%3A%5Bor%5C%3A9%2C0994505329...%5D%20%3D%20b)
So, you have this:
I am joyous to assist you at any time.
Part A: 5.25
Average speed is 5.25 mi per hr
Part B: 8 hrs because
42 divided by 5.25 is 8
Answer:
1. 135°
2. 114°
3. 118°
4. 81°
Step-by-step explanation:
Let "x" represent the measure of the indicated angle in each problem.
1. x = 135° (corresponding angles theorem)
2. x = 180° - 66° (same-side interior angles theorem)
x = 114°
3. x = 118° (alternate interior angles theorem)
4. x = 81° (alternate exterior angles theorem)
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
