Answer:
A, D
Step-by-step explanation:
When we multiply the fractions, we can get:
![\frac{1}{5^{4} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%5E%7B4%7D%20%7D)
This is also equivalent to:
![5^{-4}](https://tex.z-dn.net/?f=5%5E%7B-4%7D)
When looking at the answer choices, the only ones that equal
are A and D because:
![(5^{-2})^{2} =5^{-4}](https://tex.z-dn.net/?f=%285%5E%7B-2%7D%29%5E%7B2%7D%20%20%3D5%5E%7B-4%7D)
![5^{2}*5^{-6} = 5^{-4}](https://tex.z-dn.net/?f=5%5E%7B2%7D%2A5%5E%7B-6%7D%20%3D%205%5E%7B-4%7D)
Answer:
90% confidence interval: (70.41,86.89)
Step-by-step explanation:
We are given the following in the question:
Point estimate = 78.65
Margin of error, E = 8.24
Confidence level = 90%
Significance level = 10%
Formula:
![\text{Point estimate} \pm \text{Margin of error}](https://tex.z-dn.net/?f=%5Ctext%7BPoint%20estimate%7D%20%5Cpm%20%5Ctext%7BMargin%20of%20error%7D)
Putting the values, we get,
![z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64](https://tex.z-dn.net/?f=z_%7Bcritical%7D%5Ctext%7B%20at%7D~%5Calpha_%7B0.10%7D%20%3D%20%5Cpm%201.64)
![78.65 \pm 8.24 = (70.41,86.89)](https://tex.z-dn.net/?f=78.65%20%5Cpm%208.24%20%3D%20%2870.41%2C86.89%29)
(70.41,86.89) is the required 90% confidence interval.