Answer:
a) 
With:


b) 

c) 

d) 


Step-by-step explanation:
For this case we know the following propoertis for the random variable X

We select a sample size of n = 81
Part a
Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

With:


Part b
We want this probability:

We can use the z score formula given by:

And if we find the z score for 89 we got:


Part c

We can use the z score formula given by:

And if we find the z score for 75.65 we got:


Part d
We want this probability:

We find the z scores:



Answer:
4
Step-by-step explanation:
12 divided by 3 is 4. It's that simple!
Given:
The logarithmic expression is:

To find:
The equivalent expression of given expression by using change-of-base formula.
Solution:
The change-of-base formula is:

The given expression is:

Using the change-of-base formula, we get

Where, is a constant and c>0.
Let
, then

Therefore, the correct option is a.
11.k>-3(4r+3)/4r-5
12.k<(2x+2)/x+3