Merry Christmas and a happy new year
        
             
        
        
        
Answer:
 (x) =
(x) =  x + 8
 x + 8
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 9(x - 8) ← divide both sides by 9
 = x - 8 ( add 8 to both sides )
 = x - 8 ( add 8 to both sides )
 + 8 = x
 + 8 = x
Change y back into terms of x with x =  (x) , thus
(x) , thus
 (x) =
(x) =  x + 8
 x + 8
 
        
             
        
        
        
The volume of the sphere is expressed in the formula V= 4/3 3.14r^3 and we are given the radius of the sphere. to find the volume, we can directly substitute r as the unit of the volume to be determined is consistent with the given. Hence, via subsitution, the answer is 1.7671 cubic feet 
        
             
        
        
        
Answer:
The lower bound for a 90% confidence interval is 0.2033.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of  , and a confidence level of
, and a confidence level of  , we have the following confidence interval of proportions.
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of  .
.
For this problem, we have that:

90% confidence level
So  , z is the value of Z that has a pvalue of
, z is the value of Z that has a pvalue of  , so
, so  .
.
The lower limit of this interval is:

The lower bound for a 90% confidence interval is 0.2033.
 
        
             
        
        
        
Answer:
hope this helped you
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