Answer:
We need a sample size of at least 75.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, we find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The standard deviation is the square root of the variance. So:
With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
We need a sample size of at least n, in which n is found when M = 5. So
We need a sample size of at least 75.
It has to be the first one
Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
which is a cubic polynomial in 
with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then 
can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)
Its the connection between those numbers
The circumference of this circle is c=94.25ft
