Answer:
For this case the confidence interval is given by :
Step-by-step explanation:
Data provided
represent the sample mean for the fuel efficiencies
population mean
s=2.51 represent the sample standard deviation
n=601 represent the sample size
Confidence interval
The formula for the confidence interval of the true mean is given by:
(1)
The degrees of freedom for this case is given by:
The Confidence level for this case is 0.95 or 95%, and the significance level 
and 
and the critical value is given by 
Replcing into the formula for the confidence interval is given by:
For this case the confidence interval is given by :
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
To find the indicated angle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the adjacent side and the hypotenuse. Therefore, we should use cosine to solve.
cos(x) = 12/36
x = cos^-1(12/36)
x = 71 degrees
Hope this helps!
