Answer:
E. None of the above.
Step-by-step explanation:
The central limit theorem states that; the sampling distribution of a population mean tends towards a normal distribution with respect to an increasing sample size. It implies that as the sample size increases, the shape of a sampling distribution would approach normality as required.
Therefore, most options in the given question are importance of the theorem. Thus, none of the above is the correct choice because other choices are directly or indirectly an importance of central limit theorem.
A graph can be helpful for finding limits of integration.
The volume can be found using cylindrical shells of height (x-0.5x^2) and radius (3-x).
_____
The parabola whose area is shaded purple is the difference between the curves y=x and y=0.5x^2. The area under the parabola shaded purple is
(2/3)*height*width = (2/3)*(0.5)*2 = 2/3
The volume is that area multiplied by the circumference of the circle about which its centroid is revolved. That circle has radius 2, so its circumference is 4π. Then the volume is
V = (2/3)*4π = 8π/3
The common ration is 12/ -4 = -3
the explicit term is (-4)* -3^(n-1)
so the 5th term is -4*-3^4 = -324
Im a bit hazy about the recursive formula
i think its a(n+1) = an * -3