Find the variance of [6 ,7 ,10 ,11 ,12 ,13 ,16 ,18 ,25].
1 answer:
The variance of [6 ,7 ,10 ,11 ,12 ,13 ,16 ,18 ,25] is 34.61
The sample size (n) = 9
The mean of the distribution (x_i) is the sum of the distribution divided by the number of items in the distribution.
The variance is the average between the difference of the mean, followed by squaring the result.
Therefore, the variance of the sample given is 34.61
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The series converges to 1/(1-9x) for -1/9<x<1/9
Given the series is ∑
We have to find the values of x for which the series converges.
We know,
∑ converges to (a) / (1-r) if r < 1
Otherwise the series will diverge.
Here, ∑ is a geometric series with |r| = | 9x |
And it converges for |9x| < 1
Hence, the given series gets converge for -1/9<x<1/9
And geometric series converges to a/(1-r)
Here, a = 1 and r = 9x
Therefore, a/(1-r) = 1/(1-9x)
Hence, the given series converges to 1/1-9x for -1/9<x<1/9
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Answer: (a) 2 : 3
(b) 4 :1
Step-by-step explanation:
The Volume of a sphere is given as
and the volume of a cylinder is given as
h
The ration of their volume is the same as Volume of Sphere : Volume of Cylinder , which gives
:
h
recall that they have the same radius and the height of the cylinder is 2r , taking this into consideration, we have
:
(2r)
which gives 4 : 6 = 2 :3
(b) The area of a sphere is 4
and the surface area of the circular cylinder is
The ratio then gives
4
:
,which gives
4 : 1