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Rzqust [24]
3 years ago
14

In the equation for a confidence interval, the sample size is located in the denominator underneath the radical sign. What happe

ns to the value of the expression under the radical sign as the sample size increases?
Mathematics
1 answer:
Lorico [155]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that in the equation for a confidence interval, the sample size is located in the denominator underneath the radical sign.

In hypothesis testing we have

Confidence interval = Mean ±Margin of error

= Mean±Z critical*std dev/sqrt n

Thus we find that whenever n increases, sqrt of n increases,  margin of error decreases and as a result we find that whenever sample size increases then sqrt n also increases which in turn reduces the wirth of confidence interval.

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Write the first five terms of the sequence. an=n2 +2​
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Answer:

The first five terms of the given sequence

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Step-by-step explanation:

It is given that,

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<u>To find the first five terms</u>

a₁ = 1² + 2 = 1 + 2 = 3

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Semicircles
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Answer:

The area of the shaded portion of the figure is 9.1\ cm^2

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shaded area is equal to the area of the square less the area not shaded.

There are 4 "not shaded" regions.

step 1

Find the area of square ABCD

The area of square is equal to

A=b^2

where

b is the length side of the square

we have

b=4\ cm

substitute

A=4^2=16\ cm^2

step 2

We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):

The area of circle is equal to

A=\pi r^{2}

The diameter of the circle is equal to the length side of the square

so

r=\frac{b}{2}=\frac{4}{2}=2\ cm ---> radius is half the diameter

substitute

A=\pi (2)^{2}

A=4\pi\ cm^2

Therefore, the area of 2 "not-shaded" regions is:

A=(16-4\pi) \ cm^2

and the area of 4 "not-shaded" regions is:

A=2(16-4\pi)=(32-8\pi)\ cm^2

step 3

Find the area of the shaded region

Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:

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A=16-(32-8\pi)=(8\pi-16)\ cm^2  

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assume

\pi =3.14

substitute

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