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4 years ago

Please help me find the area of each shaded segment and round the answer to the nearest tenth :)

Mathematics

1 answer:

Keith_Richards [23]4 years ago

3 0

Hi there!

In order to solve, we need to use the formula for the area of a circle, and the angle given to find the area of the sector. Then, subtract the area of the triangle to find the area of the segment. We would use the equation : A = x/360 (pi * r^2) - 1/2(b * h). We need to plug in 90 for the angle measurement, 8 for the radius, and 8 for both the base and height.

WORK:
A = 90/360 (pi * 64) - 1/2(64)
A = 1/4(64pi) - 32
A = 16pi - 32 = ~ 18.3ft^2

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

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lisabon 2012 [21]

Answer:

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Step-by-step explanation:

1) Data given and notation

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s=2.573 represent the sample standard deviation

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A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

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$\chi^2_{\alpha/2}=32.852$

$\chi^2_{1- \alpha/2}=8.907$

And replacing into the formula for the interval we got:

$\frac{(19)(6.62)}{32.852} \leq \sigma^2 \frac{(19)(6.62)}{8.907}$

$3.829 \leq \sigma^2 \leq 14.121$

So the 95% confidence interval for the variance in the pounds of impurities would be $3.829 \leq \sigma^2 \leq 14.121$ .

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(

)

−

Explanation:

A quadratic function can be written in vertex form as:

(

)

(

−

)

where

(

)

is the vertex and

is a constant multiplier.

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(

)

(

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, so we can write:

(

)

(

−

)

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(

)

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(

−

)

Subtract

from both ends to get:

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Divide both sides by

and transpose to find:

−

So our quadratic function can be written in vertex form as:

(

)

−

(

−

)

We can multiply this out and simplify as follows:

(

)

−

(

−

)

(

)

−

(

−

)

(

)

−

(

)

−

Step-by-step explanation:

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