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labwork [276]
3 years ago
5

A circle has its center at the center of a square with 26-inch sides. Using 3.14 for pi, find the area of the square not covered

by the circle, then write a ratio of the circle’s circumference to the perimeter of the square.
Mathematics
2 answers:
AlladinOne [14]3 years ago
7 0
For squrae
area=side²
perimiter=4(side)

for circle
area=pir²
circumference=2pir

side=diameter, diameter/2=radius=side/2


find area not covered
that is areasquare-areacircle
areasquare=26²=676 sqauare inches
areaciecle, diameter=side, 26/2=13, area=pi13²=169*3.14=530.66 square inches

areanotcovered=676-530.66=145.34 square inches not coverd


ratio of perimiter to circumferece
perimiter=4*26=104
circumference=2pir=2pi13=26pi=26*3.14=81.64
circumference to perimiter is 81.64/104=0.785

earnstyle [38]3 years ago
7 0

area of square = s^2 = (26)^2  

area of circle = pi*r^2 = 3.14*(13)^2  

area of square not covered by the circle = 26^2-3.14(13)^2  

perimeter of square = 4s = 4(26) = 104  

circumference of circle = pi*d = 3.14*26  

circumference:perimeter ratio => 3.14:4

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Answer:

\hat p = \frac{14}{105}= 0.133

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:  

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If we replace the values obtained we got:

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Step-by-step explanation:

Previous concept

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

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In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

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The proportion estimated would be:

\hat p = \frac{14}{105}= 0.133

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

If we replace the values obtained we got:

0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475

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The 99% confidence interval would be given by (0.0475;0.2185)

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