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3 years ago

Find the perimeter of this figure to the nearest hundredth

Mathematics

1 answer:

Alja [10]3 years ago

8 0

Answer:

The perimeter of given figure = 56.56 ft

Step-by-step explanation:

Step(i):-

From diagram

The length of the rectangle = 10 ft

The width of the rectangle = 8 ft

Perimeter of the rectangle

= 2 ( l+w)

= 2 ( 10 + 8)

= 2 × 18

= 36

Step(ii):-

The semi circle is included in the given diagram

Now we will find the perimeter of semicircle

We know that

perimeter of the circle

p = 2πr + d

perimeter of the semicircle

P = πr + 2 r (∵ d = 2 r)

Step(iii):-

From diagram the diameter of semicircle is equal to the width of the rectangle

d = 8

d = 2 r = 8

The radius of the circle 'r' = 4

perimeter of the semicircle

P = πr + 2 r

P = 3.14 ( 4) + 8

P= 20.56

Conclusion:-

The perimeter of given figure

= perimeter of rectangle + perimeter of semicircle

= 36 + 20.56

=56.56 ft

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Suppose 52% of the population has a college degree. If a random sample of size 563563 is selected, what is the probability that

amm1812

Answer:

The value is $P(| \^ p - p| < 0.05 ) = 0.9822$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.52$

The sample size is n = 563

Generally the population mean of the sampling distribution is mathematically represented as

$\mu_{x} = p = 0.52$

Generally the standard deviation of the sampling distribution is mathematically evaluated as

$\sigma = \sqrt{\frac{ p(1- p)}{n} }$

=> $\sigma = \sqrt{\frac{ 0.52 (1- 0.52 )}{563} }$

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Generally the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5% is mathematically represented as

$P(| \^ p - p| < 0.05 ) = P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 ))$

Here $\^ p$ is the sample proportion of persons with a college degree.

$P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 )) = P(\frac{[[0.05 -0.52]]- 0.52}{0.02106} < \frac{[\^p - p] - p}{\sigma } < \frac{[[0.05 -0.52]] + 0.52}{0.02106} )$