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belka [17]
1 year ago
12

The circumference of a circle is 9 pi m. What is the area, in square meters? Express your answer in terms of pi​

Mathematics
1 answer:
Travka [436]1 year ago
5 0

Answer:

The circumference of a circle = 2πr = 9π inches

Or, 2πr = 9π

Or, r = 9/2

Or, r = 4.5 inches

The area of a circle = πr²

Or, The area of a circle = π×4.5×4.5

Or, The area of a circle = 20.25π square inches

Step-by-step explanation:

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Step-by-step explanation:

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The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $3
DerKrebs [107]

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

The parameters in this problem are given as follows:

\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5

Item a:

The probability is the <u>p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000</u>, hence:

X = 1250:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1250 - 1140}{77.5}

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

Z = \frac{X - \mu}{s}

Z = \frac{1000 - 1140}{77.5}

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is <u>one subtracted by the p-value of Z when X = 1250</u>, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the <u>p-value of Z when X = 1220</u>, hence:

Z = \frac{X - \mu}{s}

Z = \frac{1220 - 1140}{77.5}

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

More can be learned about the normal distribution at brainly.com/question/4079902

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Answer:

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Step-by-step explanation:

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Answer:

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1 year ago
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