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Alika [10]
2 years ago
6

A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the poi

nt will be in the shaded region.
about 60%

about 50%

about 30%

about 75%

Mathematics
1 answer:
liubo4ka [24]2 years ago
8 0

Answer:

The correct answer is first option 60%

Step-by-step explanation:

The radius of a circle is inscribed in an equilateral triangle with side a = a/2√3

<u>To find the area of equilateral triangle</u>

Here side be 'a'

Area of equilateral = √3a²/4

<u>To find the area of circle</u>

Here radius = a/2√3

Area = πr²

 = π(a/2√3)

 = 3.14a²/12

<u>To find the probability</u>

probability = area of circle/area of triangle

   = 3.14a²/12/ √3a²/4

   = 3.14/3√3

   = 0.6043 ≈ 60.43 %  60 %

The correct answer is first option 60%

 

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The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of m
UkoKoshka [18]

Answer:

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

X \sim N(14.7,3.7)  

Where \mu=14.7 and \sigma=3.7

Since the distribution of X is normal then we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we have;

\mu_{\bar X}= 14.70

\sigma_{\bar X} =\frac{3.7}{\sqrt{40}}= 0.59

Step-by-step explanation:

Assuming this question: The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 14.7 minutes and a standard deviation of 3.7 minutes. Let R be the mean delivery time for a random sample of 40 orders at this restaurant. Calculate the mean and standard deviation of \bar X Round your answers to two decimal places.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

X \sim N(14.7,3.7)  

Where \mu=14.7 and \sigma=3.7

Since the distribution of X is normal then we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we have;

\mu_{\bar X}= 14.70

\sigma_{\bar X} =\frac{3.7}{\sqrt{40}}= 0.59

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Answer:

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Step-by-step explanation:

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use the -3 for b and you get

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2/3+(-1/3)
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Your answer is 1/3
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Answer:

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Step-by-step explanation:

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