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vlabodo [156]
3 years ago
5

A central angle in a circle with a radius of 7in. intercepts an arc with a length of 9in. What is the radian measure of the cent

ral angle?

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0
A central angle in a circle with a radius of 7in. intercepts an arc with a length of 9in. What is the radian measure of the central angle?

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If the point (5, k) lies on the line represented by the equation 2x + y = 9, the value of k is
Paladinen [302]

Answer:

<h2>k = -1</h2>

Step-by-step explanation:

We have the point (5, k) and the equation 2x + y = 9.

Put the coordinates of the point ot the equation:

x = 5, y = k

2(5) + k = 9

10 + k = 9         <em>subtract 10 from both sides</em>

10 - 10 + k = 9 - 10

k = -1

4 0
3 years ago
The time a randomly selected individual waits for an elevator in an office building has a uniform distribution with a mean of 0.
Amiraneli [1.4K]

Answer:

The mean of the sampling distribution of means for SRS of size 50 is \mu = 0.5 and the standard deviation is s = 0.0409

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size, of at least 30, can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 0.5, \sigma = 0.289

What are the mean and standard deviation of the sampling distribution of means for SRS of size 50?

By the Central Limit Theorem

\mu = 0.5, s = \frac{0.289}{\sqrt{50}} = 0.0409

The mean of the sampling distribution of means for SRS of size 50 is \mu = 0.5 and the standard deviation is s = 0.0409

Does it matter that the underlying population distribution is not normal?

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

What is the probability a sample of 50 people will wait longer than 45 seconds for an elevator?

We have to use 45 seconds as minutes, since the mean and the standard deviation are in minutes.

Each minute has 60 seconds.

So 45 seconds is 45/60 = 0.75 min.

This probability is 1 subtracted by the pvalue of Z when X = 0.75. So

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

By the Central Limit Theorem

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

Z = \frac{0.75 - 0.5}{0.0409}

Z = 6.11

Z = 6.11 has a pvalue of 1

1-1 = 0

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

8 0
3 years ago
What is the divisibility rule(s) for 93?
My name is Ann [436]
It is prime, it can't be divided by anything, but itself and one.
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3 years ago
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Two datasets arranged in descending order are: {8, x, 4,1) and (9. y, 5,2). If the medians of
OverLord2011 [107]

Answer:

Legon fo)

Step-by-step explanation:

3 0
3 years ago
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3.<br>June has 248 oranges. She sells of these oranges. How many oranges did June sell?<br>Answer.​
uranmaximum [27]

Answer:

93. Divide 248 by 8. One eighth of 248 = 31.

June sold 3/8 of the 248 oranges.

If 1/8 = 31 and June sold 3/8 of the oranges.

Multiply 3 × 31. Therefore June sold 93 oranges.

Step-by-step explanation:

5 0
2 years ago
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