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Murljashka [212]
3 years ago
5

What is the volume.of pirámide when the height is 6in and a dimensions are 3in and 5in

Mathematics
1 answer:
blondinia [14]3 years ago
8 0

Answer:

90

Step-by-step explanation:

multiply all three numbers

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The time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes
klio [65]

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that \mu = 10, \sigma = 2

Suppose 64 visitors independently view the site.

This means that n = 64,  = \frac{2}{\sqrt{64}} = 0.25

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

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

By the Central Limit Theorem

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

Z = \frac{10.25 - 10}{0.25}

Z = 1

Z = 1 has a p-value of 0.8413.

X = 9.75

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

Z = \frac{9.75 - 10}{0.25}

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c. The value exceeded by the mean time of the visitors with probability 0.01.

The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.

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

2.327 = \frac{X - 10}{0.25}

X - 10 = 2.327*0.25

X = 10.58

So 10.58 minutes.

6 0
3 years ago
A circle has radius 50 cm. Which of these is closest to its area?
olga55 [171]

Answer:

7854 cm²

Step-by-step explanation:

3.14 x 50² = 7850

4 0
2 years ago
A group of 3 friends are splitting fruit salad at a picnic. If each person gets 11 pieces, how many total pieces of fruit are th
strojnjashka [21]

Answer:

33 Pieces total

Step-by-step explanation:

4 0
2 years ago
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If two numbers round to the same number, does that mean the numbers are equal?
Eduardwww [97]
If two numbers round to the same number it doesnt always mean they are equal, for example: 11 and 9 both round to ten but they are not the same number
3 0
3 years ago
Read 2 more answers
$5000 at 6% for 9 months what is the balance
Kay [80]
I think it's suppose to go

6% is .06 divided by 12 which is .005 times the number of months so in this case 9 so 5,000 times .005 times 9 which is 225 so 5,000 plus an interest of 225 adds up to 5,225
8 0
3 years ago
Read 2 more answers
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