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3 years ago

Please tell me the answer! I'm crying in confusion! :(

Mathematics

2 answers:

Natalka [10]3 years ago

8 0

Find the common denominator:

3 6 9
-- -- --
7 14 21

1 2 3 4 5 6 7 8
-- -- -- -- -- -- -- --- ---
3 6 9 12 15 18 21

Ok, so we know the common demonators are 9/21 and 8/21

Now we subtract 9/21 and 8/21 which is 1/21

So.. There is 1/21 pizza left!

Hope this helped :))

Inessa [10]3 years ago

6 0

First, change the fractions to a common denominator, which is 21.

so 3/7 * 3/3 = 9/21

1/3 * 7/7 = 7/21

Add the two together

9/21 + 7/21 = 16/21

Then take 21/21 - 16/21 = 5/21

There is 5/21 of the pizza left.

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Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length

Paladinen [302]

Answer:

a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b) s = 0.44

c) 0.84% of the sample means will be greater than 27.05 seconds

d) 98.46% of the sample means will be greater than 25.05 seconds

e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

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 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 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(also called standard error) $s = \frac{\sigma}{\sqrt{n}}$ .

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

In this problem, we have that:

$\mu = 26, \sigma = 2, n = 21, s = \frac{2}{\sqrt{21}} = 0.44$

a. What can we say about the shape of the distribution of the sample mean time?

By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b. What is the standard error of the mean time? (Round your answer to 2 decimal places)

$s = \frac{2}{\sqrt{21}} = 0.44$

c. What percent of the sample means will be greater than 27.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 27.05. So

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

By the Central Limit Theorem

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

$Z = \frac{27.05 - 26}{0.44}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

1 - 0.9916 = 0.0084

0.84% of the sample means will be greater than 27.05 seconds

d. What percent of the sample means will be greater than 25.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 25.05. So

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

$Z = \frac{25.05 - 26}{0.44}$

$Z = -2.16$

$Z = -2.16$ has a pvalue of 0.0154

1 - 0.0154 = 0.9846

98.46% of the sample means will be greater than 25.05 seconds

e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"

This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.

X = 27.05

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

$Z = \frac{27.05 - 26}{0.44}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

X = 25.05

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

$Z = \frac{25.05 - 26}{0.44}$

$Z = -2.16$

$Z = -2.16$ has a pvalue of 0.0154

0.9916 - 0.0154 = 0.9762

97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

8 0

3 years ago

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Inga [223]

Answer:

2ab(a + 3b)

Step-by-step explanation:

2a²b + 6ab²

Factor out 2ab

2ab(a + 3b)

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Rama09 [41]

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Answer:

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mrs_skeptik [129]

Hi Mrsdiaz1jd1977owwfvt!
OK so 2,000 boards per hour in 10 hours is 2,000*10=20,000 boards in 10 hours. So it can produce 16,500 boards in less than a day.
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4 years ago

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