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Stels [109]
3 years ago
13

The mean of four consecutive even numbers is 15. The greatest of these numbers is a1. The least of these numbers is a2.

Mathematics
1 answer:
skad [1K]3 years ago
6 0
X + (x + 2) + ( x + 4) + (x + 6)
-----------------------------------     = 15
                   4

4x + 12
---------    = 15
    4

Multiply by 4 on both sides

4x + 12 = 60
subtract 12 from both sides
4x = 48
divide by 4 on each side
x = 12
x + 2 = 14
x + 4 = 16
x + 6 = 18
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According to a report from a business intelligence company, smartphone owners are using an average of 22 apps per month. Assume
Ira Lisetskai [31]

Answer:

0.4332 = 43.32% probability that the sample mean is between 21 and 22.

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.

According to a report from a business intelligence company, smartphone owners are using an average of 22 apps per month.

This means that \mu = 22

Standard deviation is 4:

This means that \sigma = 4

Sample of 36:

This means that n = 36, s = \frac{4}{sqrt{36}}

What is the probability that the sample mean is between 21 and 22?

This is the p-value of Z when X = 22 subtracted by the p-value of Z when X = 21.

X = 22

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

By the Central Limit Theorem

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

Z = \frac{22 - 22}{\frac{4}{sqrt{36}}}

Z = 0

Z = 0 has a p-value of 0.5.

X = 21

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

Z = \frac{21 - 22}{\frac{4}{sqrt{36}}}

Z = -1.5

Z = -1.5 has a p-value of 0.0668.

0.5 - 0.0668 = 0.4332

0.4332 = 43.32% probability that the sample mean is between 21 and 22.

4 0
2 years ago
Percents
Yuki888 [10]

Answer:

Percentage: 115%

Decimal: 1.15

Fraction: \frac{23}{20}\\

Step-by-step explanation:

<u>Percentages, Fractions, and Decimals</u>

Assume we set 100% as the original price of the food that Michael consumed. When he leaves a 15% tip for the waitress, he is really paying 100%+15%=115% of the original price.

Now we express 115% as a decimal, simply dividing by 100:

115% = 115/100 = 1.15

To express it as a fraction, we simplify the division instead of calculating it:

115% = \frac{115}{100}

Simplifying by 5:

115% = \frac{23}{20}

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Step-by-step explanation:

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the opposite of the point is (1,-1)

This point is in the fourth quadrant

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Amu of unknown element = 40 - (20% * 40)
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therefore, the approximate weight of the unknown element is 38 amu.

hope this helps.
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Step-by-step explanation:

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