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Juliette [100K]
3 years ago
6

When a number is added to 1/5 of itself, the result is 24. The equation that models this problem is n + 1/5n = 24. What is the v

alue n?
Mathematics
1 answer:
Katarina [22]3 years ago
8 0

Answer:

First we need to subtract n on both sides. That will give us 1/5n = 24 - n. Then we need to divide both sides by 1/5 aka multipliying both sides by 5. Now we have n = 120-5n. Now we subtract both sides by n. That will give us 0 = 120 - 4n. Now lets add both sides by 4n. Canceling the 4n on the right side. 120 = 4n. Now we need to divide both sides by 4. 30 = n. Therefore the answer is 30

<h2><u>30 = n thats the answer</u></h2>

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The number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. A sample of 1
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Answer:

The 98% confidence interval for the population mean number of hours worked per year per person is (2146, 2193).

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The question is incomplete.

The number of hours registered in the sample are:

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The sample mean can be calculated as:

M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{15}(2051+2061+2162+2167+2169+2171+2180+2183+2186+2195+2196+2198+2205+2210+2211)\\\\\\M=\dfrac{32545}{15}\\\\\\M=2169.67\\\\\\

We have to calculate a 98% confidence interval for the mean.

The population standard deviation is know and is σ=39.

The sample mean is M=2169.67.

The sample size is N=15.

As σ is known, the standard error of the mean (σM) is calculated as:

\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{39}{\sqrt{15}}=\dfrac{39}{3.873}=10.07

The z-value for a 98% confidence interval is z=2.326.

The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_M=2.326 \cdot 10.07=23.43

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 2169.67-23.43=2146\\\\UL=M+t \cdot s_M = 2169.67+23.43=2193

The 98% confidence interval for the population mean is (2146, 2193).

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