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2 years ago

Find the inverse of each function. f(n)=n+4/2

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

3 0

Step-by-step explanation:

$f(n) = \frac{ n +4}{2} \\ let \: f(n) = y \implies \: n = {f}^{ - 1}(y) \\ \therefore \: y = \frac{ n +4}{2} \\ \\ \therefore \:2 y = n +4 \\ \\ \therefore \:2 y - 4= n \\ \therefore \:n = 2y - 4 \\ \\ \therefore \: {f}^{ - 1}(y) = 2y - 4 \\ \\ \red{ \boxed{\bold{\therefore \: {f}^{ - 1}(n) = 2n- 4} }}$

(Replacing y by n)

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Read 2 more answers

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

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Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

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3 years ago