Help please!!!!!:( Solve the equation for x. Round your answer to two decimal places. Do not include "x =" in your answer.

2 answers:

4 0

The solution to the problem is as follows:

If you use Ln you can get rid of e.

ln(e^0.4x) = ln(0.4)

0.4x = ln(0.4)

x = (ln(0.4))/0.4

<span>x = -2.29
</span>
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Anna007 [38]3 years ago

4 0

Answer:

x = ( -2.29 )

Step-by-step explanation:

The given expression is $e^{(0.4x)}=0.4$

We have to solve this equation for the value of x. We take natural log on both the sides of the equation.

$ln(e)^{0.4x}=ln(0.4)$

0.4x ln(e) = ln (0.4)

0.4x = ln (0.4) [ Since lne = 1 ]

0.4x = -0.9163

$x=\frac{0.9163}{0.4}$ = 2.29

Therefore, x = ( -2.29 ) is the answer.

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The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$