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3 years ago

Solve the equation. 5 | n | - 15 = 40

Mathematics

2 answers:

son4ous [18]3 years ago

8 0

$|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a$

Answer: n = -11 or n = 11

Ilya [14]3 years ago

6 0

Hi there!

Let's solve this equation step by step!

$5 |n| - 15 = 40$
First add 15 to both sides of the equation.

$5 |n| = 55$
Now divide both sides by 5.

$|n| = 11$

Finally we need to take a look at the meaning of the stripes between our variable. Those stripes mean we are dealing with an absolute value function. The absolute value stripes make everything between the stripes positive; also when we plug in a number. In this particular question we can plug in both -11 and 11 at the position of n, because when -11 is made positive, it fulfils the equation.

Hence,
$n = 11$ or $n = - 11$

~ Hope this helps you!

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3 years ago

In a random sample of 25 people, the mean commute time to work was 33.9 minutes and the standard deviation was 7.2 minutes. Ass

Phoenix [80]

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$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

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".

$\bar X=33.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.2 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 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,24)".And we see that $t_{\alpha/2}=1.32$