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2 years ago

Solve the following absolute value equation. −8 − 2 |5X – 17| = −14

Mathematics

1 answer:

Levart [38]2 years ago

4 0

If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to

-8 - 2 (5x - 17) = -14

-8 - 10x + 34 = -14

-10x = -40

x = 4

If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have

-8 - 2 (-5x + 17) = -14

-8 + 10x - 34 = -14

10x = 28

x = 2.8

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

$18-2.262\frac{2.75}{\sqrt{10}}=16.03$

$18+2.262\frac{2.75}{\sqrt{10}}=19.97$

Step-by-step explanation:

Information given

$\bar X=18$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.75 represent the sample standard deviation

n=10 represent the sample size

Confidence interval

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

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

The degrees of freedom are given by:

$df=n-1=10-1=9$

The Confidence is 0.90 or 90%, the significance is $\alpha=0.1$ and $\alpha/2 =0.05$ , and the critical vaue would be $t_{\alpha/2}=2.262$

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

$18-2.262\frac{2.75}{\sqrt{10}}=16.03$

$18+2.262\frac{2.75}{\sqrt{10}}=19.97$

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2 years ago

The table below gives the dimensions of a bridge and a scale model of the bridgeFind the scale factor of the model to the real b

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3 years ago

Express 3080 as a product of prime factors

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Prime Factors of 3080 =2, 2, 2, 5, 7, 11

Which is the same as = 23 x 5 x 7 x 11

Prime Factors Tree of 3080

3080
/ \
2 1540
/ \
2 770
/ \
2 385
/ \
5 77
/ \
7 11
/ \
11 1

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