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2 years ago

75 POINTS !!!!! URNGETNM EASY MATH PLEAS EIM CYRING I NEED NOW PLEAS ESOW ALL WORK AND EXPLAIN PLEASE

Mathematics

1 answer:

Naddika [18.5K]2 years ago

7 0

Answer:

$y = -2x +3\\\rule{150}{0.5}\\\text{Slope: -2}\\\text{Y-Intercept: 3}$

Step-by-step explanation:

We would have to convert the standard equation into slope-intercept form.

======================================

<h3><u>Converting the equation into Slope-Intercept Form:</u></h3>

<u /> $8x + 4y = 12\\\rule{150}{0.5}\\8x - 8x + 4y = 12-8x\\\\4y = 12-8x\\\\4y = -8x + 12 \leftarrow \text{I switched the order on the right side.}\\\\\frac{4y=-8x+12}{4}\\\\\boxed{y = -2x + 3}$

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<h3><u>Identifying the Slope and Y-Intercept:</u></h3>

<em>General slope-intercept form is: </em>

<em></em> $y=mx + b\\\rule{150}{0.5}\\\text{m - Slope}\\\text{b - Y-Intercept}$

<u />

In the equation $y = -2x + 3$ , '-2' would be the slope since it is in 'm's place, and '3' would be the y-intercept since it's in 'b's place.

<em>Therefore:</em>

<em></em> $\text{In } y=-2x+3\text{...}\\\rule{150}{0.5}\\\text{Slope: -2}\\\text{Y-Intercept: 3}$ <em></em>

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<em>Hope this helps!</em>

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Answer:

$17.67-2.92\frac{2.517}{\sqrt{3}}=13.427$

$17.67+2.92\frac{2.517}{\sqrt{3}}=21.913$

So on this case the 90% confidence interval would be given by (13.427;21.913)

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".

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

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n 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 mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=17.67$

The sample deviation calculated $s=2.517$

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

$df=n-1=3-1=2$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ 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: "=-T.INV(0.05,2)".And we see that $t_{\alpha/2}=2.92$

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

$17.67-2.92\frac{2.517}{\sqrt{3}}=13.427$

$17.67+2.92\frac{2.517}{\sqrt{3}}=21.913$

So on this case the 90% confidence interval would be given by (13.427;21.913)

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