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Sergio [31]
3 years ago
9

Find an equation for the line that passes through the points (5.-5) and (-4,-2)

Mathematics
1 answer:
ANEK [815]3 years ago
4 0

Answer:

\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (5, -5) and (-4, -2).

Substiute:

m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

-5=-\dfrac{1}{3}(5)+b

-5=-\dfrac{5}{3}+b               <em>add 5/3 to both sides</em>

-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}

Finally we have the equation of a line in the slope-intercept form:

y=-\dfrac{1}{3}x-\dfrac{10}{3}

Convert to the standard form <em>(Ax + By = C)</em>:

y=-\dfrac{1}{3}x-\dfrac{10}{3}          <em>multiply both sides by 3</em>

3y=-x-10              <em>add x to both sides</em>

x+3y=-10

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Answer:

The 95% confidence interval for the population variance is (8.80, 32.45).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population variance is given as follows:

\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}

It is provided that:

<em>n</em> = 20

<em>s</em> = 3.9

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Compute the critical values of Chi-square:

\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2, (20-1)}=\chi^{2}_{0.025,19}=32.852\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.05/2, (20-1)}=\chi^{2}_{0.975,19}=8.907

*Use a Chi-square table.

Compute the 95% confidence interval for the population variance as follows:

\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}

\frac{(20-1)\cdot (3.9)^{2}}{32.852}\leq \sigma^{2}\leq \frac{(20-1)\cdot (3.9)^{2}}{8.907}\\\\8.7967\leq \sigma^{2}\leq 32.4453\\\\8.80\leq \sigma^{2}\leq 32.45

Thus, the 95% confidence interval for the population variance is (8.80, 32.45).

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