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Marizza181 [45]
3 years ago
7

Write an equation in slope-intercept form for the following line: (-14.1) and (13,-2)

Mathematics
1 answer:
vesna_86 [32]3 years ago
8 0

Answer:

y=-\frac{1}{9}x-\frac{5}{9}

Step-by-step explanation:

(-14,1)(13,-2)

Use the slope-intercept formula:

y=mx+b

m is the slope and b is the y-intercept. Use the slope formula first:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}

Rise over run is the change in the y-axis over the change in the x-axis. Plug in the coordinates:

(-14(x_{1}),1(y_{1}))\\(13(x_{2}),-2(y_{2}))

\frac{-2-1}{13-(-14)}

Simplify parentheses (two negatives makes a positive):

\frac{-2-1}{13+14}

Simplify:

\frac{-3}{27} =-\frac{3}{27}=-\frac{1}{9}

The slope is -\frac{1}{9}. Insert into the equation:

y=-\frac{1}{9}x +b

Now, to find the y-intercept, take one of the points and substitute for the x and y values of the equation:

(13,-2)\\-2=-\frac{1}{9} (13)+b

Solve for b, the y-intercept. Simplify parentheses:

-\frac{1}{9}*\frac{13}{1}=-\frac{13}{9}

-2=-\frac{13}{9} +b

Add -\frac{13}{9}  to both sides:

-2+\frac{13}{9}=-\frac{13}{9} +\frac{13}{9}  +b\\\\-2+\frac{13}{9} =b

Simplify:

-\frac{2}{1} +\frac{13}{9}\\\\-\frac{18}{9}+\frac{13}{9}\\  \\b=-\frac{5}{9}

The y-intercept is -\frac{5}{9} . Insert this into the equation:

y=-\frac{1}{9} x-\frac{5}{9}

Finito.

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Answer:

The 95% confidence interval for true proportion of red candies is (5%, 27%).

The true proportion of red candies made by the company is different from 33%.

Step-by-step explanation:

The hypothesis to determine whether the claim made by the candy company is correct or not is:

<em>H</em>₀: The true proportion of red candies made by the company is 33%, i.e. <em>p</em> = 0.33.

<em>Hₐ</em>: The true proportion of red candies made by the company is different from 33%, i.e. <em>p</em> ≠ 0.33.

A (1 - <em>α</em>)% confidence interval can be constructed to check this claim.

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If the confidence interval consists the null value then the null hypothesis will not be rejected. Otherwise it will be rejected.

The (1 - <em>α</em>)% confidence interval for population proportion is:

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The information provided is:

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Compute the 95% confidence interval for true proportion of red candies as follows:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.167\pm 1.96\times \sqrt{\frac{0.167(1-0.167)}{42}}\\=0.16\pm0.1137\\=(0.0463, 0.2737)\\\approx(0.05, 0.27)

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