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garri49 [273]
3 years ago
12

What is the slope of a line that is perpendicular to the line y= 1/3 x - 2

Mathematics
1 answer:
drek231 [11]3 years ago
4 0

Answer:

slope = - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{1}{3} x - 2 ← is in slope- intercept form

with slope m = \frac{1}{3}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{1}{3} } = - 3

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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.

The decision rule is:

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:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The information provided is:

<em>n</em> = 42

<em>X</em> = number of red candies = 7

Compute the sample proportion of candies that are red as follows:

\hat p=\frac{X}{n}=\frac{7}{42}=0.167

The critical value of <em>z</em> for 95% confidence level is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use a <em>z</em>-table for the critical value.

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)

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

The confidence interval does not contains the null value.

Thus, the null hypothesis will be rejected at 5% level of significance.

Conclusion:

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

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