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3 years ago

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

1 answer:

6 0

Directrix y = 8
It is a horizontal line so the parabola is vertical.
The focus (2, 4) lies below the directrix,
Therefore parabola opens downwards. 
vertex will be halfway between focus and directrix, at (2, 6) 
focal length =p
= distance between focus and vertex
= 2 
y = (-1/(4p))(x - 2)² + 6 
y = (-1/8)(x - 2)² + 6
hope this helps

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2 years ago

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in a random sample of 28 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.3 minutes. assu

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Answer:

The margin of error of u is of 3.8.

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Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 28 - 1 = 27

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.7707

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$M = T\frac{s}{\sqrt{n}} = 2.7707\frac{7.3}{\sqrt{28}} = 3.8$

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error of u is of 3.8.

The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes

The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes

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3 years ago

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2 years ago

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<h3>How to find the equation of linear regression?</h3>

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

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More can be learned about linear regression at brainly.com/question/22992800

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10 months ago