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2 years ago

What is the y intercept of the line that passes through the point 3, 4 and has a slope of 3

Mathematics

1 answer:

notka56 [123]2 years ago

3 0

(0, -5)

Step-by-step explanation:

Since we are given the slope and a point on the line, we can use these to write the point-slope form of the equation of the line, which looks this this:

$y - y_1 = m(x - x_1)$

where $(x_1, y_1)$ is the point on the line and m is the slope. So the equation has the form

$y - 4 = 3(x - 3)$

To find the y-intercept, set x = 0 to get

$y - 4 = 3(0 - 3) \Rightarrow y - 4 = -9$

Solving for y, we get

$y = -5$

Therefore, the coordinates of the y-intercept is (0, -5).

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A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon

fiasKO [112]

Answer:

The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon they'd received in the mail.

This means that $n = 603, \pi = \frac{142}{603} = 0.2355$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694$

The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).

8 0

2 years ago

Write an equation to match each graph:

castortr0y [4]

From what I know this graph looks like that of a modulus function except it's shifted 1 unit to right and 1 unit below the origin.

So the original equation must be:
y = |x|

And the transformed equation (aka the equation if this graph) must be,

y+1 = |x| -1

y = |x| -2

7 0

3 years ago

Read 2 more answers

What is the best estimate of the sum of the fraction? 31/4 +17/3 +8/18

Bogdan [553]

The best estimate of the sum of the expression given is $\rm 13 \dfrac {31}{26}$