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The slope-intercept form of the equation of a line that passes through point (-2,-13) is y=5x-3. What is the point-slope form of

marissa [1.9K]

Answer:

y + 13 = 5(x + 2)

Step-by-step explanation:

<h3>Point - slope form of equation: </h3>

$\sf \boxed{\bf y - y_1=m(x-x_1)}$

Slope intercept of the line : y =5x - 3

Comparing with y = mx +b , m =slope = 5

m = 5 and Point (-2 ,-13)

y - [-13] = 5(x - [-2])

y + 13 = 5(x + 2)

4 0

2 years ago

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

butalik [34]

Answer:

a) A sample size of 5615 is needed.

b) 0.012

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 zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

99.5% confidence level

So $\alpha = 0.005$ , z is the value of Z that has a pvalue of $1 - \frac{0.005}{2} = 0.9975$ , so $Z = 2.81$ .

(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.

This is n for which M = 0.015.

We have that $\pi = 0.2$

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

$0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}$

$0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}$

$\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}$

$(\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}$

$n = 5615$

A sample size of 5615 is needed.

(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

Now $\pi = 0.12, n = 5615$ .

We have to find M.

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

$M = 2.81\sqrt{\frac{0.12*0.88}{5615}}$

$M = 0.012$

7 0

3 years ago

Which property justifies the procedure used to eliminate fractions and decimals from equations?

igor_vitrenko [27]

By multiplying both sides of an equation by a number, you can eliminate all decimals and fractions, so the answer is C.

4 0

3 years ago

What is the prime factorization of 32?

dalvyx [7]

You could’ve just looked it up

5 0

3 years ago

Read 2 more answers

I need to make a matrix in reduced row echelon form

a_sh-v [17]

Let the three apartments be A, B & C

The rent of A is $x

The rent of B is $y

The rent of C is $z

So x + y + z = 1600 .......(1)

Now

Maintenance of A is 20% of x = 0.20x

Maintenance of B is 20% of y = 0.20y

Maintenance of C is 25% of z = 0.25z

0.20x + 0.20y + 0.25z = 345

Multiplying by 100 we get

20x + 20y + 25 z = 34500

Dividing by 5 we get

4x + 4y + 5z = 6900 .......(2)

Monthly fee of A is 10% of x = 0.10x

Monthly fee of B is 20% of y = 0.20 y

Monthly Fee of C is 10% of z = 0.10z

Now

0.10x + 0.20y + 0.10 z= 1820 - 1600

0.10x + 0.20y + 0.10z = 220

Multiplying by 100 we get

10x + 20y + 10z = 22000

Dividing by 10

x + 2y + z = 2200 ....(3)

Making a Matrix of equation (1), (2) & (3)

$\left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right]$

is the required matrix

7 0

3 years ago

Read 2 more answers