All categories

2 years ago

If AB is parallel to CD and the slope of CD is -5, what sis the slope of AB?

Mathematics

2 answers:

Lady bird [3.3K]2 years ago

7 0

Answer:

The answer is D. -5

Step-by-step explanation:

Since AB is parallel to CD, their slopes are the same. Parallel actually means to have the same slope.

Pavlova-9 [17]2 years ago

6 0

For this case we have that, by definition if two lines are parallel, then their slopes are equal, that is:

$m_ {1} = m_ {2}$

In this case we have that the slope of the line CD is:

$m_ {2} = - 5$

If CD is parallel to AB, we are asked to find the slope of AB.

So:

$m_ {1} = m_ {2} = - 5$

Answer:

Option D

You might be interested in

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22$

And rounded up we have that n=426

3 0

2 years ago

The volume of a sphere is 5,000pi m3. What is the surface area of the sphere to the nearest square meter?

tia_tia [17]

Surface area of a sphere = 4πr2
the volume of a sphere= 43πr3
so 5000π=4/3πr3
> r^3 = 5000 x 3 / 4 =>
r^3 = 3750
taking cube root on both sides
r=15.53616
hope it helps

5 0

2 years ago

Read 2 more answers

Which of the following companies offers the greatest total employment compensation? Company A Company B Company C Company D Gros

san4es73 [151]

we know that

To find the company with the greatest total employee compensation package, adds each company's gross pay, paid insurance, and paid time off, then subtract the job expenses on the sum

Find the total employee compensation package for each company

Step $1$

Find the total employee compensation package for company A

$total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses$

$total\ employee\ compensation=37,600+2,800+3,100-1,200\\ total\ employee\ compensation=42,300\ dollars$

Step $2$

Find the total employee compensation package for company B

$total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses$

$total\ employee\ compensation=36,800+2,400+3,600-600\\ total\ employee\ compensation=42,200\ dollars$

Step $3$

Find the total employee compensation package for company C

$total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses$

$total\ employee\ compensation=38,100+2,100+2,900-300\\ total\ employee\ compensation=42,800\ dollars$

Step $4$

Find the total employee compensation package for company D

$total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses$

$total\ employee\ compensation=39,000+1,800+2,500-800\\ total\ employee\ compensation=42,500\ dollars$

therefore

the answer is

the company with the greatest total employee compensation package is the company C

8 0

2 years ago

Read 2 more answers

Graph the linear equation. Find three points that solve the equation, then plot on the graph. -3y=x-6

nata0808 [166]

Answer:

Step-by-step explanation: x - 6

The given equation can be re-written as y = ---------

-3

Arbitrarily choose x = 0. Then:

x - 6 0-6

y = --------- = ----------- = 2, so (0, 2) is a point on the graph which is also the

-3 -3 y-intercept

Arbitrarily choose x = 6. Then y = 0, and (6, 0) is another point on the graph

which happens to be the x-intercept

arbitrarily choose x = 12. Then y = (12 - 6) / (-3) = -2. Then (12, -2) is

another point on the

graph.

Plot (12, -2), (6, 0) and (0, 2). Draw a line through these three points.

6 0

2 years ago

Which expression has the same value as -18÷(-9)

erma4kov [3.2K]

Negative dividing by negative gives positive,
so 18:9=2

6 0

2 years ago

Read 2 more answers