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3 years ago

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Morgan drew 3 lines. • Line A moves in the same direction as Line B and the lines never intersect. • Line B forms a perfect righ

t angle (90° angle) with Line C. Which statement is correct about these lines?
A: Line B is parallel to Line
2: Line A is perpendicular to Line B
3: Line C is perpendicular to Line A
4: Line C is parallel to Line A

1 answer:

Elena L [17]3 years ago

3 0

Answer: line c is perpendicular to line a

Step-by-step explanation:

Parallel lines are two or more lines that lie next to each other

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I NEED HELP PLEASE, THANKS!! :)

Lisa [10]

Answer:

The answer is

$\frac{1372}{3} \pi \: {cm}^{3}$

Step-by-step explanation:

First you have to find the radius of sphere by dividing diameter by 2 :

$radius = diameter \div 2$

Let diameter = 14,

$radius = 14 \div 2$

$radius = 7 \: cm$

Next you have to use the volume of sphere formula :

$v = \frac{4}{3} \times \pi \times {r}^{3}$

Let r = 7,

$v = \frac{4}{3} \times \pi \times {7}^{3}$

$v = \frac{4}{3} \times \pi \times 343$

$v = \frac{1372}{3} \pi \: {cm}^{3}$

7 0

3 years ago

Graph the system of equations.<br><br> {8x+8y=642x−2y=−4

klemol [59]

<span>The graph is attached.

Explanation:
We can use the x- and y-intercepts to graph. The x-intercept of the first equation is 8, and the y-intercept is 8. The x-intercept of the second equation is -2, and the y-intercept is 2.
<span>
x-intercepts are where the data crosses the x-axis. At every one of these points, the y-coordinate will be 0; therefore we can substitute 0 for y and solve to get the value of the x-intercept.

For the first equation, we would have
8x+8(0)=64
8x=64.

Divide both sides by 8:
8x/8 = 64/8
x=8.

For the second equation,
2x-2(0)=-4
2x=-4.

Divide both sides by 2:
2x/2 = -4/2
x=-2.

y-intercepts are where the data crosses the y-axis. At every one of these points, the x-coordinate will be 0; therefore we can substitute 0 for x and solve to get the value of the y-intercept.

For the first equation,
8(0)+8y=64
8y=64.

Divide both sides by 8:
8y/8 = 64/8
y=8.

For the second equation,
2(0)-2y=-4
-2y=-4.

Divide both sides by -2:
-2y/-2 = -4/-2
y=2.

Plot these points for both equations and connect them to draw the line.</span></span>

6 0

3 years ago

In 2002, the mean age of an inmate on death row was 40.7 years with a standard deviation of 9.6 years according to the U.S. Depa

marissa [1.9K]

Answer:

The <em>95% confidence interval</em> for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Step-by-step explanation:

The <em>confidence interval</em> of the mean is given by the next formula:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$ [1]

We already know (according to the U.S. Department of Justice):

The (population) standard deviation for this case (mean age of an inmate on death row) has a standard deviation of 9.6 years ( $\\ \sigma = 9.6$ years).
The number of observations for the sample taken is $\\ n = 32$ .
The sample mean, $\\ \overline{x} = 38.9$ years.

For $\\ z_{1-\frac{\alpha}{2}}$ , we have that $\\ \alpha = 0.05$ . That is, the <em>level of significance</em> $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the <em>z-score</em> corresponding to this case is:

$\\ z_{1-\frac{\alpha}{2}} = z_{1-\frac{0.05}{2}} = z_{1-0.025} = z_{0.975}$

Consulting a cumulative <em>standard normal table</em>, available on the Internet or in Statistics books, to find the z-score associated to the probability of, $\\ P(z$ , we have that $\\ z = 1.96$ .

Notice that we supposed that the sample is from a population that follows a <em>normal distribution</em>. However, we also have a value for n > 30, and we already know that for this result the sampling distribution for the sample means follows, approximately, a normal distribution with mean, $\\ \mu$ , and standard deviation, $\\ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$ .

Having all this information, we can proceed to answer the question.

Constructing the 95% confidence interval for the current mean age of death-row inmates

To construct the 95% confidence interval, we already know that this interval is given by [1]:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

That is, we have:

$\\ \overline{x} = 38.9$ years.

$\\ z_{1-\frac{\alpha}{2}} = 1.96$

$\\ \sigma = 9.6$ years.

$\\ n = 32$

Then

$\\ 38.9 \pm 1.96*\frac{9.6}{\sqrt{32}}$

$\\ 38.9 \pm 1.96*\frac{9.6}{5.656854}$

$\\ 38.9 \pm 1.96*1.697056$

$\\ 38.9 \pm 3.326229$

Therefore, the Upper and Lower limits of the interval are:

Upper limit:

$\\ 38.9 + 3.326229$

$\\ 42.226229 \approx 42.23$ years.

Lower limit:

$\\ 38.9 - 3.326229$

$\\ 35.573771 \approx 35.57$ years.

In sum, the 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Notice that the "mean age of an inmate on death row was 40.7 years in 2002", and this value is between the limits of the 95% confidence interval obtained. So, according to the random sample under study, it seems that this mean age has not changed.

7 0

4 years ago

76.98 divided by 45.2

Stella [2.4K]

Answer:

1.7030973451327434

Step-by-step explanation:

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3 years ago

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Zinaida [17]

Answer:

y=13

Step-by-step explanation:

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2 years ago

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