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3 years ago

A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line?

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

8 0

Answer:

(5,4) & (8,-10)

Step-by-step explanation:

First step:

$y=mx+b$

You can use any number you want for b (I used 4)

$y=-\frac{4}{5} x+4$

Make x=0

$y=-\frac{4}{5} (0)+4$

$y=4$

Make y=0

$0=-\frac{4}{5} x+4$

Subtract 4 from both sides

$-4=-\frac{4}{5} x$

Divide both sides by $-\frac{4}{5}$

$x=5$

Second step:

In order to make a line perpendicular to another the slope of the second line will be the negative inverse of the first line. So $m=-\frac{4}{5}$ will be $m=\frac{5}{4}$ for the second line.

Then you just need to repeat the process in first step to get the intercepts. (Again I used a random number like -10 for b)

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4 years ago

Paul had a job during his summer vacation. He earned $8.75 per hour. He worked 20 hours per week for 8 weeks. How much money did

Elan Coil [88]

Answer:

9800 is final answer. He rich :)

Step-by-step explanation:

Alright first let's find how much he makes each day.

20 * 8.75= 175

Now there are 7 days a week so...

175 * 7=1225

He works for 8 weeks:

1225 *8= 9800

8 0

4 years ago

Find unknown measure of rectangle for width if perimeter is 62 centimeters and length is 16 cm.

SVETLANKA909090 [29]

Answer: The width of the rectangle is 3.875.

Step-by-step explanation:

Use the formula P = LW

Rearrange the formula to read W = P/L

Put the numbers in the formula and solve.

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5 0

3 years ago

"The municipal transportation authority determined that 58% of all drivers were speeding along a busy street. In an attempt to r

vredina [299]

Answer:

a) X=77 drivers

b) Power of the test = 0.404

c) Increasing the sample size.

Step-by-step explanation:

This is a hypothesis test of proportions. As the claim is that the speed monitors were effective in reducing the speeding, this is a left-tail test.

For a left-tail test at a 5% significance level, we have a critical value of z that is zc=-1.645. This value is the limit of the rejection region. That means that if the test statistic z is smaller than zc=-1.645, the null hypothesis is rejected.

The proportion that would have a test statistic equal to this critical value can be expressed as:

$p_c=\pi+z_c\cdot\sigma_p$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.58*0.42}{150}}\\\\\\ \sigma_p=\sqrt{0.001624}=0.04$

Then, the proportion is:

$p_c=\pi+z_c\cdot\sigma_p=0.58-1.645*0.04=0.58-0.0658=0.5142$

This proportion, with a sample size of n=150, correspond to

$x=n\cdot p=150\cdot0.5142=77.13\approx 77$

The power of the test is the probability of correctly rejecting the null hypothesis.

The true proportion is 0.52, but we don't know at the time of the test, so the critical value to make a decision about rejecting the null hypothesis is still zc=-1.645 corresponding to a critical proportion of 0.51.

Then, we can say that the probability of rejecting the null hypothesis is still the probability of getting a sample of size n=150 with a proportion of 0.51 or smaller, but within a population with a proportion of 0.52.

The standard error has to be re-calculated for the new true proportion:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.52*0.48}{150}}\\\\\\ \sigma_p=\sqrt{0.001664}=0.041$

Then, we calculate the z-value for this proportion with the true proportion:

$z=\dfrac{p-\pi'}{\sigma_p}=\dfrac{0.51-0.52}{0.041}=\dfrac{-0.01}{0.041}=-0.244$

The probability of getting a sample of size n=150 with a proportion of 0.51 or lower is:

$P(p$

Then, the power of the test is β=0.404.

The only variable left to change in the test in order to increase the power of the test is the sample size, as the significance level can not be changed (it is related to the probability of a Type I error).

It the sample size is increased, the standard error of the proprotion decreases. As the standard error tends to zero, the critical proportion tend to 0.58, as we can see in its equation:

$\lim_{\sigma_p \to 0} p_c=\pi+ \lim_{\sigma_p \to 0}(z_c\cdot\sigma_p)=\pi=0.58$

Then, if the critical proportion increases, the z-score increases, and also the probability of rejecting the null hypothesis.

5 0

4 years ago

Use the rules for long division to divide 724 by11

zalisa [80]

__ ← that is a bar representing that it is ongoing.
724/11=65.81
__
x65.81 1)11 cannot go into 7 so u put a x
______ 2)72 goes in 11 6 times so u put 6 next to x
11 | 724.00 3)6 times 11 is 66
-66↓ ↓ ↓ 4)subtract 66 by 72 and get 6
__↓ ↓ ↓ 5)bring down the 4 and put it next to the 6 getting 64.
64 ↓ ↓ 6)64 goes into 11 5 times
-55 ↓ ↓ 7)put the five next to the x6
___↓ ↓ 8)11 times 5 is 55
90 ↓ 9)subtract 55 from 64 and get 9
-88 ↓ 10)bring the decimal up
___ ↓ 11)gring down the zero *remember*:*a zero has unlimited
20 zeros*
-11 12)90 goes into 11 8 times so put a 8 next to x65.
__ 13)11 times 8 is 88
9 14)subtract 90 from 88 and get 2
15)bring down another zero
16)20 goes into 11 1 time so put a one next to x65.8
17)subtract 11 from 20 and get 9
18)it is not ongoing so put a bar over the answer
__
the answer is 65.81 or u can round it, 65.8182

5 0

3 years ago