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3 years ago

How many solutions do these have

Mathematics

1 answer:

V125BC [204]3 years ago

3 0

Answer:

See explanation below

Step-by-step explanation:

a. One solution (p = 1/4)

b. Infinite amount of solutions (No matter what value for p is, the equation will always be 7=7)

c. One solution (p = 12)

d. No solution (No matter what value for p is, the equation will always be 3 = -1, which wouldn't work)

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Which is the graph of x Greater-than-or-equal-to 98.6? A number line going from 95 to 103. A closed circle is at 98.6. Everythin

DENIUS [597]

Answer:

A number line going from 95 to 103. A closed circle is at 98.6. Everything to the right of the circle is shaded.

Step-by-step explanation:

We want to determine the graph of $x\geq 98.6.$

Since we have the sign, $\geq$ , we use a closed circle to show that the number 98.6 is included in the domain of definition.

Then since the sign is greater than, we shade to the right of 98.6.

The correct option is A.

3 0

3 years ago

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"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

3 years ago

8. Find the area of a circle with center

antoniya [11.8K]

Answer:

Area of circle = 50.24 units

Option J is correct answer.

Step-by-step explanation:

We need to find the area of a circle with centre (2, 3) that passes through (2,7)

The formula used to find area of circle is:

$Area\: of\: circle=\pi \:r^2$

We need to find radius.

The radius can be found using the distance between points (2,3) and (2,7)

The The distance formula is: $Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Putting values and finding length

We have: $x_1=2, y_1=3, x_2=2, y_2=7$

Putting values and finding distance

$Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance = \sqrt{(2-2)^2+(7-3)^2}\\Distance = \sqrt{(0)^2+(4)^2}\\Distance = \sqrt{0+16}\\Distance = \sqrt{16}\\Distance = 4$

So, we found Distance = 4

Therefore, the radius of circle is 4

Now, finding area:

$Area\: of\: circle=\pi \:r^2\\Area\: of\: circle=3.14\times (4) ^2\\Area\: of\: circle=3.14\times 16\\Area\: of\: circle=50.24 \:units$

So, Area of circle = 50.24 units

Option J is correct answer.

6 0

3 years ago

30 POINTS PLUS BRAINLIEST. ANSWER ALL QUESTIONS IN DETAILS,FORMULA AND STEP BY STEP.EXPLANATION FOR EACH ONE. NEEDS TO BE DONE I

Brut [27]

Answer: I think the answers below are all correct! :)

Step-by-step explanation: --> (that sign means I simplified the equation)

9-7r=-5 --> (9+5)-7r=0 --> 14-7r=0 --> 14=7r --> r=2

6x-5=4x+9 --> 6x=4x+(9+5) --> 6x=4x+14 --> 6x-4x=14 --> 2x=14 --> x=7

3(2d-1)=7d --> *multiply the parenthesis* 6d-3=7d --> -3=7d-6d -->d=-3

2(p-3)=4(3p+1) --> *multiply the parenthesis* 2p-6=12p+4 --> -10p=10 --> p=-1

___________________________________________________________

Don't know how to do the others below the boxes.

Good Luck!

8 0

3 years ago

*<br> For x = 3, evaluate the following:<br> (2x)?

Vera_Pavlovna [14]

Answer:

6is answer

x=3

2x=2×3=6

6 0

3 years ago

Read 2 more answers