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2 years ago

What is the scale factor of the dilation of triangle PRQ?

Mathematics

1 answer:

vlabodo [156]2 years ago

3 0

Answer:

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original

scale factor = $\frac{Q'R'}{QR}$ = $\frac{6}{2}$ = 3 → A

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A single card is drawn from a standard 52 card deck.

Mandarinka [93]

Step-by-step explanation:

probability of 6 of hearts = 1/52

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

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2 years ago

The length of a rectangle is four times the width minus three. If the perimeter of the rectangle is 64 meters, what is the lengt

Nastasia [14]

Answer:

L = 25 m

Step-by-step explanation:

L = 4W - 3

perimeter = 2(L + W)

64 = 2(4W - 3 + W)

divide both sides by 2:

32 = 5W - 3

add 3 to each side:

5W = 35

divide both sides by 5:

W =7

L = 4(7) - 3 = 25

6 0

2 years ago

The sum of four consecutive even integers is -28

mina [271]

I guess you want to find the 4 numbers

x + x + 2 + x + 4 + x + 6 = -28
4x + 12 = - 28
4x = - 40
x = -10

so the numbers are -10, -8, -6 ,-4.

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2 years ago

Write addition sentences (expression) where the sum is zero. <br><br> can someone make a expression

12345 [234]

All those equations answers are 0, please mark me brainiest, and hope I helped!

4 0

2 years ago

Read 2 more answers

GRE Test: The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores o

Zepler [3.9K]

Answer:

a) $\bar X=144.3$

b) The 95% confidence interval would be given by (138.846;149.754)

c) n=34

d) n=298

e) n=1190

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".

We can calculate the sample mean with this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

$\bar X=144.3$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=8.8$ represent the population standard deviation

n=10 represent the sample size

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

$\bar X=144.3$

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$144.3-1.96\frac{8.8}{\sqrt{10}}=138.846$

$144.3+1.96\frac{8.8}{\sqrt{10}}=149.754$

So on this case the 95% confidence interval would be given by (138.846;149.754)

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (5) we got:

$n=(\frac{1.960(8.8)}{3})^2 =33.05 \approx 34$

So the answer for this case would be n=34 rounded up to the nearest integer

Part d

$n=(\frac{1.960(8.8)}{1})^2 =297.493 \approx 298$

So the answer for this case would be n=298 rounded up to the nearest integer

Part e

$n=(\frac{1.960(8.8)}{0.5})^2 =1189.97 \approx 1190$

So the answer for this case would be n=1190 rounded up to the nearest integer

7 0

3 years ago