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Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5). What are the coordinates after the two transformations: Translation (x, y) --> (x - 2, y - 1) Rotation: 90 degrees counterclockwise at the origin.Immersive Reader

Answers

Answer 1

Answer:

Given :

Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5).

To Find :

The coordinates after the two transformations:

a) Translation (x, y) --> (x - 2, y - 1) .

b) Rotation: 90 degrees counterclockwise at the origin.

Solution :

Applying transition a) , we get :

R'(2-2,3-1) , S'(-2-2,1-1) , T'(-1-2,5-1)

R'( 0, 2) , S'( -4 , 0), T'( -3, 4)

Now , When any point ( h , k ) is rotated 90° counterclockwise about the origin, the new points are (-k , h) .

So , R''( -2, 0) , S''( 0, -4 ) , T''( -4 , -3 ) .

Therefore , the coordinates after transformations are

( -2, 0) ,( 0, -4 ) , ( -4 ,-3 ) .

Hence , this is the required solution .

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What sample size is needed to give a margin of error within in estimating a population mean with 95% confidence, assuming a previous sample had .

Answers

Answer:

$n = ((1.96√(\pi(1-\pi)))/(M))^2$

The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion $\pi$ (if no previous estimate use 0.5) and M is the desired margin of error.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the z-score that has a p-value of $1 - (\alpha)/(2)$ .

The margin of error is of:

$M = z\sqrt{(\pi(1-\pi))/(n)}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - (0.05)/(2) = 0.975$ , so $Z = 1.96$ .

Needed sample size:

The needed sample size is n. We have that:

$M = z\sqrt{(\pi(1-\pi))/(n)}$

$M = 1.96\sqrt{(\pi(1-\pi))/(n)}$

$√(n)M = 1.96√(\pi(1-\pi))$

$√(n) = (1.96√(\pi(1-\pi)))/(M)$

$(√(n))^2 = ((1.96√(\pi(1-\pi)))/(M))^2$

$n = ((1.96√(\pi(1-\pi)))/(M))^2$

WILL MARK BRAINLIEST ONLY HAVE 30 MINUTES

Answers

Answer:

Step-by-step explanation:

the answer is 21

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Someone help me