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lesantik [10]
3 years ago
5

polygon ABCD is defined by the points A(-4,2), B(-2,4), C(1,3), and D(2,2). match the coordinates of the points you f the transf

ormed polygons to their correct value

Mathematics
1 answer:
Tomtit [17]3 years ago
5 0

<u><em>Answer:</em></u>

D' ..................> (-2,2)

C'' .................> (3,-1)

A''' ................> (4,-2)

B'' .................> (4,2)

<u><em>Step-by-step explanation:</em></u>

<u>Before we begin, we should remember the rotation rules:</u>

<u>1- Rotation 90° clockwise:</u>

Coordinates (x,y) become (y,-x)

<u>2- Rotation 90° counter clockwise:</u>

Coordinates (x,y) become (-y,x)

<u>3- Rotation 180° clockwise:</u>

Coordinates (x,y) become (-x,-y)

<u>4- Rotation 270° counter clockwise:</u>

Coordinates (x,y) become (y,-x) ...........> same as rotation 90° clockwise

<u>Now, let's consider the given problem:</u>

<u>1- Coordinates of D' if polygon ABCD rotates 90° counter clockwise to create A'B'C'D'</u>

Original coordinates of point D are (2,2)

Rotation 90° counter clockwise means that the new coordinates will be (-y,x) which is (-2,2)

<u>2- Coordinates of C'' if polygon ABCD rotates 90° clockwise to create A''B''C''D''</u>

Original coordinates of point C are (1,3)

Rotation 90° clockwise means that the new coordinates will be (y,x) which is (3,-1)

<u>3- Coordinates of A''' if polygon ABCD rotates 180° clockwise to create A'''B'''C'''D'''</u>

Original coordinates of point A are (-4,2)

Rotation 180° clockwise means that the new coordinates will be (-x,-y) which is (4,-2)

<u>4- Coordinates of B'' if polygon ABCD rotates 270° counter clockwise to create A''B''C''D''</u>

Original coordinates of point B are (-2,4)

Rotation 270° counter clockwise means that the new coordinates will be (y,-x) which is (4,2)

Hope this helps :)

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4 0
3 years ago
Let X denote the length of human pregnancies from conception to birth, where X has a normal distribution with mean of 264 days a
Kaylis [27]

Answer:

Step-by-step explanation:

Hello!

X: length of human pregnancies from conception to birth.

X~N(μ;σ²)

μ= 264 day

σ= 16 day

If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:

X[bar] ~N(μ;σ²/n)

When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ

When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)

a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.

P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602

b. P(X[bar]>b)= 0.05

You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.

P(X[bar]≤b)= 0.95

P(Z≤(b-μ)/(σ/√n))= 0.95

The value of Z that accumulates 0.95 of probability is Z= 1.648

Now we reverse the standardization to reach the value of pregnancy length:

1.648= (b-264)/(16/√15)

1.648*(16/√15)= b-264

b= [1.648*(16/√15)]+264

b= 270.81 days

c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.

Symbolically:

P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)

P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))

P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0

d. P(X[bar]>270)= 0.1151

P(Z>(270-264)/(16/√n))= 0.1151

P(Z≤(270-264)/(16/√n))= 1 - 0.1151

P(Z≤6/(16/√n))= 0.8849

With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:

P(Z≤1.200)= 0.8849

Z= \frac{X[bar]-Mu}{Sigma/\sqrt{n} }

Z*(Sigma/\sqrt{n} )= (X[bar]-Mu)

(Sigma/\sqrt{n} )= \frac{(X[bar]-Mu)}{Z}

Sigma= \frac{(X[bar]-Mu)}{Z}*\sqrt{n}

Sigma*(\frac{Z}{(X[bar]-Mu)})= \sqrt{n}

n = (Sigma*(\frac{Z}{(X[bar]-Mu)}))^2

n = (16*(\frac{1.2}{(270-264)}))^2

n= 10.24 ≅ 11 pregnant women.

I hope it helps!

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3 years ago
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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