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exis [7]
2 years ago
10

Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k

> 0. Are Rectangle 1 and Rectangle 2 similar? Why or why not? Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1. Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1. Answer:
Mathematics
1 answer:
Alika [10]2 years ago
8 0

Yes, the two rectangles are similar, because rectangle 2 is a dilation of rectangle 1.

<h3>Are the two rectangles similar?</h3>

We know that rectangle 1 has dimensions L and W.

And rectangle 2 is made by multiplying the dimensions of rectangle 1 by a factor k > 0.

Then, rectangle 2 is just a dilation of rectangle 1, this means that in fact, the two rectangles are similar by definition.

Then:

Dimensions of rectangle 1:

  • Length = L
  • Width = W.
  • Perimeter = 2*(W + L)
  • Area = W*L

For rectangle 2:

  • Length = k*L
  • Width = k*W
  • Perimeter = 2*(k*L + k*W) = k*(2*(L + W))
  • Area = (k*L)*(k*W) = k²(L*W)

Above we can see that the perimeter of rectangle 2 is k times the perimeter of rectangle 1, and the area of rectangle 2 is k squared times the area of the rectangle 1.

If you want to learn more about similar figures:

brainly.com/question/14285697

#SPJ1

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Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement
Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.173, n = 120. So

\mu = E(X) = np = 120*0.173 = 20.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

Z = \frac{X - \mu}{\sigma}

Z = \frac{34 - 20.76}{4.14}

Z = 3.2

Z = 3.2 has a pvalue of 0.9993

X = 21

Z = \frac{X - \mu}{\sigma}

Z = \frac{21 - 20.76}{4.14}

Z = 0.06

Z = 0.06 has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0
3 years ago
12. What is the sum of angles aº+bº?
BigorU [14]

Answer:

240

Step-by-step explanation:

360-(60+60) = 240

3 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=3%5En%5E%2B%5E1%2B9%2F3%5En%5E-%5E1%2B1" id="TexFormula1" title="3^n^+^1+9/3^n^-^1+1" alt="3^n
abruzzese [7]

Answer:

Hello,

Step-by-step explanation:

\dfrac{3^{n+1}+9}{3^{n-1}+1} \\\\=\dfrac{9*(3^{n-1}+1)}{3^{n-1}+1}\\\\=9\\

4 0
2 years ago
The sum of two numbers is 58. The larger number is 6 more than the smaller number. What are the numbers?
kenny6666 [7]

Answer:

Numbers are 32, and 26.

Step-by-step explanation:

58 / 2 = 29

29 + 3 = 32 (large number)

29 - 3 = 26 (small number)

8 0
3 years ago
Read 2 more answers
Carla buys a dress that cost $20.00. She pays 7% sales tax. How much does she pay fo the dress, with tax? A. $21.40 B. $34.00 C.
Zarrin [17]

Answer:

A

Step-by-step explanation:

if its wrong sorry :( :(

7 0
2 years ago
Read 2 more answers
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