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3 years ago

7

A side of one polygon is 18 meters and the corresponding side of a second similar polygon is 24 meters. If the perimeter of the

first polygon is 16 meters and it's area is 1000 square meters find the perimeter and area of the similar polygon

1 answer:

AleksandrR [38]3 years ago

7 0

The perimeter of a polygon is proportional to its side so:
18 : 16
24 : p
p = 21.3 meters

Area is proportional to the square of the side of a polygon so:
18² : 1000
24² : x
x = 1,777.8 square meters

Note: The value of the perimeter should not be less than the length of one side. The data may be incorrect. Regardless, the method will be the same.

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An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos

Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation 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:

$p = 0.78, n = 675$

So

$\mu = E(X) = np = 675*0.78 = 526.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76$

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when $X = 0.8*675 = 540$ . So

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

$Z = \frac{540 - 526.5}{10.76}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

8 0

3 years ago

What is true about AngleQRT? Select two options.

stiv31 [10]

The complete question is

"Triangle QST is isosceles, and Line segment R T bisects AngleT. Triangle Q S T is cut by bisector R T. The lengths of sides S T and Q T are congruent. Line segments S R and R Q are congruent. Angles S T R and R T Q are congruent. What is true about AngleQRT?

Select two options. Measure of angleQRT = 90° Measure of angleQRT = Measure of angleSRT AngleQRT Is-congruent-to AngleSTQ Measure of angleQRT = 2*Measure of angleRTQ AngleQRT Is-congruent-to AngleRTQ"

The true about AngleQRT options are A abd B; ∠QRT = 90 and ∠QRT = ∠SRT

<h3>What is the congruent triangle?</h3>

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given information;

The triangle QST is isosceles with QT ≅ ST.

The ∠STR and ∠RTQ are congruent.

Now, consider two triangles ∠QTR and ∠STR

In the following triangle

TR ≅ TR

QTR ≅ STR

QT ≅ ST

Now, according to SAS rule, two congruent triangles have congruent corresponding to their sides,

1. QR ≅ SR

2. QRT ≅ SRT

Since the above two angles are congruent so, they will have the same measure

That will be 90 degree.

Hence, The correct options are; ∠QRT = 90 and ∠QRT = ∠SRT

For more information about congruent visit;

brainly.com/question/13367096

#SPJ1

5 0

1 year ago

Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax u

alexgriva [62]

Answer:b

Step-by-step explanation:

7 0

3 years ago

there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three time

hoa [83]

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

$0.05x + 0.1y + 0.25z = 3.65$

Dimes: 3 times greater than nickels:

This means that:

$y = 3x$

Quarters: One greater than double the number of nickels:

This means that:

$z = 2x + 1$

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

$0.05x + 0.1y + 0.25z = 3.65$

$0.05x + 0.1(3x) + 0.25(2x+1) = 3.65$

$0.05x + 0.3x + 0.5x + 0.25 = 3.65$

$0.85x = 3.4$

$x = \frac{3.4}{0.85}$

$x = 4$

y and z:

$y = 3x = 3(4) = 12$

$z = 2x + 1 = 2(4) + 1 = 9$

There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at brainly.com/question/17096268

4 0

3 years ago

20 POINTS PLEASE HELP DONT HAVE TO SHOW WORK 2 ATTACHMENTS PLEASE ANSWER BOTH

Allisa [31]

$5^ \frac{3}{2}$

$5 \sqrt{3}$

7 0

3 years ago