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2 years ago

The image is an example of which type(s) of symmetry

Mathematics

2 answers:

LiRa [457]2 years ago

8 0

Answer:

A. Both rotational and reflectional.

Step-by-step explanation:

We have been given an image of a regular polygon. We are asked to determine type(s) of symmetry for our given polygon.

Upon looking at our given polygon, we can see that it is a pentagon.

We know that a regular pentagon has five equal sides and five lines of symmetry.

We can see that each line of symmetry divides pentagon into two mirror images, therefore, our given pentagon has reflectional symmetry.

We know that the regular polygon has a rotational symmetry. We can find rotational symmetry of a regular polygon by multiplying 360 degrees by number of sides.

$\text{Rotational symmetry of pentagon}=\frac{360^{\circ}}{5}$

$\text{Rotational symmetry of pentagon}=72^{\circ}$

Therefore, a regular pentagon has rotational symmetry.

KonstantinChe [14]2 years ago

8 0

The image is an example of both rotational and reflectional symmetry.

The image given in the picture is that of a regular polygon. The polygon is also a pentagon because it has five equal sides and 5 equal angles.

<h2>Further Explanation</h2>

From the image, each of the symmetry divides the pentagon into two mirror images, which shows that the pentagon has refectional symmetry.

For more clarification, reflectional symmetry refers to a type of rigid motion for a 2 D shape, it is also known as line symmetry, simplest symmetry or mirror symmetry.

Reflectional symmetry is very easy to see simply because one half is the reflection of the other half.

The polygon has a rotational symmetry; rotational symmetry of any polygon can be determined by dividing 360 degree by the number of sides. The central angle of any regular polygon is 360 degree divided by the number of sides and since a pentagon has 5 sides, therefore the normal calculation will be 360 divided by 5, which is 72 degree.

Rotational symmetry is when a shape is rotated around a central point and still remains the same. This implies, a shape is said to have rotational symmetry if can be turned around a fixed point and fits the space it originally occupied.

LEARN MORE:

rotational and reflectional symmetry: brainly.com/question/1593820

KEYWORDS:

pentagon
polygon
rotational symmetry
reflectional symmetry
image

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a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message

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c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message

d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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25% of the incoming calls involve fax messages

This means that $p = 0.25$

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This means that $n = 25$

a. What is the probability that at most 4 of the calls involve a fax message?

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$ .

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.001 + 0.006 + 0.025 + 0.064 + 0.118 = 0.214$

0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b. What is the probability that exactly 4 of the calls involve a fax message?

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.

c. What is the probability that at least 4 of the calls involve a fax message?

Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$ . Then

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$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.096 = 0.904$

0.904 = 90.4% probability that at least 4 of the calls involve a fax message.

d. What is the probability that more than 4 of the calls involve a fax message?

Very similar to c.

$P(X \leq 4) + P(X > 4) = 1$

From a), $P(X \leq 4) = 0.214)$

Then

$P(X > 4) = 1 - 0.214 = 0.786$

0.786 = 78.6% probability that more than 4 of the calls involve a fax message

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So, the stickers are allotted to the 3 children in a group of

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Step-by-step explanation:

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