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Harrizon [31]
3 years ago
10

Given a group of 17 people in a party, we consider the number of times a person shakes hand with someone else. Show that there i

s always two people who shake hands with the same total number of people.
Mathematics
1 answer:
aev [14]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that there is a group of 17 people in a party.  There takes place a number of hand shakes between them.

To show that there is always two people who shake hands with the same total number of people.

If possible let each person did a different number of handshake.

We know that since there are 17 people, there cannot be more than 16 hand shakes for any one in the group.

Hence if different hand shakes must be 0,1,2...16

Consider the last person having 16 hand shakes. He has shaken hand with each other person in the group thus making it clear that no one could have done 0 hand shakes.   Since we get a contradiction, our assumption was wrong. That is, there is always two people who shake hands with the same total number of people.

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Parte de Cálculo: En cada una de las siguientes proporciones, utilizar regla de tres para determinar el valor desconocido
sineoko [7]

Answer:

<u><em>x = 4</em></u>

<u><em>x = 3</em></u>

<em><u>x = 10</u></em>

<u><em>x = 3</em></u>

<em><u>x = 16</u></em>

<em><u>x = 35</u></em>

Step-by-step explanation:

\frac{x}{5} :\frac{8}{10}

x · 10 = 5 · 8

10x = 40

10x ÷ 10 = 40 ÷ 10

<u><em>x = 4</em></u>

\frac{8}{12} :\frac{2}{x}

x · 8 = 12 · 2

8x = 24

8x ÷ 8 = 24 ÷ 8

<u><em>x = 3</em></u>

\frac{15}{3} :\frac{x}{2}

x · 3 = 15 · 2

3x = 30

3x ÷ 3 = 30 ÷ 3

<em><u>x = 10</u></em>

\frac{x}{6}:\frac{6}{12}

x · 12 = 6 · 6

12x = 36

12x ÷ 12 = 36 ÷ 12

<u><em>x = 3</em></u>

\frac{x}{8} :\frac{4}{2}

x · 2 = 8 · 4

2x = 32

2x ÷ 2 = 32 ÷ 2

<em><u>x = 16</u></em>

\frac{10}{2} :\frac{x}{7}

x · 2 = 10 · 7

2x = 70

2x ÷ 2 = 70 ÷ 2

<em><u>x = 35</u></em>

5 0
3 years ago
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Answer:

maybe do the math

Step-by-step explanation:

7 0
3 years ago
A construction company built a scale model of a building. The model was built using a scale of 3 inches = 32 feet. If the buildi
Vlad1618 [11]

Let x represent the height of the model.

We have been given that a construction company built a scale model of a building. The model was built using a scale of 3 inches = 32 feet. We are asked to find the height of the model, if  the building is expected to be 200 feet tall.

We will use proportions to solve our given problem as:

\frac{\text{Model height}}{\text{Actual height}}=\frac{\text{Model length}}{\text{Actual length}}

Upon substituting our given values, we will get:

\frac{x}{200\text{ ft}}=\frac{3\text{ in}}{\text{32 ft}}

\frac{x}{200\text{ ft}}\times 200\text{ ft}=\frac{3\text{ in}}{\text{32 ft}}\times 200\text{ ft}

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3 years ago
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Answer:

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Step-by-step explanation:

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zmey [24]
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