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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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Alisiya [41]

Let the time = x

Distance = Speed x time

One train is 75x, the other train 85x

Add together to equal total distance:

75x + 85x = 384

Simplify:

160x = 384

Divide both sides by 160:

x = 384 / 160

x = 2.4 hours

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3 years ago
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3 years ago
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Michelle is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 16 meters
Rama09 [41]

Answer:

12 meters

Step-by-step explanation:

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2 years ago
using the midpoint formula find the coordinates of the midpoint 9f each sigment with end points (4,2),(-5,-1)​
exis [7]

Answer:

The midpoint of the segment is (-0.5,0.5).

Step-by-step explanation:

Midpoint of a segment:

The midpoint of a segment is given by the mean of its coordinates.

Segment with end points (4,2),(-5,-1)​

x-coordinates: 4 and -5

y-coordinates: 2 and -1

x-coordinate of the midpoint:

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y-coordinate of the midpoint:

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2 years ago
Help? I'd Appreciate it!
kondor19780726 [428]

<u>Answer</u>

y = (1/2)x - 1


<u>Explanation</u>

The first step is to get the gradient of the line.

The two points in the line are; (2,0) and (-2, -2).

Gradient = (-2 - 0)/(-2, - 2)

                = -2/-4

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1/2 = y/(x - 2)

(x - 2) = 2y

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3 years ago
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