1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
adell [148]
3 years ago
15

10) Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friend

s or four mutual enemies, and there are either three mutual enemies or four mutual friends.
Mathematics
1 answer:
ddd [48]3 years ago
3 0

Answer with explanation:

Number of People in the group =10 People

The combination between two people is that, they can be either friends or enemies.

Total number of Possible Relation

                            =18 +16+14+12+10+8+6+4+2

                            = 90 Relations in all.

Out of 90 relations , 45 will be friends and 45 will be enemies.

⇒Now, we have to prove that, between 10 people, there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.

→→If there are three mutual friends, total number of people in the group =3 ×2=6 people in the group

And, four mutual enemies in a group means there are 2 people in each group.

So, total number of people if we combine the two groups in which there are either three mutual friends or four mutual enemies

   =6 +4

   =10

Hence proved.

→→→→Second part is ,in this group there can be either three mutual enemies or four mutual friends.

⇒If there are three mutual enemies, total number of people in the group =3 ×2=6 people in the group

And, four mutual friends in a group means there are 2 people in each group.

So, total number of people if we combine the two groups in which there are either three mutual enemies or four mutual enemies

   =6 +4

   =10

Hence proved.

You might be interested in
Determine whether more or less than the percent budgeted was actually spent.
SSSSS [86.1K]

The amount spent as a percentage of the budget can be found from

... (actual amount)/(total budget) × 100%

... = (actual amount)/3600×100%

... = ((actual amount)/36)%

For housing, this is

... (820/36)% = 22.78% . . . . less than budget for housing

For transportation, this is

... (370/36)% = 10.28% . . . . more than budget for transportation

7 0
3 years ago
A horizontal line , such as y=4, has a slope of what
SpyIntel [72]

Answer:

0

Step-by-step explanation:

A horizontal line has a slope of zero and a vertical line has an undefined slope

5 0
3 years ago
List two ordered pairs on the graph of y = 3x + 2 <br> A. 2,7 , 3,9<br> B. 2,8 , 3,11
cricket20 [7]
The answer is b. 2,8 and 3,11
8=3(2)+2
8=6+2
8=8

11=3(3)+2
11=9+2
11=11
7 0
3 years ago
In What quadrant is the point (-5, -5) located
sineoko [7]

Answer:

Since both values are negative, it can be found in the 3rd quadrant

<em>Feel free to mark this as brainliest :D</em>

4 0
3 years ago
What is the slope of the line represented by the equation y =<br> -1/2x+1/4?
Dmitry_Shevchenko [17]

Answer:

-1/2

negative

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Between x = 2 and x = 3, which function has a greater average rate of change than y = 1 3 -x ?
    8·1 answer
  • if your gross pay was $365 and your net pay was $313.90 what percent of your pay went towards deductions
    13·1 answer
  • Identify the 2-dimensional shape created from a diagonal cross section of a cone​
    7·1 answer
  • I don’t know, someone help please.
    12·1 answer
  • PLZ ANSWER QUICK IT WILL HELP A LOT!
    10·2 answers
  • Use substitution to determine which value of x makes the equation 12+x=14.2 true.
    13·2 answers
  • Write an explicit formula for the sequence -13,-6,1,8, ...
    11·2 answers
  • PLEASE HELP!!!!!!!!!!
    14·1 answer
  • Which value of k makes the equation k\2 =10
    7·1 answer
  • Two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!