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
aliina [53]
3 years ago
9

Show that in a group of five people (where any two people are either friends or enemies), there are not necessarily three mutual

friends or three mutual enemies.
Mathematics
1 answer:
sveta [45]3 years ago
8 0

Answer:

Lets call the people A,B,C,D and E. We need to find an example where there are not 3 mutual friends and not three mutual enemies.

Lets start by assuming that A has 2 friends, B and C, and 2 enemies, D and E.

Since we want A,B and C not to be mutually friends, then B and C neccesarily have to be enemies.

Now, since B and C are enemies, they cant be enemies at the same time with D, and they also cant be enemies at the same time with E. Therefore one of them has to be friends with D and one has to be friends with E.

Also, since D and E are enemies with A, they neccesarily need to be friends.

From the fact that D and E are friends, we coclude that they cant have a friend in common, as a consequence, B has to be friends with one of D and E and C has to be friend with the other. We can assume that B is friend with D and C is friend with E. If we use that, we have the following friendship configuration

---------------------

Friends of A: B, C

Enemies of A: D,E

-------------------------

Friends of B: A,D

Enemies of B: C, E

------------------------

Friends of C: A,E

Enemies of C: B,D

------------------------

Friends of D: B,E

Enemies of D: A,C

----------------------------

Friends of E: C,D

Enemies of E:  A,B

--------------------------

As you can check, there is not three mutual friends nor three mutual enemies.

You might be interested in
THIS IS A K12 QUESTION WILL GIVE BRAINLIEST NEED ANSWER NOW!!!! For which distributions is the median the best measure of the ce
vampirchik [111]

Answer:

B

Step-by-step explanation:

A, C, and D can be a possibility but they are not exactly at the middle. B is the only one that shows a slightly triangular shape, which you can see the middle that shows the best measure of the center.

Hope this helped!

5 0
3 years ago
Read 2 more answers
Rachel made a mosaic from different color rectangular tiles. Three tiles measured 312 inches by 3 inches. Six measured 4 inches
astraxan [27]
The answer is 10,344 hope this helps!
3 0
3 years ago
Read 2 more answers
Oakley charged $795 to his credit card last month. What is the first minimum payment he must make? (2 points)$25.00
DaniilM [7]

Answer:

$31.80

Step-by-step explanation:

<u><em>The complete question is</em></u>

Use the details of Oakley's new credit card to answer the question that follows. APR 11.9% compounded monthly Grace Period 28 days Minimum Payment 4% of the remaining balance or $25, whichever is higher Oakley charged $795 to his credit card last month. What is the first minimum payment he must make?

step 1

Find out the 4% of the balance of $795

0.04(795)=\$31.80

so

\$31.80 >\$25

This amount is higher than $25,

therefore

The first minimum payment he must make is $31.80

4 0
3 years ago
Consider the following operations on the number 8.82 x 10^-2. Without using a calculator, decide which would give a significantl
Ksenya-84 [330]

Correct question is;

Consider the following operations on the number 8.85 x 10^(-2). Without using a calculator, decide which would give a significantly smaller value than 8.85 x 10^(-2), which would give a significantly larger value, or which would give essentially the same value.

A) 8.85 × 10^(-2) + 6.69 × 10^(5)

B) 8.85 x 10^(-2) - 6.69 x 10^(5)

C) 8.85 x 10^(-2) x 6.69 x 10^(5)

D) 8.85 × 10^(-2) ÷ 6.69 × 10^(5)

Answer:

Option A & B yield essentially the same value.

Option C yields a significantly smaller value

Option D yields a significantly larger value

Step-by-step explanation:

Since given value for the operations is in 10^(-2) indices, then let's convert the operations numbers from 10^(5) indices to 10^(-2).

Thus;

6.69 × 10^(5) = (6.69 × 10^(-7)) × 10^(-2)

Thus;

A) 8.85 × 10^(-2) + 6.69 × 10^(5) is now;

8.85 × 10^(-2) + ((6.69 × 10^(-7)) × 10^(-2))

This gives;

[8.85 + (6.69 × 10^(-7))] × 10^(-2)

The 10^(-7) indices indicates that the initial value of 8.85 × 10^(-2) would not change much and would essentially be the same

B) 8.85 x 10^(-2) - 6.69 x 10^(5) is now;

8.85 × 10^(-2) - ((6.69 × 10^(-7)) × 10^(-2))

This gives;

[8.85 - (6.69 × 10^(-7))] × 10^(-2)

Again the 10^(-7) indices indicates that the initial value of 8.85 × 10^(-2) would not change much and would essentially be the same.

C) 8.85 x 10^(-2) x 6.69 x 10^(5) is now;

(8.85 × 10^(-2)) × ((6.69 × 10^(-7)) × 10^(-2))

This gives;

[8.85 × (6.69 × 10^(-7))] × 10^(-2)

When we multiply 8.85 by 6.69 × 10^(-7), the value gotten will be way lower than the initial value of 8.85.

Thus,this operation will give a significantly smaller value.

D) (8.85 × 10-2) ÷ (6.69 × 10^5) is now;

(8.85 × 10^(-2)) ÷ ((6.69 × 10^(-7)) × 10^(-2))

This gives;

[8.85 ÷ (6.69 × 10^(-7))] × 10^(-2)

When we carry out the operation:

8.85 ÷ (6.69 × 10^(-7)), it is essentially equal to (8.85 × 10^(7))/6.69.

This means that the new value would be significantly larger than the initial value of 8.85.

Thus,this operation yields a significantly larger value.

4 0
3 years ago
What is the z value in W×(-4+z)=mz+17
Irina-Kira [14]
There value for z would be 3-5
5 0
3 years ago
Other questions:
  • Write 5.641 in word form
    5·2 answers
  • What's the expression for 150 decreased by the quantity of 6 plus b
    7·1 answer
  • The area of a square is decreasing at a rate of 43 square inches per second. At the time when the side length of the square is 7
    14·1 answer
  • What's the answer people. Help
    13·2 answers
  • What’s pi? (i actually kno what it is i’m jus bored lol)
    7·2 answers
  • A bucket holds 10 potatoes. Hal removes and cleans 4 potatoes per minute.
    15·1 answer
  • Determine the value of x+3/8=2
    12·1 answer
  • Write to explain how you can use an array to break apart 18x12 to find the product and check if the product is reasonable.
    9·1 answer
  • Use the Pythagorean Theorem to determine the lengths of QT and RS Show your work
    6·1 answer
  • Who knows all the answers
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!