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IceJOKER [234]
3 years ago
11

Show that in any group of 101 people there are at least two persons having the same number friends (It is assumed that if a pers

on x is a friend of y then y is also a friend of x and we are only considering the friends amongst the group of people). How would you modify your proof if the number of people were not 101?
Mathematics
1 answer:
vladimir1956 [14]3 years ago
7 0

Answer:

Step-by-step explanation:

Let us assume that if possible in the group of 101, each had a different number of friends.  Then the no of friends 101 persons have 0,1,2,....100 only since number of friends are integers and non negative.

Say P has 100 friends then P has all other persons as friends.  In this case, there cannot be any one who has 0 friend.  So a contradiction.  Hence proved

Part ii: EVen if instead of 101, say n people are there same proof follows as

if different number of friends then they would be 0,1,2...n-1

If one person has n-1 friends then there cannot be any one who does not have any friend.

Thus same proof follows.

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896, -448, 224, -112 next in the sequence
faltersainse [42]
56, you are dividing by -2 each time
4 0
3 years ago
Simplify.<br><br> 42+25<br><br><br><br> A.21<br><br> B.29<br><br> C.41<br><br> D.51
bearhunter [10]

Im actually pretty sure its C because 4 to the power of 2 is 16 and then add those too up 16+25=41

8 0
3 years ago
Explain to me in words how you would find the slope of this line and explain answer
Andrews [41]
Answer:
7/3

Explanation:
The slope of the line is equal to the rise/run, or in other words, the number of units the line travels upwards over the number of units the line travels to the right.

We can identify the slope using any two points on the line. Here, we can use the two points that are marked on the picture. The second point is 7 units above the first and 3 units to the right of the first, so the slope of the line is equal to 7/3.

Another way to calculate the slope of the line is the use this formula:

(y2-y1)/(x2-x1)

The first point is at the coordinate (1,-4) and second point is at the coordinate (4,3). When we plug these two coordinates into the equation, we get this:

(y2-y1)/(x2-x1)
->(3-(-4))/(4-1)

When we simply the fraction, we would get 7/3 and that would give us the slope.

I hope this helps!
7 0
3 years ago
For which acute angles is the following statement true? The complement of the angle is smaller in measure than either of the two
Hitman42 [59]

Let the acute angle be 2x.

Its complement is 90 - 2x.

It is given that this complementary angle is less than each of the bisected angle.

Therefore, 90 - 2x < x

90 < 3x

or, x > 30.

2x > 60

Therefore, the statement is true for all angles that are greater than 60 degrees.

7 0
3 years ago
Arnoldo needs to write this system in slope-intercept form. Which shows how he could do that? 3 x minus 2 y = 6. 0.4 (20 y + 15)
kotegsom [21]

Answer:

  y = three-halves x minus 3

Step-by-step explanation:

Subtract 3x from both sides of the original equation.

  -2y = -3x +6

Divide by -2

  y = 3/2x -3

4 0
3 years ago
Read 2 more answers
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