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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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Solve for x -3x > 12
Readme [11.4K]

Answer:

x < -6

Step-by-step explanation:

x -3x > 12

Combine like terms

-2x>12

Divide by -2, remembering to flip the inequality

-2x/-2 < 12/-2

x < -6

6 0
1 year ago
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3 years ago
Which scenario is modeled by the equation (x)(0.6) = $86.46?
belka [17]

Answer: A picnic table is on sale for 60 percent off. The original price of the picnic table is x, $144.10.


Step-by-step explanation:

Given equation: (x)(0.6)=\$86.46

To find x, divide 0.6 on both sides, we get

x=\frac{\$86.46}{0.6}\\\Rightarrow\ x=\frac{\$864.6}{6}\\\Rightarrow\ x=\$144.10

Also 0.6=0.6\times100=60\%

Thus, 60\%\ of\ \$144.10=\$86.46

So the best scenario modeled by the above equation is

"A picnic table is on sale for 60 percent off. The original price of the picnic table is x, $144.10."

4 0
3 years ago
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91 rounded to the nearest hundred is 100 because 91 is closer to 100 than ? on the number line
Rufina [12.5K]

Answer:

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Write a decimal subtraction problem that requires regrouping to solve. then solve the problem
Svetach [21]
For example, think about 8.4 - 2.9.

You have to regroup because you can't subract 4 - 9.
4 turns into a 14 since you borrow from the left number, 8.
8 turns into a 7 after that.
Now, you have to subtract 14 - 9 and 7 - 2. You're answer is 5.5.
You can check your work by doing inverse opperations:
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Hope this helped you! If you need a better explaination or another example, I will be happy to help you! :)
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