In a small chess tournament, 20 matches were played. find out how many people were involved if it is known that each participant played 2 games with every other participant in the tournament.

5

Step-by-step explanation:

We are given that 20 matches were played in a small chess tournament.

We are also given that Each participant played 2 games with every other participant in the tournament.

We are required to find out how many people were involved in the game.

So, First Let no. of players involved be n

Since we are given  for every match there should be two players out of n

Thus, number of ways they can play  a match :

Since we know that each participant played 2 games with every other participant.

Thus , The total no. of games played  =

We can see that 20 matches were played in total

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Thus using the combination formula i.e.

Since total players = n and r = 2

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⇒(n+4)=0  ,  (n-5)=0

⇒ n = -4, 5

Number of players cannot be negative so neglect n = -4

Thus , Number of players involved were 5

the answer is 14ft

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet