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 inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950