Question

The number n of possible handshakes by all the people in the room is given by the function n(n) = n(n – 1)/2. for what number n of people is 66 ≤ n ≤ 300?

Answer 1

The number of possible handshakes between all the people in a room can be calculated using the formula n(n-1)/2.

Step-by-step explanation:

The number of possible handshakes between all the people in a room can be calculated using the formula n(n-1)/2, where n is the number of people in the room. In this case, we need to find the value of n for which 66 ≤ n ≤ 300. To solve this inequality, we can set up the following inequality:

n(n-1)/2 ≥ 66

n(n-1) ≥ 132

n² - n - 132 ≥ 0

(n-12)(n+11) ≥ 0

From this equation, we can see that the possible values for n are n ≥ 12 and n ≤ -11. However, since the number of people cannot be negative, we only need to consider the value n ≥ 12.

Therefore, for 12 ≤ n ≤ 300, there are n(n-1)/2 possible handshakes between all the people in the room.