1. In a room of twenty students, every person shakes hands with exactly half the people in the room.?

Question

1. In a room of twenty students, every person shakes hands with exactly half the people in the room. What is the total number of handshakes?
2. A dog is tied to a ten-foot leash that is tied to the corner of a building in the shape of a regular pentagon with thirty-foot sides. How much area does the dog have to play with?

Answer 1

!. Unless there is some freaky 3 way action happening then the total number of handshakes is 100

2> the area that the dog has is a circle with a TT r ^2 area where r = 10 less the area taken by the pentagon.
Now the area that the pentagon takes away form a circle is a quadrant of 120 degrees . This means that as a circle is 360 degrees a third of the area that the dog would have had if tied to a post in the ground is no longer available to the poor doggy.
So area now equals 2/3 TT R ^2 (the pentagon could be 100 km long it wouldn't matter it is the length of the leach being shorter than the wall that determines it ) sooooo
The answer = 2/3 TT 10^2= 209.44 square feet

Answer 2

1st guy will shake hand with 3 others, 2d with 2 greater, third with one greater, and 4th one has already shaken palms with all. so the no. o handshakes is 6. the no.of handshakes is n(n-a million)/2, the place n is not any of individuals

Answer 3

1. 100
2. 20 pi

Answer 4

The answer to both is go and figure out yourself.