My roommate and i are having a house party. we invite 15 couples. at the party, everyone must shake hands with everyone whom they do not already know. at the end of the party, i can't remember the number of people i have met, so i go ask all other people at the party how many hands they have shaken, and they each tell me a different number. you do not shake hands with yourself or your 'partner' (the person with whom you came). how many hands did my roommate shake?

There are 105 handshakes that his roommate shake.

Step-by-step explanation:

Since we have given that

Number of couples = 15

As we know the "Handshaking lemma"

Here, n = 15

So, the number of handshakes would be

Hence, there are 105 handshakes that his roommate shake.

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you