graph theory : given graph g with n vertices, prove that ? (¯) ? n
[a hint that was given to us is to consider what will happen to the maximal independent set in the compliment graph, since we know that ? (g)q ? n, where "q" is the largest independent set in g]

According to statistics a person will devote 32 years to sleeping and watching tv. the number of years sleeping will exceed the number of years watching tv by 18. over a lifetime, how many years will the person spend on each of these activities

Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.

Tim has obtained a 3/27 balloon mortgage. after the initial period, he decided to refinance the balloon payment with a new 30-year mortgage. how many years will he be paying for his mortgage in total?