2006 Regional

[gemini9525]

how do you do these?

find the sum of the solutions (prefably without a calculator):
log2 (9-2^x)=3-x
(the 2 is supposed to be a lower subscript)

a box contains 10 tennis balls numbered 1,2,3...9,10. the tennis coach randomly selects 5 balls without replacement. what's the probability that the smallest ball drawn is a 4?

how many pairs of integers(x,y) will solve the equation 6x^2-3xy-13x+5y=-11?

thank you!

[bradp]

1) x = 3 and x = 0 work
if x > 3, the left hand side won't be a real number
if x < 0, the right hand side is to big to be equal
1 & 2 don't work

3 + 0 = 3

but I would just graph it :P

2) (number of 4 member subsets from the set {5,6,7,8,9,10}) divided by (number of 5 member subsets from {1,2,3....10}

6C4 / 10C5

http://www.artofproblemsolving.com/Foru ... p?t=115151

[Kurt]

[AuSmith]