Given that f(x) =x^2 -3x+3 and g(x)= x-1/4, solve for f(g( when x=5 a.) -3 b.)1 c.)7 d.)13

OK. First calculate g(5). Put the value of x to the equation of the function g(x):

Therefore

Calculate:

hmmm... something is wrong. Maybe is

Try:

B.) 1

Next time, remember to write your expressions correctly

Answer and explanation:

There are 36 total possible outcomes with the roll of two 6-sided cubes.

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6} {2,1} {2,2} {2,3} {2,4} {2,5} {2,6} {3,1} {3,2} {3,3} {3,4} {3,5} {3,6} {4,1} {4,2} {4,3} {4,4} {4,5} {4,6} {5,1} {5,2} {5,3} {5,4} {5,5} {5,6} {6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

a) There are 21 DIFFERENT possible different outcomes.  For the purpose of the game, it doesn't matter if the first cube is a 3 and the second cube is a 6, so {3,6} and {6,3} are equivalent.

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6} {2,2} {2,3} {2,4} {2,5} {2,6} {3,3} {3,4} {3,5} {3,6} {4,4} {4,5} {4,6} {5,5} {5,6} {6,6}

b) The question asks for the fraction of the possible outcomes (not the different possible outcomes), so we have to count how many outcomes feature a 3 and divide that by the number of possible outcomes (36).

Based on the total possible outcomes: we have 11 possibilities to get a 3, out of 36, so 11 / 36 = 30.6%

If the question was about the different possible outcomes, we would have: 6 out of 21, so 28.6%

c) A bit less, because both the total and the different possible give us a probability that is a bit less than 34%... so it's unlikely the rolls would get us 34%.