A number cube has faces numbered 1 through 6, and a coin has two sides, "heads" and "tails". The
number cube will be rolled once, and the coin will be flipped once. Find the probability that the
number cube shows a 6 or the coin shows "heads." (Express your answers as fractions in lowest
terms.)

The required probability is .

Step-by-step explanation:

Let A be the event of rolling the number cube.

Let B be the event of tossing the coin.

Total number of possibilities of rolling the number cube and tossing the coin are 12 here.

where H means Head on toss of coin and T means Tails on toss of coin.

Formula for probability of an event E is:

Here, we have to find the probability of event 'E' i.e. getting a 6 on number cube and heads on coin.

Number of favorable cases are 1 and total cases are 12.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

1 and 0

step-by-step explanation: