The table below shows all of the possible outcomes of rolling a six-sided number cube and flipping a coin. which outcome is represented by x?

{(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)}

Step-by-step explanation:

Let X would represent each possible outcome of rolling a six-sided number cube and flipping a coin.

Possible outcomes of rolling a six-sided number cube = { 1, 2, 3, 4, 5, 6 }

Number of possible outcomes of rolling a six-sided number cube = 6

Possible outcomes of flipping a coin = { H, T }

Number of possible outcomes of flipping a coin = 2

Total possible outcomes represented by X are

{(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)}

Number of total possible outcomes represented by X = 6 × 2 = 12

Therefore, the outcomes {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)} represented by X.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions