Anumber cube is rolled and a coin is flipped. find the probabilities below

a) p(1 and heads)=
b) p(even and tails)=
c) p(5 or 6 and heads)=

The two events are independent, because the result of the number cube has no influence on the coin flipped, and vice versa. So, we can calculate the two probabilities independently and then multiply them.

So, we have:

P(1 and heads) = P(cube returns 1) * P(coin returns heads)

The probability of rolling 1 is 1/6, because there are 6 numbers on the cube, and they all have the same probability. Similarly, the probability of getting heads is 1/2, because it's either heads or tails with equal probability.

The other two exercises follow the exact same logic, you only need to count how many outcomes satisfy your request for both the cube and the coin, and multiply the probabilities:

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.