Lewis rolls a number cube and then chooses a card from a set of cards numbered 1 through 5. What is the probability that he will roll an even number and choose an even numbered card?

Step-by-step explanation:

The general formula for a probability is:

The favorable events for the cube to fall in a even number are:

2, 4, and 6 ⇒ 3 favorable events

and in the cube the total events are:

1, 2, 3, 4, 5, 6 ⇒ 6 total events

So the probability of rolling an even number in the cube is:

Now we do something similar to find the probability to choose a card with an even number.

The favorable events for an even numbered card are:

2, 4 ⇒ 2 favorable events

and the total number of events in the cards is:

1, 2, 3, 4, 5 ⇒ 5 total events

Thus, the probability to choose an even numbered card (according to the probability formula) is:

And finally, since we want both things to happen we must multiply both obtained probabilities:

The probability is 1/5 which is equal to 0.2 or 20%

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.