Thirty cards are numbered from 1 to 30, inclusive. if one card is drawn at random, what is the probability that the number on the card will be divisible by either 3 or 5?

Find the numbers between 1 and 30 that are divisible by 3 or 5:

Divisible by 3:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Divisible by 5:

5, 10, 15, 20, 25, 30

There are 10 numbers divisible by 3 and  6 numbers divisible by 5 for a total of 16 numbers.

The probability is 16/30, which reduces to 8/15 are divisible by 3 or 5.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1