The numbers 1-40 are written on pieces of paper and put in a box. two pieces of paper are randomly selected. what is the probability both numbers will be multiples of 4?

So we have 40 possible numbers to choose from in the beginning. There are 10 numbers which are multiples of 4, so the probability of drawing one multiple of 4 is 10/40 = 1/4.

Since we drew a number previously, we now have 39 possible numbers to choose from. Since we have to draw two numbers that are multiples of 4, we can assume that we've already drawn one, meaning that we have 9 numbers left. Therefore, the probability of drawing a second number that's a multiple of 4 is 9/39.

Now, since we need to have drawn two numbers that are multiples of 4, we multiply the first probability by the second: 1/4 * 9/39 = 9/156 = 3/52.

Answer: choice c and choice d

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

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