An integer is chosen at random from the first 40 positive integers. what is the probability that the integer chosen is divisible by 6 or 8?

1/4

Step-by-step explanation:

There are 40/8 = 5 integers in the range that are divisible by 8. There are floor(40/6) = 6 integers in the range that are divisible by 6. Of those sets of integers, one (24) is divisble by both numbers. So, altogether, there are 5+6-1 = 10 of the 40 integers that are divisible by 6 or 8.

If you choose an integer at random from the range 1–40, the probability is 10/40 = 1/4 that it will be divisible by 6 or 8.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus