suppose the absolute value of x is <4 and x is an interger. Find the probability of the absolute value of x being a factor of 36
There are only three integers less than 4.
These are 1,2,3.
They are all factors of 36, so the probability is 1.0
or 100%, depending on what your teacher is looking for
To find the probability of the absolute value of x being a factor of 36, we first need to determine the possible values of x that satisfy the condition |x| < 4.
Since x is an integer and the absolute value of x is less than 4, the possible values for x are -3, -2, -1, 0, 1, 2, and 3. These are the integers between -4 and 4, excluding -4 and 4.
Next, we need to determine which of these values are factors of 36. A number is a factor of another number if it divides it evenly without leaving a remainder. In this case, we need to check if each value of x divides 36 without leaving a remainder.
Let's check each value:
-3 is not a factor of 36 because the division 36 ÷ (-3) leaves a remainder.
-2 is a factor of 36 because the division 36 ÷ (-2) gives an even quotient (18).
-1 is a factor of 36 because the division 36 ÷ (-1) gives an even quotient (-36).
0 is not a factor of 36 because the division 36 ÷ 0 is undefined (division by zero is not possible).
1 is a factor of 36 because the division 36 ÷ 1 gives an even quotient (36).
2 is a factor of 36 because the division 36 ÷ 2 gives an even quotient (18).
3 is a factor of 36 because the division 36 ÷ 3 gives an even quotient (12).
So, out of the possible values of x, the factors of 36 are -2, -1, 1, 2, and 3. There are 5 values that satisfy the condition.
To find the probability, we divide the number of favorable outcomes (number of values that satisfy the condition) by the number of possible outcomes (total number of values for x). In this case, the probability is 5/7 or approximately 0.714.