12/3 = x/8
Cross multiply
3x = 96
Eliminate
3x/3 = 96/3
x = 32
Because the probability is uniform (equally likely) between 20 and 100 pounds, the probability distribution is uniform between 80 and 100 pounds, with the value 1/(100-20) = 1/80 chocolates/pound.
Let x = random variable that represents pounds of chocolate consumed.
Therefore
P(x < 60) = (60 - 20)*(1/80) = 1/2.
Answer: The probability is 1/2.
The absolute value function |<em>x</em>| always returns a non-negative number. It takes any number <em>x</em> and returns <em>x</em> if it's already non-negative, or -<em>x</em> if it is negative in order to make it positive.

For the equation
-3 + 4 |2<em>x</em> - 5| = 14
rearrange terms to get
|2<em>x</em> - 5| = 17/4
Now,
• if 2<em>x</em> - 5 ≥ 0, then |2<em>x</em> - 5| = 2<em>x</em> - 5. Then
2<em>x</em> - 5 = 17/4
• and if instead 2<em>x</em> - 5 < 0, then |2<em>x</em> - 5| = -(2<em>x</em> - 5), so that
-(2<em>x</em> - 5) = 17/4, or
2<em>x</em> - 5 = -17/4
In the first case,
2<em>x</em> - 5 = 17/4
2<em>x</em> = 17/4 + 5 = 37/4
<em>x</em> = 37/8
In the second case,
2<em>x</em> - 5 = -17/4
2<em>x</em> = -17/4 + 5 = 3/4
<em>x</em> = 3/8
Answer:
The difference between 19 and 8 is 11.
Step-by-step explanation:
Given:
The difference between a number and 8 is 11
Find the number.
Solution:
Let the unknown number be 
The difference between the unknown number can be written as:

We are given that the difference =11
So we can write the equation to find
as :

Using additive property to solve for 
Adding 8 to both sides to isolate
on one side.

∴ 
∴ The unknown number = 19