A factory produces 42,000 computer monitors per day. The manager of the factory claims that fewer than 660 defective computer mo
nitors are produced each day. In a random sample of 240 computer monitors, there are 2 defective computer monitors. Determine whether the manager's claim is likely to be true. Explain.
Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.
We'll let . We want to cut the bit off completely, so let's create the scalpel that'll let us do that. If , then we can also say that . Maybe I was lying a bit: the is our real scalpel here, and is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting off of ) leaves us with:
The operation was a success! We can now simply divide either side by 9 to find , which, when reduced by dividing the numerator and denominator by 3, gives us