In order to convert a fraction into a decimal, you can do one of two ways. I'll do the manual way, first since that's probably what your teacher would prefer.
First, find something that will multiply in the denominator that will equal 10,100,1000.
In this case, it will be 1,000.
1,000 ÷ 8 = 125.
So, you will multiply both the numerator and the denominator by 125.
3 x 1,000 = 375
8 x 125 = 1,000
Now, you have a BIG fraction of 375/1,000 but it's OKAY! Why? You're almost done.
Take your numerator of 375. Since your denominator has 3 zeros in it, you'll be moving your decimal 3 places to the right (from the imaginary decimal in front of the 3). So, we'll have 0.375.
So, your decimal of 3/8 is 0.375.
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Now, for the easiest way!
You will simply divide 3 ÷ 8 = 0.375
63% decrease.
0.63•80=50.4kg
80kg-50.4kg=29.6kg
$1.88 is our amount after the 380% is added!
$1.88 - 380%*x = x
Note, that when you are working with percents in a problem you need to convert the percent into a decimal value in order to properly work with it in an equation like the one above.
So, it will look like this:
$1.88 - 3.8x = x
Now onto explaining how I derived this equation in the first place, because it doesn't help you if you don't know how to do it yourself.
How a percent problem works is if you are taking some original price x, and increasing it by 380% you would take 380% of the item, and then adding it to the item. To take 380% of an item you would need to multiply the number by 380% (3.8). So, if you translate that into math it looks like this:
x + 380%*x = y
Y, in this case is $1.88. In other words it is the price AFTER you've added 380% to the cost. So I started to solve for x by subtracting 380%*x on both sides leaving us with this:
$1.88 - 3.8x = x
We need to solve the equation for x by adding 3.8x on both sides.
$1.88 = 3.8x + x
Combine like terms.
$1.88 = 4.8x
Divide both sides by 4.8.
$1.88/4.8 = x
So our original price is $1.88/4.8!
The question asks for the 380% * x part of the problem.
So we take our answer and multiply it by 3.8.
($1.88/4.8)*3.8 = $1.49 mark up!
Answer:
If a component received by the manufacturer is defective, the probability that it was produced at plant A is 0.5385 = 53.85%.
Step-by-step explanation:
We use the Bayes Theorem to solve this question.
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Defective component
Event B: Produced at plant A.
Plant A produces 70% of the components used
This means that 
Among the components produced at plant A, the proportion of defective components is 1%.
This means that 
Probability of a defective component:
1% of 70%(defective at plant A)
2% of 100 - 70 = 30%(defective at plant B). So
If a component received by the manufacturer is defective, the probability that it was produced at plant A is
If a component received by the manufacturer is defective, the probability that it was produced at plant A is 0.5385 = 53.85%.
