The process is to go step-by-step to isolate the y.
To do this, you basically run the order of operations in reverse.
In 5x+2y=10, the first thing to move away from the left side is 5x and you cancel it out by subtracting 5x from both sides:
5x+2y - 5x = 10 - 5x
The 5x's on the left cancel leaving you with:
2y = 10 - 5x
Side note: this is more commonly written as 2y = -5x+10, since we tend to write variable terms first.
Finally, to get the y fully by itself, you need to cancel the 2 that's multplied against it. To cancel multiplication, you need to divide:
The most important thing to remember here is that the 2 needs to divide into both terms on the right:
Finally, we simplify this into:
Using the Fundamental Counting Theorem, it is found that 128 different combinations are possible.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
In this problem:
- There are two options for the sleeve length, hence .
- There are four options for the size, hence .
- There are four options for the color, hence .
- There are four options for the artwork, hence .
Thus, the number of combinations is given by:
N = 2 x 4 x 4 x 4 = 128.
More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866
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Answer:
18.18% of employees rode the bus to work last year
Step-by-step explanation:
This question can be solved using a rule of three.
Last year, a proportion of x employees riding the bus was 100% = 1.
This year, 20% = 0.2 ride the bus, which is 100 + 10 = 110% = 1.1 of last year.
So
0.2 - 1.1
x - 1
0.1818*100 = 18.18%
18.18% of employees rode the bus to work last year