The sum of a number divided by 5 and 12 is 16. What is the number?
2 answers:
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Answer:
We have the system of equations:
y=1/3x+5
y=2/3x+5
To solve it graphically, we need to graph both lines and see in which point the lines intersect.
You can see the graph below, and you can see that the lines intersect in the point (0, 5)
Now, we can also solve this analytically.
We can use the fact that for the solution, we need y = y.
Then we can write:
(1/3)*x + 5 = (2/3)*x + 5
First, we can subtract 5 in both equations to get:
(1/3)*x = (2/3)*x
This only has a solution when x = 0.
Replacing x = 0 in one of the equations, we get:
y = (1/3)*0 + 5 = 5
Then the solution is x = 0, and y = 5, as we already could see in the graph.
The difference in gallons per day used is 3.6.
The formula to calculate a z-score is:
,
where X is the value used to calculate the score, μ is the mean and σ is the standard deviation. We have the z-scores so we must work backward:
For both equations, we will cancel the 1.2 by multiplying both sides:
Now we will cancel 2.2 from both equations by adding it to both sides:
3.6+2.2=X-2.2+2.2 and 0+2.2=X-2.2+2.2
5.8=X and 2.2=X
The difference in gas used per day would be given by
5.8-2.2 = 3.6.
The formula to calculate a z-score is:
where X is the value used to calculate the score, μ is the mean and σ is the standard deviation. We have the z-scores so we must work backward:
For both equations, we will cancel the 1.2 by multiplying both sides:
Now we will cancel 2.2 from both equations by adding it to both sides:
3.6+2.2=X-2.2+2.2 and 0+2.2=X-2.2+2.2
5.8=X and 2.2=X
The difference in gas used per day would be given by
5.8-2.2 = 3.6.