Answer:
The value of y is 847 for x=11
Step-by-step explanation:
It is given that y is directly proportional to the square of x
This can be written mathematically as:
![y \propto x^2](https://tex.z-dn.net/?f=y%20%5Cpropto%20%20x%5E2)
Removing the proportionality symbol introduces a proportionality constant in the equation which is denoted by k
![y = kx^2](https://tex.z-dn.net/?f=y%20%3D%20kx%5E2)
Given that "When x is 5, y is 175"
![175 = k (5)^2\\175 = k*25\\k = \frac{175}{25}\\k = 7](https://tex.z-dn.net/?f=175%20%3D%20k%20%285%29%5E2%5C%5C175%20%3D%20k%2A25%5C%5Ck%20%3D%20%5Cfrac%7B175%7D%7B25%7D%5C%5Ck%20%3D%207)
Putting the value of k
![y = 7x^2](https://tex.z-dn.net/?f=y%20%3D%207x%5E2)
Now putting x = 11
![y = 7(11)^2\\y = 7 * 121\\y = 847](https://tex.z-dn.net/?f=y%20%3D%207%2811%29%5E2%5C%5Cy%20%3D%207%20%2A%20121%5C%5Cy%20%3D%20847)
Hence,
The value of y is 847 for x=11
7/4=1.75
1.75=175%
175% of a school year is 7 quarters.
Here you go, let me know if you have a question about the steps
In order to find the price per bar, we divide the price by the amount of bars. For the first one:
15.37/10 = $1.54 per bar
The second package:
15.35/12 = $1.28 per bar.
The 10-pack costs $1.54 per bar and the 12-pack costs $1.28 per bar. The 12-pack has the better price per bar.
Now, let's look at the price per ounce. We do this in a similar way. We find the total amount of ounces in the package, and divide the price by the number of ounces.
In the first package, we multiply 10*2.1=21. We have 21 ounces in the first package. Now we divide 15.37/21. In the first package, we have 0.73 dollars per ounce.
Now, let's look at the second package. We start by multiplying 1.4*12=16.8. There are 16.8 ounces in the package. Now, we divide 15.35/16.8=0.91. So, in the second package, we have 0.91 dollars per ounce.
The cost per ounce of the 10-pack is $0.73 and the cost per ounce of the 12-pack is $0.91. The first package has the better price per ounce.
The better explanation is the second one, because I prefer the lower price per ounce, I think that the 1st pack is the better buy.