D , it’s the only one that make since
The sample % of these two populations would be 100/size (of student body at each school) x 100 so this would compare the two student bodies preferences for the particular type of candy bar. However, the actual % of the whole student body at each school would be a factor also. If the high school only had 200 students then this would be 50% representative but if the middle school had say 500 students this would only be 20% representative so this would have to be taken into account too. It might be more representative to have the same % of the student bodies respectively for the sample.
the equilibrium point, is when Demand = Supply, namely, when the amount of "Q"uantity demanded by customers is the same as the Quantity supplied by vendors.
That occurs when both of these equations are equal to each other.
let's do away with the denominators, by multiplying both sides by the LCD of all fractions, in this case, 12.
![\bf \stackrel{\textit{Supply}}{-\cfrac{3}{4}Q+35}~~=~~\stackrel{\textit{Demand}}{\cfrac{2}{3}Q+1}\implies \stackrel{\textit{multiplying by 12}}{12\left( -\cfrac{3}{4}Q+35 \right)=12\left( \cfrac{2}{3}Q+1 \right)} \\\\\\ -9Q+420=8Q+12\implies 408=17Q\implies \cfrac{408}{17}=Q\implies \boxed{24=Q} \\\\\\ \stackrel{\textit{using the found Q in the Demand equation}}{P=\cfrac{2}{3}(24)+1}\implies P=16+1\implies \boxed{P=17} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{Equilibrium}{(24,17)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7BSupply%7D%7D%7B-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7BDemand%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7DQ%2B1%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%2012%7D%7D%7B12%5Cleft%28%20-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%20%5Cright%29%3D12%5Cleft%28%20%5Ccfrac%7B2%7D%7B3%7DQ%2B1%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%20-9Q%2B420%3D8Q%2B12%5Cimplies%20408%3D17Q%5Cimplies%20%5Ccfrac%7B408%7D%7B17%7D%3DQ%5Cimplies%20%5Cboxed%7B24%3DQ%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20found%20Q%20in%20the%20Demand%20equation%7D%7D%7BP%3D%5Ccfrac%7B2%7D%7B3%7D%2824%29%2B1%7D%5Cimplies%20P%3D16%2B1%5Cimplies%20%5Cboxed%7BP%3D17%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7BEquilibrium%7D%7B%2824%2C17%29%7D~%5Chfill)
Answer:
The solution is
. Fourth option
Explanation:
Solve for x:
![2x^2+3x-7=x^2+5x+39](https://tex.z-dn.net/?f=2x%5E2%2B3x-7%3Dx%5E2%2B5x%2B39)
Move all the terms from the right to the left side of the equation, a zero in the right side:
![2x^2+3x-7-x^2-5x-39=0](https://tex.z-dn.net/?f=2x%5E2%2B3x-7-x%5E2-5x-39%3D0)
Join all like terms:
![x^2-2x-46=0](https://tex.z-dn.net/?f=x%5E2-2x-46%3D0)
The general form of the quadratic equation is:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Solve the quadratic equation by using the formula:
![\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In our equation: a=1, b=-2, c=-46
Substituting into the formula:
![\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-%28-2%29%5Cpm%20%5Csqrt%7B%28-2%29%5E2-4%281%29%28-46%29%7D%7D%7B2%281%29%7D)
![\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B4%2B184%7D%7D%7B2%7D)
![\displaystyle x=\frac{2\pm \sqrt{188}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B188%7D%7D%7B2%7D)
Since 188=4*47
![\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B4%2A47%7D%7D%7B2%7D)
Take the square root of 4:
![\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%202%5Csqrt%7B47%7D%7D%7B2%7D)
Divide by 2:
![\displaystyle x=1\pm \sqrt{47}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D1%5Cpm%20%5Csqrt%7B47%7D)
First option: Incorrect. The answer does not match
Second option: Incorrect. The answer does not match
Third option: Incorrect. The answer does not match
Fourth option: Correct. The answer matches exactly this option
Answer:
1200 per time
Step-by-step explanation: