Answer:
168
Step-by-step explanation:
7(8) + (8)(14)
56 + 112
168
<em>Assuming </em><em>the </em><em>'e' </em><em>was </em><em>a </em><em>typo</em><em>.</em>
In order to know how many shelves Yasmin needs we need to divide the number of books between the number of books per shelf
![\frac{200}{30}=6.66](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B30%7D%3D6.66)
Then we round to the nearest bigger integer in this case 7
Yasmin will need 7 shelves
So, angles A and B added together is 130° which makes the whole angle = 180°-130°=50°
The answer is 180° because it is a supplementary angle and all supplementary angles equal 180° so, all the angles added makes 180°
<u>Answer-</u>
<em>The </em><em>exponential model</em><em> best fits the data set.</em>
<u>Solution-</u>
x = input variable = number of practice throws
y = output variable = number of free throws
Using Excel, Linear, Quadratic and Exponential regression model were generated.
The best fit equation and co-efficient of determination R² are as follows,
<u>Linear Regression</u>
![y=2.155x+0.391,\ R^2=0.903](https://tex.z-dn.net/?f=y%3D2.155x%2B0.391%2C%5C%20R%5E2%3D0.903)
<u>Quadratic Regression</u>
![y=0.096x^2+0.713x+3.803,\ R^2=0.948](https://tex.z-dn.net/?f=y%3D0.096x%5E2%2B0.713x%2B3.803%2C%5C%20R%5E2%3D0.948)
<u>Exponential Regression</u>
![y=4.625e^{0.141x},\ R^2=0.951](https://tex.z-dn.net/?f=y%3D4.625e%5E%7B0.141x%7D%2C%5C%20R%5E2%3D0.951)
The value of co-efficient of determination R² ranges from 0 to 1, the more closer its value to 1 the better the regression model is.
Now,
![R^2_{Linear}< R^2_{Quadratic}< R^2_{Exponential}](https://tex.z-dn.net/?f=R%5E2_%7BLinear%7D%3C%20R%5E2_%7BQuadratic%7D%3C%20R%5E2_%7BExponential%7D)
Therefore, the Exponential Regression model must be followed.
i)
<u>Factor using completing square method</u>
![\dashrightarrow \sf y = -x^2+16x-64](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%20-x%5E2%2B16x-64)
![\dashrightarrow \sf y = -(x^2-16x+64)](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%20-%28x%5E2-16x%2B64%29)
![\dashrightarrow \sf y = -(x^2-8x-8x+64)](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%20-%28x%5E2-8x-8x%2B64%29)
![\dashrightarrow \sf y = -(x(x-8)-8(x-8))](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%20-%28x%28x-8%29-8%28x-8%29%29)
![\dashrightarrow \sf y = -((x-8)(x-8))](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%20-%28%28x-8%29%28x-8%29%29)
ii)
<u>Find zeros of a function, f(x) = 0</u>
![\dashrightarrow \sf -((x-8)(x-8))=0](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20-%28%28x-8%29%28x-8%29%29%3D0)
![\dashrightarrow \sf (x-8)=0, \ (x-8)=0](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20%28x-8%29%3D0%2C%20%20%5C%20%20%28x-8%29%3D0)
![\dashrightarrow \sf x = 8](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20x%20%3D%208)
iii)
<u>In order to find vertex use the formulae : x = -b/2a</u>
![\dashrightarrow \sf x = \dfrac{-(16)}{2(-1)}](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20x%20%3D%20%5Cdfrac%7B-%2816%29%7D%7B2%28-1%29%7D)
![\dashrightarrow \sf x = 8](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20x%20%3D%208)
Then find y:
![\dashrightarrow \sf y = -(8)^2+16(8)-64](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%20-%288%29%5E2%2B16%288%29-64)
![\dashrightarrow \sf y = 0](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20y%20%3D%200)
coordinates: (8, 0)
iv) Sketched Below: