the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.
it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.
check the picture below.
so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bparabola%20vertex%20form%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cleftarrow%20%5Ctextit%7Busing%20this%20one%7D%5C%5C%5C%5C%20x%3Da%28y-%20k%29%5E2%2B%20h%20%5Cend%7Barray%7D%20%5Cqquad%5Cqquad%20vertex~~%28%5Cstackrel%7B%7D%7B%20h%7D%2C%5Cstackrel%7B%7D%7B%20k%7D%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-5%5C%5C%20k%3D9%20%5Cend%7Bcases%7D%5Cimplies%20y%3Da%5Bx-%28-5%29%5D%5E2%2B9%5Cimplies%20y%3Da%28x%2B5%29%5E2%2B9)
![\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bwe%20also%20know%20that%20%7D%20%5Cbegin%7Bcases%7D%20x%3D-7%5C%5C%20y%3D1%20%5Cend%7Bcases%7D%5Cimplies%201%3Da%28-7%2B5%29%5E2%2B9%20%5C%5C%5C%5C%5C%5C%20-8%3Da%28-2%29%5E2%5Cimplies%20-8%3D4a%5Cimplies%20%5Ccfrac%7B-8%7D%7B4%7D%3Da%5Cimplies%20-2%3Da%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20y%3D-2%28x%2B5%29%5E2%2B9~%5Chfill)
Answer:
The 95% confidence interval of the true mean.
(29.4261 ,36.9739)
Step-by-step explanation:
<u>Step :- (i)</u>
Given sample size 'n' =15
sample of the mean x⁻ = 33.2
The standard deviation of the sample 'S' = 8.3
<u>95% of confidence intervals</u>
<u></u>
<u></u>
<u>Step:-(ii)</u>
<u>The degrees of freedom γ=n-1 = 15-1=14</u>
The tabulated value t = 1.761 at 0.05 level of significance.
now substitute all possible values, we get

After calculation , we get
(33.2-3.7739 , 33.2+3.7739
(29.4261 ,36.9739)
<u>Conclusion</u>:-
the 95% confidence interval of the true mean.
(29.4261 ,36.9739)
<em>while the two were at the movies Katie spent $40.00</em>
Step-by-step explanation:
Translations: When a figure is slid to another place on the coordinate grid (for example if i asked you to move the figure 2 units down and 4 units to the left)
Reflected: When a figure is reflected across the y-axis or the x-axis and both figures are congruent to each other.
Rotated: When a figure is rotated (for example if i asked you to rotate the figure 90 degrees)