check the picture below. So the parabola looks more or less like so.
bearing in mind that the distance "p" is the same from the vertex to the directrix or the focus point, so the vertex is therefore half-way between those two fellows, now, from 3,4 up to y = 8, there are 4 units, and the vertex is half-way, thus is at y = 6, and x = 3, (3, 6) as you see there in the picture.
the parabola is vertical, meaning the squared variable is the "x", and is opening downwards, meaning the "p" distance is negative, so since "p" is 2 units, then p = -2.
![\bf \textit{parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=3\\ k=6\\ p=-2 \end{cases}\implies 4(-2)(y-6)=(x-3)^2\implies -8(y-6)=(x-3)^2 \\\\\\ y-6=\cfrac{(x-3)^2}{-8}\implies \blacktriangleright y=-\cfrac{1}{8}(x-3)^2+6 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%0A%5C%5C%5C%5C%0A4p%28y-%20k%29%3D%28x-%20h%29%5E2%0A%5Cqquad%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Avertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%0A%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0Ah%3D3%5C%5C%0Ak%3D6%5C%5C%0Ap%3D-2%0A%5Cend%7Bcases%7D%5Cimplies%204%28-2%29%28y-6%29%3D%28x-3%29%5E2%5Cimplies%20-8%28y-6%29%3D%28x-3%29%5E2%0A%5C%5C%5C%5C%5C%5C%0Ay-6%3D%5Ccfrac%7B%28x-3%29%5E2%7D%7B-8%7D%5Cimplies%20%5Cblacktriangleright%20y%3D-%5Ccfrac%7B1%7D%7B8%7D%28x-3%29%5E2%2B6%20%5Cblacktriangleleft)
The standard deviation is a measure of a collection of values' variance or dispersion. The true mean bill for a customer at Burger Palace with 95% confidence is $13.38.
<h3>What is a standard deviation?</h3>
The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Given that the Sample mean (
) is $14.30, the Sample size(n) is 24 customers, the Standard deviation(σ) is 2.30, while for a 95% confidence interval the Z-score is 1.960. Therefore, the true mean can be written as,
μ = 13.3788 ≈ 13.38
Hence, the true mean bill for a customer at Burger Palace with 95% confidence is $13.38.
Learn more about Standard Deviation:
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Answer:
What's r?
Step-by-step explanation:
d = dimes
q = quarters
d+q = 38 coins
q=38-d
0.25q + 0.10d=6.95
0.25(38-d)+0.10d=6.95
9.5-0.25d+0.10d=6.95
-015d=-2.55
d=-2.55/-0.15 = 17
q=38-17 =21
21*0.25 =5.25
17*0.10 = 1.70
5.25+1.70 = 6.95
she had 21 quarters and 17 dimes
Given question ,
Raise v to the 5th power then triple the result
The expression is as follows :
Tripling ,
