Think of this situation as a system of equations.
let y be the price of hotdogs
let x be the price of hamburgers
5y + 2x = 8
2y + 5x = 9.50
now use your solution method of choice
substitution, elimination, matrices, etc
40.32 mpg, because 36x.12=4.32 + 36= 40.32
5 pairs of gloves, two gloves per pair, so we have 10 gloves.
If the entire pack cost $29.45, we divide that by 10 to determine the cost of a single glove:
$29.45 ÷ 10 = $2.945 which rounds to $2.95 per glove.
Making predictions about your data requires the usage of a hypothesis. They aid data analysts in determining what they want to verify or dispute.
Given,
A senior data analyst requests that a junior data analyst offer two hypotheses for a project involving data analytics.
The rationale for a hypothesis must be explained;
This is,
Hypothesis testing is a sort of statistical reasoning that uses information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially best guessed.
Here,
A hypothesis seeks to infer something from your data. Data analysts use them to show or refute what they want to prove.
Learn more about hypothesis here;
brainly.com/question/17099835
#SPJ4
let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.
![\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bhyperbolas%2C%20vertical%20traverse%20axis%20%7D%20%5C%5C%5C%5C%20%5Ccfrac%7B%28y-%20k%29%5E2%7D%7B%20a%5E2%7D-%5Ccfrac%7B%28x-%20h%29%5E2%7D%7B%20b%5E2%7D%3D1%20%5Cqquad%20%5Cbegin%7Bcases%7D%20center%5C%20%28%20h%2C%20k%29%5C%5C%20vertices%5C%20%28%20h%2C%20k%5Cpm%20a%29%5C%5C%20c%3D%5Ctextit%7Bdistance%20from%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bcenter%20to%20foci%7D%5C%5C%20%5Cqquad%20%5Csqrt%7B%20a%20%5E2%20%2B%20b%20%5E2%7D%5C%5C%20asymptotes%5Cquad%20y%3D%20k%5Cpm%20%5Ccfrac%7Ba%7D%7Bb%7D%28x-%20h%29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}](https://tex.z-dn.net/?f=%5Ccfrac%7B%28y-3%29%5E2%7D%7B1%7D-%5Ccfrac%7B%28x%2B2%29%5E2%7D%7B4%7D%3D1%5Cimplies%20%5Ccfrac%7B%5By-3%5D%5E2%7D%7B1%5E2%7D-%5Ccfrac%7B%5Bx-%28-2%29%5D%5E2%7D%7B2%5E2%7D%3D1~~%20%5Cbegin%7Bcases%7D%20h%3D-2%5C%5C%20k%3D3%5C%5C%20a%3D1%5C%5C%20b%3D2%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B1%2B4%7D%5Cimplies%20c%3D%5Csqrt%7B5%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bso%20then%20the%20foci%20are%20at%7D%7D%7B%28-2~~%2C~~3%5Cpm%20%5Csqrt%7B5%7D%29%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Band%20its%20vertices%20are%20at%20%7D%7D%7B%28-2~~%2C~~3%5Cpm%201%29%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%28-2%2C4%29%5C%5C%20%28-2%2C2%29%20%5Cend%7Bcases%7D)
now let's check for the asymptotes.
![\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2](https://tex.z-dn.net/?f=%5Cbf%20y%3D3%5Cpm%20%5Ccfrac%7B1%7D%7B2%7D%5Bx-%28-2%29%5D%5Cimplies%20y%3D3%5Cpm%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3%2B%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%5Cimplies%20y%3D3%2B%5Ccfrac%7Bx%2B2%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B6%2Bx%2B2%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7Bx%2B8%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B1%7D%7B2%7Dx%2B4%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3-%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%5Cimplies%20y%3D3-%5Ccfrac%7B%28x%2B2%29%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B6-%28x%2B2%29%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B6-x-2%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B-x%2B4%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B1%7D%7B2%7Dx%2B2)
