Answer: A. G(x)= ax=y= - f(x) is flip over x-axis. Therefore, f(x) =14x would become f(x) =-14x. Therefore, final transformed function f(x)=-14x is vertically stretch by a factor of 14 and flip over the x-axis.
A.) 1/2
B.) 3
For the first one, just plug the value of x (4) everywhere you see x in the formula.
For the second one, place 1 wherever you see f(x)
Hope this helps
For this equation, we can let c = the value of one coupon
<span>4c = 108 - 76 </span>
<span>4c = 32 </span>
<span>c= $8
Hope this helped, and if it did I'd appreciate if you marked me as brainliest as I need it to get to a higher rank. If you need any more help, feel free to add me and/or message me :)
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Answer:
Here's what I get.
Step-by-step explanation:
1. Representation of data
I used Excel to create a scatterplot of the data, draw the line of best fit, and print the regression equation.
2. Line of best fit
(a) Variables
I chose arm span as the dependent variable (y-axis) and height as the independent variable (x-axis).
It seems to me that arm span depends on your height rather than the other way around.
(b) Regression equation
The calculation is easy but tedious, so I asked Excel to do it.
For the equation y = ax + b, the formulas are
![a = \dfrac{\sum y \sum x^{2} - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}](https://tex.z-dn.net/?f=a%20%3D%20%5Cdfrac%7B%5Csum%20y%20%5Csum%20x%5E%7B2%7D%20-%20%5Csum%20x%20%5Csumxy%7D%7Bn%5Csum%20x%5E%7B2%7D-%20%5Cleft%20%28%5Csum%20x%5Cright%20%29%5E%7B2%7D%7D%5C%5C%5C%5Cb%20%3D%20%5Cdfrac%7Bn%5Csumx%20y%20%20-%20%5Csum%20x%20%5Csumxy%7D%7Bn%5Csum%20x%5E%7B2%7D-%20%5Cleft%20%28%5Csum%20x%5Cright%20%29%5E%7B2%7D%7D)
This gave the regression equation:
y = 1.0595x - 4.1524
(c) Interpretation
The line shows how arm span depends on height.
The slope of the line says that arm span increases about 6 % faster than height.
The y-intercept is -4. If your height is zero, your arm length is -4 in (both are impossible).
(d) Residuals
![\begin{array}{cccr}&\textbf{Arm Span} & \textbf{Arm Span}&\\\textbf{Height/in} &\textbf{Actual} & \textbf{Predicted}&\textbf{Residual}\\25 & 19 & 22.3 & -3.3\\40 & 41 & 38.2 & 2.8\\55 & 51 & 54.1 & -3.1\\65 & 67 & 62.6 & 4.4\\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccr%7D%26%5Ctextbf%7BArm%20Span%7D%20%26%20%5Ctextbf%7BArm%20Span%7D%26%5C%5C%5Ctextbf%7BHeight%2Fin%7D%20%26%5Ctextbf%7BActual%7D%20%26%20%5Ctextbf%7BPredicted%7D%26%5Ctextbf%7BResidual%7D%5C%5C25%20%26%2019%20%26%2022.3%20%26%20-3.3%5C%5C40%20%26%2041%20%26%2038.2%20%26%202.8%5C%5C55%20%26%2051%20%26%2054.1%20%26%20-3.1%5C%5C65%20%26%2067%20%26%2062.6%20%26%204.4%5C%5C%20%5Cend%7Barray%7D)
The residuals appear to be evenly distributed above and below the predicted values.
A graph of all the residuals confirms this observation.
The equation usually predicts arm span to within 4 in.
(e) Predictions
(i) Height of person with 66 in arm span
![\begin{array}{rcl}y& = & 1.0595x - 4.1524\\66 & = & 1.0595x - 4.1524\\70.1524 & = & 1.0595x\\x & = & \dfrac{70.1524}{1.0595}\\\\& = & \textbf{66 in}\\\end{array}\\\text{A person with an arm span of 66 in should have a height of about $\large \boxed{\textbf{66 in}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Dy%26%20%3D%20%26%201.0595x%20-%204.1524%5C%5C66%20%26%20%3D%20%26%201.0595x%20-%204.1524%5C%5C70.1524%20%26%20%3D%20%26%201.0595x%5C%5Cx%20%26%20%3D%20%26%20%5Cdfrac%7B70.1524%7D%7B1.0595%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Ctextbf%7B66%20in%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BA%20person%20with%20an%20arm%20span%20of%2066%20in%20%20should%20have%20a%20height%20of%20about%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B66%20in%7D%7D%24%7D)
(ii) Arm span of 74 in tall person
![\begin{array}{rcl}y& = & 1.0595x - 4.1524\\& = & 1.0595\times74 - 4.1524\\& = & 78.4030 - 4.1524\\& = & \textbf{74 in}\\\end{array}\\\text{ A person who is 74 in tall should have an arm span of $\large \boxed{\textbf{74 in}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Dy%26%20%3D%20%26%201.0595x%20-%204.1524%5C%5C%26%20%3D%20%26%201.0595%5Ctimes74%20-%204.1524%5C%5C%26%20%3D%20%26%2078.4030%20-%204.1524%5C%5C%26%20%3D%20%26%20%5Ctextbf%7B74%20in%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7B%20A%20person%20who%20is%2074%20in%20tall%20should%20have%20an%20arm%20span%20of%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B74%20in%7D%7D%24%7D)
Answer: x(4x
4
−3)
Step-by-step explanation:
GCF = xx
x(
x
4x
5
+
x
−3x
)
x(4x
4
−3)