60 square feet= $287.00 + $80.00
= $367
1 square feet= $367 / 60
= $6.116666667
= $6.12 (to 2dp) ( answer)
Answer:
32 red
28 white
20 blue
Step-by-step explanation:
.40 x 80 = 32 red
.35 x 80 = 28 white
.25 x 80 = 20 blue
The totals have to equal the total number of strands.
A scatter diagram has points that show the relationship between two sets of data.
We have the following data,
![\left\begin{array}{ccccccc}\mathrm{x}&3&7&15&32&74\\\mathrm{y}&40&35&30&25&17\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5Cbegin%7Barray%7D%7Bccccccc%7D%5Cmathrm%7Bx%7D%263%267%2615%2632%2674%5C%5C%5Cmathrm%7By%7D%2640%2635%2630%2625%2617%5Cend%7Barray%7D%5Cright)
where <em>x</em> is the average number of employees in a group health insurance plan and <em>y</em> is the average administrative cost as a percentage of claims.
To make a scatter diagram you must, draw a graph with the independent variable on the horizontal axis (<em>in this case x</em>) and the dependent variable on the vertical axis (<em>in this case y</em>). For each pair of data, put a dot or a symbol where the x-axis value intersects the y-axis value.
Linear regression is a way to describe a relationship between two variables through an equation of a straight line, called line of best fit, that most closely models this relationship.
To find the line of best fit for the points, follow these steps:
Step 1: Find
and
as it was done in the below table.
Step 2: Find the sum of every column:
![\sum{X} = 131 ~,~ \sum{Y} = 147 ~,~ \sum{X \cdot Y} = 2873 ~,~ \sum{X^2} = 6783](https://tex.z-dn.net/?f=%5Csum%7BX%7D%20%3D%20131%20~%2C~%20%5Csum%7BY%7D%20%3D%20147%20~%2C~%20%5Csum%7BX%20%5Ccdot%20Y%7D%20%3D%202873%20~%2C~%20%5Csum%7BX%5E2%7D%20%3D%206783)
Step 3: Use the following equations to find intercept a and slope b:
![\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 147 \cdot 6783 - 131 \cdot 2873}{ 5 \cdot 6783 - 131^2} \approx 37.05 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 5 \cdot 2873 - 131 \cdot 147 }{ 5 \cdot 6783 - \left( 131 \right)^2} \approx -0.292\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%20%20%20%20%20%20%20a%20%26%3D%20%5Cfrac%7B%5Csum%7BY%7D%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Csum%7BX%7D%20%5Ccdot%20%5Csum%7BXY%7D%20%7D%7Bn%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%7D%20%3D%20%20%20%20%20%20%20%20%20%20%20%20%20%5Cfrac%7B%20147%20%5Ccdot%206783%20-%20131%20%5Ccdot%202873%7D%7B%205%20%5Ccdot%206783%20-%20131%5E2%7D%20%5Capprox%2037.05%20%5C%5C%20%5C%5Cb%20%26%3D%20%5Cfrac%7B%20n%20%5Ccdot%20%5Csum%7BXY%7D%20-%20%5Csum%7BX%7D%20%5Ccdot%20%5Csum%7BY%7D%7D%7Bn%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%7D%20%20%20%20%20%20%20%20%3D%20%5Cfrac%7B%205%20%5Ccdot%202873%20-%20131%20%5Ccdot%20147%20%7D%7B%205%20%5Ccdot%206783%20-%20%5Cleft%28%20131%20%5Cright%29%5E2%7D%20%5Capprox%20-0.292%5Cend%7Baligned%7D)
Step 4: Assemble the equation of a line
![\begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~37.05 ~-~ 0.292 \cdot x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20y~%26%3D~a%20~%2B~%20b%20%5Ccdot%20x%20%5C%5Cy~%26%3D~37.05%20~-~%200.292%20%5Ccdot%20x%5Cend%7Baligned%7D)
Answer:
x-1 = 0 or x-7 =0
x=1 or x=7
Step-by-step explanation:
(x-1) (x-7) =0
Using the zero product property
x-1 = 0 or x-7 =0
x-1+1 =0 +1 or x-7+7 =0+7
x=1 or x=7