Answer:
Step-by-step explanation:
<u>Distance:</u>
<u>Speed:</u>
<u>Time:</u>
- t = d/s
- t = 7/8 : 3/8 = 7/8 * 8/3 = 7/3 = 2 1/3 min
Given the data points, (x, y) of a linear function: (2, 11), (4, 10), (6, 9), (12, 6), what is the function? What is the slope?
NeX [460]
Answer:
The function is
.
The slope is
.
The y-intercept is
.
Step-by-step explanation:
Our aim is to calculate the values <em>m</em> (slope) and <em>b</em> (y-intercept) in the equation of a line :
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
We have the following data:
![\begin{array}{c|cccc}x&2&4&6&12\\y&11&10&9&6\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Ccccc%7Dx%262%264%266%2612%5C%5Cy%2611%2610%269%266%5Cend%7Barray%7D)
To find the line of best fit for the points given, you must:
Step 1: Find
and
as it was done in the table below.
Step 2: Find the sum of every column:
![\sum{X} = 24 ~,~ \sum{Y} = 36 ~,~ \sum{X \cdot Y} = 188 ~,~ \sum{X^2} = 200](https://tex.z-dn.net/?f=%5Csum%7BX%7D%20%3D%2024%20~%2C~%20%5Csum%7BY%7D%20%3D%2036%20~%2C~%20%5Csum%7BX%20%5Ccdot%20Y%7D%20%3D%20188%20~%2C~%20%5Csum%7BX%5E2%7D%20%3D%20200)
Step 3: Use the following equations to find <em>b</em> and <em>m</em>:
![\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 36 \cdot 200 - 24 \cdot 188}{ 4 \cdot 200 - 24^2} \approx 12 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 4 \cdot 188 - 24 \cdot 36 }{ 4 \cdot 200 - \left( 24 \right)^2} \approx -0.5\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%09%09%09%09%09%09%09b%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%09%09%09%09%09%09%09%20%20%20%20%20%20%5Cfrac%7B%2036%20%5Ccdot%20200%20-%2024%20%5Ccdot%20188%7D%7B%204%20%5Ccdot%20200%20-%2024%5E2%7D%20%5Capprox%2012%20%5C%5C%20%5C%5Cm%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%09%09%09%09%09%09%09%3D%20%5Cfrac%7B%204%20%5Ccdot%20188%20-%2024%20%5Ccdot%2036%20%7D%7B%204%20%5Ccdot%20200%20-%20%5Cleft%28%2024%20%5Cright%29%5E2%7D%20%5Capprox%20-0.5%5Cend%7Baligned%7D)
Step 4: Assemble the equation of a line
![\begin{aligned} y~&=~b ~+~ m \cdot x \\y~&=~12 ~-~ 0.5 \cdot x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20y~%26%3D~b%20~%2B~%20m%20%5Ccdot%20x%20%5C%5Cy~%26%3D~12%20~-~%200.5%20%5Ccdot%20x%5Cend%7Baligned%7D)
The graph of the regression line is:
Answer:
False
Step-by-step explanation:
9 is a multiple of 3 but not 6
2. They are both straight lines. The solution of a linear system is where the two lines intersect, and if they're both straight lines, then they can only cross once.
See the picture attached.
2 * 7 = 14 (the number of tiles for each row) 23 - 14 = 9 (the number of tiles subtracted from how many tiles that are taken away) 9 tiles are in the seventh row.