Point A is located at (2, 8) and point B is located at (8, 5). What point partitions the directed line segment AB⎯⎯⎯⎯⎯ into
2 answers:
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Giving the table below which shows <span>the percent increase of donations made on behalf of a non-profit organization for the period of 1984 to 2003.
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Year: 1984 1989 1993 1997 2001 2003
Percent: 7.8 16.3 26.2 38.9 49.2 62.1
The scatter plot of the data is attached with the x-axis representing the number of years after 1980 and the y-axis representing the percent increase <span>of donations made on behalf of a non-profit organization.
To find the equation for the line of regression where </span><span>the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.
![\begin{center} \begin{tabular}{ c| c| c| c| } x & y & x^2 & xy \\ [1ex] 4 & 7.8 & 16 & 31.2 \\ 9 & 16.3 & 81 & 146.7 \\ 13 & 26.2 & 169 & 340.6 \\ 17 & 38.9 & 289 & 661.3 \\ 21 & 49.2 & 441 & 1,033.2 \\ 23 & 62.1 & 529 & 1,428.3 \\ [1ex] \Sigma x=87 & \Sigma y=200.5 & \Sigma x^2=1,525 & \Sigma xy=3,641.3 \end{tabular} \end{center}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%0A%5Cbegin%7Btabular%7D%7B%20c%7C%20c%7C%20c%7C%20c%7C%20%7D%0A%20x%20%26%20y%20%26%20x%5E2%20%26%20xy%20%5C%5C%20%5B1ex%5D%20%0A%204%20%26%207.8%20%26%2016%20%26%2031.2%20%5C%5C%20%20%0A%209%20%26%2016.3%20%26%2081%20%26%20146.7%20%5C%5C%20%0A13%20%26%2026.2%20%26%20169%20%26%20340.6%20%5C%5C%20%0A17%20%26%2038.9%20%26%20289%20%26%20661.3%20%5C%5C%20%0A21%20%26%2049.2%20%26%20441%20%26%201%2C033.2%20%5C%5C%20%0A23%20%26%2062.1%20%26%20529%20%26%201%2C428.3%20%5C%5C%20%5B1ex%5D%0A%5CSigma%20x%3D87%20%26%20%5CSigma%20y%3D200.5%20%26%20%5CSigma%20x%5E2%3D1%2C525%20%26%20%5CSigma%20xy%3D3%2C641.3%20%20%0A%5Cend%7Btabular%7D%0A%5Cend%7Bcenter%7D)
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Recall that the equation of the regression line is given by
where
and
Thus, the equation of the regresson line is given by
The graph of the regression line is attached.
Using the equation, we can predict the percent donated in the year 2015. Recall that 2015 is 35 years after 1980. Thus x = 35.
The percent donated in the year 2015 is given by
Therefore, the percent donated in the year 2015 is predicted to be 90.5
</span>
Year: 1984 1989 1993 1997 2001 2003
Percent: 7.8 16.3 26.2 38.9 49.2 62.1
The scatter plot of the data is attached with the x-axis representing the number of years after 1980 and the y-axis representing the percent increase <span>of donations made on behalf of a non-profit organization.
To find the equation for the line of regression where </span><span>the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.
</span>
Recall that the equation of the regression line is given by
where
and
Thus, the equation of the regresson line is given by
The graph of the regression line is attached.
Using the equation, we can predict the percent donated in the year 2015. Recall that 2015 is 35 years after 1980. Thus x = 35.
The percent donated in the year 2015 is given by
Therefore, the percent donated in the year 2015 is predicted to be 90.5
Answer:
2.5 second
Step-by-step explanation:
The equation is missing in the question.
The equation is, , where 'h' is the height and 't' is time measured in second.
Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :
Now the differentiating the equation with respect to time t, we get
For maximum height,
So,
Therefore, the ball takes 2.5 seconds time to reach the maximum height.