Find f(x) =32 f(x)=3x-1
1 answer:
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Answer:
or
or equivalently:
or
Step-by-step explanation:
To express the Fahrenheit temperature <em>as a linear function of the Celsius temperature</em>, F(c), we can proceed as follows.
We can use here <em>the two-point form</em> <em>equation</em> of a line:
[1]
We are asked to express the <em>Fahrenheit temperature</em> as a function of <em>Celsius temperature</em>, so the independent variable, in this case, is <em>x</em> (Celsius temperature) and the dependent variable is <em>y</em> (Fahrenheit temperature).
When temperature is zero degree Celsius (), the Fahrenheit temperature is 32 (
).
When the Celsius temperature is 100 (), the corresponding Fahrenheit temperature is 212 (
).
Then, using [1], we have:
.
It could be also be written as:
=
, as it commonly appears in books.
Then <em>the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c</em>) is ( solving the equation for <em>y </em>) :
or
.
Or equivalently:
or
We can check this using the given values from the question:
For 0 Celsius degrees, the Fahrenheit temperature is:
= 32 Fahrenheit degrees.
For 100 Celsius degrees, the Fahrenheit temperature is:
= 212 Fahrenheit degrees.
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.
</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.
![\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)
</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
</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