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$x$ | $y$ |
900 | 70 |
988 | 80 |
1000 | 82 |
1010 | 84 |
1200 | 105 |
1205 | 108 |
$y=0.\text{121}x-38.841,\text{\hspace{0.17em}}r=0.998$
Graph $f(x)=0.5x+10$ . Pick a set of 5 ordered pairs using inputs $x=\text{\u22122},\text{1},\text{5},\text{6},\text{9}$ and use linear regression to verify that the function is a good fit for the data.
Graph $f(x)=-2x-10$ . Pick a set of 5 ordered pairs using inputs $x=\text{\u22122},\text{1},\text{5},\text{6},\text{9}$ and use linear regression to verify the function.
$\left(\text{\u22122},\mathrm{-6}\right),\left(\text{1},\text{\u221212}\right),\left(\text{5},\text{\u22122}0\right),\left(\text{6},\text{\u221222}\right),\left(\text{9},\text{\u221228}\right)$ ; $y=\mathrm{-2}x\mathrm{-10}$
For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years:
$\left(\text{46},\text{1},\text{6}00\right),\left(\text{48},\text{1},\text{55}0\right),\left(\text{5}0,\text{1},\text{5}0\text{5}\right),\left(\text{52},\text{1},\text{54}0\right),\left(\text{54},\text{1},\text{495}\right)$ .
Use linear regression to determine a function $P$ where the profit in thousands of dollars depends on the number of units sold in hundreds.
Find to the nearest tenth and interpret the x -intercept.
$\left(\text{189}.\text{8},0\right)$ If 18,980 units are sold, the company will have a profit of zero dollars.
Find to the nearest tenth and interpret the y -intercept.
For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:
$\text{(2500,2000),(2650,2001),(3000,2003),(3500,2006),(4200,2010)}$
Use linear regression to determine a function $y,$ where the year depends on the population. Round to three decimal places of accuracy.
$y=0.00587x+\text{1985}.4\text{1}$
Predict when the population will hit 8,000.
For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:
$\left(\text{46},\text{25}0\right),\left(\text{48},\text{3}0\text{5}\right),\left(\text{5}0,\text{35}0\right),\left(\text{52},\text{39}0\right),\left(\text{54},\text{41}0\right)$ .
Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .
$y=\text{2}0.\text{25}x-\text{671}.\text{5}$
Predict when the profit will exceed one million dollars.
For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:
$\text{(46,250),(48,225),(50,205),(52,180),(54,165)}\text{.}$
Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .
$y=-\text{1}0.\text{75}x+\text{742}.\text{5}0$
Predict when the profit will dip below the $25,000 threshold.
Determine whether the algebraic equation is linear. $2x+3y=7$
Yes
Determine whether the algebraic equation is linear. $6{x}^{2}-y=5$
Determine whether the function is increasing or decreasing.
$f\left(x\right)=7x-2$
Increasing.
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