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guapka [62]
3 years ago
10

Three people whowork full time are working together on a project but their totaltime on the project is to be equivalent to that

of only one person working full time. If one of the people is budgetedforone half of the time to the project and the second person foe one third of her time what part of the third workers time should be budgeted to this project
Mathematics
1 answer:
Art [367]3 years ago
7 0
The answer is (1/3). So first you need to determine the fraction of time the second person worked. Multiply (1/2)x(1/3) and you will get (1/6). All the values need to add up to 1, so you can make the equation (1/2)+(1/6)+x=1. Solve for x and you will get (1/3).
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The equation of the regression line is:

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Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}

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Step 3: Use the following equations to find a and 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{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}

Step 4: Assemble the equation of a line

\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}

The graph of the regression line is:

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