Concept explainers
a.
To graph the given data.
a.
Explanation of Solution
Given information:
The works and number of minutes they will take to finish job is,
Workers | Minutes |
9 | 80 |
16 | 40 |
18 | 35 |
8 | 90 |
15 | 60 |
11 | 60 |
9 | 70 |
17 | 30 |
9 | 70 |
15 | 50 |
11 | 80 |
12 | 70 |
Graph:
b.
To draw a line to fit to show the trend
b.
Explanation of Solution
Given information:
The works and number of minutes they will take to finish job is,
Workers | Minutes |
9 | 80 |
16 | 40 |
18 | 35 |
8 | 90 |
15 | 60 |
11 | 60 |
9 | 70 |
17 | 30 |
9 | 70 |
15 | 50 |
11 | 80 |
12 | 70 |
c.
To write the equation of line.
c.
Answer to Problem 4.4.2P
The equation of line is
Explanation of Solution
Given information:
The graph is,
Formula used:
Equation of line in slope intercept form,
Equation of line in
1
Slope is,
3
Calculation:
Let the two points be,
(9, 8) and (15, 50).
Substituting the values in the formula of slope,
So,
On solving,
Hence, slope is 7.
Substituting the values in the equation of line in slope point form,
Converting it into slope intercept form,
Opening the brackets,
Shifting left hand side value to right hand side,
On solving,
Hence, the equation of line in slope-intercept form is,
Conclusion:
The equation of line is
d.
To calculate how long the workers will take to complete the task.
d.
Answer to Problem 4.4.2P
A group of 6 workers will finish the work in 95mins.
Explanation of Solution
Given information:
Number of workers are 6.
Graph for the given data is,
Formula used:
Graph evaluating.
Calculation:
Checking the value of “y” in the graph when “x” is 6
Concluding from the graph,
When
Hence, a group of 6 workers will finish the work in 95mins.
Conclusion:
A group of 6 workers will finish the work in 95mins.
e.
To number of workers needed
e.
Answer to Problem 4.4.2P
14 workers are required to complete work in 45 mins.
Explanation of Solution
Given information:
The time in which the work should be finished is 45mins
The equation of line is
The graph is,
Formula used:
Substitution and equation solving.
Calculation:
Substituting the value in the equation,
Shifting right hand side values to left hand side,
On solving,
Cross- multiplying both sides,
On solving,
Rounding off,
Hence, 14 workers are required to complete work in 45 mins.
Conclusion:
14 workers are required to complete work in 45 mins.
f.
To calculate the y-intercept
f.
Answer to Problem 4.4.2P
The y- intercept is -55.
Explanation of Solution
Given information:
The equation for the given data set is
Formula used:
Equation of line is,
Where, m is slope
c is y-intercept
Calculation:
Comparing with the equation of line and the equation of the given data set,
The y- intercept is,
The y-intercept in this situation tells the total time it will take for 0 workers to do the work.
From the equation the value of y- intercept is negative, which should have been positive, because the time cannot be negative.
Conclusion:
The y- intercept is -55.
Chapter ISG Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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