Concept explainers
a.
To Draw: A
a.
Explanation of Solution
Given: In an experiment, student measured the speed s (in meters per second) of a ball t second after it was released, the result are shown in the below table.
Time, t | Speed, s |
0 | 0 |
1 | 11.0 |
2 | 19.4 |
3 | 29.2 |
4 | 39.4 |
Calculation:
Graph a scatter plot on the above table data is given below.
Conclusion: The plot is increasing
b.
To find: An equation of a line that seems to fit the data best.
b.
Answer to Problem 147RE
The equation of a line that seems to fit the data best is
Explanation of Solution
Given: In an experiment, student measured the speed s (in meters per second) of a ball t second after it was released, the result are shown in the below table.
Time, t | Speed, s |
0 | 0 |
1 | 11.0 |
2 | 19.4 |
3 | 29.2 |
4 | 39.4 |
Calculation:
The equation of a line passing through two points
From the scatter plot select two points as (0,0),(4,39.4), then the equation of a line passing through two points as (0,0),(4,39.4), is,
The equation of a line that seems to fit the data best is
c
To find: A linear model for the data and identify the
c
Answer to Problem 147RE
The equation of linear regression line is
The regression coefficient is 0.9993
Explanation of Solution
Given: In an experiment, student measured the speed s (in meters per second) of a ball t second after it was released, the result are shown in the below table.
Time, t | Speed, s |
0 | 0 |
1 | 11.0 |
2 | 19.4 |
3 | 29.2 |
4 | 39.4 |
Calculation:
The equation for the regression line is given below.
Using linear regression calculator on above result data table, linear regression line is,
Thus, the regression coefficient is 0.9993.
d.
To estimate: The speed of the ball after 2.5 seconds.
d.
Answer to Problem 147RE
The speed of the ball after 2.5 seconds is 24.65 meter/second.
Explanation of Solution
Given: In an experiment, student measured the speed s (in meters per second) of a ball t second after it was released, the result are shown in the below table.
Time, t | Speed, s |
0 | 0 |
1 | 11.0 |
2 | 19.4 |
3 | 29.2 |
4 | 39.4 |
Calculation:
The regression line is
To estimate the speed of the ball after 2.5 seconds, substitute x =2.5 in regression line equation.
So, speed of the ball after 2.5 seconds is 24.65 meter/second.
Chapter 1 Solutions
Precalculus with Limits: A Graphing Approach
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning