The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24 -hour period. Let x represent the time of day, where x = 0 corresponds to 6 a.m. These data can be approximated by the model y = 0.026 x 3 − 1.03 x 2 + 10.2 x + 34 , 0 ≤ x ≤ 24. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. (e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24 -hour period. Let x represent the time of day, where x = 0 corresponds to 6 a.m. These data can be approximated by the model y = 0.026 x 3 − 1.03 x 2 + 10.2 x + 34 , 0 ≤ x ≤ 24. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. (e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Solution Summary: The author explains how to draw the scatter plot and graph of the model in the same viewing window by using the graphing utility.
The table shows the temperatures
y
(in degrees Fahrenheit) in a city over a
24
-hour
period. Let
x
represent the time of day, where
x
=
0
corresponds to 6 a.m.
These data can be approximated by the model
y
=
0.026
x
3
−
1.03
x
2
+
10.2
x
+
34
,
0
≤
x
≤
24.
(a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window.
(b) How well does the model fit the data?
(c) Use the graph to approximate the times when the temperature was increasing and decreasing.
(d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period.
(e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
Manuel is investigating how long his phone's battery lasts (in hours) for various brightness levels (on
a scale of 0-100). His data is displayed in the table and graph below.
Brightness Level (x)
30
49
65
67
69
80
85
85
Hours (y)
6.6
4.6
4.1
4.3
3.5
2.8
3.1
10+
7
2
10
20
30
40
60
70
80
100
Brightness Level
a) Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the
equation.
SANOH
An insurance company determines that a linear relationship exists between the cost of fire damage in major
residential fıres and the distance from the house to the nearest fire station. A sample of 15 recent fires in a
large suburb of a major city was selected. For each fire, the following variables were recorded:
x= the distance between the fire and the nearest fire station (in miles)
y= cost of damage (in dollars)
The distances between the fire and the nearest fire station ranged between 0.7 miles and 6.1 miles.
The correlation between cost and distance is 0.961. Test if the correlation is significant at a=.10.
O No, the correlation is not significant because 0.961 does not exceed the critical value.
O Yes, the correlation is significant because 0.961 exceeds the critical value.
No, the correlation is not significant because 0.961 exceeds the critical value.
O Yes, the correlation is significant because 0.961 does not exceed the critical value.
O No, the correlation is not…
Chapter 2 Solutions
College Algebra Real Mathematics Real People Edition 7
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