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.
Suppose you flip a fair two-sided coin four times and record the result.
a). List the sample space of this experiment. That is, list all possible outcomes that could
occur when flipping a fair two-sided coin four total times. Assume the two sides of the coin are
Heads (H) and Tails (T).
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