Concept explainers
(a)
To draw: a
(a)
Answer to Problem 109AYU
Explanation of Solution
Given:
Decade, x | Major Hurricanes Striking United States, H |
1921-1930, 1 | 5 |
1931-1940, 2 | 8 |
1941-1950, 3 | 10 |
1951-1960, 4 | 8 |
1961-1970, 5 | 6 |
1971-1980, 6 | 4 |
1981-1990, 7 | 5 |
1991-2000, 8 | 5 |
Calculation:
Figure 1 shows the scatter diagram. A cubic relation may exist between the two variables x and H.
Figure 1
Conclusion:
Therefore, the scatter diagram is drawn.
(b)
To find: the cubic function of best fit
(b)
Answer to Problem 109AYU
The cubic equation of best fit to the data is
Explanation of Solution
Calculation:
Upon executing the CUBIC Regression Program, obtained results are shown in Figure 2. The output that the utility provides shows us the equation
The cubic equation of best fit to the data is
Figure 2
Conclusion:
The cubic equation of best fit to the data is
(c)
To predict: the number of major hurricanes that struck the United States
(c)
Answer to Problem 109AYU
The no. of major hurricane is 6.
Explanation of Solution
Calculation:
The cubic equation of best fit to the data is
In Figure 1, point
The no. of major hurricane that struck the United States between 1961 through 1970 can be calculated as
The no. of major hurricane is 6.
Conclusion:
The no. of major hurricane is 6.
(d)
To draw: a graph of the cubic function of best fit
(d)
Answer to Problem 109AYU
Explanation of Solution
Calculation:
Figure 3 shows the graph of the cubic function of best fit on the scatter diagram. The function fits the data reasonably well. The cubic function of best fit passes through all the point very nearly.
Figure 3
Conclusion:
Therefore, the required graph is drawn.
(e)
To predict: the number of major hurricanes and explain whether the result appear to agree with what the scientists believe.
(e)
Answer to Problem 109AYU
The no. of major hurricane is 10.
The result appears to agree with what these scientists believe.
Explanation of Solution
Calculation:
In Figure 1 point
The no. of major hurricane that struck the United States between 2001 and 2009 can be calculated as
Therefore the no. of major hurricane that struck the United States between 2001 through 2009 is equal to 10.
From Figure 3 at the point
So, the result appears to agree with what these scientists believe.
Conclusion:
Therefore the no. of major hurricane is 10 and the result appears to agree with what these scientists believe.
(f)
To find: whether the given statement support or contradict the prediction
(f)
Answer to Problem 109AYU
The prediction supports our result in part €
Explanation of Solution
Given:
From 2001 through 2010,10 major hurricanes struck the United States.
From 2001 through 2009, 10 major hurricanes struck the United States.
Our prediction in part (e) shows that the no. of major hurricane in United States is equal to 10.
The answer is yes, this prediction supports our result in part (e).
Conclusion:
Therefore, theprediction supports our result in part €
Chapter 4 Solutions
Precalculus
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