Provide an appropriate response.Suppose that a histogram is constructed for the frequency table shown below:
The class 60-69 has twice the frequency of the class 70-89. In the histogram, will the area of the bar for the class 60-69 be twice the area of the bar for the class 70-89? In other words, will areas be proportional to frequencies in this histogram? Explain your thinking. Are there any conditions under which areas are proportional to frequencies in histograms?
What will be an ideal response?
The areas of the bars for the two classes will actually be the same. This is because the bar for the class 60-69, while it is twice as tall as the bar for the class 70-89, is also only half the width because the class widths are not the same. Heights, not areas are proportional to frequencies. For classes of equal width, areas will also be proportional to frequencies.
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For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes.f(x) = 
A. removable discontinuity at (-2, 0);
x-intercept: (-2, 0), y-intercept: 
;
asymptotes: x = -5, y = 1
B. removable discontinuities: 
, 
;
x-intercept: (2, 0), y-intercept: 
;
asymptotes: x = 5, y = 1
C. removable discontinuities: 
, (-2, 0);
x-intercept: (-2, 0), y-intercept: 
;
asymptotes: x = 5, y = 1
D. removable discontinuity at 
;
x-intercept: (2, 0), y-intercept: 
;
asymptotes: x = -5, y = 1
Refer to the weighted voting system 
and the Banzhaf definition of power. (The four players are P1, P2, P3, and P4.)The number of winning coalitions is
A. 7. B. 15. C. 8. D. 1. E. none of these
The graph of a function f is given. Use the graph to answer the question.What are the x-intercepts?
A. (-30, 0), (35, 0) B. (-50, 0), (-30, 0), (35, 0), (50, 0) C. (-30, 0), (35, 0), (50, 0) D. (-30, 0)
Divide and simplify to the form a + bi.
A. 
+ 
i
B. 
+ 
i
C. 
+ 
i
D. 4 - 22i