E-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let f ( t ) represent the number of tax returns made through e-file in the year t . ( Source: efile ) Year Number of Tax Returns Made through E-File 2007 80.0 2008 89.9 2009 95.0 2010 98.7 2011 112.2 2012 112.1 2013 114.4 2014 125.8 (a) Find f ( 2014 ) − f ( 2007 ) 2014 − 2007 and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let t = 7 correspond to 2007. (d) Use the model found in part (c) to complete the table. t 7 8 9 10 11 12 13 14 N (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let x = 7 correspond to 2007. How does the model you found in part (c) compare with the model given by graphing utility?
E-Filing The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let f ( t ) represent the number of tax returns made through e-file in the year t . ( Source: efile ) Year Number of Tax Returns Made through E-File 2007 80.0 2008 89.9 2009 95.0 2010 98.7 2011 112.2 2012 112.1 2013 114.4 2014 125.8 (a) Find f ( 2014 ) − f ( 2007 ) 2014 − 2007 and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let t = 7 correspond to 2007. (d) Use the model found in part (c) to complete the table. t 7 8 9 10 11 12 13 14 N (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let x = 7 correspond to 2007. How does the model you found in part (c) compare with the model given by graphing utility?
The table shows the numbers of tax returns (in millions) made through e-file from 2007 through 2014. Let f(t) represent the number of tax returns made through e-file in the year t. (Source: efile)
Year
Number of Tax Returns Made through E-File
2007
80.0
2008
89.9
2009
95.0
2010
98.7
2011
112.2
2012
112.1
2013
114.4
2014
125.8
(a) Find
f
(
2014
)
−
f
(
2007
)
2014
−
2007
and interpret the result in the context of the problem.
(b) Make a scatter plot of the data.
(c) Find a linear model for the data algebraically. Let N represent the number of tax returns made through e-file and let
t
=
7
correspond to 2007.
(d) Use the model found in part (c) to complete the table.
t
7
8
9
10
11
12
13
14
N
(e) Compare your results from part (d) with the actual data.
(f) Use a graphing utility to find a linear model for the data. Let
x
=
7
correspond to 2007. How does the model you found in part (c) compare with the model given by graphing utility?
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.
Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.
Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.
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