College Freshmen The percentage, y , of college freshmen who smoke cigarettes decreased steadily from the year 2004 to the year 2014 and can be approximated by the linear equation y = − .46 x + 6.32 where x represents the number of years since 2004. Thus, x = 0 represents 2004, x = 1 represents 2005, and so on. ( Source: The American Freshman: National Norms .) a. What interpretation can be given to the y -intercept of the graph of the equation? b. In 2014, approximately what percent of college freshmen smoked? c. In what year did approximately 2.6% of college freshmen smoke?
College Freshmen The percentage, y , of college freshmen who smoke cigarettes decreased steadily from the year 2004 to the year 2014 and can be approximated by the linear equation y = − .46 x + 6.32 where x represents the number of years since 2004. Thus, x = 0 represents 2004, x = 1 represents 2005, and so on. ( Source: The American Freshman: National Norms .) a. What interpretation can be given to the y -intercept of the graph of the equation? b. In 2014, approximately what percent of college freshmen smoked? c. In what year did approximately 2.6% of college freshmen smoke?
Solution Summary: The author explains how the y-intercept of the graph shows the percentage of college freshmen who smoke cigarette in the year 2004.
College Freshmen The percentage, y, of college freshmen who smoke cigarettes decreased steadily from the year 2004 to the year 2014 and can be approximated by the linear equation
y
=
−
.46
x
+
6.32
where x represents the number of years since 2004. Thus,
x
=
0
represents 2004,
x
=
1
represents 2005, and so on. (Source: The American Freshman: National Norms.)
a. What interpretation can be given to the y-intercept of the graph of the equation?
b. In 2014, approximately what percent of college freshmen smoked?
c. In what year did approximately 2.6% of college freshmen smoke?
Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
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