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use problem 15 of this section to show that in n independent trials with probability p of successproblem 15draw a graph
draw a graph of the equation y x1 - x for x between 0 and 1 what is the maximum value of y why does this show that the
is a score of 70 on a 100 question true-false test consistent with the hypothesis that the test taker was just guessing
show that the variance for n independent trials with two outcomes and probability p of success is given by np1-p what
we have a nickel dime and quarter in a cup we withdraw two coins first one and then the second without replacement what
draw the minimum number of drawings of trees you can so that each tree with five vertices has one of those drawings
does every tree have a vertex of degree 1 if the answer is yes explain why if the answer is no try to find additional
the internal path length of a binary tree is the sum taken over all internal see exercise 62-11 vertices of the tree of
the height of a rooted or binary tree with one vertex is 0 otherwise it is 1 plus the maximum of the heights of its
aleft right child of a vertex in a binary tree is the root of a left right subtree of that vertex a binary tree is a
it may seem clear to some people that the breadth first number of a vertex is the number of vertices previously added
create a breadth first search tree centered at vertex 12 for the graph in figure 68 and use it to compute the distance
find a tree with more than one vertex that has the property that all the rooted trees you get by picking different
draw all rooted trees on 6 vertices with four leaf vertices if you would like to label the vertices as we did in the
draw all rooted trees on 5 vertices the order and the place in which you write the vertices down on the page is
a binary tree is a full binary tree if each vertex has either two nonempty children or two empty children a vertex with
a binary tree is a special kind of rooted tree that has some additional structure that makes it tremendously useful as
draw the minimum number of drawings of trees you can so that each tree with six vertices is represented by exactly one
find the strongest condition you can that has to be satisfied by a graph that has a path starting and ending at
try to find an interesting condition involving the degrees of the vertices of a simple graph that guarantees that the
suppose v 2k and consider a graph g consisting of two complete graphs one with k vertices x1xk and one with k 1
what is the minimum number of new bridges that would have to be built in kumlonigsberg and where could they be built in
if we built a new bridge in kumlonigsberg between the island and the top and bottom banks of the river could we take a
the hypercube graph qn has as its vertex set the n-tuples of zeros and ones two of these vertices are adjacent if and
we form the hamiltonian closure of a graph by constructing a sequence of graphs gi with g0 g and gi formed from gi-1