Show that for any k > 3, any tree with a vertex of degreek must have at least k leaves. The proof that uses summations of the result that a tree always has two leaves is probably easiest to adapt here. You will want to assume ng > 1 in the summations

Q: A bit is a 0 or a 1. A bit string of length 7 is a sequence of 7 digits, all of which are either 0…

A: Given: A bit is 0 or 1. A bit string of length 7 is a sequence of 7 digits. To find: a) Total number…

Q: Use induction to prove that every tree is bipartite.

A: We Know that a bipartite graph is a graph whose vertices can be divided into two disjoint and…

Q: 2yy" = 1 + (y')² 2

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Q: How many three-digit numbers are possible under each condition? (a) The leading digit cannot be zero…

A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

Q: You may be familiar with the formula for the sum of a finite geometric progression: if a and r are…

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Q: Given a cube that has a side length of one, find out the greatest number of points that can be put…

A: Given a cube that has a side length of one, find out the greatest number of points that can be put…

Q: Use induction to prove the theorem: A tree with n vertexes has n-1 edges.

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Q: A sequence bo, b1, b2, ... is defined by letting bo = 5 and b = 4+bk-1 for each integer k> 1. Show…

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Q: Carry out all the steps in the the division algorithm for 78 and 15. This means show how to find q…

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Q: Jse generating functions to show that every positive integer can be written in exactly one way as a…

A: A generating function is a way to encode an infinite sequence of numbers by treating them as the…

Q: Show that if h+1 distinct integers are, Chasen from the Set El,2,en.,4n}. then there are always two…

A: To show that choosing n+1 distinct integers from the set {1, 2, 3, ..., 4n} then there are always…

Q: Prove the property of the Fibonacci numbers, F(n) = 5(n 4) + 3F(n-5), for n ≥6

A: We have to prove the property of the given Fibonacci numbers F(n) = 5F(n-4) + 3F(n-5) ,  for n≥6

Q: An n×n magic square is a square array of numbers (n > 1) such that the sum of every row, of every…

A: Given a n×n magic square

Q: 8) sle) = [x-02] + 4 y -3 -2 3. 4 x

A: To understand the behaviour of the function in terms of the graph, let's construct a table of values…

Q: x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10 What does this prove about the sum of these natural numbers?

A: The sum of the given equation is calculated as follows.

Q: If given a sequence of five consecutive integers (e.g. 1,2,3,4,5), then the sum of these integers is…

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Q: Suppose that a1, a2, a3, . .. is a sequence of sequences of zeros and ones. aj is a11, a12, a13, ·…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.