To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

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Answer 1

Question

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

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Suppose an experiment was conducted to compare the mileage(km) per litre obtained by competing brands of petrol I,II,III. Three new Mazda, three new Toyota and three new Nissan cars were available for experimentation. During the experiment the cars would operate under same conditions in order to eliminate the effect of external variables on the distance travelled per litre on the assigned brand of petrol. The data is given as below: Brands of Petrol Mazda Toyota Nissan I 10.6 12.0 11.0 II 9.0 15.0 12.0 III 12.0 17.4 13.0 (a) Test at the 5% level of significance whether there are signi cant differences among the brands of fuels and also among the cars. [10] (b) Compute the standard error for comparing any two fuel brands means. Hence compare, at the 5% level of significance, each of fuel brands II, and III with the standard fuel brand I. [10]

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Use the method of undetermined coefficients to solve the given nonhomogeneous system.X' = −1 33 −1 X + −4t2t + 2 X(t) =

Answer 2

Question

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

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Answer 3

Question

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

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Answer 4

Question

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

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Answer 5

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

Answer 6

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

Answer 7

Chapter 12.1, Problem 27E

To determine

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

Answer 8

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

Answer 9

To determine

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

Answer 10

Expert Solution & Answer

Answer 11

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Answer 12

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Answer 13

Ch. 12.1 - Prob. 1TFQ Ch. 12.1 - Prob. 2TFQ Ch. 12.1 - Prob. 3TFQ Ch. 12.1 - Prob. 4TFQ Ch. 12.1 - Prob. 5TFQ Ch. 12.1 - Prob. 6TFQ Ch. 12.1 - Prob. 7TFQ Ch. 12.1 - Prob. 8TFQ Ch. 12.1 - Prob. 9TFQ Ch. 12.1 - Prob. 10TFQ

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

Solution Summary: The author explains that a tree with two vertices of degree 3 must have at least four edges. If the result isn't true, then there are two and at most three.

To prove: that a tree with vertices of degree 3 must have at least four vertices of degree1.

To prove: The result of (a) is the best possible: A tree with two vertices of degree 3 need not have five vertices of degree 1.

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Chapter 12 Solutions