The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Question

Page < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.

Answer 1

Question

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

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Page < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.

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Answer 2

Question

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

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Answer 3

Question

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

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Answer 4

Question

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

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Answer 5

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

Answer 6

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Answer 7

Chapter 6.B, Problem 16E

Part a:

To determine

The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Answer 8

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Answer 9

Part b:

To determine

The five-number summary and draw a box plot for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Refer explanation.

Answer 10

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Answer 11

Part c:

To determine

The standard deviation for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Answer 12

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Answer 13

Part d:

To determine

The standard deviation for each of the two data sets using range rule of thumb for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

Answer 14

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

Answer 15

Part e:

To determine

To compare: The two data sets in terms of their center and variation for the given table which gives average sales tax rate in six east coast and six western states.

East coast states Western states
Florida 6.8% California 8.25%
Massachusetts 6.25% Arkansas 1.76%
Maryland 6.00% Oregon 0%
New Hampshire 0% Washington 8.92%
New York 8.49% Arizona 8.25%
Rhode Island 7.00% Utah 6.76%

The average of sales tax rate in east coast states and western states are almost same. Variation is more in western states.

Answer 16

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The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

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The mean, median, and range for each of the two data sets for the given table which gives average sales tax rate in six east coast and six western states.

Chapter 6 Solutions

East coast states	Western states
Florida	6.8%	California	8.25%
Massachusetts	6.25%	Arkansas	1.76%
Maryland	6.00%	Oregon	0%
New Hampshire	0%	Washington	8.92%
New York	8.49%	Arizona	8.25%
Rhode Island	7.00%	Utah	6.76%