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CalculusFinite Mathematics and Applied Calculus (MindTap Course List)Tourism in the 1990s The following table gives the number of people (in thousands) who visited Australia and South Africa in 1998: 14 To Australia South Africa From North America 440 190 Europe 950 950 Asia 1,790 200 You estimate that 5% of all visitors to Australia and 4% of all visitors to South Africa decide to settle there permanently. Take A to be the 3 × 2 matrix whose entries are the 1998 tourism figures in the above table, and take B = [ 0.05 0.04 ] and C = [ 0.05 0 0 0.04 ] . Compute the products AB and AC . What do the entries in these matrices represent?BuyFind*arrow_forward*

7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 5.2, Problem 73E

Textbook Problem

**Tourism in the 1990s** The following table gives the number of people (in thousands) who visited Australia and South Africa in 1998:^{14}

To |
Australia |
South Africa |

From North America |
440 | 190 |

Europe |
950 | 950 |

Asia |
1,790 | 200 |

You estimate that 5% of all visitors to Australia and 4% of all visitors to South Africa decide to settle there permanently. Take *A* to be the

Compute the products *AB* and *AC*. What do the entries in these matrices represent?

Expert Solution

To determine

**To calculate:** The products *AB* and *AC* and what do the entries represent where *A* is the

To | Australia | South Africa |

From North America | 440 | 190 |

Europe | 950 | 950 |

Asia | 1790 | 200 |

**Given Information:**

*A* is the

To | Australia | South Africa |

From North America | 440 | 190 |

Europe | 950 | 950 |

Asia | 1790 | 200 |

**Formula used:**

A matrix with *m* rows and *n* columns is of dimension *m* and *n* are positive integers.

For matrices *A* with dimension *B* with dimension *AB* is defined if the number of columns in *A* equal number of columns in *B*,

For matrices *A* with dimension *B* with dimension *AB* is the matrix of dimension *AB* is the sum of product of corresponding entries of row *i* of *A* and column *j* of *B*.

**Calculation:**

Consider *A* is the

To | Australia | South Africa |

From North America | 440 | 190 |

Europe | 950 | 950 |

Asia | 1790 | 200 |

Write the table as a matrix *A*.

Thus, tourism in

Consider, the product *AB*.

Recall that a matrix with *m* rows and *n* columns is of dimension *m* and *n* are positive integers.

Since, number of rows in

Substitute *m* and *n* in

Thus, dimension of

Since, number of rows in

Substitute *m* and *n* in

Thus, dimension of

Since, number of rows in

Substitute *m* and *n* in

Thus, dimension of

Recall that for matrices *A* with dimension *B* with dimension *AB* is the matrix of dimension *AB* is the sum of product of corresponding entries of row *i* of *A* and column *j* of *B*

Finite Mathematics and Applied Calculus (MindTap Course List)

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Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

For each set of sample outcomes below, use Formula 6.2 to construct the 95 confidence interval for estimating ,...

Essentials Of Statistics

8688 Express the limit as a derivative and evaluate. limh016+h42h

Calculus (MindTap Course List)

Knight and Haslam (2010) found that office workers who had some input into the design of their office space wer...

Statistics for The Behavioral Sciences (MindTap Course List)

Investments In Hedge Funds Investments in hedge funds have increased along with their popularity. The assets of...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the limit, if it exists. 27. limx164x16xx2

Single Variable Calculus

Let X1, X2,..., Xn be a random sample from a pdf f(x) that is symmetric about , so that X is an unbiased estima...

Probability and Statistics for Engineering and the Sciences

Counting: Grading One professor grades homework by randomly choosing 5 out of 12 homework problems to grade. (a...

Understanding Basic Statistics

Solve the equations in Exercises 126. (x+1)3+(x+1)5=0

Finite Mathematics

In Exercise 9 to 16, use a calculator to find the indicated cosine ratio to four decimal places. cos73

Elementary Geometry For College Students, 7e

Use the triangle in Illustration 2 for Exercises 25-30. ILLUSTRATION 2 Find sinA.

Elementary Technical Mathematics

Reduce the following fractions to lowest terms. a. 270810 b. 175232

Contemporary Mathematics for Business & Consumers

Let X = {a, b, c, d, e} be the universal set. Determine whether Dc Morgans law (A B) = A B holds true for the...

Mathematical Excursions (MindTap Course List)

11. Rewards As a reward for a record year, the Ace Software Company is randomly selecting 4 people from its 500...

Mathematical Applications for the Management, Life, and Social Sciences

Graph the following points and their opposites on the real number line: 1, -2, and 4.

Intermediate Algebra

Find f'(x). Compare the graphs of f and f' and use them to explain why your answer is reasonable. f(x) = x4 2x...

Single Variable Calculus: Early Transcendentals

Finding a Taylor Series In Exercises 5-16, use the definition of Taylor series to find the Taylor series, cente...

Calculus of a Single Variable

Condensing a Logarithmic Expression In Exercises 99-106, write the expression as the logarithm of a single quan...

Calculus: Early Transcendental Functions (MindTap Course List)

Exercises
1. List all cyclic subgroups of the group in Example of section.
Example 3.
We shall take and ob...

Elements Of Modern Algebra

Graph each of the following lines. y=2x

Trigonometry (MindTap Course List)

limx1x3x21x = _____. a) 1 b) 1 c) 0 d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

A definite integral for , where C is the curve given by x = 3t, y = t, t [0, 1] is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercise 5 to 9, use a compass and a straightedge to complete the constructions. Given: Point N on line s Co...

Elementary Geometry for College Students

GAME OF CHANCE Refer to Exercise 26. Suppose Diane has decided to stop playing after she has accumulated a sum ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding a Directional DerivativeIn Exercises 2528, use the gradient to find the directional derivative of the f...

Multivariable Calculus

Slope Field In Exercises 6772, use a computer algebra system to (a) graph the slope field for the differential ...

Calculus (MindTap Course List)

The following data show the pattern of results that was obtained in a study by Liguori and Robinson (2001) exam...

Research Methods for the Behavioral Sciences (MindTap Course List)

The solution of the following problems requires more than one formula and the rearrangement of formulas. Use C=...

Mathematics For Machine Technology

A study of smartphone users shows that 68% of smartphone use occurs at home and a user spends an average of 410...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain the general advantages and disadvantages of within-subjects designs compared to between-subjects design...

Research Methods for the Behavioral Sciences (MindTap Course List)

In addition to the fiber contents given in the previous exercise, sugar content (in grams per serving) for the ...

Introduction To Statistics And Data Analysis

Find the slope of the line PQ, if possible. P(a+b,b);Q(b,ba)

College Algebra (MindTap Course List)

Consumption of alcoholic beverages by young women of drinking age in the United Kingdom, the United States, and...

Statistics for Business & Economics, Revised (MindTap Course List)

15. In the following profit payoff table for a decision problem with two states of nature and three decision al...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Motor Vehicle Accidents in New York City. In a one-year period, New York City had a total of 11,232 motor vehic...

Essentials Of Statistics For Business & Economics

Fibonacci Variation: A single pair of rabbits (male and female) is born at the beginning of ayear. Assume thefo...

Discrete Mathematics With Applications

Examine and discuss the following system: Dx2Dy=t2(D+1)x2(D+1)y=1.

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

28. a. Use Jeffersons Method to apportion the bureau seats in Exercise 16. b. Use Adamss Method to apportion th...

Mathematics: A Practical Odyssey

Hollings Functional Response Curve The total number P of prey taken by a predator depends on the availability o...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

f(x) , a continuous probability function, is equal to 112 , and the function is restricted to 0x12 . What Is P ...

Introductory Statistics