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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 5.2, Problem 76E

Textbook Problem

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**Population Movement** Assume that the percentages given in Exercise 75 also describe the population movements from 2009 to 2010. Use two matrix multiplications to estimate, from the data in Exercise 75, the population in each region in 2010.

To determine

**To calculate:** The population in each region in

To | Northeast | Midwest | South | West |

From Northeast | 0.9923 | 0.0016 | 0.0042 | 0.0019 |

Midwest | 0.0018 | 0.9896 | 0.0047 | 0.0039 |

South | 0.0056 | 0.0059 | 0.9827 | 0.0058 |

West | 0.0024 | 0.0033 | 0.0044 | 0.9899 |

**Given Information:**

The population is broken by region as

To | Northeast | Midwest | South | West |

From Northeast | 0.9923 | 0.0016 | 0.0042 | 0.0019 |

Midwest | 0.0018 | 0.9896 | 0.0047 | 0.0039 |

South | 0.0056 | 0.0059 | 0.9827 | 0.0058 |

West | 0.0024 | 0.0033 | 0.0044 | 0.9899 |

**Formula used:**

In the matrix equation *A* has entries equal to the coefficients of the left hand side of the system of equations and the matrix *X* is the column matrix of the unknowns in the system and the matrix *B* is the column matrix and has entries equal to the coefficients of the right hand side of the system of equations.

**Calculation:**

Consider, the population is broken by region as

To | Northeast | Midwest | South | West |

From Northeast | 0.9923 | 0.0016 | 0.0042 | 0.0019 |

Midwest | 0.0018 | 0.9896 | 0.0047 | 0.0039 |

South | 0.0056 | 0.0059 | 0.9827 | 0.0058 |

West | 0.0024 | 0.0033 | 0.0044 | 0.9899 |

Since, in

Write the *A*.

Thus,

Write the table as a matrix *P*.

Thus,

To calculate the population in

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*

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Find the functions (a) f g, (b) g f, (c) f f, and (d) g g and their domains. 33. f(x) = 3x + 5, g(x) = x2 +...

Single Variable Calculus

Cricket Chirps: Temperature Anyone who has been outdoors on a summer evening has probably heard crickets. Did y...

Understanding Basic Statistics

a. If a constant c is added to each xi in a sample, yielding yi = xi + c, how do the sample mean and median of ...

Probability and Statistics for Engineering and the Sciences

Solve the equations in Exercises 126. 2x3x2x3x+1=0

Finite Mathematics

11. An agency charges $100 per person for a trip to a concert if 70 people travel in a group. But for each pers...

Mathematical Applications for the Management, Life, and Social Sciences

Calculate the missing information based on the format of the income statement.
Net Sales Cost of Goods Sold Gro...

Contemporary Mathematics for Business & Consumers

Simplify 6x23x7x25x2 by combining similar terms.

Intermediate Algebra

In Exercises 23 to 40, let U {p, q, r, s, t}, D = (p. r, s, t}, E = {q, s), F = {p, t}, and G = {s}. Determine ...

Mathematical Excursions (MindTap Course List)

A circle is inscribed in a triangle having sides of lengths 5 in., 12 in., and 13 in. If the length of the radi...

Elementary Geometry For College Students, 7e

Change each decimal to a percent: 0.08

Elementary Technical Mathematics

Use the guidelines of this section to sketch the curve. y=x3x2

Single Variable Calculus: Early Transcendentals

Greens Theorem: Region with a Hole Let R be the region inside thee llipse x=4cos, y=3sin and outside the circle...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding a Limit In Exercises 43-46, find the limit. Use a graphing utility to verify your result. (Hint: Treat ...

Calculus of a Single Variable

18. Let be the smallest subring of the field of rational numbers that contains . Find a description for a ty...

Elements Of Modern Algebra

Use a calculator to find each of the following. Round all answers to four places past the decimal point. cos64

Trigonometry (MindTap Course List)

The moment about the xz-plane of solid E whose density is ρ(x, y, z) = x is:

Study Guide for Stewart's Multivariable Calculus, 8th

If f(x) = sin 2x, an upper bound for |f(n + 1)(x)| is
2
2n
2n + 1
22n

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

In Exercises 16, find maximum and/or minimum valuess of the objective function on the feasible set S. Z=2x+3y

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 29 to 34, draw the line described. Through -2,1 and perpendicular to the line that has intercepts ...

Elementary Geometry for College Students

Using the Root Test In Exercises 39-52, use the Root Test to determine the convergence or divergence of the ser...

Calculus (MindTap Course List)

Changing the Order of Integration In Exercises 45-50. sketch the region R of integration and change the order o...

Multivariable Calculus

Finding Cross ProductsIn Exercises 31 and 32, find (a) uv, (b) vu, and (c) vv. u=0,2,1v=1,3,4

Calculus

In Exercises 1-20, construct a truth table for the symbolic expressions. (rp)(qp)

Mathematics: A Practical Odyssey

Explain the basic distinction between probability sampling methods and nonprobability sampling methods and reco...

Research Methods for the Behavioral Sciences (MindTap Course List)

There has been a trend toward less driving in the last few years, especially by young people. From 2001 to 2009...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

How many binding posts can be cut from a brass rod 4212 inches long if each post is 178 inches long? Allow 332 ...

Mathematics For Machine Technology

Perform the operations and simplify. y5+2y3+7-y5-2y3-7

College Algebra (MindTap Course List)

What is a ceiling effect, and how can it be a problem?

Research Methods for the Behavioral Sciences (MindTap Course List)

After the 2010 earthquake in Haiti, many charitable organizations conducted fundraising campaigns to raise mone...

Introduction To Statistics And Data Analysis

Refer to Table 1.6. a. What is the average miles per gallon for city driving? b. On average, how much higher is...

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