BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Question

Chapter 3.6, Problem 47E

To determine

To write: An inequality that can be used to find the x -values for which A(x) is less than V(x) .

Expert Solution

Answer to Problem 47E

The required inequality is x2−890x−70000<0 .

Explanation of Solution

Given information:

The model of the driver’s reaction time A(x) to audio stimuli: A(x)=0.0051x2−0.319x+15,16≤x≤70

The model of reaction time V(x) to visual stimuli: V(x)=0.005x2−0.23x+22,16≤x≤70

Age of the driver = x

Calculation:

The given equations are:

A(x)=0.0051x2−0.319x+15,16≤x≤70 and V(x)=0.005x2−0.23x+22,16≤x≤70

Take A(x)<V(x) .

0.0051x2−0.319x+15<0.005x2−0.23x+220.0051x2−0.005x2−0.319x+0.23x+15−22<00.0001x2−0.089x−7<010000(0.0001x2−0.089x−7)<(0)10000

Simplify the above expression further.

10000(0.0001x2−0.089x−7)<(0)10000x2−890x−70000<0

Hence, the required inequality is x2−890x−70000<0 .

To determine

To calculate: The solution of the inequality using a graphing calculator. Also, describe the use of the domain 16≤x≤70 to determine a reasonable solution.

Expert Solution

Answer to Problem 47E

The required solution of the inequality is (16,70) .

Explanation of Solution

Given information:

The model of the driver’s reaction time A(x) to audio stimuli: A(x)=0.0051x2−0.319x+15,16≤x≤70

The model of reaction time V(x) to visual stimuli: V(x)=0.005x2−0.23x+22,16≤x≤70

Age of the driver = x

Calculation:

The given equations are:

A(x)=0.0051x2−0.319x+15,16≤x≤70 and V(x)=0.005x2−0.23x+22,16≤x≤70

The graph of inequality is shown below:

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 3.6, Problem 47E , additional homework tip 1

From the above graph, the interval where the red graph is below the blue graph is the solution of the inequality.

This means the interval (16,70) is the solution of the inequality.

The given domain helps to obtain the proper solution of the inequality.

Hence, the required solution of the inequality is (16,70) .

To determine

To determine: Whether the driver would react more quickly to a traffic light changing from green to yellow or a the siren of an approaching ambulance.

Expert Solution

Answer to Problem 47E

The driver would react more quickly to a traffic light than to a siren.

Explanation of Solution

Given information:

The model of the driver’s reaction time A(x) to audio stimuli: A(x)=0.0051x2−0.319x+15,16≤x≤70

The model of reaction time V(x) to visual stimuli: V(x)=0.005x2−0.23x+22,16≤x≤70

Age of the driver = x

Calculation:

The given equations are:

A(x)=0.0051x2−0.319x+15,16≤x≤70 and V(x)=0.005x2−0.23x+22,16≤x≤70

The graph of inequality is shown below:

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 3.6, Problem 47E , additional homework tip 2

From the above graph, the interval where the red graph is below the blue graph is the solution of the inequality.

This means the interval (16,70) is the solution of the inequality.

The given domain helps to obtain the proper solution of the inequality.

It is seen in the graph that the blue graph (visual stimuli) is above the red graph (audio stimuli). This means that the driver would react more quickly to a traffic light.

Hence, the driver would react more quickly to a traffic light than to a siren.

Chapter 3.6, Problem 46E

Chapter 3.6, Problem 48E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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An inequality that can be used to find the x -values for which A ( x ) is less than V ( x ) .

Concept explainers

Videos

To write: An inequality that can be used to find the x -values for which A(x) is less than V(x) .

Answer to Problem 47E

Explanation of Solution

To calculate: The solution of the inequality using a graphing calculator. Also, describe the use of the domain 16≤x≤70 to determine a reasonable solution.

Answer to Problem 47E

Explanation of Solution

To determine: Whether the driver would react more quickly to a traffic light changing from green to yellow or a the siren of an approaching ambulance.

Answer to Problem 47E

Explanation of Solution

Chapter 3 Solutions