Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…

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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 A Bridge To Success Algebra 2: 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 A Bridge To Success Algebra 2: 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 A Bridge To Success Algebra 2: 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

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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