Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
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Question
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Chapter 3.6, Problem 33E
To determine

To graph: The data of the table.

Expert Solution
Check Mark

Answer to Problem 33E

  P=7.5686t+352.7

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

Using graphing utility to find the graph of linear regression model and coefficient of determination.

  Precalculus with Limits: A Graphing Approach, Chapter 3.6, Problem 33E , additional homework tip 1

The above graph show linear model of given data.

The model is P=7.5686t+352.7

The coefficient of determination is 0.9786

To determine

To graph: The data of the table and find the power model.

Expert Solution
Check Mark

Answer to Problem 33E

  P=248.55t0.2351

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

Using graphing utility to plot the points and draw the graph.

  Precalculus with Limits: A Graphing Approach, Chapter 3.6, Problem 33E , additional homework tip 2

The above graph show power model of given data.

The model is P=248.55t0.2351

The coefficient of determination is 0.9438

To determine

To graph: The data of the table and find the exponential model.

Expert Solution
Check Mark

Answer to Problem 33E

  P=366.63(1.016)t

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

Using graphing utility to plot the points and draw the graph.

  Precalculus with Limits: A Graphing Approach, Chapter 3.6, Problem 33E , additional homework tip 3

The above graph show exponential model of given data.

The model is P=366.63(1.016)t

The coefficient of determination is 0.9866

To determine

To graph: The data of the table and find the logarithmic model.

Expert Solution
Check Mark

Answer to Problem 33E

  P=168.58+111.66lnx

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

Using graphing utility to plot the points and draw the graph.

  Precalculus with Limits: A Graphing Approach, Chapter 3.6, Problem 33E , additional homework tip 4

The above graph show logarithmic model of given data.

The model is P=168.58+111.66lnx

The coefficient of determination is 0.9289

To determine

To choose: The best fit model for given data.

Expert Solution
Check Mark

Answer to Problem 33E

Exponential model

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

There are total four different model for same data with coefficient of determination.

Linear model, P=7.5686t+352.7

Coefficient of determination, r2=0.9786

Power model, P=248.55t0.2351

Coefficient of determination, r2=0.9468

Exponential model, P=366.63(1.016)t

Coefficient of determination, r2=0.9866

Logarithmic model, P=168.58+111.66lnx

Coefficient of determination, r2=0.9289

In all above model, the best coefficient of determination nearest to 1 for exponential model.

So, choose exponential model.

To determine

To predict: The populations of Luxembourg for the years 2014 through 2018.

Expert Solution
Check Mark

Answer to Problem 33E

Exponential model

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

There are total four different model for same data with coefficient of determination.

Linear model, P=7.5686t+352.7

Coefficient of determination, r2=0.9786

  Year20142015201620172018t2425262728PLinear534.4541.9549.5557.1564.6

Power model, P=248.55t0.2351

Coefficient of determination, r2=0.9468

  Year20142015201620172018t2425262728Ppower524.7529.7534.7539.4544.1

Exponential model, P=366.63(1.016)t

Coefficient of determination, r2=0.9866

  Year20142015201620172018t2425262728Pexp539.8545.2553.9562.8571.8

Logarithmic model, P=168.58+111.66lnx

Coefficient of determination, r2=0.9289

  Year20142015201620172018t2425262728Plog523.4527.9532.4536.6540.6

In all above model, the best choose exponential model.

To determine

To choose: The best model for population.

Expert Solution
Check Mark

Answer to Problem 33E

Exponential model

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

There are total four different model for same data with coefficient of determination.

Linear model, P=7.5686t+352.7

Coefficient of determination, r2=0.9786

  Year20142015201620172018t2425262728PLinear534.4541.9549.5557.1564.6

Power model, P=248.55t0.2351

Coefficient of determination, r2=0.9468

  Year20142015201620172018t2425262728Ppower524.7529.7534.7539.4544.1

Exponential model, P=366.63(1.016)t

Coefficient of determination, r2=0.9866

  Year20142015201620172018t2425262728Pexp539.8545.2553.9562.8571.8

Logarithmic model, P=168.58+111.66lnx

Coefficient of determination, r2=0.9289

  Year20142015201620172018t2425262728Plog523.4527.9532.4536.6540.6

In all above model, the best choose exponential model.

To determine

To verify: The choice of model for parts (e) and (g).

Expert Solution
Check Mark

Answer to Problem 33E

Exponential model

Explanation of Solution

Given: The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with t=9 corresponding to 1999.

  Year199920002001200220032004200520062007200820092010201120122013t91011121314151617181920212223P427.4433.6439.0444.1448.3455.0461.2469.1476.2483.8493.5502.1511.8524.9537.0

Yes, In both parts models same. That is exponential model.

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Chapter 3.6, Problem 32E
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Chapter 3.6, Problem 34E

Chapter 3 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Prob. 74ECh. 3.1 - Prob. 75ECh. 3.1 - Prob. 76ECh. 3.1 - Prob. 77ECh. 3.1 - Prob. 78ECh. 3.1 - Prob. 79ECh. 3.1 - Prob. 80ECh. 3.1 - Prob. 81ECh. 3.1 - Prob. 82ECh. 3.1 - Prob. 83ECh. 3.1 - Prob. 84ECh. 3.1 - Prob. 85ECh. 3.1 - Prob. 86ECh. 3.1 - Prob. 87ECh. 3.1 - Prob. 88ECh. 3.1 - Prob. 89ECh. 3.1 - Prob. 90ECh. 3.1 - Prob. 91ECh. 3.1 - Prob. 92ECh. 3.1 - Prob. 93ECh. 3.1 - Prob. 94ECh. 3.1 - Prob. 95ECh. 3.1 - Prob. 96ECh. 3.1 - Prob. 97ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - 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Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Prob. 81ECh. 3.4 - Prob. 82ECh. 3.4 - Prob. 83ECh. 3.4 - Prob. 84ECh. 3.4 - Prob. 85ECh. 3.4 - Prob. 86ECh. 3.4 - Prob. 87ECh. 3.4 - Prob. 88ECh. 3.4 - Prob. 89ECh. 3.4 - Prob. 90ECh. 3.4 - Prob. 91ECh. 3.4 - Prob. 92ECh. 3.4 - Prob. 93ECh. 3.4 - Prob. 94ECh. 3.4 - Prob. 95ECh. 3.4 - Prob. 96ECh. 3.4 - Prob. 97ECh. 3.4 - Prob. 98ECh. 3.4 - Prob. 99ECh. 3.4 - Prob. 100ECh. 3.4 - Prob. 101ECh. 3.4 - Prob. 102ECh. 3.4 - Prob. 103ECh. 3.4 - Prob. 104ECh. 3.4 - Prob. 105ECh. 3.4 - Prob. 106ECh. 3.4 - Prob. 107ECh. 3.4 - Prob. 108ECh. 3.4 - Prob. 109ECh. 3.4 - Prob. 110ECh. 3.4 - Prob. 111ECh. 3.4 - Prob. 112ECh. 3.4 - Prob. 113ECh. 3.4 - Prob. 114ECh. 3.4 - Prob. 115ECh. 3.4 - Prob. 116ECh. 3.4 - Prob. 117ECh. 3.4 - Prob. 118ECh. 3.4 - Prob. 119ECh. 3.4 - Prob. 120ECh. 3.4 - Prob. 121ECh. 3.4 - Prob. 122ECh. 3.4 - Prob. 123ECh. 3.4 - Prob. 124ECh. 3.4 - Prob. 125ECh. 3.4 - Prob. 126ECh. 3.4 - Prob. 127ECh. 3.4 - Prob. 128ECh. 3.4 - Prob. 129ECh. 3.4 - Prob. 130ECh. 3.4 - Prob. 131ECh. 3.4 - Prob. 132ECh. 3.4 - Prob. 133ECh. 3.4 - Prob. 134ECh. 3.4 - Prob. 135ECh. 3.4 - Prob. 136ECh. 3.4 - Prob. 137ECh. 3.4 - Prob. 138ECh. 3.4 - Prob. 139ECh. 3.4 - Prob. 140ECh. 3.4 - Prob. 141ECh. 3.4 - Prob. 142ECh. 3.4 - Prob. 143ECh. 3.4 - Prob. 144ECh. 3.4 - Prob. 145ECh. 3.4 - Prob. 146ECh. 3.4 - Prob. 147ECh. 3.4 - Prob. 148ECh. 3.4 - Prob. 149ECh. 3.4 - Prob. 150ECh. 3.4 - Prob. 151ECh. 3.4 - Prob. 152ECh. 3.4 - Prob. 153ECh. 3.4 - Prob. 154ECh. 3.4 - Prob. 155ECh. 3.4 - Prob. 156ECh. 3.4 - Prob. 157ECh. 3.4 - Prob. 158ECh. 3.4 - Prob. 159ECh. 3.4 - Prob. 160ECh. 3.4 - Prob. 161ECh. 3.4 - Prob. 162ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.5 - Prob. 61ECh. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.5 - Prob. 71ECh. 3.5 - Prob. 72ECh. 3.5 - Prob. 73ECh. 3.5 - Prob. 74ECh. 3.5 - Prob. 75ECh. 3.5 - Prob. 76ECh. 3.5 - Prob. 77ECh. 3.5 - Prob. 78ECh. 3.5 - Prob. 79ECh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Prob. 75RECh. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Prob. 98RECh. 3 - Prob. 99RECh. 3 - Prob. 100RECh. 3 - Prob. 101RECh. 3 - Prob. 102RECh. 3 - Prob. 103RECh. 3 - Prob. 104RECh. 3 - Prob. 105RECh. 3 - Prob. 106RECh. 3 - Prob. 107RECh. 3 - Prob. 108RECh. 3 - Prob. 109RECh. 3 - Prob. 110RECh. 3 - Prob. 111RECh. 3 - Prob. 112RECh. 3 - Prob. 113RECh. 3 - Prob. 114RECh. 3 - Prob. 115RECh. 3 - Prob. 116RECh. 3 - Prob. 117RECh. 3 - Prob. 118RECh. 3 - Prob. 119RECh. 3 - Prob. 120RECh. 3 - Prob. 121RECh. 3 - Prob. 122RECh. 3 - Prob. 123RECh. 3 - Prob. 124RECh. 3 - Prob. 125RECh. 3 - Prob. 126RECh. 3 - Prob. 127RECh. 3 - Prob. 128RECh. 3 - Prob. 129RECh. 3 - Prob. 130RECh. 3 - Prob. 131RECh. 3 - Prob. 132RECh. 3 - Prob. 133RECh. 3 - Prob. 134RECh. 3 - Prob. 135RECh. 3 - Prob. 136RECh. 3 - Prob. 137RECh. 3 - Prob. 138RECh. 3 - Prob. 139RECh. 3 - Prob. 140RECh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CTCh. 3 - Prob. 26CTCh. 3 - Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 1CLTCh. 3 - Prob. 2CLTCh. 3 - Prob. 3CLTCh. 3 - Prob. 4CLTCh. 3 - Prob. 5CLTCh. 3 - Prob. 6CLTCh. 3 - Prob. 7CLTCh. 3 - Prob. 8CLTCh. 3 - Prob. 9CLTCh. 3 - Prob. 10CLTCh. 3 - Prob. 11CLTCh. 3 - Prob. 12CLTCh. 3 - Prob. 13CLTCh. 3 - Prob. 14CLTCh. 3 - Prob. 15CLTCh. 3 - Prob. 16CLTCh. 3 - Prob. 17CLTCh. 3 - Prob. 18CLTCh. 3 - Prob. 19CLTCh. 3 - Prob. 20CLTCh. 3 - Prob. 21CLTCh. 3 - Prob. 22CLTCh. 3 - Prob. 23CLTCh. 3 - Prob. 24CLTCh. 3 - Prob. 25CLTCh. 3 - Prob. 26CLTCh. 3 - Prob. 27CLTCh. 3 - Prob. 28CLTCh. 3 - Prob. 29CLTCh. 3 - Prob. 30CLTCh. 3 - Prob. 31CLTCh. 3 - Prob. 32CLTCh. 3 - Prob. 33CLTCh. 3 - Prob. 34CLTCh. 3 - Prob. 35CLTCh. 3 - Prob. 36CLTCh. 3 - Prob. 37CLTCh. 3 - Prob. 38CLTCh. 3 - Prob. 39CLTCh. 3 - Prob. 40CLTCh. 3 - Prob. 41CLTCh. 3 - Prob. 42CLTCh. 3 - Prob. 43CLTCh. 3 - Prob. 44CLTCh. 3 - Prob. 45CLTCh. 3 - Prob. 46CLTCh. 3 - Prob. 47CLT
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