Assignment
Problem 1. Optimization Models
A company produces and sells two types of coolants (C1 and C2) by mixing three grades of solvents (A, B, and C) in different proportions.
Minimum percentages of grade A solvent and maximum percentages of grade C solvent allowed for each type of coolant are specified. The company has to produce at least a specified minimum quantity of each type of coolant. The table below presents these requirements, along with the selling price of each type of coolant.
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Minimum percent of grade A allowed
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Maximum percent of grade C allowed
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Minimum Quantity Required (gallons)
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Selling price per gallon
|
|
C1
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40%
|
30%
|
100,000
|
$4
|
|
C2
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20%
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60%
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100,000
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$3
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Availability of the three grades of solvents and their costs are as follows:
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Grade
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A
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B
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C
|
|
Maximum quantity available per day (gallons)
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60,000
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60,000
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90,000
|
|
Cost per gallon
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$3
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$2
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$1
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The company wants to maximize profits subject to the specified constraints.
Formulate the problem as a linear program, find the optimal solution, and answer the following questions:
a. What is the maximum profit attainable?
b. How many gallons of each solvent are used to produce each type of coolant under the optimal solution?
c. At most how much should the company be willing to pay for one additional gallon of grade A solvent (beyond its current availability of 60,000 gallons)?
Problem 2. Linear Regression
The data file "trainFinal.csv" contains observations on 12 variables: class, x1, x2, ..., x10, y
Run a regression to predict the output variable y based on the 10 input variables x1, x2, ..., x10.
(a) Interpret the regression results to complete the table below. Specify the coefficient estimates (rounded to 2 decimal places) under the column "Coefficient Estimate". Specify whether the coefficient estimates are significant (Yes or No) at the 0.1% level under the column "Significant"
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Coefficient Estimate
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Significant?
|
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Intercept
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|
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x1
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|
|
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x2
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|
|
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x3
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|
|
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x4
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|
|
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x5
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|
|
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x6
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|
|
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x7
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|
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x8
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|
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x9
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|
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x10
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|
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(b) Predict the expected value of y for the 10 examples in the data file "newFinal.csv" and report the predicted values (rounded to 1 decimal place) in the table below.
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x1
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x2
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x3
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x4
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x5
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x6
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x7
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x8
|
x9
|
x10
|
y
|
|
0.36
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0.30
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0.68
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0.38
|
0.02
|
0.61
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0.53
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0.52
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0.35
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0.78
|
|
|
0.23
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0.79
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0.59
|
0.53
|
0.77
|
0.07
|
0.90
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0.37
|
0.18
|
0.34
|
|
|
0.80
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0.96
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0.35
|
0.69
|
0.19
|
0.59
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0.85
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0.55
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0.75
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0.68
|
|
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0.56
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0.48
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0.80
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0.85
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0.50
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0.23
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0.22
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0.65
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0.84
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0.31
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|
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0.75
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0.39
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0.47
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0.02
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0.19
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0.23
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0.99
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0.03
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0.65
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0.87
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0.55
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0.44
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0.62
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0.09
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0.53
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0.45
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0.91
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0.52
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0.33
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0.62
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0.20
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0.70
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0.24
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0.81
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0.22
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0.01
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0.82
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0.67
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0.40
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0.46
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0.68
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1.00
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0.00
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0.86
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0.06
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0.63
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0.47
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0.45
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0.03
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0.30
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|
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0.08
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0.49
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0.97
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0.08
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0.68
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0.82
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0.89
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0.82
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0.47
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0.96
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|
|
0.27
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0.33
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0.69
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0.77
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0.26
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0.52
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0.23
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0.23
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0.50
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0.34
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Problem 3. Classification Tree Inductive Learning
Train a decision tree classifier using the observations from the data file "trainFinal.csv" to classify the output binary variable "class" based on the 10 input variables: x1, x2, ..., x10.
(a) Specify the rules obtained in the form:
IF Then class = ?
(b) Use the rules obtained to predict the output class for the observations in data file "testFinal.csv" and present your confusion matrix.
(c) Use the rules obtained to predict the output class for the 10 observations in data file "newFinal.csv" and present your confusion matrix.
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x1
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x2
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x3
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x4
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x5
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x6
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x7
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x8
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x9
|
x10
|
class
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0.36
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0.30
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0.68
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0.38
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0.02
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0.61
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0.53
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0.52
|
0.35
|
0.78
|
|
|
0.23
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0.79
|
0.59
|
0.53
|
0.77
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0.07
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0.90
|
0.37
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0.18
|
0.34
|
|
|
0.80
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0.96
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0.35
|
0.69
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0.19
|
0.59
|
0.85
|
0.55
|
0.75
|
0.68
|
|
|
0.56
|
0.48
|
0.80
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0.85
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0.50
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0.23
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0.22
|
0.65
|
0.84
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0.31
|
|
|
0.75
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0.39
|
0.47
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0.02
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0.19
|
0.23
|
0.99
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0.03
|
0.65
|
0.87
|
|
|
0.55
|
0.44
|
0.62
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0.09
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0.53
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0.45
|
0.91
|
0.52
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0.33
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0.62
|
|
|
0.20
|
0.70
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0.24
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0.81
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0.22
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0.01
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0.82
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0.67
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0.40
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0.46
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|
|
0.68
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1.00
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0.00
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0.86
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0.06
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0.63
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0.47
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0.45
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0.03
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0.30
|
|
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0.08
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0.49
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0.97
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0.08
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0.68
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0.82
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0.89
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0.82
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0.47
|
0.96
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|
|
0.27
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0.33
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0.69
|
0.77
|
0.26
|
0.52
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0.23
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0.23
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0.50
|
0.34
|
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Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also include a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also Include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.
Attachment:- Data-FIles.rar