Pathways to Math Literacy
Pathways to Math Literacy
2nd Edition
ISBN: 9781260189346
Author: sobecki, David
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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Chapter 2.3, Problem 10G

In Questions 9-13, perform each calculation. Then describe whether the result is an area or a volume, and make an educated guess as to what type of figure you think the result measures. (If necessary, round results to one decimal place.)

( 2  ft ) ( 5  ft ) ( 10  ft )

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4. (i) Let a be a positive constant and f(x) = ax² e −4x x = R. Find a such that f(x) is a probability density function. [6 Marks] (ii) Let X be a random variable with probability density function in (i) (a) Find (A), the characteristic function of the random variable X. (b) Using (A), calculate E(X) and Var(X). [15 Marks] [14 Marks]
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Chapter 2 Solutions

Pathways to Math Literacy

Ch. 2.1 - Fill in each blank. a. 120isof500. b. 11isof20. c....Ch. 2.1 - Perform each calculation. Convert fractions to...Ch. 2.1 - Put this list in order from least to greatest....Ch. 2.1 - There are three different measures that well study...Ch. 2.1 - There are three different measures that well study...Ch. 2.1 - There are three different measures that well study...Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - The spreadsheet summarizes the results for one...
Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - Compute the other two measures of average, then...Ch. 2.1 - Find the other two measures of average, and...Ch. 2.1 - How many total points can be earned in the course?Ch. 2.1 - What percentage of the total score is accounted...Ch. 2.1 - If you dont show up for the first exam and take a...Ch. 2.1 - What would your final percentage be if you score...Ch. 2.1 - Try this problem to see if you understand the...Ch. 2.1 - Suppose that the instructor who wrote the test in...Ch. 2.1 - Suppose that the instructor who wrote the test in...Ch. 2.1 - Type a short answer to each question. Describe the...Ch. 2.1 - Name...Ch. 2.1 - Name...Ch. 2.1 - Name...Ch. 2.1 - Name...Ch. 2.2 - Perform each operation a. 35 b. (2)6 c....Ch. 2.2 - Perform each operation a. 12+202 b. (4)(6)7 c....Ch. 2.2 - Perform each operation a. 20+2(94)2 b. 33242 c....Ch. 2.2 - Perform each operation a. ((801)3)2 b....Ch. 2.2 - Provide a couple more examples of where an input...Ch. 2.2 - What is a variable?Ch. 2.2 - Prob. 2CCh. 2.2 - Consider the following relationships, where one...Ch. 2.2 - If we wanted to know the cost of a 7-mile cab...Ch. 2.2 - Evaluate the cost formula for m=4, then attach...Ch. 2.2 - When using the formula A=P+Prt in a given...Ch. 2.2 - Now forget about formulas for a second, and...Ch. 2.2 - Now substitute the values provided in Question 5...Ch. 2.2 - Complete the table of values for your shiny new...Ch. 2.2 - Whats the value of the account after 2 years?Ch. 2.2 - How long does it take for the account to reach a...Ch. 2.2 - Evaluate this formula for P=10,000,t=40,andr=0.06....Ch. 2.2 - Write a formula that describes the value of an...Ch. 2.2 - Use a calculator or spreadsheet to complete this...Ch. 2.2 - Whats the value of this account after 20 years?Ch. 2.2 - To the nearest year, how long does it take the...Ch. 2.2 - Try this problem to see if you understand the...Ch. 2.2 - Try this problem to see if you understand the...Ch. 2.2 - Try this problem to see if you understand the...Ch. 2.2 - Name...Ch. 2.2 - Type a short answer to each question. What is a...Ch. 2.2 - Type a short answer to each question. When two...Ch. 2.2 - Type a short answer to each question. Describe the...Ch. 2.2 - Type a short answer to each question. How do the...Ch. 2.2 - If we were to find a formula that relates the...Ch. 2.2 - The formula D=R+0.05R2 describes the total...Ch. 2.2 - If youre driving at 25 miles per hour through a...Ch. 2.2 - How slow would you have to go in order to decrease...Ch. 2.2 - At the scene of an accident, a traffic...Ch. 2.2 - According to the U.S. Department of...Ch. 2.2 - What are some factors that would affect stopping...Ch. 2.3 - Add the quantities if possible, or describe why...Ch. 2.3 - If possible, rewrite the quantities so they can be...Ch. 2.3 - Perform each multiplication. a. 4y6y b. (4km)(6km)...Ch. 2.3 - To find the amount of simple interest earned,...Ch. 2.3 - The temperature in degrees Fahrenheit can be...Ch. 2.3 - Notice that each of the small boxes in the figure...Ch. 2.3 - When length is measured in inches, the correct...Ch. 2.3 - Use your answer from Question 1 to write a formula...Ch. 2.3 - This time, we have a three-dimensional figure made...Ch. 2.3 - When length is measured in centimeters, the...Ch. 2.3 - Use your answer from Question 4 to write a formula...Ch. 2.3 - My friend David Najar is an acclaimed artist. The...Ch. 2.3 - The volume of a cylindrical oil storage tank can...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - Perform each multiplication. For parts a and b,...Ch. 2.3 - Use the formula P=a+b+c to find the perimeter of...Ch. 2.3 - Prob. 11CCh. 2.3 - Prob. 12CCh. 2.3 - Try this problem to see if you understand the...Ch. 2.3 - Try this problem to see if you understand the...Ch. 2.3 - Try this problem to see if you understand the...Ch. 2.3 - Type a short answer to each question. Why are...Ch. 2.3 - Type a short answer to each question. What does it...Ch. 2.3 - The calculation below is intended to find the...Ch. 2.3 - Find the fix needed to correct the mistake in the...Ch. 2.3 - Use your corrected formula to find the volume of...Ch. 2.3 - What percentage of the volume of the can is filled...Ch. 2.3 - After performing the division in Question 4, what...Ch. 2.3 - Racquetballs have a radius of about 2.8 cm. If...Ch. 2.3 - Golf balls also come in packages of three, but...Ch. 2.4 - Write each fraction in lowest terms. a. 1218 b....Ch. 2.4 - Write each fraction with the given denominator. a....Ch. 2.4 - Perform each operation, and reduce your answer if...Ch. 2.4 - Simplify each fractional expression by dividing...Ch. 2.4 - Use the table on the previous page to find an...Ch. 2.4 - Write two different conversion factors based on...Ch. 2.4 - There are two ways we could multiply our...Ch. 2.4 - What are the units for the other calculation? Do...Ch. 2.4 - So how many liters of magic potion are in the...Ch. 2.4 - According to our handy-dandy conversion chart, 1...Ch. 2.4 - Use one of the two conversion factors to convert...Ch. 2.4 - Now heres one of the great things about...Ch. 2.4 - My house is just about 15 miles from the Gulf of...Ch. 2.4 - Convert 0.44 L of love potion into dLandkL by...Ch. 2.4 - Dr. Phails potion also comes in a 0.75-gallon...Ch. 2.4 - According to the table of equivalences,...Ch. 2.4 - Use the idea from Question 11 to convert your...Ch. 2.4 - Based on what you just did, fill in the blank to...Ch. 2.4 - Explain what is meant when we say a car is...Ch. 2.4 - The entire 450mL of Dr. Phails Love Potion (from...Ch. 2.4 - Simplify the rate you wrote in Question 2 so that...Ch. 2.4 - It might seem like it would be really complicated...Ch. 2.4 - While in production, the love potion needs to be...Ch. 2.4 - Use the appropriate formula to convert 200F to...Ch. 2.4 - Use one of the two formulas provided to convert...Ch. 2.4 - Use a calculator or spreadsheet along with an...Ch. 2.4 - According to the online dosage guide for one brand...Ch. 2.4 - A dosage of 1,700 mg of cefadroxil is to be...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Type a short answer to each question. Describe the...Ch. 2.4 - Type a short answer to each question. Whats a...Ch. 2.4 - Type a short answer to each question. Whats a...Ch. 2.4 - Type a short answer to each question. How can we...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.5 - Locate 40, 15, 15, 27, and 2 on the number line.Ch. 2.5 - The pie chart shows the distribution of grades on...Ch. 2.5 - The bar graph shows the number of students that...Ch. 2.5 - The scatter plot shows the final grades for all 31...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - Now well practice estimation using a bar graph....Ch. 2.5 - Prob. 12CCh. 2.5 - Now well practice estimation using a bar graph....Ch. 2.5 - Now well practice estimation using a bar graph....Ch. 2.5 - Another type of graph that we often have to...Ch. 2.5 - Another type of graph that we often have to...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Reflections Type a short answer to each question....Ch. 2.5 - Reflections Type a short answer to each question....Ch. 2.5 - Prob. 4RCh. 2.5 - According to a survey reported by the Nielsen...Ch. 2.5 - Write the set of described numbers using the...Ch. 2.5 - Shopping provides a really good example of the...Ch. 2.5 - Shopping provides a really good example of the...Ch. 2.5 - Shopping provides a really good example of the...Ch. 2.5 - Estimation is useful for tipping when youre dining...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.6 - Convert each fraction into percent form. a. 1240...Ch. 2.6 - Find the area of a building made up of three...Ch. 2.6 - Using only the fact that 1yd=3ft, convert 10 cubic...Ch. 2.6 - Using only the fact that 12in.=1ft, convert 5,000...Ch. 2.6 - Find the relative change if you win $5,000,000 and...Ch. 2.6 - Compare the relative change for the two scenarios...Ch. 2.6 - Your instructor tells you that youre going to get...Ch. 2.6 - For Questions 4 and 5, write a sentence that...Ch. 2.6 - For Questions 4 and 5, write a sentence that...Ch. 2.6 - For Questions 6 and 7, write a statement using the...Ch. 2.6 - For Questions 6 and 7, write a statement using the...Ch. 2.6 - Suppose that $435 million is spent for...Ch. 2.6 - Suppose that only $440 million is budgeted for...Ch. 2.6 - A news article reports that this program has been...Ch. 2.6 - Write a sentence or two describing the 5.4% cut...Ch. 2.6 - When youre buying carpet, do you want an...Ch. 2.6 - Find the area of the bedroom only in square...Ch. 2.6 - Find the area of the closet in square inches.Ch. 2.6 - Each of the doorways shown is 30 inches wide, and...Ch. 2.6 - What is the total carpeted area? Convert the total...Ch. 2.6 - Write a sentence or two describing how the...Ch. 2.6 - Find the percent error in the estimate. Round to...Ch. 2.6 - Not everyone realizes this, but when you buy...Ch. 2.6 - Use the actual error in the estimate to find the...Ch. 2.6 - One suggestion for estimating carpet is to measure...Ch. 2.6 - List some situations where relative change is a...Ch. 2.6 - Try this problem to see if you understand the...Ch. 2.6 - Try this problem to see if you understand the...Ch. 2.6 - Try this problem to see if you understand the...Ch. 2.6 - Type a short answers to each question. How would...Ch. 2.6 - Type a short answers to each question. Both Shawna...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.7 - Find the mean of the numbers listed. 23 34 45 56...Ch. 2.7 - The pie chart represents the breakdown of...Ch. 2.7 - In an average year, there is at least some...Ch. 2.7 - Write a verbal description of each interval...Ch. 2.7 - Write an inequality that describes each interval....Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Fill in the second column of the table below. Step...Ch. 2.7 - Fill in the third column of the table by squaring...Ch. 2.7 - Find the mean of the values in the third column of...Ch. 2.7 - Find the standard deviation by computing the...Ch. 2.7 - Describe the pattern made by the seed pods, and...Ch. 2.7 - Use the information just given about and to fill...Ch. 2.7 - Based on your diagram, about what percentage of...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Type a short answers to each question. Describe...Ch. 2.7 - Type a short answers to each question. What can we...Ch. 2.7 - In Lesson 2-1, you found the mean of the exam...Ch. 2.7 - According to numerous online resources, the mean...Ch. 2.7 - Write an expression of the form P(inequality) that...Ch. 2.7 - In a group of 500 women, how many would you expect...Ch. 2.7 - On one campus, about 95% of students work between...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.8 - There are 52 cards in a standard deck, equally...Ch. 2.8 - When you roll one six-sided die, whats the...Ch. 2.8 - Convert each percentage to decimal form: a. 87 b....Ch. 2.8 - Add the numbers across each of the 10 rows, and...Ch. 2.8 - On average, how much did you win per roll?Ch. 2.8 - Add the answers from Question 2 for every group in...Ch. 2.8 - Congratulations: Youve just found the expected...Ch. 2.8 - What is the probability of getting a 1 when...Ch. 2.8 - What is the probability of getting any individual...Ch. 2.8 - Complete the second column of this table by...Ch. 2.8 - Find the sum of the values in the third column....Ch. 2.8 - Obviously, playing this game for free would ROCK:...Ch. 2.8 - Lets say you were setting up this game somewhere...Ch. 2.8 - If you were charging $2 to play, the outcomes for...Ch. 2.8 - Using the scores provided, find the percentage of...Ch. 2.8 - Use information on the grading scale to fill in...Ch. 2.8 - The points out of 100 earned for each category is...Ch. 2.8 - The overall grade, out of 100, is the sum of all...Ch. 2.8 - What letter grade did Christine earn?Ch. 2.8 - Which category would you say had the most negative...Ch. 2.8 - So lets say that you have the following scores in...Ch. 2.8 - So lets say that you have the following scores in...Ch. 2.8 - So lets say that you have the following scores in...Ch. 2.8 - Whats the net gain if you land on blue? Write your...Ch. 2.8 - Compute and record the probability for each gain...Ch. 2.8 - Calculate and record the product for each X*P(X)....Ch. 2.8 - Whats the expected value? Record in the table,...Ch. 2.8 - A game of chance is called a fair game if the...Ch. 2.8 - A game favors the player if the players expected...Ch. 2.8 - If you played this game 100 times, how much would...Ch. 2.8 - Try these problems to see if you understand the...Ch. 2.8 - Try these problems to see if you understand the...Ch. 2.8 - Prob. 3DYGICh. 2.8 - Prob. 4DYGICh. 2.8 - For all but one bet in standard American roulette,...Ch. 2.8 - Betting on 0, 00, 1, 2, and 3 in roulette has an...Ch. 2.8 - What makes a grading system weighted?Ch. 2.8 - Name one thing you learned or discovered in this...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Next, well study a traditional carnival game that...Ch. 2.8 - Find the expected value of this game. The table,...Ch. 2.8 - Would you prefer to be the player in this game, or...Ch. 2.8 - What should the player expect to happen if he...Ch. 2.8 - The grading structure for my Calc 2 class last...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Compute the mean, median, and mode for the lengths...Ch. 2 - A prepaid calling card starts with a value of $40....Ch. 2 - Compute the standard deviation for the lengths of...Ch. 2 - The table shows the number of points possible on...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - According to www.boeing.com/, the Boeing 747...Ch. 2 - Use your calculator or a spreadsheet to complete...Ch. 2 - How many gallons would be remaining after 1,000...Ch. 2 - How many miles were flown if there were 56,000...Ch. 2 - Write a sentence or two using the terms input,...Ch. 2 - Which is most likely the correct way to compute...Ch. 2 - The formula A=r2 can be used to find the area of a...Ch. 2 - The formula V=r2h can be used to find the volume...Ch. 2 - In Questions 15 and 16, simplify each expression....Ch. 2 - In Questions 15 and 16, simplify each expression....Ch. 2 - Determine the number of cups that are in a 2-liter...Ch. 2 - Determine the speed in inches per second of a...Ch. 2 - A 5-k race is 5 kilometers long. How long is that...Ch. 2 - Convert 68 Fahrenheit to Celsius.Ch. 2 - Write a brief summary of Polyas 4-step...Ch. 2 - If in a typical month your cell-phone bill is...Ch. 2 - A seven-passenger van can transport at most seven...Ch. 2 - On March 1, 2017, the Dow Jones Industrial Average...Ch. 2 - If a jet was fueled with 68,000 lbs of fuel and...Ch. 2 - Runners often keep a training log to keep track of...Ch. 2 - Runners often keep a training log to keep track of...Ch. 2 - Runners often keep a training log to keep track of...Ch. 2 - It has been reported that credit card debt for...Ch. 2 - Write an expression that describes the probability...Ch. 2 - Use the empirical rule to find P(2,162x5,462) and...Ch. 2 - Suppose you decide to set up a simple dice-rolling...Ch. 2 - Suppose you decide to set up a simple dice-rolling...Ch. 2 - The grading structure for a Stats course is...
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