Wilmu MAT205 Complete Course Latest 2022 June (Full)

MAT205 Intro Survey of Mathematics

Week 1 Discussion

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. The host then says to you, “Do you want to pick door No. 2 instead of door No. 1?” Is it to your advantage to switch your choice?  Use what you have learned about probability so far to defend your choice.

 

MAT205 Intro Survey of Mathematics

Week 2 Discussion

Please watch this video:

Experimental Probability (Links to an external site.)

What is the theoretical probability of rolling a fair die and obtaining a 1?  If you roll a fair die 6 times, how many times would you expect, theoretically, of obtaining a 1?  What if you performed an experiment and rolled the die 6 times. Will you definitely obtain your theoretical answer? Why is experimental probability often different than theoretical probability?  What do you think you should expect if you increase the number of trials, that is, rolls of the die?  Why?

 

MAT205 Intro Survey of Mathematics

Week 3 Discussion

You and a friend are playing a game with a pair of six-sided dice.  To determine a winner, you each roll the dice and total them.  Your friend wins if the total is 5, 6, 7, or 8.  You win if the total is 2, 3, 4, 9, 10, 11, or 12.  Is this game fair?  Why or why not?  Use what you have learned about probability so far to defend your choice.  

 

MAT205 Intro Survey of Mathematics

Week 4 Discussion

If you were given a large data set, such as the sales over the last year of Amazon’s top 100 customers, what might you be able to do with these data? What might be the benefits of describing the data?  How would you display the data?

 

MAT205 Intro Survey of Mathematics

Week 5 Discussion

Describe a data set where the mean would be the most appropriate measure of center.  Describe a data set where the mean is not the most appropriate measure of center.  What measure of center should be used and why?

 

MAT205 Intro Survey of Mathematics

Week 6 Discussion

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?  Justify your answer.

 

MAT205 Intro Survey of Mathematics

Week 7 Discussion

A kidney stone treatment study found that treatment A had 81 out of 87 successful trials in small stone treatments and 234 out of 270 successful trials in large stone treatments. Treatment B had 234 out of 270 successful trials in small stone treatments and 55 out of 80 trials successful in large stone treatments. Overall which treatment had a better success rate and why?

 

MAT205 Intro Survey of Mathematics

Week 9 Discussion

The parabola is a shape found in nature as well as used in architecture.   Find examples of parabolas, man-made or naturally forming, in the world around you.  If possible, provide a picture along with a description of the image.

 

MAT205 Intro Survey of Mathematics

Week 10 Discussion

Use the Internet to research parabolic devices in use today.  List those that you are familiar with or any that you use.  How have these devices made your life easier?

 

MAT205 Intro Survey of Mathematics

Week 11 Discussion

Find a real-life example of exponential growth or decay.  Describe the growth or decay and make predictions of where the growth or decay could be 50 years from now.

 

MAT205 Intro Survey of Mathematics

Week 12 Discussion

1. Create a compound interest word problem, using this formula A=P(1+r/n)^(nt) or this formula A=Pe^(rt). Set up the word problem, clearly defining the known and unknown values using complete sentences. Do not solve your problem! Do this by Wednesday at 11:59 pm EST.

 

2. Solve another student's problem. Select a problem that no one else has solved yet.  Solve it by explaining all of your work by Friday at 11:59 pm EST.

3. Check your own problem and provide feedback or show the correct method and solution by Sunday at 11:59 pm EST.

 

MAT205 Intro Survey of Mathematics

Week 13 Discussion

Explain the relationship between the graphs of exponential and logarithmic functions.  Refer to the online resources to help form your response.

 

MAT205 Intro Survey of Mathematics

Week 14 Discussion

Discuss the beauty of mathematics.  What part of mathematics touches your heart, soul, or mind?  Where have you seen mathematics naturally in the world around you?

 

 

 

MAT205 Intro Survey of Mathematics

Week 3 Project 

Probability Island

You will collect the data for the population of an island community. Then you will use and evaluate probability models. You will be using this data for the next parts of your project.

Your ship is carrying 150 passengers  75 adult females and 75 adult males  all in good health.  An intense storm occurs and your ship hits rocks and wrecks off the coast of a deserted island in the Pacific Ocean.  This island has the necessary natural resources for human survival. 

The ages of your passengers are recorded in the table below.

 

MAT205 Intro Survey of Mathematics

Week 7 Project

Statistics Island

Directions

For all calculations, show your workand/or explain how you used the calculator to compute.

1.Your population is thriving on your island.  The data you have collected now needs to be displayed and analyzed.  Use the charts you created in the Probability Island project to complete the table below.Use the total number of births per year to fill in chart 3. Round to two decimal places if necessary

Chart 3 – Births

Mean   

Median               

Mode   

Range  

Standard Deviation        

2. Is your standard deviation for a population or a sample?  Why did you select that answer?

3. Find the following values using your data from chart 1 on the first project.

Chart 4

Lowest value    

First Quartile (Q1)           

Median (Q2)     

Third Quartile (Q3)         

Highest value    

Interquartile range         

4. Create a box and whisker plot using the answers from question 3.  Be sure to include the number line and label it.  

5. Label Graph 1.  Using the mean and standard deviation from Chart 3, label the mean.  Then label up to 3 standard deviations above and below the mean.

Graph 1

6. a. Find the probability of the number of births annually being less than 1 bycalculating the z-score using the formula the formula z=(x-μ)/σ.

Then use the Area Under a Normal Distribution Curve tableor your calculator (Normalcdf).

b. Find the probability of the number of births annually being greater than 2.  Calculate the z-score.  Then find the probability by using the Area Under a Normal Distribution Curve table or your calculator.

MAT205 Intro Survey of Mathematics

Week 11 Project

Graphing Island

Directions

Your population is thriving on your island.  The data you have collected now needs to be displayed and further analyzed.  Use the charts you created in the probability portion in weeks 1-3for this part of the project.  Always show your calculations or explain how you used technology.  Take a picture of your calculator if you used that or submit your excel worksheet.

1.            a. Create a Scatter Plot using the total population for each of the years from the Probability Island. The horizontal axis should always represent time.

b. Use linear regression or a trendline in Excel to find the equation of the best fit line. 

c. Find the Correlation Coefficient.  Explain what this means for your data.

d. Use the equation to predict the population in year 20.

2.            a.Use the first and last data points of the total population for each of the years from the Probability Island to find a linear equationto model the data.

b. Graph the equation.

c. Compare the slope of the Linear Regression Line of question 1 with the slope of this line.  Provide an explanation of why they may similar or differ.

d. Use the equation to predict the population in year 20.

3.            a. Assume that (0,150) represents the vertex of a quadratic equation.  Find a quadratic equation using thetenth-year population as another point.   

b.            Graph the equation.

c.             Use the equation to predict the population in year 20.

4.            Using the equation y = 2x2 -9x +4,explain and demonstrate how to find the x-intercepts, the y-intercept, the axis of symmetry, and the vertex of a quadratic equation.