If you net $14.25 per hour and work 40 hours a week, 4 weeks per month, and have monthly expenses of: rent $825.50, car payment $458.79, utilities $110, food $150, gas $105, phone $125.25, savings $225, and insurance $118.36, what do you have left to invest for your retirement?

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Week3 My Money

My Money
3-68. If you net $14.25 per hour and work 40 hours a week, 4 weeks per month, and have monthly expenses of: rent $825.50, car payment $458.79, utilities $110, food $150, gas $105, phone $125.25, savings $225, and insurance $118.36, what do you have left to invest for your retirement? LU 3-2(1)

3-69. Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $29.95 per day plus 14 1/2 cents Page 85
per mile. Mark drove 410.85 miles. How much does Mark owe? LU 3-2(1)

3-70. Nursing home costs are on the rise as consumer affairs.com reports in its quarterly newsletter. The average cost is around $192 a day with an average length of stay of 2.5 years. Calculate the cost of the average nursing home stay. LU 3-2(1)

3-71. Bob Ross bought a smartphone on the web for $89.99. He saw the same smartphone in the mall for $118.99. How much did Bob save by buying on the web? LU 3-2(1)

3-72. Russell is preparing the daily bank deposit for his coffee shop. Before the deposit, the coffee shop had a checking account balance of $3,185.66. The deposit contains the following checks:
No. 1 $ 99.50 No. 3 S8.75 No. 2 110.35 No. 4 6.83

Russell included $820.55 in currency with the deposit. What is the coffee shop’s new balance, assuming Russell writes 110 new checks? LU 3-2( 1 I excel

3-73. The United Nations claims India will overtake China as the world’s most populous country within seven years. If China has 1.436 billion people and India has 1.345 billion people. what is the difference in population? LU 3-2(1)

What is your maximum height on the Ferris wheel? What is your minimum height on the Ferris wheel? How far off the ground is the centre of the Ferris wheel? What is the radius of the Ferris wheel?

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MARK BREAKDOWN

Knowledge/Understanding

Overall marks for communication: /5C
1. For each of the following: determine if the graph is periodic, and if it is periodic state the period and the amplitude.
Periodic (Y/N): Periodic (Y/N):
if periodic: if periodic:
Period: Period:
Amplitude: Amplitude:

2. Determine an equation if the given base graph has been transformed as follows. (4marks).siny x= compressed vertically by a factor of3 1 , reflected in the x–axis, translated120 to the right, and 5.5 units upward.
________________________

3. For the function, state the following. (4)( ) 25.42430sin4 −+= xy
phase shift____________________ period ______ vertical displacement ____________________ amplitude ______ range ____________________

5. Determine: amplitude, horizontal and vertical phase shift, period ( 4)

6. If the base graph issiny x= describe, in words, the transformations that occur to . (3)

__________________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
Application
7. For each function, state the following, draw a sketch, then graph.. (10)
a. p.s._______________ per. ____ v.d. _______________ amp. ____ range__________
b.( ) 2150sin2 ++= xy p.s._______________ per.____ v. d._____________ amp.____range_________

Inquiry

8. A radio transmission tower sways in a strong wind so that the top moves back and forth as much as 56 cm with a period of 6.0 s. This motion can be modeled using a sine function. (7 marks)
a) Sketch a graph of the sideways displacement of the tower, d, from its normal position as a function of time, t, for 12.0 s.
b) Graph it the function (hint: you need to find amplitude, period, h shift, axis of the curve if they apply to your graph)

9. The height of a rider on a Ferris wheel, in metres, can be modelled by the function h(x) = 9 sin(x − 90)+ 10 ,where x is the rotation angle, in degrees, that you’re on the ride. (5)
a. What is your maximum height on the Ferris wheel?
b. What is your minimum height on the Ferris wheel?
c. How far off the ground is the centre of the Ferris wheel?
d. What is the radius of the Ferris wheel?

What is the student’s mean score in the class BEFORE the final exam? What is the student’s mean score in the class AFTER the final exam? Calculate the normal non-weighted average of the 5 grades and compare to the weighted average in part b.

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DISCUSSION ESSAY

To be sure that all math formatting is properly displayed, you are strongly encouraged to reload this page after opening. You should also reload this page if “Math Error” appears in place of math problems.

The following problems reflect the reading material you had to prepare for this week. From the list below, choose one problem, write it down, and solve it in detail (show all of your steps). You should pick a problem that has not yet been attempted if you can. Please label your solution with the corresponding question number. In your solutions, you are only to use the math concepts that have been covered in this course up to this point.

1. A student receives test scores of 50, 75, and 90. The student’s final exam score is 82 and homework score is 75. Each test is worth 15% of the final grade, the final exam is 35% of the final grade and the homework grade is 20% of the final grade.
a) What is the student’s mean score in the class BEFORE the final exam?
b) What is the student’s mean score in the class AFTER the final exam?
c) Calculate the normal non-weighted average of the 5 grades and compare to the weighted average in part b.

2. The scores for a competency test are approximately symmetric and bell-shaped, with a mean score of 65, with a standard deviation of 4.
a) Can we use the Empirical Rule on this data set? Why?
b) Assuming that we can use the Empirical Rule on this data set, find the percentage of scores between 57 and 73.
c) Provide a statistical argument using your knowledge of the standard deviation to complete this sentence: Most taking this test do not make a score of 77 or above because __________________. (Consider data values outside two standard deviations to be unusual and outside of three standard deviations to be an outlier.)

3. The average SAT verbal score is 490, with a standard deviation of 96.

a) Use the Empirical Rule to determine what percent of the scores lie between 298 and 586.
b) To some, a score of 600 may seem very high compared to the mean of 490. Use the standard deviation to explain why we would not say 600 is unusually high. (Consider data values outside two standard deviations to be unusual and outside of three standard deviations to be an outlier.)

4. Consider the following grades on a test: 98, 51, 94, 67, 94, 73, 75, 89, 22, 99, 84, 89, 87, 93, 81, 92, 71, 61, 10 The mean is 75. Create a stem and leaf display of the data and then answer the following question:

True or False:

a) Most students made C’s.
b) Most students made right around the mean of 75.
c) There was a balanced amount of A’s, B’s, C’s, D’s, and F’s.
d) Half of the grades were below 75 and half above.

Additional discussion topic for this question: When you think of a test average of 75, what automatically comes to your mind about the grades? For most of us, the grades above with an average of 75 does not fit the mold of what we believe an average of 75 means.

Explain the formula in the text for angle measure in the Cartesian model. Find the perpendicular line from (2, 3) to t = {(x, A 1 2x + 3v = 5).

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EXERCISES 11.1

  1. Explain the formula in the text for angle measure in the Cartesian model.
  2. Find the perpendicular line from (2, 3) to t = {(x, A 1 2x + 3v = 5).
  3. Find a coordinate function for f = {(x, A I 2x + 3y = 51.

11.2 THE POINCARE DISK MODEL FOR HYPERBOLIC GEOMETRY

 

Define the number of years that have passed after 1960 as the predictor variable x, and the mean CO2 measurement for a particular year as y. Create a linear model for the mean CO2 level in the atmosphere, y = mx + b, using the data points for 1960 and 2015.

/in /by

MATH 163 Fall 2022

Applications Project

Pre-Calculus I is a general education course designed to assist students in the development of critical life skills.  One of the goals of this assignment is to assess student competence for each of these objectives:

  1. Written and Oral Communication— articulate a solution to mathematical problems (CCO20),
  2. Critical Analysis and Reasoning— produce and compare graphs of functions, using transformations, symmetry, end behavior, and asymptotes (CCO16),
  • Technological Competence— apply appropriate technology to the solution of mathematical problems (CCO21),
  1. Scientific and Quantitative or Logical Reasoning— identify domain and range of functions (CCO4), and
  • Personal and Professional Ethics— construct a solution to real world problems using problem solving methods individually and in groups (CCO18).

 

ASSIGNMENT: 
Over the last decade, at least, there has been much talk about climate change.  There have been discussions concerning the role humans have played in the altering of Earth’s atmosphere and the real and potential impact on life as we have come to know it.  Finally, there have been attempts already made to stop or reverse any negative results that may have been or that may be caused as humans continue to produce and consume goods and services in our ever-expanding societies.

In this assignment you will have the opportunity to investigate four scenarios related to the issues climate change.

Purpose:  The purpose of this assignment is to provide you, the student, with an opportunity to demonstrate your level of mastery of the mathematical and logical concepts that are presented in this pre-calculus course.

Audience:  The audience for this assignment is your pre-calculus professor, or any individual with a sound knowledge of the topics covered in the questions posed along with each scenario.

Directions:  Please respond to TWO of the THREE scenarios with complete ideas and sentences.  Be clear and succinct in your submissions.  Also, make sure to provide all required technology displays or output.

 

ASSIGNMENT SPECIFICATIONS: 

PICK ONLY 2 out of the 3 problems below to complete.

  • Cut and paste all technology displays and outputs, as needed, directly into the final document.
  • Your project should be typed; however, mathematical calculations may submitted as photo within the document.
  • Please delete these directions on pages 1, 2, &3. Keep the project scenarios.  You will answer each part of the scenario directly below the question asked.
  • Both CCBC and Purdue University offer very good online references at: ·

http://www.ccbcmd.edu/Resources-for-Students/Tutoring-and-Academic- Coaching/Writing-Center- and-Online-Writing-Lab/Documenting-and-Citing-Sources.aspx

http://owl.english.purdue.edu/owl/resource/747/01/

 

SUBMISSION GUIDELINES:

  • Send electronically with your name and class to dtruszkowski@ccbcmd.edu

Instructions on how to use Desmos, Excel, and Calculators to sketch a graph of an equation, to make a table and plot points, and to find an equation that models your data (i.e., the linear regression line or the line of best fit)

  1. Desmos
  2. To create a new graph, go to comand just type your expression in the expression list bar. As you are typing your expression, the calculator will immediately draw your graph on the graph paper. You can graph a single line by entering an expression like y = 2x + 3.
  3. Finding an equation that best fits your data in Desmos
  4. Go to comand choose Start Graphing.
  5. Click the plus sign in the upper left and choose Add Item > table
  6. Type your data in the table.
  7. Click on the wrench in the upper right to change the graph settings.
  8. Modify your x, and y values to reflect your data.
  9. Adjust the values of the sliders until the graph of the equation most closely fits your data points.
  10. On the DESMOS Calculator, type and select all to access the sliders to adjust the slope m and y-intercept b. Please use the following links for more directions on how to use DESMOS to sketch a graph of an equation, to make a table and plot points, and to find an equation that fits your data. Below are online videos that will help with explanation. Watch them in order. Please copy and paste the following links to the google site to avoid any possible error.
  11. Helpful videos:

https://learn.desmos.com/tables

https://learn.desmos.com/graphing

https://www.youtube.com/watch?v=4NTf551hHQE

 

  1. Excel
  2. You can also use Excel to get a regression line (line that models your data). These are the steps:
  3. Open Excel and fill your data in two columns: 1st column representing the x coordinates and second column representing the y coordinates of your points.
  4. Select both columns by highlighting them.
  5. Go to insert and at the chart part of the menu, you will see the scatterplot. Click on it and select the first scatterplot option. A scatterplot of your data will appear on the screen
  6. You can either click on the “Add chart element” at the top left of the menu or just click on the “plus” sign at the top corner of the scatterplot. Check the trendline box. It will show the trendline (regression line). To add an equation for the trendline, click on the arrow next to the trendline option and it will show you “more options”. You scroll down until you see “display the equation” and you check that box. The equation of the trendline will appear on the screen. It is usually in a “small” font and a little hard to read. You can move it around the screen and change the font and make it bigger.
  7. The following link shows these steps: https://www.youtube.com/watch?v=L_a8Z0BVjyM

 

  • Calculators: How to find the linear regression line:

 

  1. Casio fx-115ES Plus
  2. Press Mode, then 3 for STAT, then 2 for A+BX.
  3. Input all of your independent data under the X column, and all of the dependent data under the Y column.
  4. Press AC to exit edit mode safely.
  5. Press SHIFT & 1 to enter STAT/DIST mode.
  6. Press 5 for Reg.

 

  1. Casio fx-991EX
  2. Press MENU, then 6 for Statistics, then 2 for y=a+bx.
  3. Input all of your independent data under the x column, and all of the dependent data under the y column.
  4. Press AC to exit edit mode safely.
  5. Press OPTN.
  6. Press 3 for Regression Calc. Everything is now on your screen, although you may need to scroll down to find relevant information.
  7. When you are finished, your calculator will still be in y=a+bx Statistics mode. Press MENU, then 1 to return to Calculator mode.

 

  1. TI-84 Plus or similar

Press STAT, then ENTER to input your data.

  1. Input all of your independent data under the L1 column, and all of your dependent data under the L2 column
  2. Press 2ND & MODE to quit out of edit mode.
  3. Re-Press STAT, but this time scroll over to CALC.
  4. Scroll down to LinReg(ax+b).
  5. Press ENTER to select LinReg(ax+b).
  6. Scroll down to highlight CALCULATE.
  7. Press ENTER to see all of the data. This will display the correlation, slope of line of best fit (called a), and the y-intercept of the line of best fit (called b).

 

Math 163 Applied Project

  • Carbon Dioxide Emissions

Carbon emissions contribute to climate change, which has serious consequences for humans and their environment. According to the U.S. Environmental Protection Agency, carbon emissions, in the form of carbon dioxide (CO2), make up more than 80 percent of the greenhouse gases emitted in the United States (EPA, 2019). The burning of fossil fuels releases CO2 and other greenhouse gases. These carbon emissions raise global temperatures by trapping solar energy in the atmosphere. This alters water supplies and weather patterns, changes the growing season for food crops, and threatens coastal communities with increasing sea levels (EPA, 2016).

The amount of CO2 emitted per year A (in tons) for a vehicle that averages x miles per gallon of gas, can be approximated by the function .

  1. Interpret the interval [20, 25] in the context of the question and then calculate and interpret the average rate of change.
  2. Determine the average rate of change of the amount of CO2 emitted in a year over the interval [35, 40], and interpret its meaning.

 

  1. Provide an interpretation of the difference between the values found in parts a) and b) and state the implications in the context of vehicle emissions of CO2. Be sure to discuss what the difference is between the average miles per gallon of 20-25 versus 35-40. Is one more ideal? Provide an explanation of your reasoning. (Department of Energy, 2019)

 

 

  • Carbon Dioxide Change

As humans continue to burn fossil fuels, the amount of CO2 in the atmosphere increases.  Scientists measure atmospheric CO2 in parts per million (ppm), which means the number of CO2 molecules for every one million molecules of other atmospheric gases such as oxygen and nitrogen.  Scientists have been tracking the amount of CO2 in the atmosphere at the Mauna Loa Observatory in Hawaii since 1958.

The table below shows the CO2 measurements recorded for the years 1959-2018.

Year Mean Year Mean Year Mean Year Mean Year Mean
1959 315.97 1972 327.45 1985 346.12 1998 366.70 2011 391.65
1960 316.91 1973 329.68 1986 347.42 1999 368.38 2012 393.85
1961 317.64 1974 330.18 1987 349.19 2000 369.55 2013 396.52
1962 318.45 1975 331.11 1988 351.57 2001 371.14 2014 398.65
1963 318.99 1976 332.04 1989 353.12 2002 373.28 2015 400.83
1964 319.62 1977 333.83 1990 354.39 2003 375.80 2016 404.24
1965 320.04 1978 335.40 1991 355.61 2004 377.52 2017 406.55
1966 321.38 1979 336.84 1992 356.45 2005 379.80 2018 408.52
1967 322.16 1980 338.75 1993 357.10 2006 381.90
1968 323.04 1981 340.11 1994 358.83 2007 383.79
1969 324.62 1982 341.45 1995 360.82 2008 385.60
1970 325.68 1983 343.05 1996 362.61 2009 387.43
1971 326.32 1984 344.65 1997 363.73 2010 389.90

(Source: U.S. Department of Commerce/National Oceanic & Atmospheric Administration. https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html )

  1. Use these data to make a summary table of the mean CO2 level in the atmosphere as measured at the Mauna Loa Observatory for the years 1960, 1965, 1970, 1975, …, 2015.

 

  1. Define the number of years that have passed after 1960 as the predictor variable x, and the mean CO2 measurement for a particular year as y. Create a linear model for the mean CO2 level in the atmosphere, y = mx + b, using the data points for 1960 and 2015 (round the slope and y-intercept values to three decimal places).  Use Desmos or Excel (directions are included in this assignment) to sketch a scatter plot of the data in your summary table and also to graph the linear model over this plot.  Comment on how well the linear model fits the data.

 

  1. Looking at your scatter plot, choose two years that you feel may provide a better linear model than the line created in part b). Use the two points you selected to calculate a new linear model and use Desmos to plot this line as well.  Provide this linear model and state the slope and y-intercept, again, rounded to three decimal places.

 

  1. Use the linear model generated in part c) to predict the mean CO2 level for each of the years 2010 and 2015, separately. Compare the predicted values from your model to the recorded measured values for these years. What conclusions can you reach based on this comparison?

 

  1. Again, using the linear model generated in part c), determine in which year the mean level of CO2 in the atmosphere would exceed 420 parts per million.

 

  • Sea-Level Rise

The Arctic ice cap is a large sheet of sea ice that contains an estimated 680,000 cubic miles of water.  If the global climate were to warm significantly as a result of the greenhouse effect or other climactic change, this ice cap would start to melt (NASA, n.d.).  More than 200 million people currently live on land that is less than 3 feet above sea level.  There are several large cities in the world that have a low average elevation, including Miami, Florida (pop. 463,347) at 7 feet, Shanghai, China (pop. 24,180,000) at 13 feet, and Boston, Massachusetts (pop. 685,094) at 14 feet.  In this part of the project you are going to estimate the rise in sea level if the ice cap were to melt and determine whether this event would have a significant impact on the people living in these three cities (US Government, 2019).

  1. The surface area of a sphere is given by the expression , where is its radius.  Although the shape of the earth is not exactly spherical, it has an average radius of 3,960 miles.  Estimate the surface area of the earth to the nearest million square miles.
  2. Oceans cover approximately 71% of the total surface area of the earth. How many square miles of the earth’s surface are covered by oceans (again, rounded to the nearest million)?
  3. Approximate the potential sea-level rise if half the Arctic ice cap were to melt. This can be done by dividing the volume of water from the melted ice cap by the surface area of the earth’s oceans.  Convert your answer into feet.
  4. Discuss what your approximation of the potential sea-level rise implies for the cities of Miami, Boston, and Shanghai. What are some possible social, economic, or political impacts for these cities and the people who live there? Based on your specified impact, what could be an appropriate and ethical response?
  5. The Antarctic ice cap contains approximately 6,300,000 cubic miles of water. Approximate the potential sea-level rise if half the Antarctic ice cap were to melt, and discuss the implications for the cities of Miami, Boston, and Shanghai.

 

References:

EPA. (2016, December 20). Climate Change Impacts | US EPA. Retrieved December 13, 2019, from https://19january2017snapshot.epa.gov/climate-impacts_.html
EPA. (2019, May 13). Overview of Greenhouse Gases. Retrieved December 13, 2019, from https://www.epa.gov/ghgemissions/overview-greenhouse-gases
Department of Energy. (n.d.). Department of Energy. Retrieved December 13, 2019, from https://www.energy.gov/
United States Government. (2019, September 5). U.S. Geological Survey. Retrieved December 13, 2019, from https://www.doi.gov/hurricanesandy/usgs
NASA. (n.d.). Arctic Sea Ice Minimum | NASA Global Climate Change. Retrieved December 13, 2019, from https://climate.nasa.gov/vital-signs/arctic-sea-ice/

 

Identify the place value for the following: LU 3-1(1) 3-1. 7.5328 3-2. 229.448 1

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DRILL PROBLEMS

Identify the place value for the following: LU 3-1(1) 3-1. 7.5328  3-2. 229.448 1
Round the following as indicated: LU 3-1(1) eleventh Hundredth Thousandth  3-3. .7391 3-4. 6.8629 3-5. 5.8312 3-6. 6.8415 3-7. 6.5555 3-8. 75.9913
Round the following to the nearest cent: LU 3-1(1) 3-9. $4,822.775 3-10. S4,892.046
Convert the following types of decimal fractions to decimals (round to nearest hundredth as needed): LU 3-1(2 3-11. 3-15. — 8 100 91 100 3-12. 3-16. 3-13. 3-17. 61 3-14. 610 —3 10 979 1,000 16 61 1,000 1.000 100

Convert the following decimals to fractions. Do not reduce to lowest terms. LU 3-1(2)
3-18. .9 3-19. .71 3-20. .009 3-21. .0125 3-22. .609 3-23. .825 3-24. .9999 3-25. .7065

Convert the following to mixed numbers. Do not reduce to the lowest terms. LU 3-1(2)
3-26. 7.1 3-27. 28.48
3-28. 6.025

Write the decimal equivalent of the following: LU 3-1(2)
3-29. Five thousandths 3-31. Eighty-five ten thousandths Rearrange the following and add: LU 3-2(1) 3-33. .115, 10.8318, 4.7, 802.4811 Rearrange the following and subtract: LU 3-2(1) 3-35. 9.2 – 5.8 3-36. 7 – 2.0815
3-30. Three hundred three and two hundredths
3-32. Seven hundred seventy-five thousandths 3-34. .005, 2,002.181, 795.41, 14.0, .184 3-37. 3.4 – 1.08

Estimate by rounding all the way and multiply the following (do not round final answer): LU 3-2(1)
3-38. 6.24 x 3.9 = Estimate
3-40. 675 x 1.92 = Estimate
3-39. .413 x 3.07 = Estimate
3-41. 4.9 x .825 = Estimate

Divide the following and round to the nearest hundredth: LU 3-2(1) 3-42. .8931 = 3 3-43. 29.432 .0012
3-44. .0065 ÷ .07 3-46. 8.95 ÷ 1.81
3-45. 7,742.1 ÷ 48 3-47. 2,600 = 381

Convert the following to decimals and round to the nearest hundredth: LU 3-1(2) 3-48. 1 – 5 3-49. I 3-50. – 8 25 6
3-51.
5
8

Complete these multiplications and divisions by the shortcut method (do not do any written calculations): LU 3-2(3)
3-52. 96.7 ÷ 10 3-55. .86 ÷ 100 3-58. 750 x 10 3-61. 7.9132 x 1,000
3-53. 258 = 100 3-56. 9.015 x 100 3-59. 3,950 ÷ 1,000
3-54. 8.51 x 1,000 3-57. 48.6 x 10 3-60. 8.45=10

Provide an interpretation of the difference between the values found in parts a) and b) and state the implications in the context of vehicle emissions of CO2. Discuss what the difference is between the average miles per gallon of 20-25 versus 35-40. Is one more ideal? Provide an explanation of your reasoning.

/in /by

MATH 163 Fall 2022

Applications Project

Pre-Calculus I is a general education course designed to assist students in the development of critical life skills.  One of the goals of this assignment is to assess student competence for each of these objectives:

  1. Written and Oral Communication— articulate a solution to mathematical problems (CCO20),
  2. Critical Analysis and Reasoning— produce and compare graphs of functions, using transformations, symmetry, end behavior, and asymptotes (CCO16),
  • Technological Competence— apply appropriate technology to the solution of mathematical problems (CCO21),
  1. Scientific and Quantitative or Logical Reasoning— identify domain and range of functions (CCO4), and
  • Personal and Professional Ethics— construct a solution to real world problems using problem solving methods individually and in groups (CCO18).

 

ASSIGNMENT: 
Over the last decade, at least, there has been much talk about climate change.  There have been discussions concerning the role humans have played in the altering of Earth’s atmosphere and the real and potential impact on life as we have come to know it.  Finally, there have been attempts already made to stop or reverse any negative results that may have been or that may be caused as humans continue to produce and consume goods and services in our ever-expanding societies.

In this assignment you will have the opportunity to investigate four scenarios related to the issues climate change.

Purpose:  The purpose of this assignment is to provide you, the student, with an opportunity to demonstrate your level of mastery of the mathematical and logical concepts that are presented in this pre-calculus course.

Audience:  The audience for this assignment is your pre-calculus professor, or any individual with a sound knowledge of the topics covered in the questions posed along with each scenario.

Directions:  Please respond to TWO of the THREE scenarios with complete ideas and sentences.  Be clear and succinct in your submissions.  Also, make sure to provide all required technology displays or output.

 

ASSIGNMENT SPECIFICATIONS: 

PICK ONLY 2 out of the 3 problems below to complete.

  • Cut and paste all technology displays and outputs, as needed, directly into the final document.
  • Your project should be typed; however, mathematical calculations may submitted as photo within the document.
  • Please delete these directions on pages 1, 2, &3. Keep the project scenarios.  You will answer each part of the scenario directly below the question asked.
  • Both CCBC and Purdue University offer very good online references at: ·

http://www.ccbcmd.edu/Resources-for-Students/Tutoring-and-Academic- Coaching/Writing-Center- and-Online-Writing-Lab/Documenting-and-Citing-Sources.aspx

http://owl.english.purdue.edu/owl/resource/747/01/

 

SUBMISSION GUIDELINES:

  • Send electronically with your name and class to dtruszkowski@ccbcmd.edu

Instructions on how to use Desmos, Excel, and Calculators to sketch a graph of an equation, to make a table and plot points, and to find an equation that models your data (i.e., the linear regression line or the line of best fit)

  1. Desmos
  2. To create a new graph, go to comand just type your expression in the expression list bar. As you are typing your expression, the calculator will immediately draw your graph on the graph paper. You can graph a single line by entering an expression like y = 2x + 3.
  3. Finding an equation that best fits your data in Desmos
  4. Go to comand choose Start Graphing.
  5. Click the plus sign in the upper left and choose Add Item > table
  6. Type your data in the table.
  7. Click on the wrench in the upper right to change the graph settings.
  8. Modify your x, and y values to reflect your data.
  9. Adjust the values of the sliders until the graph of the equation most closely fits your data points.
  10. On the DESMOS Calculator, type and select all to access the sliders to adjust the slope m and y-intercept b. Please use the following links for more directions on how to use DESMOS to sketch a graph of an equation, to make a table and plot points, and to find an equation that fits your data. Below are online videos that will help with explanation. Watch them in order. Please copy and paste the following links to the google site to avoid any possible error.
  11. Helpful videos:

https://learn.desmos.com/tables

https://learn.desmos.com/graphing

https://www.youtube.com/watch?v=4NTf551hHQE

 

  1. Excel
  2. You can also use Excel to get a regression line (line that models your data). These are the steps:
  3. Open Excel and fill your data in two columns: 1st column representing the x coordinates and second column representing the y coordinates of your points.
  4. Select both columns by highlighting them.
  5. Go to insert and at the chart part of the menu, you will see the scatterplot. Click on it and select the first scatterplot option. A scatterplot of your data will appear on the screen
  6. You can either click on the “Add chart element” at the top left of the menu or just click on the “plus” sign at the top corner of the scatterplot. Check the trendline box. It will show the trendline (regression line). To add an equation for the trendline, click on the arrow next to the trendline option and it will show you “more options”. You scroll down until you see “display the equation” and you check that box. The equation of the trendline will appear on the screen. It is usually in a “small” font and a little hard to read. You can move it around the screen and change the font and make it bigger.
  7. The following link shows these steps: https://www.youtube.com/watch?v=L_a8Z0BVjyM

 

  • Calculators: How to find the linear regression line:

 

  1. Casio fx-115ES Plus
  2. Press Mode, then 3 for STAT, then 2 for A+BX.
  3. Input all of your independent data under the X column, and all of the dependent data under the Y column.
  4. Press AC to exit edit mode safely.
  5. Press SHIFT & 1 to enter STAT/DIST mode.
  6. Press 5 for Reg.

 

  1. Casio fx-991EX
  2. Press MENU, then 6 for Statistics, then 2 for y=a+bx.
  3. Input all of your independent data under the x column, and all of the dependent data under the y column.
  4. Press AC to exit edit mode safely.
  5. Press OPTN.
  6. Press 3 for Regression Calc. Everything is now on your screen, although you may need to scroll down to find relevant information.
  7. When you are finished, your calculator will still be in y=a+bx Statistics mode. Press MENU, then 1 to return to Calculator mode.

 

  1. TI-84 Plus or similar

Press STAT, then ENTER to input your data.

  1. Input all of your independent data under the L1 column, and all of your dependent data under the L2 column
  2. Press 2ND & MODE to quit out of edit mode.
  3. Re-Press STAT, but this time scroll over to CALC.
  4. Scroll down to LinReg(ax+b).
  5. Press ENTER to select LinReg(ax+b).
  6. Scroll down to highlight CALCULATE.
  7. Press ENTER to see all of the data. This will display the correlation, slope of line of best fit (called a), and the y-intercept of the line of best fit (called b).

 

Math 163 Applied Project

  • Carbon Dioxide Emissions

Carbon emissions contribute to climate change, which has serious consequences for humans and their environment. According to the U.S. Environmental Protection Agency, carbon emissions, in the form of carbon dioxide (CO2), make up more than 80 percent of the greenhouse gases emitted in the United States (EPA, 2019). The burning of fossil fuels releases CO2 and other greenhouse gases. These carbon emissions raise global temperatures by trapping solar energy in the atmosphere. This alters water supplies and weather patterns, changes the growing season for food crops, and threatens coastal communities with increasing sea levels (EPA, 2016).

The amount of CO2 emitted per year A (in tons) for a vehicle that averages x miles per gallon of gas, can be approximated by the function .

  1. Interpret the interval [20, 25] in the context of the question and then calculate and interpret the average rate of change.
  2. Determine the average rate of change of the amount of CO2 emitted in a year over the interval [35, 40], and interpret its meaning.

 

  1. Provide an interpretation of the difference between the values found in parts a) and b) and state the implications in the context of vehicle emissions of CO2. Be sure to discuss what the difference is between the average miles per gallon of 20-25 versus 35-40. Is one more ideal? Provide an explanation of your reasoning. (Department of Energy, 2019)

 

 

  • Carbon Dioxide Change

As humans continue to burn fossil fuels, the amount of CO2 in the atmosphere increases.  Scientists measure atmospheric CO2 in parts per million (ppm), which means the number of CO2 molecules for every one million molecules of other atmospheric gases such as oxygen and nitrogen.  Scientists have been tracking the amount of CO2 in the atmosphere at the Mauna Loa Observatory in Hawaii since 1958.

The table below shows the CO2 measurements recorded for the years 1959-2018.

Year Mean Year Mean Year Mean Year Mean Year Mean
1959 315.97 1972 327.45 1985 346.12 1998 366.70 2011 391.65
1960 316.91 1973 329.68 1986 347.42 1999 368.38 2012 393.85
1961 317.64 1974 330.18 1987 349.19 2000 369.55 2013 396.52
1962 318.45 1975 331.11 1988 351.57 2001 371.14 2014 398.65
1963 318.99 1976 332.04 1989 353.12 2002 373.28 2015 400.83
1964 319.62 1977 333.83 1990 354.39 2003 375.80 2016 404.24
1965 320.04 1978 335.40 1991 355.61 2004 377.52 2017 406.55
1966 321.38 1979 336.84 1992 356.45 2005 379.80 2018 408.52
1967 322.16 1980 338.75 1993 357.10 2006 381.90    
1968 323.04 1981 340.11 1994 358.83 2007 383.79    
1969 324.62 1982 341.45 1995 360.82 2008 385.60    
1970 325.68 1983 343.05 1996 362.61 2009 387.43    
1971 326.32 1984 344.65 1997 363.73 2010 389.90    

(Source: U.S. Department of Commerce/National Oceanic & Atmospheric Administration. https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html )

  1. Use these data to make a summary table of the mean CO2 level in the atmosphere as measured at the Mauna Loa Observatory for the years 1960, 1965, 1970, 1975, …, 2015.

 

  1. Define the number of years that have passed after 1960 as the predictor variable x, and the mean CO2 measurement for a particular year as y. Create a linear model for the mean CO2 level in the atmosphere, y = mx + b, using the data points for 1960 and 2015 (round the slope and y-intercept values to three decimal places).  Use Desmos or Excel (directions are included in this assignment) to sketch a scatter plot of the data in your summary table and also to graph the linear model over this plot.  Comment on how well the linear model fits the data.

 

  1. Looking at your scatter plot, choose two years that you feel may provide a better linear model than the line created in part b). Use the two points you selected to calculate a new linear model and use Desmos to plot this line as well.  Provide this linear model and state the slope and y-intercept, again, rounded to three decimal places.

 

  1. Use the linear model generated in part c) to predict the mean CO2 level for each of the years 2010 and 2015, separately. Compare the predicted values from your model to the recorded measured values for these years. What conclusions can you reach based on this comparison?

 

  1. Again, using the linear model generated in part c), determine in which year the mean level of CO2 in the atmosphere would exceed 420 parts per million.

 

  • Sea-Level Rise

The Arctic ice cap is a large sheet of sea ice that contains an estimated 680,000 cubic miles of water.  If the global climate were to warm significantly as a result of the greenhouse effect or other climactic change, this ice cap would start to melt (NASA, n.d.).  More than 200 million people currently live on land that is less than 3 feet above sea level.  There are several large cities in the world that have a low average elevation, including Miami, Florida (pop. 463,347) at 7 feet, Shanghai, China (pop. 24,180,000) at 13 feet, and Boston, Massachusetts (pop. 685,094) at 14 feet.  In this part of the project you are going to estimate the rise in sea level if the ice cap were to melt and determine whether this event would have a significant impact on the people living in these three cities (US Government, 2019).

  1. The surface area of a sphere is given by the expression , where is its radius.  Although the shape of the earth is not exactly spherical, it has an average radius of 3,960 miles.  Estimate the surface area of the earth to the nearest million square miles.
  2. Oceans cover approximately 71% of the total surface area of the earth. How many square miles of the earth’s surface are covered by oceans (again, rounded to the nearest million)?
  3. Approximate the potential sea-level rise if half the Arctic ice cap were to melt. This can be done by dividing the volume of water from the melted ice cap by the surface area of the earth’s oceans.  Convert your answer into feet.
  4. Discuss what your approximation of the potential sea-level rise implies for the cities of Miami, Boston, and Shanghai. What are some possible social, economic, or political impacts for these cities and the people who live there? Based on your specified impact, what could be an appropriate and ethical response?
  5. The Antarctic ice cap contains approximately 6,300,000 cubic miles of water. Approximate the potential sea-level rise if half the Antarctic ice cap were to melt, and discuss the implications for the cities of Miami, Boston, and Shanghai.

 

References:

EPA. (2016, December 20). Climate Change Impacts | US EPA. Retrieved December 13, 2019, from https://19january2017snapshot.epa.gov/climate-impacts_.html
EPA. (2019, May 13). Overview of Greenhouse Gases. Retrieved December 13, 2019, from https://www.epa.gov/ghgemissions/overview-greenhouse-gases
Department of Energy. (n.d.). Department of Energy. Retrieved December 13, 2019, from https://www.energy.gov/
United States Government. (2019, September 5). U.S. Geological Survey. Retrieved December 13, 2019, from https://www.doi.gov/hurricanesandy/usgs
NASA. (n.d.). Arctic Sea Ice Minimum | NASA Global Climate Change. Retrieved December 13, 2019, from https://climate.nasa.gov/vital-signs/arctic-sea-ice/

 

Identify the following types of fractions: 2-1. LU 2-1(1) 2-2. LU 2-1(2) 2-5. 12 2-3. 25 —9 10 Convert the following to mixed numbers: 91 2-4. 11 921 13 10 15

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Math Week 2

DRILL PROBLEMS

Identify the following types of fractions: 2-1. LU 2-1(1) 2-2. LU 2-1(2) 2-5. 12 2-3. 25 —9 10 Convert the following to mixed numbers: 91 2-4. 11 921 13 10 15

Convert the following to improper fractions: LU 2-1(2) 2-6. 8-7 2-7. 19 8 3

Reduce the following to the lowest terms. Show how to calculate the greatest common divisor by the step approach. LU 2-1(3) 44 2-8. . — 2-9. 38 52

Convert the following to higher terms. LU 2-1(3) 2-10. 9= — 10 70

Determine the LCD of the following (a) by inspection and (b) by division of prime numbers: LU 2-2(2) 2-11.
_3 4′ _5 6′ _1 5 Check _7 12′

Inspection

2-12. 5 75 2 6′ 18’9′ 72 Inspection
2-13. 1 3 5 1 4’32’48’1 Inspection

Check
Check

Add the following and reduce to lowest terms: LU 2-2(1), LU 2-1(3) 2-14. 3 + –3 2-15. 3+ 4 9 9 7 21 2-16. 6 I + a 2-17. 63+9 1 24 8 8 8 2-18. 9 9 + 6 1 10 10

Subtract the following and reduce to lowest terms: LU 2-2(3), LU 2-1(3)
2-19. 11 2-20. 14-3 – 105 — – 12 12 8 8 2-21. 121 –4? 9 3

Multiply the following and reduce to lowest terms. Do not use the cancellation technique for these problems. LU 2-3(1), LU 2-1(3)
2-22. 2-24. 17 x –4 2 87 x 64 8 2-23. –5 x –3 6 8

Multiply the following. Use the cancellation technique. LU 2-3(1), LU 2-1(2)
2-25. -4x —30 x —6 10 60 10
2-26. 3-3x –8x 4-9 4 9 12

Divide the following and reduce to lowest terms. Use the cancellation technique as needed. LU 2-3(2), LU 2-1(2)
2-27. 12 ÷ 4 2-28. 18= –1 9 5
2-29. 4?_ 12 2-30. 35_31 3 6 2

What are the differences between innovation and invention? What different types of innovations do you know? Explain how the success of companies like Apple and Google is due partly to the state.

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DISCUSSION QUESTIONS

  1. What are the differences between innovation and invention? What different types of innovations do you know? Please give 3-5 examples.
  2. Explain how the success of companies like Apple and Google is due partly to the state.
  3. What role should marketing play in the early stages of product innovation?

 200 – 300 words.