## Description

# MAT 126 SURVEY OF MATHEMATICAL METHODS COMPLETE CLASS

**MAT 126 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material – Ashford**

**Week 1 Written Assignment**

Following completion of your readings, complete exercises 35 and 37 in the “Real World Applications” section on page 280 of *Mathematics in Our World*.

For each exercise, specify whether it involves an arithmetic sequence or a geometric sequence and ** use the proper formulas where applicable**. Format your math work as shown in the Week One Assignment Guideand be concise in your reasoning. Plan the logic necessary to complete the exercise before you begin writing. For an example of the math required for this assignment, please review the Week One Assignment Guide.

The assignment must include (** a**) all math work required to answer the problems as well as (

**) introduction and conclusion paragraphs.**

*b*Your introduction should include three to five sentences of general information about the topic at hand. The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems. Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.

**Week 1 DQ**

All numbers in our real number system are the product of prime numbers. Complete the following steps for this discussion:

List the ages of ** two **people in your life, one older than you and one younger than you. It would be best if the younger person was 15 years of age or younger. Find the prime factorizations of your age and the other two persons’ ages. Show your work listed by name and age. Make sure your work is clear and concise. Find the LCM and the GCF for each set of numbers. Again, be clear and concise. Explain or show how you arrived at your answers. In your own words, explain the meaning of your calculated LCM and GCF for the ages you selected. Do not explain how you got the numbers; rather

**. Be specific to your numbers; do not give generic definitions.**

*explain the meaning of the numbers***Week 1 Quiz**

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained none of the three writing instruments?

The process of arriving at a specific conclusion based on previously accepted general statements is called ___________ reasoning

Which property of real numbers does the following equation demonstrate?

Perform the indicated operations: -42÷6+(-7)

Find the number of subsets the set has. {1, 2, 3, 4, 5, 6, 7, 8, 9}

State whether the following sequence is arithmetic, geometric, or neither.

Which of the following phrases does not describe the number -¾?

**Week 2 Written Assignment**

Following completion of your weekly readings, read “Are You Sure It’s Fat Free?” on page 286 of *Mathematics in Our World*.

Gather three of your favorite packaged foods; perhaps one from each: breakfast, lunch and dinner. Use the model explained in the “Are You Sure It’s Fat Free?” to analyze, through the mathematical formula explained, the fat content ** and protein content** from your foods. To analyze the protein content use

**, rather than the 9 calories for grams of fat.**

*4 calories per gram of protein*The assignment must include (** a**) all math work required to answer the problems as well as (

**) introduction and conclusion paragraphs.**

*b*Your introduction should include three to five sentences of general information about the topic at hand. The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems. Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.

The assignment must be formatted according the APA (6th edition) style, which includes a title page and reference page. For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar, in your online course.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.

# WEEK 2 QUIZ

Find the LCM of 29 and 116

Solve the proportion. x//10

Which property of the real numbers is illustrated by the following statement?

Perform the addition on the 12-hour clock. 5 + 11

Find the value of 327 in the mod 7 system

Simplify: 5(-3*x* + 3)

Evaluate the formula *P* = 2*l* + 2*w* when *l* = 4 in. and *w* = 4 in

Joe has $10,000 to purchase a used car. If the sales tax is 7% and the fee for title and license plates is $200, what is the maximum amount Joe can spend for a car?

Write 23 in base five

**Week 2 DQ1**

This Discussion should be an eye opener for most students. We will look at our food shopping trends and how we spend our money. The outcomes should reveal some interesting facts.

Save a cash register receipt from a shopping trip to the food market, or borrow one from a family member or friend. The cost of four prepackaged food items that are sold by weight and the cost of at least three fresh fruits, or vegetables need to appear on the receipt. If you have no access to a receipt with these items, then you will need to go to the store and write down the cost information, or find a grocery advertisement online. Do not use liquids such as milk, juice, or soda because these are sold by volume and not by weight. Also, do not include ingredients like flour, sugar, oil, dry beans, etc. because these items are not prepackaged foods. Fruits and vegetables are sold by the pound. Add up your prices per pound for the fruits and vegetables and find the average cost per pound. (Example: If bananas are .79 per pound and apples are .59 per pound, the average is calculated like this: (.79 + .59)// per pound on average for the two fruits.) Locate the weight of your prepackaged food items. (For example, on a box of Frosted Flakes it says 15 oz.) Add up all of the weights for your prepackaged items in ounces, and then add up all of the costs for your four prepackaged items. From the totals, find the** average cost per ounce** of prepackaged items.

**Week 2 DQ2**

This Discussion will help us learn to develop our own mathematical models, write down the equations and then solve the equations for unknown values using algebraic methods.

Refer back to Week One Discussion and use the names and ages of yourself and the other two people you selected. Make sure one is older than you and one is younger than you. In years, how old was the older person when you were born? Write an equation that models how old in years each of you will be, when your ages add up to 150 years old. For example, if age and the eldest person was a year older than you, you would write their age as x + 1. Then the equation would be: x + (x+1) = 150. Explain the reasoning which helped you develop your equation. Solve for your future ages. Are your answers reasonable, do they add up to 150? In years, how old were you when the youngest person was born? At some point during the lives of you and the youngest person, your age will be three times his/her age ** at that moment**. Write an equation which models how old in years each of you will be when you are three times as old as the younger person. Explain the reasoning which helped you develop your equation. Solve the equation for your ages when you are three times as old as the youngest person. Are your answers reasonable?

**Week 3 Quiz**

Determine whether or not the network is traversable

Janet invested $26,000, part at 6% and part at 3%. If the total interest at the end of the year is $1,080, how much did she invest at 6%?

The difference between the ages of two friends is 37 years. The sum of their ages is 55 years. Find the age of the older friend

Write the equation in the slope-intercept form.

4*x* – 10*y* = 11

Identify angles 2 and 7 as alternate interior, alternate exterior, corresponding, or vertical

Adult tickets for a play cost $19 and child tickets cost $17. If there were 36 people at a performance and the theatre collected $646 from ticket sales, how many children attended the play?

Which quadrilateral is a trapezoid?

Determine whether or not the network is traversable

**Week 3 DQ1**

This Discussion will concentrate on functions and graphs. Understanding the definitions of words is the essence of mathematics. When we understand the meaning of words, finding a solution is much easier because we know what task the problem is asking us to complete.

**Part 1**

In your own words, define the word “function.” Give your own example of a function using a set of at least 4 ordered pairs. The **domain **will be any four integers between 0 and +10. The **range **will be any four integers between -12 and 5. **Your example should not be the same as those of other students or the textbook**. There are thousands of possible examples. Explain why your example models a function. This is extremely important for your learning. Give your own example of at least four ordered pairs that ** does not**model a function. The

**domain**will be any four integers between 0 and +10. The

**range**will be any four integers between -12 and +5.

**Your example should not be the same as those of other students or the textbook**. There are thousands of possible examples. Explain why your example

**model a function.**

*does not***Part 2**

Select any two integers between -12 and +12 which will become solutions to a system of two equations. Write** two equations** that have your two integers as solutions. Show how you built the equations using your integers.

**Your solution and equations should not be the same as those of other students or the textbook**. There are infinite possibilities. Solve your system of equations by the

**addition/subtraction method**. Make sure you show the necessary 5 steps. Use the example on page 426 of

*Mathematics in Our World*as a guide.

**Week 3 DQ2**

This Discussion tests your ability to use a ruler and convert from Standard English measure to Metrics. You will then apply your knowledge of the geometric measurements of area and volume through real world problems.

Choose a room in your house. Measure the length, the width, and the height. Make sure you use feet and inches. Most rooms are not a whole number, such as 10 feet; they are 10 feet and 3 inches, or 9 feet 6 inches, etc.**
NOTE**: Do not use decimal numbers for the feet. For example, do not write 10.3 to mean 10’3”, because that is incorrect. Convert the measurements to all inches for step 2, and then convert back to square feet for step 3. Record your dimensions and, using the appropriate formula, find the surface area of the room. A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon. If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room? One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions. Find the volume in cubic centimeters. Be neat and precise. If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work.

**Week 4 Written Assignment**

Following completion of your readings, complete exercise 4 in the “Projects” section on page 620 of*Mathematics in Our World*.

Make sure you build or generate at least ** five **more Pythagorean Triples using one of the many formulas available online for doing this. After building your triples, verify each of them in the Pythagorean Theorem equation.

The assignment must include (** a**) all math work required to answer the problems as well as (

**) introduction and conclusion paragraphs.**

*b*Your introduction should include three to five sentences of general information about the topic at hand. The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems. Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.

The assignment must be formatted according the APA (6th edition) style, which includes a title page and reference page. For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar, in your online course.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.

# WEEK 4 QUIZ

A tie pin which sells for $200.00 has a markup rate of 30% on the selling price. Find the amount of the markup and the cost.

Find the missing value

A single card is drawn from a deck. Find the probability of selecting a 3 or a club

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is yellow?

The odds against an event are 8:8. Find the probability that the event will occur.

Express 3.46 as a percent

A coat was reduced from $250 to $200. Find the percent of the reduction in price

Express 81.6% as a decimal

**Week 4 DQ1**

The purpose of this Discussion is to analyze a financial plan that portrays a somewhat typical budgeting scheme. You will calculate expenses, a mortgage payment, and the effects of interest and financing on your budget. ** Show your math work for every answer **and identify the answers with words.

Select the first three letters of your last name. Each letter has a numerical place value in the alphabet. For example, D is 4, L is 12, and Z is 26. Add the three place values together. For example, Wallace would yield WAL, which is 23+1+ Multiply your sum by 1500. This is your yearly income for Week Four Discussion 1. Please use the following monthly expenses: Car payment = $283.15, Car insurance = $72, Utilities (includes water and power) = $242.77, Internet = $32, and Cell Phone = $79.95. You also have a yearly educational bill of $7980 which includes textbooks and classes. Calculate your monthly income. What percent of your monthly income is the car payment? Subtract the sum of your monthly expenses. Use this value to calculate what percent of your income is now available to spend for food, clothing, and your rent or mortgage. Use the plan at the bottom of page 538, “Mathematics in Our World Revisited,” to calculate the monthly mortgage payment established by your monthly income. Assume you can afford a down payment equal to 25% of your yearly income. What is the total purchase price can you afford for a home? Would this amount allow you to purchase a home in the area where you live?

**Week 4 DQ2**

This Discussion allows you to demonstrate your understanding of the similarities and differences between classical probability and empirical probability.

In your own words, describe ** two **main differences between classical and empirical probabilities. Gather coins you find around your home or in your pocket or purse. You will need an

**of coins (any denomination) between 16 and 30. You do not need more than that. Put all of the coins in a small bag or container big enough to allow the coins to be shaken around. Shake the bag well and empty the coins onto a table. Tally up how many heads and tails are showing. Do**

*even number***of this experiment, and record your findings**

*ten repetitions***time. State how many coins you have and present your data in a table or chart. Consider just your first count of the tossed coins. What is the observed probability of tossing a head? Of tossing a tail? Show the formula you used and reduce the answer to lowest terms. Did any of your ten repetitions come out to have exactly the same number of heads and tails? How many times did this happen? How come the answers to the step above are not exactly ½ and ½? What kind of probability are you using in this “bag of coins” experiment? Compute the average number of heads from the ten trials (add up the number of heads and divide it by 10).**

*every***Week 5 Written Assignment**

Following completion of your readings, answer the following two questions from “Chapter 12 Supplement” of*Mathematics in Our World*.

Select ** one even problem** from exercises 1 through 10 on page 810. Select

**from exercises 11 through 22 on pages 811-812.**

*one even problem*As you answer the questions above, identify what types of misrepresentation or misuse have been demonstrated by referring to the bold headings in the “Chapter 12 Supplement” (e.g., Suspect Samples, Asking Biased Questions, Misleading Graphs, etc.).

** a**) all math work required to answer the problems as well as (

**) introduction and conclusion paragraphs.**

*b*The assignment must be formatted according the APA (6th edition) style, which includes a title page and reference page. If you would like to refer to APA samples and tutorials, please visit the Ashford Writing Center, located in the left navigation toolbar.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.

# WEEK 5 QUIZ

If a student’s rank in a class of 400 students is 44, find the student’s percentile rank

To select a _________ sample, the population is divided into disjoint subgroups according to some characteristics like income level, and then a few individuals are selected randomly from each of the subgroups to be in the sample

Find the area under the normal distribution curve to the right of *z* = –3.24

Kate scored in the 95th percentile rank on an exam. If 400 students took the exam, how many students scored lower than Kate?

Find the median and the mean for the data set below.

5.4 2.0 6.8 3.1 2.9 4.7 2.1 5.0 1.9 3.4

For the 20 test scores shown, find the percentile rank for a score of 86.

75 63 92 74 86 50 77 82 98 65 71 89 75 66 87 59 70 83 91 73

Use a scatter plot to deternine the relationship between the *x* values and the *y* values

Fran’s percentile rank on an exam in a class of 500 is 85. Kelly’s class rank is 60. Who is ranked higher?

**Week 5 DQ**

This Discussion will give you the opportunity to calculate or identify the three measures of central tendency. You will be asked to select an appropriate real life situation in which one measure would be more appropriate than the other two measures of center.

Select a topic of interest to you and record the topic in your posting, for example: “What is the average number of hours people watch TV every week?” ** Make sure the question you ask will be answered with a number, rather than answers with words**. Write a hypothesis of what you expect your research to reveal. Example: Adults 21 years and over watch an average of 2.5 hours of TV per day. Sample at least fifteen people and record their data in a simple table or chart; study the examples from Section 12-3. You can gather your data at work, on the phone, or via some other method. This is your “Sampling Design.” Which of the four sampling techniques best describes your design? Explain in moderate detail the method you used to gather your data. In statistics this venture is called the “Methodology.” Make sure you break your sample into classes or groups, such as males/females, or ages, or time of day, etc. Calculate the mean, median, and mode for your data as a whole. Now calculate the mean, median, and mode of each of your classes or groups. Indicate which measure of central tendency

**best**describes your data and

**why**. Then compare your results for each class or group, and point out any interesting results or unusual outcomes between the classes or groups. This is called a “comparative analysis” – using our results to explain interesting outcomes or differences (i.e., between men and women). Comment on at least two of your classmates’ postings. Make sure you comment on their hypothesis (topic), their design, and whether you agree or do not agree with their best measure of central tendency.

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