Real world applications
XXX
MAT126: Survey of Mathematical Methods
Instructor: XXX
May 20, 2012

In this assignment I would like to talk about arithmetic sequences and geometric sequences and want to give an example each how to calculate with those sequences. First I want to give a short definition of each sequence. “An arithmetic sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount. This amount is known as the common difference.” (Bluman, A. G. 2500, page 221) An example for an arithmetic sequence is:

1, 3, 5, 7, 9, 11, … (The common difference is 2. (Bluman, A. G. 2500, page 221) “A geometric sequence is a sequence of terms in which each term after the first term is obtained by multiplying the preceding term by a nonzero number. This number is called the common ratio.” (Bluman, A. G. 2005, p. 225) Here you can see that there is always added 2. 1 + 2 = 3; 3 + 2 = 5; 5 + 2 = 7; 7 + 2 = 9; …

An example for a geometric sequence is:
2, 10, 50, 250, 1250, … (The common ratio is r = 5 (Bluman, A. G. 2005, p. 225) Here you can see that the 2 is multiplied by 5, which is 10. Then the 10 is also multiplied by 5, which is 50 and so on. 2 x 5 = 10; 10 x 5 = 50; 50 x 5 = 250; 250 x 5 = 1250; …

In this assignment I have solved two exercises, one referring to arithmetic sequences and one referring to geometric sequences.

Exercise 35:
A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the next 10 feet will cost $125, the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower? (Bluman, A. G. 2005, page 230) I have calculated it this way:

n = the number of terms together; n = 9 (because the CB radio tower will be 90 feet high. One term are 10 feet, so 90 feet are 9 terms) d = common...

...Week 4 Assignment1MAT126
August 5th 2013
Following completion of your readings, complete exercise 4 in the “Projects” section on page 620 of Mathematics in Our World. In the two step process is to sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this. Then after building the triples, verify each of them in the Pythagorean Theorem equation.
The Pythagorean Theorem is based on Euclidian Geometry among the relation between the three sides of a right triangle which basically states a2+b2=c2. Or the fact that a2 = one side of the right triangle + b2 = 2nd side of the right triangle equals C2 or the hypotenuse.
For this assignment I figured I would do 2 proof types for each triple.
For any natural number m>1,
a2+b2=c2
(2m)2 + (m2-1)2 = (m2+1)2
Example1:
m= 4
2m = 8 = side A of right
m2-1 = 15 = side B of right
m2+1 = 17 = side C of the right (Hypotenuse)
Pythagorean triple (8,15,17)
Proof:
(2m)2 + (m2-1)2 = (m2+1)2
(2*4)2+(42-1)2=(42+1)2
(8)2+(16-1)2=(16+1)2
64+225=289
Proof2:
a2+b2=c2
82+152=172
64+225=289
Example2:
m=6
2m=12 = side A of right
m2-1 =...

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This document MAT126Week1 Quiz contains solutions on these questions:
1. In a survey of 24 college students, it was found that 16 were taking an English class, 17 were taking a math class, and 10 were taking both English and math. How many students were taking a math class only?
2. Find the general term of the set. {8, 12, 16, 20, 24, . . .}
3. Let U = {5, 10, 15, 20, 25, 30, 35, 40}
4. 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 exactly two of the three writing instruments?
5. Write the set using set-builder notation: {natural numbers greater than 11}.
6. Find the number of subsets the set has. {1, 2, 3, 4, 5, 6, 7, 8, 9}
7. Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find A ? B.
8. Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 7 8 10 13 17 22 28 ____
9. The process of arriving at a general conclusion based on the observation of specific examples is called ___________
10. Which...

...MAT 222: Intermediate Algebra
Title Page
Solving a proportion as we learned this week, means that you are missing an import number in your equation or fraction, and you need to solve for that missing value. As in my example, I did not know what percentage of bills we each should pay. We knew each other’s salaries; but we really had to sit down, crunch numbers, and figure it out.
For this week’s assignment we were asked to work through two proportions. For the first proportion, number 56 on page 437 of Elementary and Intermediate Algebra by Dugopolski: estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population?
Beginning to solve this equation first, we needed to make a proportion with the number of tagged bears in the sample and in the population:
Number of the tagged bears in the sample compared to the sample size equals the number of tagged bears in the population: Population size. The population size is “x”, we need to solve for “x” as such:
2/100 = 50/x
Cross multiply or use the extremes means property
2 * x = 100 * 50
2x = 5000
Because we want to solve for “x” we must isolate it by dividing both sides by two.
x = 5000/2 = 2500
Answer: x= 2500 bears
For the second problem, number 10 on...

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This work MAT126Week1Assignment - Geometric and Arithmetic Sequence shows "Survey of Mathematical Methods" and contains solutions on the following problems:
First Problem: question 35 page 230
Second Problem: question 37 page 230
Mathematics - General Mathematics
Week One 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 Guide and 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 ( b ) introduction and conclusion paragraphs.
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...

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MAT 540 WEEK1 TO 11(Strayer)
MAT540 Week1 Homework
Chapter 1, Problems 2, 4, 12, 14, 20, 22
2. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $60,000.The variable cost of recapping a tire is $9.The company charges $25 to recap a tire.
a. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire Company operation.
4. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the company.
12. If Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer from $0.40 per pound to $0.60 per pound, what effect will the change have on the break-even volume?
14. If Evergreen Fertilizer Company increases its advertising expenditures by $14,000 per year, what effect will the increase have on the break-even volume computed in Problem 13?
Reference Problem 13: If Evergreen Fertilizer Company changes its production process to add a weed killer to the fertilizer in order to increase sales, the variable cost per pound will increase from $0.15 to $0.22. What effect will this change have on the break-even volume computed in...

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Ashford MAT 222 WEEK1 TO 5
Week1, Assignment, Solving Proportions
Read the following instructions in order to complete this assignment:
1. Solve problem 56 on page 437 of Elementary and Intermediate Algebra. Set up the two ratios and write your equation choosing an appropriate variable for the bear population.
2. Complete problem 10 on page 444 of Elementary and Intermediate Algebra. Show all steps in solving the problem and explain what you are doing as you go along.
3. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:
Your solution to the above problems, making sure to include all mathematical work, and an explanation for each step
A discussion of the following: What form of an equation do you end up with in problem 10? What do you notice about the coefficient of x compared to the original problem? Do you think there might be another way to solve this equation for y than with the proportion method? How would you do it?
An incorporation of the following four math vocabulary words into your paper. Use bold font to emphasize the words in your writing. (Do not write definitions for the words; use them appropriately in sentences describing...

...of the calories come from fat. The package states this amount as well, but they rounded it down to 3% even. This is the only package that seems to be extremely close to accurate.
The last package I chose was cheetos puffs. Now this is my favorite snack food of all time and I consume quite a bit of them on a daily basis, so I am hoping that the damage isn’t too devastating.
Total grams of fat= 10g
Calories per gram of fat= 4
Total calories= 150
Work: 10x4=40 (40/150)*100= .2666*100= 26.67= 26.67%
This means that 26.67% of the calories are from fat. Whereas the package states that the percentage is 15%. This is much worse than I was hoping it would be, but I am not at all surprised by this development.
After completing this assignment I much more aware of how careful I need to be when making my food choices. Sometimes I take the convenience of a meal into mind more so than the actual health of it all. It is definitely time for us to start calculating what exactly our food is consisted of, and what we are putting in our bodies.
References
Bluman, A. G. (2011). Mathematics in our world (1st ed. Ashford University Custom). United States: McGraw-Hill....

...able to evaluate own ability to lead others
When during initial meetings the manager elicits the attention and the respect of all the employees, by explaining the objectives that should be reached within a time frame mainly selling a number of products within a set time frame and try to attract clients namely in the range of hundred a week. The manager appreciates the talents of the employees and tells them so specifically; “I know that you can succeed; I have full trust in all of you. However in case you need clarification or information or direction I am at your full disposal whenever you feel you want to contact me, all of you have been duly trained and I have been through your personal files and know that you can make it, so we can start as from today”. Frank two-way discussions between the manager and the employees will do away with any pent-up feelings and employees will relish the opportunity to provide their verbal contributions. This informal opportunity to disseminate and accumulate information will be the right forum to avail oneself of the entire information possible, do away with misinformation and disintegrate prejudices. Every week an analysis is carried out by the manager to check whether the objectives have been reached or whether new adjustments have to be made or maybe change the benchmark in so doing the manager has the ability to know where he stands for future reference and adapts the approaches for his personnel...