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# Algebra

### Percent markup

You belong to a wholesale buying club. You can order items from the club with a markup of 8% over the wholesale price. A local retail store, which gets its merchandise at the same wholesale price, offers to sell you those same items at 10% off the shelf price. What does the retail store's markup have to be for it to be cheaper f

### Explaining the Sum of a Sequence

You want to explain 2+ 4 + 6 + . . . + 2n = n (n + 1), to a class of students with diverse learning styles. Use the Four-Step Problem-Solving Process: 1) State the problem in words. 2) What are you trying to find? 3) What are the unknowns? 4) What information do you obtain from the problem? 5) Gi

### Solving Systems of Equations Word Problems.

One serving of Cornie breakfast cereal contains 2 grams of protein and 25 grams of carbohydrate. One serving of Oaties breakfast cereal contains 4 grams of protein and 20 grams of carbohydrate. How many servings of each would provide exactly 24 grams of protein and 210 grams of carbohydrate? please show calculation

### Disproving an Intersection Equality by Couterexample and Writing a Converse

Let A, B, and C be any three sets and consider the sentence: If A &#8745; B = A &#8745; C then B = C. (a) Prove in detail that this statement is false. (Give a counterexample.) (b) Write the converse of the above statement and show through an example that it is true (no proof is necessary).

### Word Problem: How Many Litres Used

There were 4.91 liters of solution B available in the science lab. Wayne used 0.87 of that amount. By rounding to the greatest place, estimate how many of liters he used? Please show all steps used.

### Solve groups and proofs

1.) Show that Z(II_alpha G_alpha)=II_alpha Z(G_alpha) 2.) Show that (G_1 x G_2 x ... x G_n)' = G'_1 x G'_2 x ... x G'_n 3.) Under what circumstances is G_1 x G_2 x ... x G_n solvable? Note that II_alpha is the product over all alpha of an index set.

### Radical Functions and Word Problems

Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work. (You may type cuberoots as cbrt(x) and show raising to the nth power as ^n, like x^3.) Find x: a) (1/4) = 3 - (2x-1)/(x+2) b) x^(2/3) = 125 c) cbrt(x) - 4 = 2 2) Solve algebraically and chec

### Project Management : Network Diagrams, Start and Finish Times and Crashing

Wild Cat Petroleum Company has struck oil on their latest drilling project in central Africa. You are responsible for developing a minimum cost schedule to bring the first wellhead into production. Unfortunately, local workers are not available due to the continuing unrest in the surrounding territory (a lingering civil war).

### Deducting Miles as a Business Expense

Question Jane Manning, an outside business woman, uses her car for both business and pleasure. Last year, she traveled 30,000 miles using 900 gallons of gas. Her car gets 40 miles per gallon on the Highway, and 25 mpg in the city. She can deduct all highway travel, but no city travel, on her taxes.

### Word problem

A local horse rancher died early one morning and his will bequeathed his herd of racehorses to his three sons. The will specified that the herd must be divided exactly; and 1/2 of the horses should go to the eldest son, 1/3 of the horses to the second son, and 1/9 of the horses to the youngest son. Unfortunately for the sons at

### Writing equations from description

A company pays a monthly rent of \$3,000 per month for the office space and it pays \$1,000 to each employee every month (there is a total of 12 employees). In addition each employee gets a bonus of \$10 for each unit they complete during the month. The company's revenue is \$18 for each unit completed by the employees. Answer the f

### Calculating EMI for a loan

You want to buy a car. Based on your current finances, you have up to \$3,200 in savings that you can use for a down payment. You believe you can afford no more than \$160 per month in loan payments. Offer Number 1: An individual you trust will sell you a used car for 10% off the Blue Book value of \$9,800. Your company credit u

### Regression and Cost Functions

Chapter: 1, exercise 18 18. Refer to the Wage data, which reports information on annual wages for a sample of 100workers. Also included are variables relating to industry, years of education, and gender for each worker. a. Which of the 12 variables are qualitative and which are quantitative? b. Determine the level of me

### Linear second order recurrence sequence

Find a closed form for uo = 2 u1 = 7 un + 2 = 2un + 1 + 8un (n = 0,1,2,3,.......) (The o,1 and n terms are subscript). The techniques given is using a auxillary equation - finding a generalised solution where A and B are unknown constants. Finding A and B using the initial terms: Auxillary equation r^2 - 2r - 8 (r -

### Solving Values for Functions

1.Here is a nonlinear function: f(x) = sqrt(x) - 3 Inputs: f(4) and f(9) 2. f(x) = x^2 f(4) 3.F(x) =2x-5² X = 10 X = 20 4.Linear Equation y = 3x+7 function x=10 Two equations f(10) = 3(x) -20 f (20) = 10(x) -50a

### Generating Equations from Description

Identify the variables and write equations that describe each situation. Also solve the generated equations. 1. Two complimentary angles have degree measures p and 3p-6. 2. American pro. plans to lay off 10% of its employees in its aerospace division and 15% of the employees in its agricultural division. If altogether 12%

### MTH133: Unit 1 Individual Project - B

For noninteger answers, please write your answer as a fraction rather than a decimal. To show your work, you will need to include o the algebra used to compute the solution to any equations. o the formula with substituted values. o the final calculated answer with units Please see attachmen

1. Show work here: Final Answer: 2. Solve . You must show all work to receive full credit. Show work here: Final Answer: 3. The cell phone service for the CEO of a small company is \$39.99 a month plus \$0.10 per minute for long distance. In a month w

### Unsolvable series

Find the derived series for S_4 Show that S'_n=A_n if n is not equal to 2 and conclude that S_n is not solvable if n is greater than or equal to 5. I need a detailed proof of this to study please.

### Greatest common divisor

2. (a) Determine gcd(987, 320). (b) Determine integers x and y such that 987x + 320y = gcd(987, 320). 3. (a) Determine gcd(&#8722;2193, 1008). (b) Determine integers x and y such that 1008x &#8722; 2193y = gcd(&#8722;2193, 1008).

### Problem from Lewis Carroll

Problem from Lewis Carroll: There are two cups, the first one contains 50 spoonfuls of brandy, the second one 50 spoonfuls of water. Someone takes a spoonful from the cup with brandy and empties it into the water cup, mixes well, and then takes a spoonful of the mixture and empties it into the first (brandy) cup. Does

### Prime simple subgroups

a) Show that if |G|= pq, where p and q are prime, then G is not simple. b) Show that the only simple groups of order less than 36 are of prime order.

### QUARDS.

ATTACHED FILE. MTH133 Unit 4 - Individual Project - A Name: 1) State the domain of the following and provide a brief explanation for your answer: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the following graphs

### Mathematics

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to

### Proofs : Grorups, Subgroups and Indexes

1.) If |G|=p^n for some prime p, and 1 is not equal to H, a normal subgroup of G, show that H intersect Z(G) is not equal to 1. 2.) Suppose G is finite, H is a subgroup of G, [G:H]=n and |G| does not divide n!. Show that there is a normal subgroup K of G, with K not equal to 1, such that K is a subgr

### Determining Maximum Area: Enclosing a Pasture Example

A farmer has \$2250 to spend on fencing material to enclose a pasture using an existing river as one side. If the fencing material costs \$25 per yard, what is the maximum area he can enclose in square feet?

### Simplify and Solve Length of Side

Jim's nephew owns a triangular plot of land. The perimeter fence that surrounds the land measure 121 feet. The shortest side is 15 feet longer than one-half the longest side. The second longest side is 4 feet shorter than the longest side. What is the length of each side.

### Variation

Direct, Inverse, and Joint Variation Write a formula that expresses the relationship described by each statement. Use k for the constant in each case 6. m varies directly as p 8. u varies inversely as n. 18. c varies inversely as d, and c _ 5 when d _ 2. Solve the variation problem 26. n varies directly as q, an

### Simplifying and Solving Problems with Exponents

Solve for x 6x+21-4x+21=4 4x-6=x+3 Simplify (-3x-3x^5-3)+(-9x^5 - 3+7x) a)-12x^5 -6x-6, b)-12x^5 -46x+4, c)-12x^5 +4x, d)-12x^5 +4x-6 Simplify (8g^3 +6)-(3g^2 -3)+(3g^3 + 2g^2) Simplify (4x^3 + 4x^2 + 4)-(5x^3 - 7x^2 +6x - 4) a)-x^3 +11x^2 -6x+8, b)x^3 -11x^2 +6x, c)-x^3-11x^2 -6x, d) -x^3-11x^2+6x+8

### 'Why do we have to learn the metric system?'

One or more of the students in your class asks: "Why do we have to learn the metric system?" How do you respond? A student in your class calculating the slope between points (8,5) and (8,20) gets 15/0. Using their calculator, the result of 15/0 shows "Error". They ask you "How can a calculator make an error?".