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Basic Algebra

Substituting series expansions into each other

Consider the formal power series f(x) = x + x^2/2 + x^3/6 + x^4/24 and g(x) = x - x*/2 + x^3/3 - x^4/4. Compute by hand the first five coefficients (i.e., up to the coefficient of x^4) of (a) h(x) = x^f(x) (d) k(x) = log(1 + g(x)) (c) m(x) = (h o k)(x)

The solution of basic algebra problems

Use Equation Editor to write mathematical expressions and equations. 1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C = 6,000/(200 - 2x) a. What is the cost to remove 75% of the pollutant? b. What is the cost to remove 90% of the pollutant? c. What is the cost to remove 99% of t

Find the generating function for the strings

Find the generating function with respect to length for the set of {0,1}- strings having the property that each block of 1's contains an even number of 1's and each block of 0's contains an of number of 0's.

simplifying the square and finding values

2. simplify the square of 96b(cubed)/144a(4th power) 3. Find the value(s) of b that would make the following true: 5b(squared)-125=0. 4. Solve using the quadratic formula: 2x(squared)+2x=3. 5. State the number of zeroes for each equation: x(squared)=4x x(squared)+9=6x x(squared)+25=0 6. a mode

total overtime wages

Consider the following aggregate production planning problem: January February Dema Demand 100 units 120 units Produ Production plan

Profit equation as a function of output using demand equation

Mickey Mouse has a trap company with fixed costs of $89,000 and operating costs of $50 per trap and a market demand curve of: price=950-.10(output). Since Mick can't set his price find the revenue equation for his mousetrap business. a) Construct the profit equation as a function of output using the demand equation. What doe

The Malthusian and Logistic Models of Population Growth

Please see the attached file. This is one question but broken in parts. Formula for Malthusian Model: dP/dt = r*P Formula for Logistic Model: dP/dt=rP(1-P/K) PS> I Prefer hand written work showing the steps if it is neat. It's up to you..I just have a hard time reading fractions & exponents in a word document etc.

In what ways can the cycle of inequality be broken in schools?

Savage Inequalities is a wonderful book to reference here as it does point to the problem of inequitable funding. In other words the poor stay poor because the school is funded disproportionally from community to community. This then impacts society's views of certain minorities and the poor, but then it also continues to fuel t

Calculate the value of given bonds.

Question 1 Pacific Homecare has three bond issues outstanding. All three bonds pay $100 in annual interest plus $1,000 at maturity. Bond S has a maturity of five years, Bond M has a 15-year maturity, and Bond L matures in 30 years. a. What is the value of these bonds when the required interest rate is 5 percent, 10 per


Question 19 of 19 4.0 Points The ABC Cement Corporation produces three varieties of high quality cements that are supplied to construction companies. The annual demand for all these varieties and their corresponding probabilities for the year 2010 are as follows. the year 2010 are as follows. Variety Demand (in tons) Probabil

Algebra word problem

The butcher, the baker, and the candlestick maker purchased a lottery ticket together and won $36,000 in the weekly lottery drawing. Since the three friends each have different risk tolerances and investment strategies, they decided that each of them would receive a certain amount of money to invest for the future. The butc

Basic Algebra: Polynomial, Exponent and Percentage

See attachment and please show your work. 1. Add (7x^3 - 6x^2 + 8x) + (6x^3 + 8x^2 -13) 2. Subtract. (2v^5 + 7v) - (-8v^5 - 6v + 7) 3. Subtract. (8x^4 + 4x^3 - 1) - (9 x^2 - 3x + 8) 4. Find the hole using the percent equation. 35 patients is 50% of what number of patients? 5. Use the product rule to simplify the ex

Determining Payments for a Loan

Eric is paying $39 per week to pay off a loan for $14,568.  How many weeks will he have to make payments to pay off the loan? How much will his last payment be?

Integral Domains and Principal Integral Domains

See attached file. I am having problems with a couple of abstract algebra problems regarding integral domains and principal integral domains (PIDs). A commutative ring satisfied the DCCP if <a1> ⊇ <a2> ⊇ <a3> ⊇ ... implies that an ~ an+1 ~ ... for some n ≥ 1. Show that an integral domain R has DCCP if and only

Sketching Graph Function Calculators

1. If f(x) = x^2 - 3x determine the following (i) f(-2) (ii) f(-2a) (iii) f(2-a) 2. (i) Use your calculator to sketch a graph of the function f(x) = 2/sqrt(9 - x^2) (ii) Explain the restrictions to the domain of the function. (iii) Name and describe the feature of the graph th

Number and Inequalities

Question 2 Number and Inequalities 1.A cylindrical vessel with one end open is made from a given piece of material. Show that its volume is greatest if the height and radius are equal. 2. a,b,c are non zero rational numbers. Show that if: ³√a + ³√b + ³√c = 0 And if none of ³√a , ³√b , ³√c is rat

Factoring help is given.

ection 6.2 Factor the trinomial completely: Questions 66/67 66. 5b3 - 5b2 - 60b (the small numbers indicate to the 3rd and 2nd powers respectively). 70. 6n^4 - 18n^3 + 12n^2 Section 6.3 Questions 56/58 Factor the trinomial completely. 56. 8y3 - 16y 2 + 6y 58. 10y3 + 5y 2 - 5y Section 6.

Algebra: estimate numbers

Radio Stations The approximate number of radio stations on the air for selected years from 1950 to 2000 is shown in the table. x (year) 1950 1960 1970 y (stations) 2800 4100 6800 x (year) 1980 1990 2000 y (stations) 8600 10,800 12,600 Make a line graph of the data. Be sure to label both axes. Discuss ways to es

Four Steps for Solving Quadratic Equations

Explain the four steps for solving quadratic equations? Can any of the steps be eliminated? Can any of the steps be changed? Would you add any steps to make it easier, or to make it easier to understand?

Use algebra to solve these problems about firms' costs and prices.

1. A company has a total cost of $50.00 per unit at a volume of 100,000 units. The variable cost per unit is $20.00. What would the price be if the company expected a volume of 120,000 units and used a markup of 50%? a) $75.00 b) $62.50 c) There is not enough information in the problem to answer d) $67.50 2. Umbrella Co

Annuities are explicated.

Part I. Basic Computations 1. Mike's Sport Shop deposits $3,600 at the end of each year for 12 years at 7% annual interest. a. How much will this ordinary annuity be worth at the end of the 12 years? (5 points) Answer: b. How much more will this annuity be worth (annuity due) if Mike deposits the money at the

Algebra Problems to Finding Speed

Please help with answers to the attached question/problems. I need the detail instructions as to how problems are figured out. Section 2.2 Question 58 1/3x + 1/4 =1/6-x Question number 72 5x = 15-2 (x + 7) Section 2.3 Question Number 32 (Word problem) There were 77 birds on the endanger species list in 20

Exercise and Heart Rate Polynomial Problem

** Please see the attached file for the complete problem description ** I need help of Exercise 79. Please look at attachment where I marked the question that I need help. 79. Exercise and Heart Rate The polynomial given by 1.6t^2 -28t + 200 calculates the heart rate shown in Figure 5.4(b) where t represents the elapsed t

Lowest Common Denominator

Provide answers and step by step instructions on the problems: 1. What is the value of "y" for the given value of x and z y= x +z x=3 z=15 2. Rewrite each fraction with the Lowest Common Denominator 4/15, 2/9, 3/5 43/36 + 3/5 + ¼ 3. Order of operations evaluate the following 5 x (3-2) to the 8th

Algebra Questions Velocity

MATH133 Unit 3 - Individual Project 2 Solve algebraically. Trial and error is not an appropriate method of solution. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type 3x as cuberoot (x) and show raising to the nth power a

Four Methods for Solving a Quadratic Equation

Four different methods of solving a quadratic equation have been discussed: factoring, the square root property, completing the square, and the quadratic formula. Explain under what circumstances each method would be preferred over any of the other methods. Give an example for each circumstance.

Algebra word problems

I am having difficulties with two practice word problems attached. Please help. Word Problems: 1. The octane rating of a gasoline is a measure of the amount of isooctane in the gas. Subaru recommends 91-octane gasoline for the 2008 Legacy 3.0 R. How much 87-octane gas and 93-octane gas should Kelsey mix in order to make 12 g

Linear Formula & Money Problems

In 2000, the average cost of tuition and fees at public four- year colleges was $3500, and in 2005 it was $5100. The supporting information is listed below. Note that the known value for 2001 is $3700. 1.) Cost of Tuition Plot (00,162) and (5,201) to see the shape of the line Slope= (201-162)/5 = 7.8

Exponential Smoothing Model: Review

In an exponential smoothing model, if the smoothing constant (alpha) were equal to 0, then a. the forecast would never change. b. the forecast would be the same as the forecast for the naive model. c. the MAD would always equal 0. d. the forecast would be impossible to calculate.