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Basic Algebra

Racial Inequalities: An Analysis

See the attachments. - White households have on average 22 times the wealth of average Black households and 18 times the wealth of average Latino households - On average, more money is spent on White children than Black and other non-White children in public schools - Public schools are nearly as segregated today as the

Reflection of a line across the line y = x

(a) Write the equation of a line that intersects the negative x-axis and the positive y-axis at points not equidistant from the origin (0, 0). (b) Draw the line. (c) Draw the line that is the reflection of your line across the line y=x. (d) Find the equation of the line drawn in Part (c). Do not convert fractions, if a

Solving equations algebraically

Solve the following equations algebraically. 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 ty sqrt 3 (x) as cuberoot (x) and shraising to the nth power as ^n, like x ^3 is typed x^3. a) t sqrt (2/3) =4 b)5 sqrt (x + 1 )= 3 c)

Algebra: Celebrity Body Mass Index

The United States is becoming more health conscious, and as a result, the problem of obesity has gotten more attention. The Body Mass Index (BMI), relates a person's height and weight, and is often used to determine if someone is overweight. The table below tells the weight status for a given BMI. BMI Weight Status Below 18.5

Let A and B be arbitrary n x n matrices whose entries are real numbers. (a) Use basic matrix laws only to expand (A + B)^2. Explain all steps. (b) Is (A - B)(A + B) = A^2 - B^2 ? Explain as you did in part (a).

1. Given the matrices A, B and C, compute: (a) AC + BC (It is much faster if you use the distributive law for matrices first.) (b) 2A - 3A (c) Perform the Boolean Product operation on the following zero-one matrices. Please refer to the attachment for the complete question. 2. We know that matrix algebra behaves si

Exponential and Logarithmic Functions - Compound Interest

Examples of Exponential and Logarithmic Functions. Excercises to follow. Explanation: Start by writing the beginning amount into cell C1 (pink). The program automatically copies that number to cell B5 (pink), which is the beginning amount for the first period. Type the multiplier into cell C3 (blue). The program automa

Solving by Elimination and Dependent and Inconsistant Systems

1. Solving a system by elimination. Solve each system of equations: a. 2x - y + 3z = 14 b. X + y = 2z = -5 c. 3x + y - z = 2 d. x - 3y + 2z = -11 e. 2x + 4y + 3z = -15 f. 3x - 5y - 4z = 5 2. Dependent and Inconsitent systems. Solve each system: a. 4x - 2y - 2z = 5 b. 2x - y - z = 7 c. -4x + 2y + 2z = 6 3. Paranoia

Force diagrams, vectors and equations of motion

A parachutist and her parachute have a combined mass of 80 kg. She steps out from an aircraft travelling horizontally at 90m s−1 at a height of 300m above the ground, and falls for 5 seconds before instantaneously opening her parachute. In the free fall phase of the motion, take the origin of coordinates to be a point on the g

Introductory Algebra

1. Simplify by factoring. Assume that all variables under radicals represent nonnegative numbers. √(36x^6) Answer or note that the square root is not a real number. Show all work. 2. Use the quotient rule to simplify. Provide answer using exponential notation. Show all work. -12a^5b^6c^12 / 3a^2b^3c^9 3. The amo

Simultaneous Equations: Word Problems

For Halloween, Mr. Olowitz bought 8 bags of candy bars and 4 bags of lollipops for a total cost of $51.56. Later that day he realized he didn't have enough candy and went back to the same store and bought 3 more bags of candy bars and 3 more bags of lollipops for a total cost of $23.82. While in the store on his second trip, Mr.

Approximating real zero, free falling object and profit

Question #1 Given f(x)=6x^4-7x^3-23x^2+14x+3, graph using a graphing tool. Use the graph to approximate each real zero as a decimal, accurate to the nearest tenth. Question #2 For a body falling freely from rest (neglecting air resistance), the distance the body falls varies directly as the square of the time. If an objec

Algebraic Synthetic Division

See the attached file. In problems 1 through 4, write out the polynomial that has the listed factors: Example: (x), (x-1) ANS: x2-x 1. (x-2), (x+3) 2. x, (x-2), (x-1) 3. (x-2i), (x+2i) 4. x, (x-1), (x+1), (x-2) In problems 5 through 8, write the polynominal having the listed roots: 5. i 6. 2, 1,

Simplifying exponential equations

32. Zero exponent. Simplify each expression. 5y^2z(y^-3z^-1) 38. Changing the sign of an exponent. Write each expression without negative exponents and simplify. 5^-2xy^-3 3x^-2 52. The quotient rule for exponents. Simplify each expression. 2r^-3t^-1 10r^5t^2∙t^-3 64. Use the rules of exponents to simplify eac

Miscellaneous algebra questions

1. Rationalize the denominator. √13 - √14 / √13 + √14 2. The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/4 foot wide, 1/2 foot high, and 16 feet long can support 30 tons, find how much a similar beam can sup

Payoff and Opportunity Loss Tables

In the following payoff and opportunity loss tables circle and label the payoff or loss associated with the following decision-making criteria under uncertainty. a. maximax b. maximin c. equally likely d. minimax Payoff Table State of Nature Alternatives A

Inequality in the criminal justice system concerning race

A discussion on inequality in the criminal justice system concerning race. Analyzed are the three videos listed below. Links: - http://www.nytimes.com/video/2012/06/12/opinion/100000001601732/the-scars-of-stop-and-frisk.html - http://abcnews.go.com/video/playerIndex?id=6953414 - http://www.youtube.com/watch?v=VQHdbW36XjE

Divisibility property in mathematics

One of the most often misunderstood concepts in math is divisibility. Divisibility is a different operation than division and the two are often confused. The solution describes the seven key properties of divisibility and proves them mathematically to show the reader that they are true and why they are important. The seven

Mathematics: Fundamental Algebra and Graphing

1. The cost, c, in dollars of a car rental is 10 + , where m is the number of miles driven. Graph the equation and use the graph to estimate the cost of car rental if the number of miles driven is 34. A) About 24 dollars B) About 15 dollars C) About 36.5 dollars D) About 19 dollars 2. Graph the two lines x + 2y

Explanation of Mathematical Expressions Using Examples

I am confused with the concept of mathematical expressions. How can I tell when a collection of operations and numbers is an expression? Is "234x + - ÷ 14 - 23 46 -" an expression? Can you help me understand this concept? Thanks

Applying Algebraic Formulas

1. Against the wind small plane 858 miles in 2 hours an 10 min. Return trip took 1 hr. and 50 min. What was the speed of the wind? What was the speed of the plane in still air? 2. A basketball scored 12 times during 1 game. He scored a total of 19 points, 2 for each 2 point shot, and 1 for each free throw. How many 2 pt.

Antibiotics Study

The following paragraphs are taken from the article, "Antibiotics' Role in Heart Attacks to Be Focus of Study." (Source: The Morning Call, April 5, 1999.) "Could taking an antibiotic spare heart patients future heart attacks, bypass surgery or death? "Researchers hope to find out with a large, federally funded study based

Energy of a particle attached to 3 springs

I am having trouble with the type of question listed below and any help would be greatly appreciated. I have attached a diagram also. A block P of mass m is attached to three springs whose other ends are attached to fixed points A, B and C. I have listed the stiffnesses of the three springs and their natural lengths below. Th

Complete Induction Proof Help

I'm currently working on this problem and I know that P(1) = 0, P(2) = 1, P(3) = 3, P(4) = 6 so P(i+1) = P(i) + i but I'm kind of confused how to structure it... Here is the complete question: Consider a 1-player game using a bag of n marbles. The player starts by dividing the bag of marbles into two groups (so that each g

Function Multiplication, Equation of a Circle & Tangent Line

Please see the attached file for the complete solution. (1) The table gives the values of the functions f and g. Use the table to evaluate the expressions below. If there is not enough information given, state the information you would need to evaluate the expression. x 0 1 2 3 4 5 3 5 0 2 1 4 2 7 1 5 3 0 a.] g(f

Zero Factor Property and Inequalities

The zero factor property: A) p^2 - p = 42 B) 16x - x^3 = 0 C) (x + 2)(x + 3) = 20 Solve each equation for y. Assume a and b are positive numbers: D) y^2 + ay + by + ab = 0 Applications: E) Tennis court dimensions. In singles competition, each player plays on a rectangular area of 117 square yards.

Abstract Algebra: Homomorphisms, Isomorphisms, and Automorphisms

Problem 1. Prove that Z / <n> ≈ Z_n , where n ∈ Z and n > 1. Problem 2. Prove that θ : g --> a^{-1} ga for a fixed a ∈ G and all g ∈ G defines an automorphism of G. Problem 3. Prove if H is the only subgroup of order n in a group G, then H is a normal subgroup of G. ** Please see the attachment for formatted q

Abstract Algebra: Prove Some Results About Subgroups

1. Define (C_G)(H) = {g is a number in G: g h = h g for all h is a number in H), where H is a subgroup of the group G. Prove that (C_G)(H) is a subgroup of G. Note: (C_G)(H) is called the centralizer of H in G. 2. Define (N_G)(H) = {g is a number in G: gH = Hg], where H is a subgroup of the Group G. Prove that (N_G)(H) is a s

Abstract Algebra: Identity Element of the Group

1. Prove that is a is a number in G, a group, and ab = b for some b of G, then a = e, the identity element of the group. 2. Consider the set of polynomials with real coefficients. Define two elements of this set to be related if their derivatives are equal. Prove that this defines an equivalence relation. 3. Let H be a s

Standard Form and Factored Form

Please refer to the attached document for the full problem set. 20. Consider the polynomial P(x), shown in both standard form and factored form. P(x) = (1/10)x^4 - (1/2)x^2 + (41/10)x - 3 = (1/10)(x+3)(x-1)(x-2)(x-5) (a) Which sketch illustrates the end of behaviour of the polynomial function? (b) State the y-intercept.