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    Basic Algebra

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    Finding the Number of Motor Vehicle Deaths

    The number of motor vehicles deaths increased by 13.75 times from 1912 to 2003. There were 39,525 more deaths in 2003 than in 1912. Find the number of motor vehicle deaths in each of the two years. Note that the number of motor vehicles on the road increased from 1 million to 230 million between 1912 and 2003.

    Algebra Problems Simplification

    Simplify the following expression. square root of negative 8 square root of negative 24 Simplify the following expression; express in terms of i. square root of negative 48 Simplify the following quotient of complex numbers into the form a + bi. negative 8 minus 8i over 1 plus 2i

    Annual profit functions

    Annual profit in thousands of dollars is given by the function, P(x) =5000 -(1000/(x -1)), where x is the number of items sold in thousands, x > 1. I need to find out how to come up with this solution? Find the profit for 5 different values of x. P(x) = 5000 - (1000/(x-1) P(2) = 5000 - (1000/1) = 4000 P(3) = 5000 - (1000/2)

    Proof about integers and rationals

    let x,y,z,w be rational numbers a) Let epsilon>0. If x is epsilon-close to y, then y is epsilon-close to x. b) Let epsilon, gamma >0. If x is epsilon-close to y, and y is gamma-close to z, then x and z are (epsilon + gamma)-close. c) Let epsilon>0. If y and z are both epsilon close to x, and w is between y and z (i.e..

    Find x value in quartic equation

    To solve the quartic equation, one of the approaches is to seek squares on both sides. For example, to find x, in ax^4+bx^2+cx=d. One way is to convert the equation to the following format: (square root of a x^2+e)^2=(gx+h)^2. However, when a, e, g and b becomes irrational number, it is difficult to apply this strategy. Here, I

    Asymptotic Behaviors of Various Functions

    1) Determine the order of the following expressions as ??0: ?(?(1-?) ), (4?)^2 ?, 1000?^(1?2), ln?(1+?), (1-cos??)/(1+cos?? ), ?^(3?2)/(1+sin?? ), ?^(3?2)/(1-cos?? ), sech ^(-1) ?, exp?(tan?? ), ln[1+(ln?(1+2?))/(1-2?)], ln[1+(1+2?)/(?(1-2?))], ?_0^? exp?(-s^2)ds. 2) Arrange the following in descending order for ??0.

    Word problem

    A girl is celebrating her seventh birthday. Each guest is served one large slice of chocolate cake, a hamburger, French fries, and some oranges. Identify the food groups mentioned above. If one slice of chocolate cake contains 35g of carbohydrate, 15g of fat and 5g of protein, calculate the kilocalories that each slice

    Scale factor after dilation

    find the scale factor after a dilation centered at the origin if H(4*square root of 2, -3 square root of 5), P (-2 * square root of 2, 2 * square root of 5) and H(square root of 128, - square root of 180) P(- square root of 32, square root of 80)

    Congruent Modulo m

    Please submit solution as a PDF or MS Word file. Prove proposition 4. Proposition 4: If m?2 is a fixed integer and a,b,c?Z then: (1) a?a mod m (2) If a?b mod m then b?a mod m (3) If a?b mod m and b?c mod m, then a?c mod m Much thanks!

    How to calculate net income

    Company reports the following operating results for the month of August: Sales $350,000 (units 5,000); variable costs $210,000; and fixed costs $90,000. Management is considering the following independent courses of action to increase net income. 1. Increase selling price by 10% with no change in total variable costs. 2. R

    Two Proofs for a Modern Algebra Class

    Please help me learn how to write these two proofs correctly for my Modern Algebra class. Please submit all work as either a PDF or MS Word file. ** Please see the attached file for the complete problem description **

    Samples of Basic Algebra

    1. If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4 marbles can be drawn? 2. Seven workers decide to send a delegation of 2 to their supervisor to discuss their grievances. a. How many different delegations are possible? b. If it is decided that a certain employe

    Concept Checks for Binomial Coefficients

    1. Determine the binomial coefficient for the fifth term in the expansion of (x+y)^9 Write the binomial expansion for each expression: 1. (a-b)^7 Write the indicated term of each binomial expansion: 1. Twelfth term of (2x+y^2)^16

    Slopes, Lines and Graphs

    An airplane climbs from sea level to a cruising altitude of 31,500 feet at a rate of 6300 ft/min. After cruising for 20 minutes, the airplane begins its descent at a rate of 3500 ft/min. If we were to sketch a graph of the airplane's flight pattern, which measurement would the x-axis represent? Which measurement would the y-axis

    Properties of Logarithms and Simplification of Expressions

    Use the properties of logarithms to rewrite each expression. Simplify the result if possible. 1. log2 ((2*square root 3)/5) Given log10 (2) = 0.3010 and log10 (3) = 0.4771, find each logarithm without using a calculator. 2. log10 (20/27)

    Variation Problems

    Solve each variation problem: 1. If m varies jointly as z and p, and m=10 when z=2 and p=7.5, find m when z=5 and p=7. 2. Current in a circuit: The current in a simple electrical circuit varies inversely as the resistance. If the current is 50 amps when the resistance is 10 ohms, find the current if the resistance is 5

    College Algebra: Polynomial Functions

    For each polynomial function, find all zeros and their multiplicities: 1. f(x)=(x+1)^2(x-1)^3(x^2-10) Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions: 1. Zeros of 2, -3, and 5; f(3)=6 2. Zero of 4 having multiplicity 2 and zero of 2 having multiplicity 1; f(1)= -18

    Problems in Galois Theory Involving a Cubic PolynomialK

    Let f be a cubic monic polynomial and char K not 3. a. Show how to make a change of variables x' = x - lamda in f (x) = 0 to reduce to a monic equation where the coefficient of x^2 is zero b. Suppose K = R. Let D be the discriminant of f. Prove that f has one real root if D < 0 and three real roots if D > or equal to 0. c. Le

    Forward Rate for the Japenese Yen

    Use the information below to answer the following questions. (Do not include the dollar signs ($). Round your answers to 4 decimal places, (e.g., 32.1616)) CURRENCY PER U.S. $ Japan Yen 115.76 6-months forward 112.91 Canadian Dollar

    Double angular formula

    Find the exact value of a) sin a/2, b) cos a/2, C) tan a/2 tan a= 4/3, a lies in quadrant 3 sin a/2 = cos a/2 = tan a/2 = (type an exact answer, using radicals as needed. simplify answer)

    Applications of rational expressions

    Look at the example application of rational expressions on page 315 of your textbook. Then, using the Internet, locate a Web site that has an additional example that interests you. (Use the search words "rational expressions applications.") Following the example of problems 51-54 on page 315, formulate two to three values for yo

    Expected value of certainty in investments

    What is expected value under certainty of the following investments, and the expected value of perfect info In a good market in a bad market Houses +10 -5 Dogs +7 -4 Cats +5 -2 Chances of bad market 60%

    Half angle formulas

    Use the given information to find the exact value of a) sin alpha/2 = b) cos alpha/2 = c) tan alpha/2 = when sec alpha = -17/8, alpha lies in quadrant 2 (Type an exact answer, using radicals as needed. simplify answer)

    Solving and graphing Quadratic equations

    Some homework practice I would like your assistance to prepare for exam. 1. Y^2-6y+9=8 ( exact solutions to three decimal places) Y=_______ 2. Solve 7x+x(x-4) = 0 the solution is x = _________ Find the x intercepts of f(x) = 7x+x(x-4) the x intercepts are _____ 3. F(x) = -1/2x^2 The vertex is _______

    Factor the following expression completely.

    Please explain how to solve the given problems. Factor the following expression completely. 1. 81m^3-63m^4+8m^5 Solve each quadratic equation by whatever method you choose. Round the answer to the nearest tenth, if necessary. If there is no answer, mention that clearly. 2. 56-y^2 = 0 3. 5x^2+13x-1=0 4. x^2+3x=-6

    Mathematics and Language

    1. Is math independent of human influence? Why or why not? 2. Why is it important for math to have its own language? What other disciplines have their own language?