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# Algebra

### The production costs modeled in a linear equation

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total \$49,345., and the variable costs will be \$9.75 per book

### Word Problem

Here is the question: A small city contains 2500 people. If the population doubles every 25 years. How large will the population be in 225 years?

### Example of a Mixture Type of Problem

1. If a < b, then -a > -b. Why? 2. What is the inherent meaning and justification of cross-multiplication as it applies to solving an inequality? 3. How can you differentiate between a function and an equation? 4. Give an example of a mixture type of problem along with the answer.

### Finding the Wingspan of a Bird

I need help figuring this problem out. find the average weight in pounds of a type of bird of your choice. Use the rational exponent equation L = 2.43 * W^0.3326 to estimate the wingspan L in feet of the bird that weighs W pounds (Rockswold, 2006). Include in your post the type of bird and the average weight and show the calc

### Compounding interest daily with logs

1.Maria invests \$5000 which compounds daily over 8 years. When she withdraws the money she has \$6205.51 whta was her interest rate? 2. Consider an investment of \$10,000 at 6.8% interest for 20 years. Fiind the amount if it was compounded quarterly.

### Quantitative Reasoning

Part 1. Computation of Indices Below is information on food items for the years 2000 and 2004. Item 2000 2004 Price Quantity Price Quantity Margarine (pound) \$0.81 18 \$0.89 27 Shortening (pound) 0.81 5 0.94 9 Milk (½ gallon) 1.44 70 1.43 65 Potato chips 2.91 27 3.07 33 A. Compute a simple price index for each of

### Qudaratic Function

For the quadratic function f(x) = x2 + 6x â?" 7, I have to give the coordinates of the x-intercept(s), y-intercept(s), and vertex of the parabola. If the parabola has a maximum or minimum, I have to give its coordinates.

### Discriminants and Parabolas

First Part: What is the discriminant? Explain what information the discriminant gives us and why this information is important. What does the discriminant tell us about the graph of a quadratic equation? Second Part: What is a parabola and where does it come from? What important information is given by the vertex of a p

### the investment needed today

If I wanted to have \$150,000.00 when I retire in 10 years and I'm investing into a high yield bond that pays 7% compounded annually, what do I have to invest today to achieve my goal? Tell me the formula and solve the equation.

### Finding an Equation and Obtaining a Graph

1) Find the equation of the line that is perpendicular to the line x-3y+16=0 and passes through the point (1,7). 2) Suppose the graph f(x) is given, describe how the graph of the function f(x-2)+3 can be obtained.

### Linear Congruence Reduce and Change

Please help me solve this congruence: 21x = 4 (mod 76). I do not know how to reduce/change mods like when they go from 8x = 6 (mod 14) to x=6 mod 7. I do not understand this, so please describe every single step in your solution when you do stuff like that. I do know how to find the GCD of 2 numbers so you do not need to t

### intersection points for feasible regions

10. Provide an appropriate response. If a system has four inequalities, the number of corner points of the feasible region must be? . a. at least three, but not more than four b. exactly four c. exactly three d. at least one, but not more than four

### size of Otto's garden last year

Last year Ottoâ??s garden was square. This year he plans to make it smaller by shortening one side 5 feet and the other 8 feet. If the area of the smaller garden will be 180 square feet, then what was the size of Ottoâ??s garden last year?

### Need detailed help with word problems: Solving simultaneous equations from word descriptions using variuos methodolgies

Write a system of two equations in two unknowns for each problem. Solve each system by substitution. See Examples 8 and 9. 92. Investing her bonus. Donna invested her \$33,000 bonus and received a total of \$970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest

Solve each system by addition. See Examples 1â?"3. See the Strategy for the Addition Method box 8. x + y = 7 x - y = 9 12. x - 2y = - 1 - x + 5y = 4 16. 3x + 5y = - 11 x - 2y = 11 22. 2x = 2 â?" y 3x + y = - 1 Solve each system by the addition method. Determine whether the equations are independent, depen

### Solving help

Demand for a popular athletic shoe is nearly constant at 800 pairs per week for a regional division of a national retailer. The cost per pair is \$54. It costs \$72 to place an order, and annual holding costs are charged at 22% of the cost per unit. The lead time is two weeks. a. What is the EOQ? b. What is the reorder point? c

### I need help solving this

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below. Medium Cost Per Ad # Reached Exposure Quality TV 500 10000 30 Radio 200 3000 40 Newspaper 400 5000 25 If the number of TV ads cannot e

### variation problems solved

10. Write each equation in slope-intercept form. y + 3 = - 3(x - 6). See Example 1. 24. Find the equation of the line that goes through the given point and has the given slope. Write the answer in slope-intercept form. (-1, - 5), - 8. See Example 1. 56. Find the equation of each line. Write each answer in slope interce

### Math problem

Library Assignment When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where â??vâ? is the initial velocity (speed) in ft/sec and â??kâ? is the initial height in feet (as if you were on top of a tower or buil

### Standard Form of a Quadratic Function

Express the quadratic functions in standard form: 1)x^2-4x 2)2x^2+6x 3)5x^2+10x+6 4)2x^2-16+39 5)x^2+8x 6)2x^2+8x+14 7)3-12x-12x^2.

### Algebra Problems: Rational Expressions and Equations

I could use some help with these problems, thanks! 1. After completing the fencing job from two weeks ago, the company sends you to construct some fencing near a river. Your client wants you to enclose a corral adjacent to a river as in the diagram below. [see attachment] a. Write an equation that represents

### the Cauchy condensation test

1. Use the Cauchy condensation test to establish the divergence of the series/;' a. sum(1/(n log(n)) b. sum(1/[n(log(n))(log log (n))]) 2. Show that if a series is conditionally convergent, then the series obtained by its positive terms is divergent, and the series obtained by its negative terms is divergent. 3. give an exam

### sigma-algebra..

Let X= R ( realnumbers): consider the set of all half lines open to the left U= {(a, infinity) : a element R} and the set A = U Union { empty set, R}. is set A a sigma algebra? What if we replace set U with the set V = {(a, infinity), (- infinity, b) : a,b are elements of R} of all half lines on R? is A a sigma algebra?

### Graphs and Functions

Answer following questions showing your work for all problems. Part I Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. a. Y = 3X2 b. (X-1)2 + (Y-8)2 = 16 c. (X+2)2 + (Y-4)2 =

### Functions and Models

Answer the following questions and if required to do calculations please show your work: 1. What is a function? 2. What is a linear function? 3. What form does a linear function take? (I.e., What is the standard mathematical notation of a linear function?) 4. What is the formula for determining the slope of a li

### The graphs of the following systems are given in (a) through (d). Match each system with the correct graph.

Section 7.1 #22 The graphs of the following systems are given in (a) through (d). Match each system with the correct graph. 3x-5y = -9 5x-6y = -8 Section 7.1 #24 The graphs of the following systems are given in (a) through (d). Match each system with the correct graph. 4x + 5y = -2 4y -x = 11 Section 7.

### Prove that a given collection of sets is a sigma-algebra

Let A be a sigma algebra of subsets of R (Real numbers) and suppose I is a closed interval which is in A. Let A(I) denote the collection of all subsets of I which are in A. prove that A(I) is a sigma algebra of subsets of I.

### Example Algebra Word Problem

The distance in miles that can be seen on the surface of the ocean is given by d = 1.4 *square root of h, where h is the height above the surface of the water. How many feet high above the water (to be nearest tenth) would a pirate have to climb to see 16 miles?

### Word Problems

1. Find the quotient of 10 and 2 added to the product of 20 and 2. 2. The formula N=0.07x + 4.1 models the number of women, N, in millions, enrolled in U.S. colleges x years after 1984. How many years after 1984 is the projected enrollment for women expected to reach 6.2 million? In which year is this expected? 3.The o

### Algebra: Goldsmith Example Question

A goldsmith has two alloys that are different purities of gold. The first is three-fourths part gold and the second is five-twelfths pure good. How many ounces of each should be melted and mixed in order to obtain a 6-oz mixture that is two-thirds pure gold?