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# Algebra

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### 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?

### the solution set solved

(x+7)(x-11)(x+5)>0 A. The solution set is {x| }. (Use at least one inequality or compound inequality to express your answer.) B. The solution is all real numbers. C. There is no solution.

### Find all solutions of x^16 = 1 Mod 19

Solve the equation x^6 = 1 in F_19. Do not use brute force. I know I can just substitute in x=0 ... x=18, but rather than doing that, I would like to know a more clever method so I can solve such equations easily in general.

### Square size

Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?

### Decide how you would prefer to commute to work each day.

Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in days, is graphed on a rectangular coordinate system where time is on the horizontal axis. Further suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C=p*a^t where p is the number of cars on the roa

### Solve the equations for the different bicycle models that can be made daily, with any of the techniques - graphing, substitution, elimination, and matrix.

As a business owner, there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company's products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble. Model B takes 3 hours to assemble. Model

### How many solutions can be created from a specific amount of numbers/characters/digits

How many passwords can be created from the 36 alpha-numeric characters (26 alpha characters and 10 numerical digits 0 to 9), assuming passwords can be 8 or 9 alpha-numeric characters in length with a minimum of 2 characters being numerical digits? Explain each step of the process by which you arrived at the answer, showing th

### Various Methods and Deciding Consistency

Write equation slope intercept line satisfying the following condition. The line passes though (-6, 4) and is perpendicular to the line that has an x intercept 3 and a y intercept -9 Solve each system or state the system is inconsistent or dependent. x/2= y+8/4, x+3/2=y+5/4 Solve by using the substitution method. x/4

### Calculating Total Distance

Eva enters a walkathon that covers a total distance of 12 miles. She runs part of the distance at a rate of 6 mph and walks the remaining distance at a rate of 4 mph, completing the course in 2 hours and 30 minutes. How far did Eva run? How many hours did she spend running?

### Existing Slopes and Pairs of Points

The math Problems that I need help with are below. #1) Find the slope, if it exist, of the line containing the pair of points. (8,10) and (9,-6) The slope m= What? #2 Find the slope and the y- intercept F(x) = -10x -3 The slope is what? The y- intercept is (0, what o

### Algeba Word Problem

Flying against the wind, an airplane travels 6030 km in 9 hours. Flying with the wind, the same plane travels 7600km in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?

### Determing Unions, Intersections, and Subsets

Set X = {5, 7, 11, 16, 21, 702}, Set Y = {2, 5, 8, 11, 19, 702} a. What is the union of Sets X and Y? b. What is the intersection of Sets X and Y c. Create your own set Z that is a subset of Set X.

### Desalination Exponential Equation

1. Desalination. More cities are supplying some of their fresh water through desalination, the process of removing the salt from the ocean water. The worldwide desalination capacity has grown exponentially from 15 million m^3 per day in 1990 to 55 million m^3 per day in 2007. a) Find the exponential growth rate k and write an e

### Null and convergent sequences

Please show all the work. (a) Use the definition of a null sequence to prove that the sequence {an} given by an = (-1)^(n+1) / (n^3 - 3) , n = 1, 2, ... is null. (b) Determine whether or not each of the attached sequences {an} converges. Find the limit of each convergent sequence.

### Area of a Square and Polynomial Region

88. Area of a square. Find a polynomial A(x) that represents the area of the shaded region in the accompanying figure. 96. Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)^2 represents the value of the investment af

### Renting a Condo

A Condo is renting at \$1,100 per month. I have two options, if I sign up for 12 month, I get 1 month free offer. Or I can use the money from that 1 month and spread it throughout the 12 month. My question is, if I would to go ahead and use that free month (\$1100) and spread it to 12 month, what would my newly adjusted monthly re

### Solving various algebraic equation problems

1. Find the value of x, 52 degrees, 137 degrees 2. find the x- intercept and y- intercept of the line given by the equation 9x - 5y = 13 3. find the points line 1- 3x + 13y = 12 line 2- 3x + 5y = 12

### Population Growth.

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2015. Please show th

### 2-4 Paragraphs.... Research Solve equations with radicals and exponents

Part 1: Using the Library, web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mile