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# Algebra

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### Price of Gold

Suppose the current price of gold is \$650 an ounce. Hotshot consultants advises that gold prices will increase at an average rate of 12% for the next two years. After the growth rate will fall to a long-run trend of 3% per year. What is the price of 1 million ounces of gold produced in eight years? Assume that gold prices have a

### Mixed Algebra Questions

1. Insurance settlement. Gary invested one-third of his insurance settlement in a CD that yielded 12%. He also invested one-third in Tara's computer business. Tara paid Gary 15% on this investment. If Gary's total income from these investments was \$10,800 for 1 year., then what was the amount of his insurance settlement? 2.

### Commutative & Associative Properties

#12 (Commutative & Associative Properties) -8 + 12 - 9 - 15 + 6 - 22 + 3 #34 (Distributive Property) Use distributive property to write each sum or difference as a product. 7b - 49 #54 Multiplication Property of Zero x * 5 = 5x #26 (Using the Properties in Computation) Perform each computation. Make use of appropri

### Sylow's Theorem Problems

Verify that if H is a subgroup of G, and a ? G, then aHa^-1 is a subgroup of G. Prove that if H is a finite subgroup of G, and a ? G, then |aHa^-1| = |H|. (Suggestion: The mapping h ? aha^-1 is one-to-one.) Explain why if H is a Sylow p-subgroup of a finite group, then so is each conjugate of H. Prove that if a finite g

### Find the Equation of the Line

Find an equation of the line passing through the pair of points. Write the equation in the form Ax + By = C. Show Work. (-7,6),(-8,-4) A. -10x-y = 76 B. x+y = 76 C. -10x + y = 76 D. 10x + y = -76

### Simplifying Equations and Solving Functions

1. Simplify: (-5a^3b^2)^4 a^12b^5/b^-7 2. let f(x)=3x^2 and g(x)=x-4 -Find the composite function (f o g)(x) and simplify -Find (f o g)(-1) 3. Find the exact solutions and simplify as much as possible 4x^2+5=4x

### Investments and Interval Notation

1. Suppose \$8,500 is invested in an account at an annual interest rate of 3.7% compunded continuosly.How long (to the nearest tenth of a year) will it take the investment to double in size? 2. Solve, and write the answer in interval notation x+5/x-7 ? 0 3. Solve: ?3x+10=-x

### Operations with Functions

1. Solve: 7^3x-4=49 2. Let f(x)=x^2+10x40 -find vertex -state the range of the function -on what interval is the function increasing? 3. Multiply and Simplify (7+6i)(2+9i) Write the answer in the form a+bi, where a and b are real numbers.

### Concentration of a Solution for Water Distribution

1. The total weight of a container and liquid is 14.40 lbs. The tare weight of the container is 6.10 lbs. If 97% of the liquid is water, what is the weight of the chemical added to it? Multiple Choice: a) 0.25 lbs b) 0.28 lbs c) 2.50 lbs d. 8.05 lbs. 2. How many gallons of water should be mixed with 2 lbs of dry

### Capacity Word Problem

The two NCAA stadiums with the largest capacities are beaver Stadium (Penn State) and Michigan Stadium (Univ. of Michigan). Beaver Stadium has a capacity of 1081 more than Michigan Stadium. If the combined capacity for the two stadium is 213,483, find the capacity for each stadium.

### Fundamental Math: Algebraic Number Theory

See the attached file. 1) Compute the Cayley tables for the additive group Z and for the multiplicative group Z of non-zero elements in Z. 2) Let G be a group written additively. Recall that the order of an element a is the minimal natural number n such that na = 0. If such n does not exits then one says that the order

### Population Growth Analysis

Population growth in Ethiopia: In 2006, the estimated population in Ethiopia was 75 million people with a relative growth rate of 2.3%. a. Write an equation that models the population growth in Ethiopia, letting 2006 be year 0. b. Based on the model, what is the expected population in Eithiopia (to the nearest million) in

### Hydrogen concentration

The pH of solution A is 4.2, while the pH of solution B is 8.2. Find the Hydrogen Ion concentration of Solution A. How much greater is it than that of solution B? (It says to use scientific notation using multiplication symbols in the math palette as needed and to round to the nearest tenth).

### Totals

A man who owns a sound system store wants to advertise all the different kinds of stereos he offers. He carries 9 different CD players, 7 different receivers, 10 different kinds of speakers. Assume that a sound system consists of one of each. How many different sound systems can he advertise?

### Algerbra Problems

1. Find the slope and y intercept of the graph Y=0.7x+5 2. Write an equation of the line with the indicated slope and y intercept. Slope= 15 Y intercept = 9 3. Find the slope of the graph 2x-3y=18 4. Write the equation of the line through each indicated point with the indicated slope. Write the final

### Word Problem about Division using Standard Form

Dropping less than 2 inches per mile after emerging from the mountains a river drains into the ocean. One day's discharge at its mouth, 5.6 trillion gallons, could apply to all of country X's households for four months. Based on this how much water does the avg. household use each month? Assume 200 million households in coun

### Seismographs and Half-Life

Question 1: A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.9 x 10^2 µm. Find this earthquake's magnitude on the Richter scale. Question 2: An artifact was found and tested for its carbon-14 content. If 81% of the original carbon-14 was still present, what is its probable age

### Cartesian Coordinates and Graphs

Please evaluate the following expressions: 92-7(8) 6(32-17) 6(32)-17 Please use the function f(x) = -3x+5 when f (2), (-1) ,(.5) , (-3) and plot the following on Cartesian coordinates: (2,3) (4,-1) (-.5,3.5) (-1.5,-4) (-5,3)

### Square Root Property and Its Form

What is the square root property and what is it used for? In what form should an equation be in order to use the square root property? When should the square root property be used instead of factoring? Use the following to explain. (3t-2)^2=108

### Square Root versus Factoring

What is the square root property and what is it used for? In what form should an equation be, in order to use the square root property? When should the square root property be used instead of factoring? Use the following to explain. 10-4p^2=21

### Classification of Positive Integers

The positive integers are classified into two types, A and B; a number is A if and only if it is the sum of two (distincts) A numbers, or the sum of two (distincts) B numbers. a) Classify the numbers 1,2, 3 as A and B. b) Prove that if n, n+1, n+2 are A numbers, then every integer >= n is an A number. c) Find the smalle

### Fahrenheit to Celsius conversion

26. The formula for converting Fahrenheit temperature, F, to Celsius, C, is C = 5(F-32)/9. If Celsius temperature ranges from -6 degree C to 15 degree C, inclusive, what is the range for the Fahrenheit temperature? 27. Find the solution(s) for the equation. |4x - 8| + 11 = 23

### Writing an Equation of a Relationship

I need help with the following problem: Write an equation that expresses the relationship. Then solve the equation for m. b varies directly as the cube of u and inversely as m. b=? (use k as the constant of variation) m=?

### A person invested \$7200 for 1 year, part at 4%, part at 10%, and the remainder at 15%. The total annual income from these investments was \$863. The amount of money invested at 15% was \$1400 more than the amounts invested at 4% and 10% combined. Find the amount invested at each rate.

A person invested \$7200 for 1 year, part at 4%, part at 10%, and the remainder at 15%. The total annual income from these investments was \$863. The amount of money invested at 15% was \$1400 more than the amounts invested at 4% and 10% combined. Find the amount invested at each rate. The person invested \$__ at 4%, \$__ at 10%,

### Synthetic Division

How would you explain the performance of synthetic division to someone else? Use the problem (2x3 - 3x2 - 11x + 7)/(x + 3) to support your explanation.

### Finding Slope from the Equation of a Line

Please help with the following algebra problems. Provide step by step calculations as well as explanations. If possible, provide an additional example. The equation of a line is given below. Find the slope of a line that is: a. Parallel to the line with the given equation. b. Perpendicular to the line with the given equa

### Linear Equation Example Question

Begin by solving the linear equation for Y. This will put the equation in slope-intercept form. Then, find the slope and the y-intercept of the line with this equation: 2y=x (this must stay in fraction format).

### Computing the balance in the account

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A 19,000 deposit in an account with an APR of 2.5%. The balance in the account after 1 year is approximately \$ (Round to the nearest cent as needed.) The balance in the account

### Operator R(theta) for matrix representation

Assume the operator R(theta) transforms a vector v (in two-dimensional real space) by swinging it around counterclockwise through an angle theta. How can I show that the operator R(theta) has the matrix representation cos(theta) -sin(theta) sin(theta) cos(theta) That is supposed to be a matrix.

### Traveling Salesman Problem

Provide an example of when the traveling salesman problem can be used to find the best solution to a problem pertaining to grocery stores.