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# Algebra

### Family of ideals in a ring

Show that the intersection of any family of ideals in a ring is an ideal. Show that the ideal generated by a subset S of a ring R is the intersection of all ideals J of R such that S <= J <=R.

### Finance/Accounting Problem1. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times: 2. Compute the future value of a \$100 cash flow for the following combinations of discount rates and times:

1. Present Values. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times: 1. r = 8 percent. t = 10 years. 2. r = 8 percent. t = 20 years. 3. r = 4percent. t = 10 years. 4. r = 4 percent. t = 20 years. 2. Future Values. Compute the future value of a \$100 cash flow fo

Adjusting the saddle: The saddle height on a bicycle should be 109% of the riders inside leg measurement L. (www.harriscyclery.com) Write an equation expressing the fact that the saddle height for Brenda is 36 in.

### Arithmetic and Geometric Sequences and Series

Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any two consecutive terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 t

### Ratio of Imports to Exports

If United States imports increased 20 percent and exports decreased 10 percent during a certain year, the ratio of imports to exports at the end of the year was how many times the ratio at the beginning of the year?

### Break-even, Charges and Investments

1. A theatre spends \$5000. building a set for a new play. Each performance of the play costs the theatre \$700. The theatre sells \$1200. worth of tickets for each performance. How many performances must the theatre put on to break even? 2. An amusement park charges admission plus a fee for each ride. Admission plus two

### Functions

Determine whether each relation is a function: x^2 = 1 + y^2 y = (square root of x + 5) Determine the domain and range of each relation y = 2x - 3 Graph each function and state the domain and range y = 0.3x y = l x-2 l

### Basic Ratio Equations for Job Direct or Indirect

1) Is the ratio between number of workers and time required to complete a job direct or indirect? 2) The formula for profit (P) is cost (C) minus overheard (O). Write an equation for profit and then translate it to solve for cost 3) Solve for t d=rt My solution was t=d/t. Is that correct 4) Solve for S (C-S)/n=R

### How long, in seconds, does she have to get out of the way ( a story is 12 feet).

The height (h) (in feet) of an object that is dropped from the height of (s) feet is given the formula h=s-16t^2, where (t) is the time the object has been falling. A 5 foot tall woman on a sidewalk looks overhead and sees a window washer drop a bottle from the fifth story. How long, in seconds, does she have to get out of the w

### Arithmetic and Geometric Sequences and Series

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any two consecutive terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: c) Using the formula for the sum of an arithmetic sequence, what is the sum of the fi

### Earthquakes and the Richter Scale

The intensity level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weakest possible tremor. -What is the formula for measuring earthquakes? -Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in

### Discriminants

If I am using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the val

### Sums of Geometric Sequences : Checkerboard Problem

A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on givin

### Arithmetic Sequence

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: 1. What is d, the difference between any 2 terms 2. Using the formula for the nth term of an arithmetic sequence, what is 101st term? 3. Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms? 4. U

### Solving Equations

1. Square root 0f x-1=3 2. The square root of x3 = 8 3. The square root of x2 = x an identity (true for all values of x)? 4. V = s3. Find the length of a side of a cube if the Volume is 729 cm3.

### Factor using trial and error.

Factor the following trinomial using the trial and error 4x^2 +12x-5

### Real life application of line, parabola, hyperbola and exponential graphs.

Relate a real life application to the specific graph(s) line, parabola, hyperbola, exponential. Then describe the characteristics of each application as related to the graph.

### Algebra - Frequency Distribution Concepts

1. The objective of statistics is best described as: A) To make inferences about a sample based on information we get from a population B) To use population mean, ? as an estimate of the sample mean, C) To make inferences about a population based on information we get from a sample taken from the population D) To make in

### Time Distance Formula

It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour: How far have you traveled after 3 hours, 4 hours? How far have you traveled after t hours? i.e. write a linear function that expresses the distance t

### Sums of Geometric Sequences : Checkerboard Problem

A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Crane came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Crane insisted on giving

### Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9, ..... to find the following: a. What is d, the difference between any 2 terms b. Using the formula for the nth term of an arithmetic sequence, what is 101st term? c. Using the formula for the sum of an arithmetic series, what is the sum of the first 20 term? what is the sum o

### Please solve these equations related to arithmetic sequence and geometric sequence

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for

### Checkerboard Problem: Sums of Geometric Sequences

Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat." As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he

### Arithmetic and Geometric Sequences and Series

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, rational,

### Using the index of a series as the domain and the value of the series as the range, is a series a function?

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

### Chinese Remainder Theorem

Need to prove two parts and must follow the Chinese Remainder Theorem. Let be polynomials with integer coefficients of the same degree d. Let be integers which are relatively prime in pairs (i.e., ( for i j). Use the Chinese Remainder Theorem to prove there exists a polynomial f(x) with integer coefficients and of degre

### Algebra Questions: arithmetic sequence, geometric sequence

Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula

### Writing Equations from Word Problems - Airplane

A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?

### Remainders of Euclidean Algorithms

Let b = r_0, r_1, r_2, ... be the successive remainders in the Euclidean Algorithm applied to a and b. Show that every 2 steps reduces the remainder by at least one half. In other words, verify that r_{i+2} < (1/2)r_{i}, for every i = 0,1,2,.... Conclude that the Euclidean algorithm terminates in at most 2log_{2}(b) steps, where

### Factoring

What is factoring by grouping? When factoring a trinomial, why is it necessary to write the trinomials in four terms?