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# Algebra

### Fermat's little theorem

How many different substitution ciphers are there? Explain. Fermat's little theorem, which says that if p is a prime number then (n^p) â?' n is always divisible by p is fundamental to many modern methods of cryptography. The important point is that if one restricts attention to possible remainders when divided by p (that

### Green House Gases

Green House Gases. Carbon Dioxide CO2 is a green house gas in the atmosphere that may raise average temperatures on Earth. The burning of fossil fuels could be responsible for the increased levels in carbon dioxide. If current trends continue, future concentrations of atmospheric carbon dioxide in parts per million (ppm) could r

### Assessing a family of sets

Suppose F is a family of sets. Prove that there is a unique Set A that has the following two properties. a) F is a subset of P(A) and b) For all of B (F is a subset of P(B) then A is a subset of B Should use an upset down A for all of B. For the word then an arrow should be used.

### Five years ago, you bought a house for \$151,000.

Five years ago, you bought a house for \$151,000. You had a down payment of \$30,000, which meant you took out a loan for \$121,000. Your interest rate was \$5.75% fixed. You would like to pay more on your loan. You check your bank statement and find the following information. Escrow payment: \$211.13 Principle and Interest pay

### Equations

Explain the difference between an identity, a conditional equation, and an inconsistent equation. Give an example of each and explain why it is so

### Orders of different groups

If Bn is the groups of upper triangular invertible matrices, On is the orthogonal group, SOn is the spacial orthogonal group (n means that the matrices are nxn) and Fp is the prime field, compute the orders of the groups: a) Bn(Fp); b) O2(F7); c) O3(F2); SO3(F3).

### Evaluating a decay function from a model

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 3% inflation decays according to P=Ae^(-0.03t). How long, rounded to a tenth of year, will it be before a pension of \$80,000 per year has a purchasing power of \$40,000?

### To prove that some quotient group is solvable.

Hello everyone, here's a problem I need help with! Let G be a group, and let K be a subgroup of G. If K_i is normal to G, for each i = 1, 2, ..., n, write K = K_1 (intersect) K_2 (intersect) ... (intersect) K_n. THE QUESTION: If G / K_i is solvable for each i, show that G / K is solvable. I'm sorry if it's hard to r

### Marshmallows do Sachi and Masami put into their ice cream

1. Sachi and Masami have their own secret recipe for making ice cream. They will tell you how much cream they use, but the won't tell you how many marshmallows they put in. Sachi will give you a few clues. She says, "we put in more than 39. We put in fewer than 64. Masami always puts the marshmallows in 3 at a time, with non

### word problem

The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 45 said they had taken physics, 67 said they had taken chemistry and 22 said they had taken both. Seventeen said they had taken neither. How many recent high school grads were surveyed? Show

### Word Problem with Variables

A bakery makes a special marble rye bread using white flour, light rye flour, and dark rye flower. If they use three fifths as much light rye as dark rye but the amount of white flour is 20% of the amount of dark rye, how much light rye flour is needed to make a 1000 gram loaf? (assume the flour makes up all the weight of the fi

### Estimating the Number of Worms

Biology: Some types of worms have a remarkable ability to live without moisture. The following table from one study shows the number of worms W surviving after x days without moisture. x (days) 0 20 40 80 120 160 W (worms) 50 48 45 36 20 3 (

### The equation for MAD is provided.

14 Given the following weekly demand figures, what is the MAD at the end of week 5? Week Demand Forecast 1 100 120 2 120 130 3 110 120 4 130 125 5 160 145 A. 4.0 B. 11.8 C. 12.0 D. 13.0 E. 15.0 22. You are given that the forecast for period 6 was 70 while the actual demand for

### WORD PROBLEM

In a multiple-choice test, each question has five options. Students will get 4 points for each correct answer; lose 2 points for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your

### Slope Intersection Form

In this set of exercises you are to use your knowledge of equations of lines to model the average annual cost of tuition and fees. 1. Cost of Tuition In 2000, the average cost of tuition and fees at private four-year colleges was \$16,200, and in 2005 it was \$20,100. Sketch a line that passes through the points (2000, 16200)

### Grouping Problems for Car Dealerships

A car dealership interviewed every driver who came onto their lot on Tuesday. This produced the following results: there were 61 people who owned trucks and 115 people who owned cars. If 14 people owned both a truck and a car and 8 people owned neither, how many people were interviewed?

### Health Care Economical Sustainability

Imagine you own a health and wellness company. Your company employs numerous fitness trainers and exercise professionals. As part of your company's community outreach program, you have agreed to visit a meeting of the local nurses association. Your audience is personal trainers, nutritionists, and nurses. They require that all p

### Word Problem: High School Classes Example

The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 45 said they had taken physics, 67 said they had taken chemistry and 22 said they had taken both. Seventeen said they had taken neither. How many recent high school grads were surveyed?

### Assessing Positive Numbers

(Not necessarily whole numbers). Explain why we can write a=m_1b+r1 where m_1 is a non-negative integer and 0 less than or equal to r_1 less than b. Why are m_1 and r_1 unique? Continuing in this fashion, we can next write b=m_2r_1+r_2 with 0 less than or equal to r_2 less than r_1 and m_2 a non-negative integer. This procedure

### Expressing the common interest formula

Find the amount that should be set aside today to yield the desired future amount. Future amount needed = 13,000 Interest rate = 4% Compounding period = quarterly Investment time = 4 years The present value is ___? (round to the nearest cent as needed).

1. The time (sec) it takes for an object to fall from a height of h(ft) is expressed by the following equation: h = 16t^2 a. Solve this equation for t. b. A penny dropped from the top of the Prudential Tower takes 7.34 seconds to hit the ground; how tall is the tower?

### Linear relations problem: Worldwide HIV infections

In 2004, there were an estimated 39 million HIV infections worldwide with an annual infection rate of 4.9 million. (a) Solve the equation graphically and find the slope's intercept form of a line that approximates the cumulative number of HIV infections in millions during year x, where x = 2004. (b) Estimate the number of HIV

### Word Problem for Possible Vacation Destinations

Use the five steps for problem solving to answer the following question. Please show all of your work. The Hansons are considering two possible vacation destinations. A trip out west will cost \$1075 in total airfare plus an average of \$450 per day in expenses. A trip south will cost \$1500 in total airfare plus an average of \$

### MATH133 Unit 5 Individual Project -A

See the attachment for full description. 1) Solve a) e^0.05t = 1600 b) ln(4x) = 3 c) log2 (8 - 6x) = 5 d) 4 + 5e^-x = 9 2) Describe the transformations on the following graph of f(x) = log(x). State the placement of the vertical asymptote and x-intercept after the transformation. For example, vertical shift up 2 or ref

### Interest Rates and Compound Interest

If a bank is advertising that a new person can open an account with a 3 3/4 interest rate compounded annually and you invests \$5000in an account at this rate and makes no deposits or withdrawals find the amount of money you will have to the nearest cent after three years can you give me step by step help to solving this question

### Graphs are emphasized.

1. 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 = 36 d. Y = X2 + X 2. Find the equation for each of the following i

### Label as arithmetic or geometic sequence.

A person hired a firm to build a CB radio tower, the firm charges \$100.00 for labor for the first 10 feet, after that the cost of the labor for each succeeding 10 feet is \$25.00 more than the preceding 10 feet. That is, the next 10 feet will cost \$125.00 the next 10 feet will cost \$ 150.00 etc. How much will it cost to build a

### Arithmetic Sequence - Apply the proper formula where applicable.

A company decides to fine it workers for parking violations on its property. The first offense carries a fine of \$25.00 the second offense is \$30.00 the third offense is \$35.00 and so on. what is the fine for the eight offense? Please show your work and whether you use arithmetic sequence or a geometric sequence and use the p