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Normal subgroup

Let N be a normal subgroup of G, a in G, and C the conjugacy class of a in G. a) Prove that a in N if and only if C is contained in N. b) If C_i is any conjugacy class in G, prove that C_i is contained in N or the intersection of C_i and N is empty. c) Use the class equation to show that |N| = |C_1| + ...+ |C_k|, where C_1, .

Velocity issues

All boulders and rocks (large enough not to be buffeted by air current) appear to take the same time to hit bottom. My conjecture, observes Galileo, leader of the team, is that there is a universal gravitational constant which affects all objects, large or small. Knowing, as he does, that if such a constant exists, call it g f

Question problem of tickets sold

There were 377 tickets purchased for a major league baseball game. The general admission ticket cost $6.50and the upper box ticket cost $10.00. The total amount of many spent was $3168.00. How many of each kind of tickets were purchased? General Admission ???? Upper Box tickets ??? Please show work

real roots graphs

The graph of y = −11x 2 + 154x − 535 is a parabola that opens in the direction _____. It has vertex ______, y-intercept _____, and ____ real roots. up, (7, 4), 154, 2 down, (7, 4), −535, 2 down, (7, 4), −535, 1 down, (−7, 4), 154, 1 None of the above

Dropped objects

All boulders and rocks (large enough not to be buffeted by air current) appear to take the same time to hit bottom. My conjecture, observes Galileo, leader of the team, is that there is a universal gravitational constant which affects all objects, large or small. Knowing, as he does, that if such a constant exists, call it g f

Calculating Total Interest from Investments

A comprehensive investment plan is made for a person with a total investment of $26,300. The money is broken into three investments. Part of the money is invested into a retirement account 5.1% interest per year, part is invested in a saving account earning 2.8% interest per year, and part is invested into a certificate of depos

Word problem

The natural stride up a staircase has a slope of 3/5, meaning that a run of 5 inches has a rise of 3 inches. The model for a standard staircase is y=(3/5)x. Find the rise for a staircase constructed at a mansion which has a run of 12 inches.

Set up of the proportion and the steps to solve

Library Research Assignment 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.

Barstow word problem

Barstow industrial supply has decided to raise 427.52 million in additional funding via a rights offering. the firm will issue one right for each share of stock outstanding. the offering consists of a total of $860,000 new shares. the current market price of the stock is $35. currently, there are 5.16 million shares outstanding.

Quadratic Residue Question

Let p be an odd prime and b be a quadratic residue of p. For p=19 for which pâ?¡3 (mod 4), show by direct calculation that the pairs 1 and 18, 2 and 17, 3 and 16, and so on, have one quadratic residue and one quadratic nonresidue.

System of Equations: Length of a Storm

Two storms occurred in one week in a certain area. in the first storm 25ml of rain fell per hour, and in the second strom 30ml of rain fell per hours. Rain lasted a total of 55 hours, resulting in a total rainfall of 1525 ml. How long did each storm last?

Rate per hour?

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1525. What was the rate charged per hour by each mechanic if the sum of the two rates was $130 per hour?

number of gallons consumed

1st car has fuel efficiency of 15 miles per gallon. Second car has fuel efficiency of 40 miles per gallon. during a week the two cars combined went a total of 1225 miles with a total gas consumpton of 40 gallons. How many gallons were consumed by each car?

Cauchy Sequence and Completeness of a Metric Space

Let X be a complete metric space. If F_n is a sequence of nonempty closed subsets of X such that F_n+1 is contained in F_n and the limit as n-->infinity of the diameter(F_n) = 0, show that the interesection of all F_n is nonempty.

Word problem

The number N, in millions, of the hearing impaired individuals of age x can be approxiamted by N= -0.00006x^3 + .006x^2 -0.1x +1.7. Approximate to the nearest million the number of impaired individuals of ages 50 and 60. age 50 = age 60 =

displacement as a function of time.

1. The Starship USS Enterprise is travelling in a straight flight path through the Delta Quadrant to investigate the Sontaran Nebula when its sensors detect a disturbance in the fabric of the space-time continuum. Captain Jean Luc Picard orders Lt. Commander Data to reverse course. However, as Data does this, the effect of the

Help with formulas for word problems is provided.

Q1. Lisa can shovel snow from her driveway in 35 min. Bill can do he same job in 50 min. How long would it take lisa and bill to shovel the driveway if they worked together. Q2. Kathy bicycles 6 KM/h faster than Carlos. In the same time it takes Carlos to bicycle 45 km, Kathy can bicycle 63 km. How fast does each bicyclist

Solve: Equating the Distance

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 9:10 am. If train B passes the same station at 9:25 am, at what time will train B catch up to train A?

Predicting Life Expectancy

In 1991, the life expectancy of males was 72.5, in 1996 it was 74.7 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991. E(t)=_____t + _____ Round to nearest tenth Use the function to predict the life expectancy in 2005 E(14)=_____ Round to nearest tenth.

Finding All Numbers which the Rational is Undefined

1. Add 8/r-2 + 8/r+2 2. Simplify by removing factors of 1 w^2-4/2-w 3. Solve x-6/x+6=2/5 4. Simplify by removing factors of 1 80v^6x^7/50v^2x^2 5. Simplify if possible 5/49z^3+1/35z^2 6. Solve 5-y/8-y=3/y-8 7. Find all numbers which the rational is undefined - 8. Multiply and simplify 9x^7/8r^6*64r^8/81

Determining Vacuum Strokes

Please show all the steps for easier understanding. Problem #1 A vacuum pump removes 15% of the air that is in a container at the beginning of a stroke. If m_r is the mass of air in the container after the rth stroke: (i) Express m_2 and m_3 in terms of the original mass m_0. (ii) How many strokes are required to obtai

Examining money invested in stocks, bonds and money market

You have a total portfolio of $20,000 to either invest in stocks, invest in bonds, or save in a money market. You want to have at least two times more money in stocks than in bonds. You estimate that stocks will provide 2 times more money this year than money markets. Lastly, you want to have $4,000 less in money market than

Feature Films Addition and Elimination Methods

Is (-2,6) a solution to 7x + 3y=4 AND 8x + 7y = 26 Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, state that Solve using the addition (elimination) method. Solve using the addition (elimination) method Solve using the substitution method Solve using the substitution

Number of positive integer solutions

Please show all the work. If n is a (fixed) positive integer what is the number of solutions (x,y) (with x and y positive integers) to the equation 1/x + 1/y = 1/n . Carefully explain your reasoning.

Counting Animals at the Zoo Problems

Monica and Marty are llamas at petting zoo. They like to count the visitors that pet them. Total of 105 people pet both Monica and Marty. 2.5 times as many people pet Monica as Marty. How many people petted Monica and how many petted Marty. Amy was soaking poor feet. Together Amy and Marcus walked total 10.5 miles. Amy walked

least squares method to solve a coin problem

I do a fair flip of a fair coin until I get heads for the first time. If I get heads for the first time on the nth throw, Sally pays me 2^n dollars. How much does she pay me on average? Solve by simulation (least squares)

Determining amount of sales

As a salesperson at Kim's Furniture, Yolanda has a choice between two options for receiving monthly pay. With one option, she receives a base salary of $412 and gets an additional 20% commission on the sales she makes. With the other option, she doesn't receive a base salary but gets 24% commission on the sales she makes. What a

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.