rules-of-exponents.jpg- which is located in attachments

Pick two of the exponent rules listed above and explain it in your own words. Provide an example to each rule you chose to illustrate the rule.

Create two exercises about the rules you explained above, so your classmates work it out.

Substantive Guidelines: Demonstrate and explain with words how you worked your classmates’ exercises.

Respond to (2) peers:

Peer (1) Kristine:

Hello Class,

To divide exponents with the same base, the base remains the same, and the exponents are subtracted.

Example:

a4 /a2= a4-2

a2

Zero exponent rule states that any exponent raised to the 0 power is always equal to 1.

Example:

a0=1

Questions:

1) x20/x10=

2) (7x4y4)0=

Peer (2) Diana:

The multiplication rule of exponents says that for any ax x ay = ax y .

For example, if x=3 and y=4, then a3 x a4 = a7 .

The Power of a Power rule says that for any (ax)y = ax*y.

For example, if x=3 and y=4, then (a3)4 = a3*4 = a12.

Questions:

1. Use the multiplication rule to solve the equation a5 x a7.

2. Use the Power of a Power rule to solve the equation (a9)8.

## Read 2 equations and find the errors, then rewrite in correct form

Paper details For this discussion (and the remaining discussions in the course), you will be asked to “Find the Error” within the solutions from a hypothetical student in the class.

Explain in which step the error lies, what the error is, and how to correct the error. After explaining the student’s errors, provide a complete step-by-step solution correctly solving the problem. Try to write your explanations as if you are addressing a student who may not fully grasp the topic (hence the error).

There may be multiple errors throughout a solution. Try to catch them all.

Don’t underestimate the challenge of spotting and explaining errors in a solution. It is not enough to simply provide a correct solution, but starting with solving the problem (correctly) yourself may help enlighten you. However, be careful…just because the sample student didn’t follow the exact same steps in the same order that you did, does not necessarily mean that those steps are incorrect. So, make sure to consider the validity of their methods when they vary from yours.

## math 143 lab

Paper details MAT 143 Signature Assignment

BUYING MY CAR LAB

Learning outcomes:

Upon completion students will be able to…

Research and calculate all the costs associated with the purchase of a car.

Calculate a budget including monthly net total.

Use the gathered car information and the budget information to determine if the individuals studied will be able to purchase the selected car.

Reflect upon the budgets and the practicality of being able to purchase a car.

Scoring/Grading rubric:

This assignment will be graded twice. Once using the rubric listed below for the ability to analyze data using quantitative concepts. And a second time for a mathematical/content grade. The second grade will count as 5% of your overall grade.

COMPETENCY: INFORMATION TECHNOLOGY AND QUANTITATIVE LITERACY

KEY INDICATOR 2: STUDENT APPLIES QUANTITATIVE CONCEPTS TO ANALYZE DATA.

Score

Description

Score Blank

Indicates an assignment was not Submitted.

Score 0

Indicates submission of an assignment that does not allow for sufficient or appropriate scoring of skill, for example, an assignment that was plagiarized.

Score 1

Beginning

Uses the quantitative analysis of data as the basis for drawing unclear conclusions from this work.

Score 2

Emerging

Uses the quantitative analysis of data as the basis for drawing plausible conclusions from this work.

Score 3

Emerging

Uses the quantitative analysis of data as the basis for drawing reasonable and appropriately qualified conclusions from this work.

Score 4

Proficient

Uses the quantitative analysis of data as the basis for drawing insightful, carefully qualified conclusions from this work.

**”Reprinted [or Excerpted] with permission from Assessing Outcomes and Improving Achievement: Tips and tools for Using Rubrics, edited by Terrel L. Rhodes. Copyright 2010 by the Association of American Colleges and Universities.”

Introduction:

In this project, you will…

Select a car to purchase.

Analyze the costs involved in purchasing and maintaining the car you selected.

Calculate the number of hours you need to work each week to maintain the vehicle.

Calculate monthly budget for two individuals.

Evaluate whether the individuals can afford to add the car selected to their monthly expenditures.

Assignment Instructions:

This assignment has three parts:

Questions 1 – 14 will help you complete the first table

Questions 15 – 19 will allow you to reflect on the information in your table.

Managing a budget: Nick’s car buying experience

You will work through each question below and show your work. You will need to record your answers for each question in the spaces provided in the table on the following page. You will notice that the table question numbers align with the question numbers below. Once you complete the chart for questions 1 -14, you have another set of questions to answer, which are numbered 15 – 19, located after the table. Use the information from your chart to help you answer questions 15 – 19.

Note: Show your work below each item, then put your final answers on the car calculations worksheet. The car calculations worksheet will be graded.

Choose a car (new or used) that you would like to purchase. Be sure to think about the type of car that you would realistically consider purchasing in the next couple of years (not your ultimate dream car). Once you have selected a car, verify that you can find maintenance information for your car on the Edmunds site (see number 7 below). If your car is not listed on the Edmunds site, please pick a similar car which is listed on the Edmunds site and use it for the rest of your calculations. List the car information, including the make, model, year, and list price in item one of the table.

Determine the amount of your down payment. For this project, make a 10% downpayment and fill in the amount in item 2 of the table. In the real world, individuals can choose a different amount, and in fact some loans do not require a downpayment.

Calculate the 3% tax (in N.C., we pay a 3% highway use tax in lieu of state sales tax). The tax is based on the list price. Source: Link to government highway use tax website.

Calculate the total amount to be financed. To find the total amount financed, take the list price minus the deposit plus the highway use tax.

Determine the interest rate for the car. Link to State Employee’s Credit Union Website to research rates. Or, if you prefer, you can look up the rates on another legitimate website (cite your source). Decide on the term of a loan (number of years) that would be reasonable for you. List your rates, term, and source in the table.

Calculate your monthly payment, total installment price, finance charge, and yearly payments using the formulas in the book from Unit 3 Section 3. To find the yearly amount, take the monthly payment times 12.

Insurance rates are calculated on many factors such as: Age, Gender, Driving Record, Make/Model/Year of car, number of years driving etc….Insurance rates will vary per individual, however for this project, use the following average rates provided by my insurance agent: $2000/year for full coverage on a new car, $1500/year for full coverage on a used car.

Include the Department of Motor Vehicles Fee of $28 per year.

Calculate the maintenance cost per year by going to Link to the Edmunds True Cost to Own Your Car Website. Divide the 5 Yr Total maintenance amount by 5 to get the average annual cost. Include your work in the middle column of the table and your one year maintenance cost in the right column.

Calculate fuel costs based on your car’s average MPG (look it up!) and the average cost of a gallon of gas ($2.75/gallon). You will need to estimate how many miles you drive per year. If you have no idea, you can use 12,000 miles, which is the national average.

Calculate the county taxes. Tax rate schedules for all counties and municipalities can be found on the Internet (search for property tax rates). For this project, we will assume that everyone lives in Mecklenburg County. Use the following rate: Mecklenburg has a tax of $0.8157 per $100 of the car’s value.

Calculate the city/municipal taxes. Tax rate schedules for all counties and municipalities can be found on the Internet (search for property tax rates). For this project, we will assume that everyone lives in the city of Charlotte. Use the following rate: Charlotte has a tax of $0.437 per $100 of the car’s value.

Example for questions 11 and 12: If your car has a value of $12,000, then the Mecklenburg county tax is ($0.8157)(12,000/100) = $97.88.

Calculate the Grand Total (rows 6 through 12: the sum of yearly payments, insurance, DMV fee, maintenance, fuel, and taxes,).

Calculate the Super Grand Total(over entire length of loan): (Grand Total times # years of loan, plus down payment)

Car Calculations Worksheet

Question Number

Descriptions and work space

Fill this column with your numbers.

# 1

Record your Car’s Make, Model and Year:

Make:

Model:

Year:

List price of Car:

# 2

Down payment: (10 %)

# 3

N.C. Highway Use Fee: (3% of list price)

# 4

Total amount to be financed:

# 5

Interest rate: _________ and length of loan: __________

Source:

Leave Blank

# 6

Monthly Payment:

Total Installment Price:

Finance Charge:

Yearly amount:

# 7

Insurance costs (yearly):

# 8

Department of Motor Vehicles fee (yearly):

# 9

Total maintenance costs (yearly):

# 10

Fuel costs (yearly):

# 11

County taxes (yearly):

# 12

City taxes (yearly):

# 13

Grand Total (yearly):

(the sum of yearly payments, insurance, DMV fee, maintenance, fuel, and taxes)

# 14

Super Grand Total (over entire length of loan):

(Grand Total * # years of loan, plus down payment)

If you have a job making minimum wage at $7.25 an hour, how many hours do you need to work per month just to pay your car expenses? How many hours do you need to work per week to pay your car expenses (assuming there are 4 weeks per month)? Make sure to answer both questions.

(Hint: To calculate your car expenses, divide your Grand Total by 12) Show your work.

How many hours do you need to work per month and per week if you make $8.25 an hour? Show your work.

How many hours do you need to work per month and per week if you make $10.00 an hour? Show your work.

Complete the chart for the yearly cost of the car. In the space below write the Grand Total and the cost of the car over the life of the loan (Super Grand Total). Based on your calculations do these figures make sense? Discuss whether these numbers are higher or lower than you expected and whether you personally would be able to afford this vehicle. Make sure you consider and discuss other life expenses. All verbal responses must be in complete sentences. Your response should be at least 6 sentences.

Grand Total:

Super Grand Total:

Review your answers from number 16, 17 and 18. Based upon the information from your car calculations, would an individual be able to afford this car if they earned $7.25 per, $8.25 per hour or $10.00 per hour? Give details to justify your reasoning and discuss your options. Make sure you consider and discuss other life expenses. All verbal responses must be in complete sentences. Your response should be at least 6 sentences.

Managing a Budget

Managing a Budget is the third part of your assignment. Here, walk-through Nick’s car buying experience and help him crunch some numbers. Answer the questions below and complete the tables with the appropriate information. There are another five questions (20 – 25) to answer after completing Nick’s financial calculations.

Your good friend Nick needs some financial advice. He is thinking about buying a car and a house. Help Nick calculate his expenses and give him some friendly advice on his planned purchases. Here is Nick’s story. Nick just graduated from CPCC in nursing and received his LPN license. He is starting his new job and will be making 68,000 a year. He will have to pay 19% of his income to pay for taxes and social security (SS) and 5% of his income to a forced employer retirement plan.

How much of his income will he have left to spend? Fill in the table below:

Description

Amount

Income

Amount Paid to Taxes and SS

Amount Paid to Retirement Account

Amount Left to Spend

Help Nick evaluate his budget. His current rent payment is $1,000 a month and his utilities total $200 each month. Nick spends $100 on a bundle for his house phone, cell phone, internet and cable bill every month. He has always believed that it is important to live a healthy lifestyle so he spends $450 a month on groceries and $99.00 a month for a gym membership. His health insurance for the month totals $250.00.

Nick does not have much time to go out but he makes sure that he treats himself to dinner and a movie at least twice a month that costs $50.00 each time. He always puts away $350 each month into his personal savings account for retirement so he will not use this money for paying bills. Nick also puts away $25.00 each week for a vacation fund (assume that there are 4 weeks in a month). Nick loves his lattes and spends $4.50 on coffee 3 times a week.

Nick wants to purchase a car but is not sure if it will fit his budget. Please compute Nick’s income and expenses using the chart below and determine if he can afford buying a new car.

Monthly Expenses: Enter the monthly expenses for each item, then add them together to find your Total Monthly Expenses.

Monthly Expenses

Description

Amount

Home

Mortgage/Rent/HOA

Utilities (Gas, Electric, Water)

Phone/Internet Bundle

Food

Groceries

Health

Health Club

Health Insurance

Entertainment

Dining Out/Movies

Vacation

Savings

(Put into an account each month)

Other

Total Monthly Expenses

Add up all the rows

Fill in the summary table below to see if they are on budget. Subtract the expenses from the income to find the monthly net total.

Monthly Budget Summary

Amount

Monthly Income Total

Monthly Expenses Total

Monthly Net Total

Based upon the information from your car calculations, would Nick be able to afford the car you selected? Give details to justify your reasoning and discuss Nick’s options. All verbal responses must be in complete sentences. Your response should be at least 6 sentences.

Nick would like to buy his dream house for $300,000. He finances the whole purchase price of $300,000. Calculate his monthly payment if he secures a home mortgage loan at 3% APR for 30 years.

Financial advisors use a general rule that your monthly payment for your home mortgage should not be more than one third your monthly income. Use the amount Nick has left to spend from number 20 to calculate his monthly income. Discuss whether Nick will be able to afford his dream house in number 23. Give details to justify your reasoning and discuss Nicks’s options. All verbal responses must be in complete sentences. Your response should be at least 6 sentences.

Each year Nick’s employer takes 5% of his income and deposits it into a forced employer retirement plan. Instead of making one deposit, Nick’s Employer makes monthly deposits of 1/12th of the annual amount taken out of his paycheck. If Nick works for the company for 30 years, how much money will be in the account if he earns 5% interest each year. Hint: Use the regular deposit formula (annuity) from page 248 in the book). Assume poor Nick does not get a raise during the 30 years, and the monthly deposit stays the same for 30 years.

What does it mean if your Monthly Net Total is positive, negative, or zero? Explain which situation has more advantages, having a positive, negative or zero Monthly Net Total. All verbal responses must be in complete sentences. Your response should be at least 6 sentences.

What have you learned from this project? All verbal responses must be in complete sentences. Your response should be at least 6 sentences.

## Math week 7

Paper details This final week of new work is focused on aspects of logic and logical methods of thinking and problem solving.

One important area is inductive and deductive reasoning. We use these types of reasoning to draw conclusions or make decisions or solve problems.

. Explain why inductive reasoning was involved.

Explain why this was a use of deductive reasoning.

## assignment 7

Paper details Important: Show your hand-written work. No work, no credit

1a.) what is the volume of the rock with a density of 3 2.5g / cm and a mass of 78g?

1b). what is the mass of an 8.0cm3 cube of lead? The density of lead is11.4g/cm3

2a.) How far away was a lightning strike if thunder is heard 8.00 seconds after the flash is seen. Assume that sound traveled at 350.0m/s during the storm.

2b.) what is the acceleration of a 23kg cart if the net force on it is 47N?

3a.) How long will be required for a car to go from a speed of 27.0m/s to a speed of 32.0m/s if the acceleration is 2 3.0m / s?

3b) A 1500kg car accelerates uniformly from 14m/s to 23m/s in 10.0s. What was the net force exerted on the car?

## Measurements

Paper details Research the flag for the state in which you live and share a picture of the flag. Determine the number of lines of symmetry in the flag, and describe the lines of symmetry you discover. Provide an example of a math situation to which you could apply lines of symmetry.