Kelly has 36 coins in her purse, only nickels and quarters. She has eight more quarters than nickels. How many nickels and quarters does she have?

# Category: Algebra homework help

This is a graded discussion: 100 points possible

due Dec 4

Module 2 Discussion: A Formula Investigation

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Module2A Formula Investigation

Discussion

Please read through all sections before proceeding to the next page and refer back whenever necessary.

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Introduction

Formulas are models of problem solutions. In Module 1, you learned how to evaluate and manipulate formulas from many different application areas. This allows you to use a formula in many ways. Specifically, if there are n variables in the formula, there are n different representations of it. You can solve any of the n variables in terms of the (n-1) other variables to solve even more problems without rethinking the process. Thus, formulas allow you to reach solutions more quickly. Formulas can help you predict solutions also.

This module week, you will work with a specific formula to investigate what happens when a variable value in the formula is changed. Recall that I = PRT is the formula for simple interest where I is the simple interest accumulated from multiplying the original amount of money, Principal, by the interest rate per year given as a percent, and Time, in years.

The total amount of money, A, you accumulate at the end of T years, if you are saving money, is given by the formula A = P + I. This is the same formula for the amount of money you have paid back on a loan after T years.

Borrowing and saving money are things you are going to do throughout life. This formula is only the tip of the iceberg for financial literacy. Let’s have some fun with it!

Before taking out a loan, it is essential to know the repayment terms and how your interest rate and the time of the loan will affect the total loan balance. For simplicity, you are using the flat rate method where each monthly payment contains an equal principal and interest amount. This is not an amortization problem.

In this discussion, you will examine how a formula is used to explain the effects of changing variable values.

Please proceed to the Prepare section.

Prepare

Think of a big-ticket item you might need to take out a loan to purchase. Dream big! What have you always wanted? This could be a boat, car, motorcycle, or a trip around the world, but not a house. (A house loan has many other considerations.) Research the cost of this item and be sure to bookmark the link.

Review the terminology from pages 132-133 of the textbook if necessary. Think about any computational sub-steps that need to be taken. Note that in simple interest, the monthly payment is the same each month.

Select a reasonable interest rate for your item (between 2% and 10% is standard). It does not have to be a whole number. Then, select a time period to pay off your loan (between 3 and 12 years is common). It is standard to be a whole number.

Please proceed to the Initial Post section.

Initial Post

For your initial post, respond to the following prompts.

· Describe the item you are taking a loan out for and state the purchase price. For purposes of the assignment, assume the price includes all taxes, etc.

· Include the direct URL so your peers can view your big-ticket item.

· Using the simple interest formula, state your chosen interest rate and amount of time for your loan.

· Show the formula with numbers and describe the steps to compute the interest on the loan, I, and the total amount of the loan, A. You may use a calculator to perform the computations.

· Think about, then show the equations with numbers and describe the steps to compute the monthly payment, M, for the life of the loan. You may use a calculator to perform the computations.

· Explain one way to verify your monthly payment is correct. Show the formula and use a calculator for the computations.

Submit your initial post to the discussion by the fourth day of the module week. You must make your initial post before you can see your classmates’ posts.

Please proceed to the Response Prompts section.

Response Prompts

Read a selection of your classmates’ postings and reply to at least two using the following prompts. Your replies should address all parts of the prompt and be completed by the seventh day of the module week.

Reply 1

Respond to at least one classmate’s initial post by answering the following:

· Think about then show the formula with numbers for what happens to the interest, the total amount of a loan, and monthly payments of your classmate’s loan if the time was reduced by one and a half years at the start of the loan. You may use a calculator to perform the computations.

· Explain why your classmate will pay a different amount (more or less) for the loan in the end. Were you surprised by the results? Why or why not?

· If this was your loan and dream object, discuss one change you could make in your life to make the new monthly payment possible. What would you expect to happen if the time was increased at the start of your classmate’s loan? Why?

Reply 2

Respond to a different classmate’s initial post by answering the following:

· What do you think will happen if the interest rate provided in your classmate’s post was decreased by one percentage point at the start of the loan? Explain why.

· Confirm your answer. Show the formula with numbers and compute the new interest your classmate will pay with this new interest rate. You may use a calculator to perform the computations.

· Compare the interest of the two loans. Share with your classmate how much interest will be saved over the loan length.

Review the Discussion Rubric for detailed grading information.

Please proceed to the Why? section.

Why?

General Education Competencies

Critical Thinking

The student will apply knowledge at the synthesis level to define and solve problems within professional and personal environments.

Quantitative Reasoning

The student will demonstrate the use of digitally enabled technology (including concepts, techniques, and tools of computing), mathematics proficiency and analysis techniques to interpret data for the purpose of drawing valid conclusions and solving associated problems.

Your donut shop has perfected a method for the perfect glazed icing by slowly mixing whole milk to confectioner’s sugar while exposed to low heat. Your mixing tank starts with 10 fluid ounces of milk and 10 ounces of sugar. You continue adding sugar at a rate of 10 ounces per minute and milk at 2 ounces per minute, as depicted by the two equations below:

S=10+10t

M=10+2t

Where S represents the number of ounces of sugar, M represents the ounces of milk, and t represents the time in minutes.

Where S represents the number of ounces of sugar, M represents the ounces of milk, and t represents the time in minutes.

Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Create a rational equation to represent the concentration (C) in ounces of sugar per ounce of milk.

Part 2: Find the domain of the concentration equation.

Part 3: Will we ever encounter a time where the rational equation is undefined? Explain your reasoning.

Part 4: Calculate the concentration after five minutes.

Part 5: How long does it take to reach a concentration of 4 ounces of sugar per ounce of milk?

select ONE of the top best 100 mathematicians with the link provided.

Top 100 Best Mathematicians

https://fabpedigree.com/james/mathmen.htm

Write 5-10 pages research papers, see the guide below to help you write your own research papers.

These are the major components of an APA-style paper:

1.Title page

2.Author Name

3. Name of the institution with which the author is affiliated

4. Body, which includes the following:

o Headings and, if necessary, subheadings to organize the content o In-text citations of research sources

5.References page

Scenario

You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram attached below:

Assessment Instructions

SHOW and EXPLAIN all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Find the total area of flower bed.

Part 2: Write the area of the flower bed as an equation using multiplication of two binomials.

Part 3: Solve your equation from Part 2.

Part 4: Identify the extraneous solution and explain how it was determined to be extraneous.

Part 5: Find the width of the part of the flower bed with the daisies.

Scenario

The height, in feet, of an object shot upwards into the air with an initial velocity, in feet per second, of vi, after t seconds is given by the formula:

Use the equation above to answer questions about a model rocket is launched from the ground into the air with an initial velocity of 384 feet per second. Use the graph below to help answer the questions.

Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Create the equation for the height of the rocket after t seconds.

Part 2: Find the time it takes for the rocket to reach a height of 0. Interpret both solutions.

Part 3: Find the time it takes to reach the top of its trajectory.

Part 4: Find the maximum height.

Part 5: Find the time it takes to reach a height of 925 feet. Round your answer to the nearest tenth.

Scenario

You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram attached below:

Assessment Instructions

SHOW and EXPLAIN all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Find the total area of flower bed.

Part 2: Write the area of the flower bed as an equation using multiplication of two binomials.

Part 3: Solve your equation from Part 2.

Part 4: Identify the extraneous solution and explain how it was determined to be extraneous.

Part 5: Find the width of the part of the flower bed with the daisies.

The graph attached below is provided by a ride-sharing service in your area showing the cost, in dollars, of a ride by the mile.

Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Calculate the base fee (in dollars) charged by the ride-share service.

Part 2: Calculate the rate of increase in cost in dollars per mile.

Part 3: Identify the slope and y-intercept of the equation in the graph.

Part 4: Write the slope-intercept equation of the line in the graph.

Part 5: Use your equation from part 4 to extrapolate the cost of a 30-mile ride.

Scenario

A friend has given you left-over landscaping bricks. You decide to make a garden bed and surround it with the bricks. There are 86 bricks, and each brick is 8 inches long. You would like the garden bed to be slightly more than twice as long as it is wide, as shown in the diagram below. You have also given yourself a budget of $115 for additional materials should you need them. Your local home improvement store sells the same bricks for $1.25 per brick. The displayed sides present the number of bricks on each side, where x is a number of bricks.

Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Write an equation representing the perimeter of the garden bed.

Part 2: Calculate how many bricks are used on each side of the garden bed.

Part 3: Determine the length of each side after the bricks are added.

Part 4: Write an inequality that represents how many bricks can be purchased within your budget. Let y represent the number of bricks.

Part 5: Will you be able to make another complete layer of bricks on top and stay within your budget? Hint: your budget is only for the second layer of bricks.