You make a purchase at a local hardware store, but what you've bought is too big to take home in your car. For a small fee, you arrange to have the hardware store deliver your purchase for you. You pay for your purchase, plus the sales taxes, plus the fee. The taxes are 7.5% and the fee is $20. (i) Write a function t(x) for the total, after taxes, on the purchase amount x. Write another function f(x) for the total, including the delivery fee, on the purchase amount x. (ii) Calculate and interpret (f o t)(x) and (t o f )(x). Which results in a lower cost to you

Answers

Answer 1

Answer:

[tex]f(x) = 1.075x[/tex]

[tex]t(x) = x + 20[/tex]

[tex](f\ o\ t)(x) = 1.075x + 21.5[/tex]

[tex](t\ o\ f)(x) = 1.075x + 20[/tex]

Explanation:

Given

[tex]Tax = 7.5\%[/tex]

[tex]Fee = \$20[/tex] -- delivery

Solving (a): The function for total cost, after tax.

This is calculated as:

[tex]f(x) = Tax *(1 + x)[/tex]

Where:

[tex]x \to[/tex] total purchase

So, we have:

[tex]f(x) = x * (1 + 7.5\%)[/tex]

[tex]f(x) = x * (1 + 0.075)[/tex]

[tex]f(x) = x * 1.075[/tex]

[tex]f(x) = 1.075x[/tex]

Solving (b): Include the delivery fee

[tex]t(x) = x + Fee[/tex]

[tex]t(x) = x + 20[/tex]

Solving (c): (f o t)(x) and (t o f)(x)

[tex](f\ o\ t)(x) = f(t(x))[/tex]

We have:

[tex]f(x) = 1.075x[/tex]

So:

[tex]f(t(x)) = 1.075t(x)[/tex]

This gives:

[tex]f(t(x)) = 1.075*(x + 20)[/tex]

Expand

[tex]f(t(x)) = 1.075x + 21.5[/tex]

So:

[tex](f\ o\ t)(x) = 1.075x + 21.5[/tex]

[tex](t\ o\ f)(x) = t(f(x))[/tex]

We have:

[tex]t(x) = x + 20[/tex]

So:

[tex]t(f(x)) = f(x) + 20[/tex]

This gives:

[tex]t(f(x)) = 1.075x + 20[/tex]

We have:

[tex](f\ o\ t)(x) = 1.075x + 21.5[/tex] ---- This represents the function to pay tax on the item and on the delivery

[tex](t\ o\ f)(x) = 1.075x + 20[/tex] --- This represents the function to pay tax on the item only

The x coefficients in both equations are equal.

So, we compare the constants

[tex]20 < 21.5[/tex] means that (t o f)(x) has a lower cost


Related Questions

You are concerned about attacks directed at your network firewall. You want to be able to identify and be notified of any attacks. In addition, you want the system to take immediate action to stop or prevent the attack, if possible. Which tool should you use

Answers

Answer:

Intrusion Prevention System (IPS)

Explanation:

Firewall can be defined as a network security device that monitors incoming and outgoing network traffic and decides whether to allow or block specific traffic based on a defined set of security rules.

Simply stated, a firewall is a network security protocol that monitors and controls inbound and outbound traffic based on set aside security rules.

A firewall is used to control access to a computer or network, as it creates a barrier between a computer or a network and the internet in order to protect against unauthorized access.

Basically, it is a network security device or security system pre-installed on most computers to essentially inspect data being transmitted to or from a computer

Thus, the tool you should use is an intrusion prevention system (IPS).

is computers takes lots of time to do any mathematical calculations.​

Answers

Answer:

I think the answer is a computer take lost of time to do any mathematical calculations because problem in the book or questions.

Hope this helps you ^^

Equi Technologies offers cloud computing services to several data centers around the world. It hosts services in the cloud, which can be accessed by clients through Equibrowse-a Web browser designed by Equi Technologies. In the context of cloud computing services, it is evident that Equi Technologies provides _____.

Answers

Answer:

The answer is "Software as a service".

Explanation:

The software license strategy permits access to the software via a remote server through subscription-based access to the software. Rather than installing software on each user's PC, SaaS lets them access applications via the Internet.

For a number of reasons, it could save you money. Purchase/installation costs and also ongoing maintenance and upkeep are avoided, which is the primary benefit. SaaS apps may be easily downloaded and managed without breaking the bank on hardware parts and upgrades.

Which kind of image is indispensable and needs added text to go with it?

Answers

Answer:

A chart and a graph

Explanation:

Tables should be used when (a) the reader need not refer to specific numerical values. (b) the reader need not make precise comparisons between different values and not just relative comparisons. (c) the values being displayed have different units or very different magnitudes. (d) the reader need not differentiate the columns and rows.

Answers

Answer: (c) the values being displayed have different units or very different magnitudes

Explanation:

A table is refered to as an arrangement of data in rows and columns. Tables are used in research, communication, and data analysis.

Tables are used in the organization of data which are too complicated or detailed to describe and the use of table give a clearer description. Tables should be used when the values being displayed have different units or very different magnitudes. Tables can also be used in highlighting patterns or trends.

In what ways can technology help you be more productive? (Select all that apply.)
Enables you to create electronic documents that present your ideas clearly and effectively
Enables you to communicate with people anywhere in the world
Enables you to store documents on a thumb drive
Enables you to eliminate procrastination habits

Answers

Answer:

Enables you to create electronic documents that present your ideas clearly and effectively.

Enables you to communicate with people anywhere in the world.

Enables you to store documents on a thumb drive.

Explanation:

Technology is the use or application of scientific knowledge to the way we live life. In other words, we can say that technology is the branch of knowledge that deals with the use of technical means in everyday life.

One of the ways that technology can help people be more productive is that it enables one to create electronic documents that clearly and effectively present one's ideas. It also helps in the communication process, especially in between long distances. Added to that, technological use also enables us to store documents on a thumb drive and enables easy transfer of documents and files.

Thus, the correct answers are the first, second, and third options.

Plz help help help


What was the first electromechanical digital computer?

For your kind information I would like to tell you that don't search on internet because it will show ENIAC and that is not the answer the answeris may be ABC or MARK I. I am just confused, Please help me

Answers

Explanation:

For your kind information the answer of the question is MARK I.

Answer:

What was the first electromechanical digital computer?

=⟩ Mark I was the first electromechanical digital computer.

Hope it helpful to you

Considering what you know about dominant and recessive genes, what are the possible genotypes for brown eyed babies? What are the possible genotypes for blue eyed babies? Explain how you came to this response making sure to discuss dominant and recessive genes.

Answers

Answer:

B = Brown, b = blue

BB & BB = 100% Brown, 0% Blue

BB & Bb = 100% Brown, 0% Blue

Bb & Bb = 75% Brown, 25% Blue

Bb & bb = 50% Brown, 50% Blue

bb & bb = 0% Brown, 100% Blue

Explanation:

Reference the Punnett square. The brown gene when mixed with a blue gene  in one of the four squares is always dominant.

Which of the following statements is true about scalability? Choose 3 options.

Horizontal scaling has fewer limits than vertical scaling.

Scalability refers to the ability of hardware components to increase their capacity.

Scalability should be considered very early in the project.

The cloud offers services to automatically scale your system and balance the workload between components.

An example of vertical scaling is adding a new server to the network.

Answers

Answer:

Horizontal scaling has fewer limits than vertical scaling.

The cloud offers services to automatically scale your system and balance the workload between components.

Scalability should be considered very early in the project.

Explanation:

Hope this helps :) If not, please let me know what answers are wrong

The statements that is true about scalability are:

The clouds provide resources to scale the system and balance the workload between components

Scalability should be considered at the beginning of the project.

Horizontal scaling has fewer limits than vertical scaling.

Horizontal scaling is a type of scaling by adding more machines to your po of resources.

It is also called adding more power.

The difference between scaling up and scaling out is that horizontal scaling simply adds more machine resources to your existing machine infrastructure.

Vertical scaling is simply known to adds power to your existing machine infrastructure by increasing power from CPU or RAM to existing machines.

Conclusively, Scalability part of a system that handle a growing amount of work by adding resources to the system.

Learn more from

https://brainly.com/question/17661222

describe in detail what each step would look like if you ran into a software error.

Answers

Answer:

First you have to identify the problem.

Second Gather information.

Third iterate through potential solutions.

Fourth Test your solution.

Explanation:

There are many different ways to handle errors in software but this is the way I do it.

Hope this helps :)

After running into a software error, a user needs to first determine the reason for the error, work towards a solution and then execute the solution discovered.

Software Error

A software error occurs when an error or unusual behaviour is observed in a piece of software and which can be reproduced after certain actions are performed that are in line with the stated rules of the software developer. In other words, a software error does not occur if the software was not used as directed by the software developer.

You can learn more about software errors here https://brainly.com/question/18497347

#SPJ6

Hey, um guys help me as my laptop will not turn off properly as whenever i turn it off, it will turn back on by me pressing a key please help!!! URGENT!!!

Answers

Answer:

hold the power key until you restart.

Explanation:

write down the appropriate technical term of following statements.​

Answers

Answer:

it is not seeing full. please give full

Lori Redford, who has been a member of the Project Management group, was recently promoted to manager of the team. She has been added as a member of the Managers group. Several days after being promoted, Lori needs to have performance reviews with the team she manages but she cannot access the performance management system. As a member of the Managers group, she should have the Allow permission to access this system. What is most likely preventing her from accessing this system

Answers

Answer:

she is still a member of the Project Management group

Explanation:

The most likely reason for this is that she is still a member of the Project Management group. This would prevent her from accessing the performance management system. The performance management system most likely allows access to the Managers Group but denies access to the Project Management Group. Therefore, since the deny access overrides the allow access, it would ultimately cause Lori to be unable to access the system. In order to fix this, she would simply need to leave the Project Management Group.

state whether the following statement are true or false​

Answers

The following statement is true , Please mark me brainliest

Which of these functions may be used with positional arguments? Select four options.

AVERAGE
COUNTIF
COUNT
SUM
MAX

Answers

Answer:

AVERAGE

COUNT

SUM

MAX

Explanation:

The functions that may be used with positional arguments include:

AVERAGE

COUNT

SUM

MAX

The basic functions formulae include SUM, AVERAGE, COUNT, MAX and MIN.

SUM: This is the sum total of all the numbers in the rows.

COUNT: This is the used to count the range of cells that contains numbers.

AVERAGE: This is the average of all the numbers in the rows.

MIN: This is the lowest number in the rows.

MAX: This will return the highest number that is found in the set of values.

It should be noted that the COUNTIF is not used with positional arguments.

What is the purpose of requirements gathering and analysis?

Answers

Answer:

The purpose of Requirements Analysis is to discover unknown requirements, i.e., to turn unknown requirements into known requirements. Users' needs that were not expressed during requirements gathering and elicitation can be uncovered through Requirements Analysis.

Explanation:


Emilio wants to add a name field for his clints. From the ribbon, which icon should be selected?

Answers

your answer is (more fields) then press enter

________ is the type of security loss that involves computer criminals invading a computer system and replacing legitimate programs with their own unauthorized ones that shut down legitimate applications and substitute their own processing to spy, steal, and manipulate data.

Answers

Answer:

Usurpation

Explanation:

In context of CIBS-210 it is known as Usurpation

Explain What Peer to Peer Networking is.

Answers

Answer:

peer to peer networking is like when joining together works

Programming languages create codes that represent binary numbers so that programmers can write in a language closer to natural speech.

Answers

Answer:

True

Explanation:

A software can be defined as a set of executable instructions (codes) or collection of data that is used typically to instruct a computer how to perform a specific task and to solve a particular problem.

This ultimately implies that, programming languages are designed and developed for creating codes that represent binary numbers (0s and 1s), so that programmers or software developers can write in a language closer to natural speech i.e the human language.

What are the uses of magnetic force?​

Answers

Explanation:

Computer hard drives use magnetism to store the data on a rotating disk. More complex applications include: televisions, radios, microwave ovens, telephone systems, and computers. An industrial application of magnetic force is an electromagnetic crane that is used for lifting metal objects.

Answer:

Examples of magnetic force is a compass, a motor, the magnets that hold stuff on the refrigerator, train tracks, and new roller coasters. All moving charges give rise to a magnetic field and the charges that move through its regions, experience a force.

I Hope this will help you if not then sorry :)

what allows an individual or company to share a post with an audience however they are designed to be used with mobile devices and limit the size of posts

Answers

Answer:

E-mail

Explanation:

The sending of messages via the Internet is known as e-mail. It is one of the most often utilised functionalities for sending text, files, pictures, and other attachments across a communications network.

A podcast lets a person or corporation to share articles with an audience, but it is geared for usage on mobile devices and has a capacity restriction.

donde veo haikyuu en español sin lag ni virus :C (la segunda, tercera y cuarta temporada)

Answers

Answer:

keep in English language

Explanation:

keep in English

ou have a company network that is connected to the internet. You want all users to have internet access, but you need to protect your private network and users. You also need to make a web server publicly available to internet users. Which solution should you use

Answers

Server and network is 2 different things, just put the server on a different network.  ;) duh

Explanation:

what is the example of HTML?​

Answers

Answer:

For example, content could be structured within a set of paragraphs, a list of bulleted points, or using images and data table

Similarities between in line css and internal css

Answers

Answer:

inline css is used to style a specific html element. for this css style, you'll only need to add the style attribute to each html tag, without using selectors. this css type is not really recommended, as each html tag needs to be styled individually. managing your website may become too hard if you only use inline css.

Explanation:

queens

The mainframe computer are the ____ and most ____ computers..​

Answers

Answer:

Mainframe computer are the larger system computers and most expensive computer.


b. "The actual use and implementation of computer started after third generations".
Justify this statement in your own words.

Answers

Answer:

The use of computers and planning of them didnt start until after the third generation.

Explanation:

Hope it helps✌✌

Answer: The computers of third generation used IC which replaced transistors. Now' the computers were more faster ,smaller and reliable so people started to use them often for many purposes ..So the actual use and implementation of computer started after third generations

What is thesql command to list the total sales by customer , month , and product, with subtotals by customer and by month and a grand total for all product sales

Answers

Answer:

The answer is below

Explanation:

The the sql command to list the total sales by customer , month , and product, with subtotals by customer and by month and a grand total for all product sales is:

SELECT S.CUS_CODE, T.TM_MONTH, S.P_CODE,

SUM(S.SALE_UNITS*S.SALE_PRICE) AS "TOTSALES"

FROM DWDAYSALESFACT AS S INNER JOIN DWTIME AS T ON S.TM_ID =

T.TM_ID

GROUP BY S.CUS_CODE,T.TM_MONTH,S.P_CODE WITH ROLLUP;

Define Artificial Intelligence(AI) in 5 sentence​

Answers

Answer:

Artificial intelligence (AI) refers to the simulation of human intelligence in machines that are programmed to think like humans and mimic their actions. ... The ideal characteristic of artificial intelligence is its ability to rationalize and take actions that have the best chance of achieving a specific goal.

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