Find a finite inseparable extension that is not a simple extension.

Answers

Answer 1

The field extension K = F(x), where F is a field of characteristic 2 and x satisfies the equation x^2 + x + 1 = 0, serves as an example of a finite inseparable extension that is not a simple extension.

A finite inseparable extension refers to an extension field where every element is inseparable over the base field. On the other hand, a simple extension is an extension field generated by a single element. To find a finite inseparable extension that is not a simple extension, we can consider a specific example.

Let's work with the base field F of characteristic 2 (where 2 does not have an inverse) and construct the field extension K = F(x), where x satisfies the equation x^2 + x + 1 = 0. This is a quadratic polynomial without any roots in F since the characteristic of F is 2. Therefore, K is a degree 2 extension over F.

To show that K is inseparable, we can examine the minimal polynomial of x over F, which is x^2 + x + 1. Taking the derivative of this polynomial with respect to x, we get 1. Since the derivative is non-zero, it implies that K is inseparable over F.

Now, let's demonstrate that K is not a simple extension. Suppose K is generated by a single element, say y. Then every element in K can be expressed as a polynomial in y with coefficients in F. However, we know that K contains elements such as x that are not expressible as polynomials in y. Therefore, K cannot be a simple extension.

In conclusion, the field extension K = F(x), where F is a field of characteristic 2 and x satisfies the equation x^2 + x + 1 = 0, serves as an example of a finite inseparable extension that is not a simple extension.

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Related Questions


Which character is often used to identify registered trademarks and is available on the Insert tab and Symbols group?

Answers

Answer:"TM"

Explanation:

Answer:

TM

Explanation:

because its used to identify, trademarks and etc. mark brainliest! i also got 100 on the quiz

What term is used to describe how mobile computing allows individuals to initiate real-time contact with other systems anywhere, any time since they carry their mobile device everywhere?.

Answers

Broad reach  term is used to describe how mobile computing allows individuals to initiate real-time contact with other systems anywhere, any time since they carry their mobile device everywhere.

What exactly does mobile computing communication entail?

A form of communication known as mobile communications does not require a direct physical link between the sender and the recipient. During conversation, it makes it easier for users to travel from one physical location to another.

Most popular forms of technology for communication-

GSM stands for Global Systems for Mobile Communications.Orthogonal Frequency Division Multiplexing (OFDM) is a technique used in the Long Term Evolution (LTE), Code Division Multiple Access (CDMA), and Universal Mobile Telecommunication System (UMTS) systems.

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The HTML tag that begins the visible part of the web page is


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The HTML tag that begins the visible part of a web page is the "body" tag.

What is the HTML tag?

The "body" tag is used to define the main content area of a web page, and it is where most of the text, images, and other elements that make up the page are placed.

The body tag is defined as follows:

<body>

 <!-- content goes here -->

</body>

Therefore, Within the body tag, you can add various HTML elements, such as headings, paragraphs, lists, images, and more, to create the content of the web page. The content that you add to the body tag will be displayed in the browser window when the page is loaded.

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Answer:<body>

Explanation:

What is a captcha? how has the collective efforts of internet users contributed to analyzing images through captchas?

Answers

Captcha is a spam prevention tool integrated into many user-facing websites.

What is a Captcha?

The captcha tool is a modern-day internet invention that helps to separate human internet users from bots any time they interact on a website. What this tool does is provide a series of challenges that only a human mind would easily understand and perform, such as asking the user to type in letters into a box, or identify certain images.

Indeed, the collective efforts of internet users have contributed to preventing spam traffic on websites today as a result of captcha integration on websites.

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Which laptop has the larger non volatile storage capacity

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There are many laptops available with different specifications and storage options. However, some of the laptops with larger non-volatile storage capacity include:

1. MacBook Pro (16-inch): This laptop offers storage options ranging from 512GB to 8TB.

2. Dell XPS 15: This laptop offers storage options ranging from 256GB to 2TB.

3. HP Spectre x360: This laptop offers storage options ranging from 256GB to 2TB.

4. ASUS ROG Zephyrus G14: This laptop offers storage options ranging from 512GB to 1TB.

5. Acer Aspire 5: This laptop offers storage options ranging from 256GB to 1TB.

It is important to note that the storage capacity of a laptop depends on the model and can vary.

________ are programs that attach themselves to legitimate programs. Group of answer choices Direct-propagation worms Worms Payloads Viruses

Answers

Answer:

Worms / Viruses / Trojan Horse Virus

Explanation:

A worm is a standalone program that can self-replicate and spread over a network. Unlike a virus, a worm spreads by exploiting a vulnerability in the infected system or through email as an attachment masquerading as a legitimate file.

A computer network that is restricted to the organization it serves; an internal internet.t/f

Answers

A computer network that is restricted to the enterprise it serves is called an internal internet. Therefore, the statement given is a true statement.

An internal internet also referred to as an intranet is a local network that  is only accessible to people within an enterprise. The internal internet is the most restricted network. It can be stated as the internal internet is a private network setup within an enterprise that is used to securely share organizational information and computing resources among its employees.

Therefore, it is concluded that the internal internet or intranet is the restricted computer network to be used by the enterprise only.

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Consider the following instruction stream: 1. 2. 3. 4. 5. 5. 7. add t3, to, ti lw t2, 0(t3) neg t2, t2 addi t2, t2, 1 lw t4, 4(t3) add t4, t4, t2 sw t4, 4(+3) (2 points each) a. Assume all load and store instructions (lw and sw) require 12 clock pulses while all other instructions require 5 clock pulses. What is the CPI of this instruction stream? b. If the clock frequency is 1 GHz, what is the CPU time for part a? C. Assume the first lw instruction (instruction 2) now requires 18 clock pulses but the following lw and sw (instructions 5 and 7) only require 6 clock pulses. What is the new CPI of this instruction stream? d. If the clock frequency is 1 GHz, what is the CPU time for part c? e. The number of clock pulses for the first lw instruction increased from 12 in part a to 18 in part c. Despite this increase, part c has a better CPU time. Why does part c have a better CPU time?

Answers

(a) CPI = 5.5, (b) CPU time = 5.5 ns, (c) CPI = 4.8, (d) CPU time = 4.8 ns,   (e) shorter load times in c.

a. The total number of clock cycles required for this instruction stream is:

5 + 12 + 5 + 5 + 12 + 5 + 5 = 49

The average CPI (cycles per instruction) is:

49/7 = 7

b. The CPU time is given by:

CPU time = Instruction count x CPI / Clock rate

Assuming 1 instruction per clock cycle, the instruction count is equal to the number of clock cycles, which is 49.

Therefore, the CPU time is:

49 / (1 x \(10^9\) ) = 49 ns

c. The new total number of clock cycles required for this instruction stream is:

5 + 18 + 5 + 5 + 6 + 5 + 6 = 45

The new average CPI is:

45/7 = 6.43

d. The CPU time is:

45 / (1 x \(10^9\) ) = 45 ns

e. Although the first lw instruction requires more clock cycles in part c, the overall CPI for the instruction stream is lower because the subsequent lw and sw instructions require fewer clock cycles. This reduces the average CPI for the instruction stream, resulting in a better CPU time despite the increased clock cycles for the first lw instruction. This highlights the importance of optimizing instruction scheduling and taking into account the impact of subsequent instructions on overall performance.

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Your team has already created a WBS for the ABC product launch project. You are kicking off phase 2 of this project, which is the product development phase. Which of the following is an example of what might appear in the second level of your project's WBS?

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In the second level of the project's Work Breakdown Structure (WBS) for the product development phase, you might find more specific deliverables or components that contribute to the overall development of the ABC product. Here is an example:

Second level of the WBS:

1. Product Development Phase

  1.1 Concept Design

      - Conduct market research

      - Define product requirements

      - Generate product concepts

  1.2 Detailed Design

      - Develop product specifications

      - Create 3D models and prototypes

      - Perform engineering analysis

  1.3 Testing and Validation

      - Conduct functional testing

      - Perform reliability testing

      - Validate product performance

  1.4 Manufacturing Preparation

      - Design manufacturing processes

      - Create production plans

      - Source raw materials and components

In this example, the second level of the WBS breaks down the product development phase into four sub-categories: concept design, detailed design, testing and validation, and manufacturing preparation. Each sub-category represents a distinct area of focus within the product development phase and includes specific tasks or activities related to that area.

Note: The specific structure and content of the WBS can vary depending on the project's requirements and the organization's preferences. The example provided above is just one possible representation.

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You may use Linux to make a ______________ of the hard drive.
A. Bootable copy
B. Screen shot
C. New version
D. Forensically valid copy

Answers

You may use Linux to make a forensically valid copy of the hard drive. Hence, D. is the correct answer.

A redundant copy of your computer's system disk is called a bootable backup. The operating system and application software are identical to those on your system drive. Additionally identical are the user configuration and all data files.

Including all files, directories, and unallocated, free, and slack space, a forensic image (forensic copy) is a direct bit-by-bit, sector-by-sector replica of a physical storage device.

A screenshot is an image that captures the contents of a computer monitor. It is sometimes referred to as a screencap or screengrab. Using screenshots, you can record exactly what's on your screen for later sharing or reference.

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how do you determine whether a column contains one of a particular set of values without using an and condition?

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In order to determine whether a column contains one of a particular set of values without using an AND condition, one can use the IN operator. The IN operator enables a user to specify multiple values in a WHERE clause and retrieve only those rows where a column matches at least one value in the specified set.

The IN operator in SQL is a comparison operator that allows us to define multiple values in a WHERE clause. It is used to retrieve rows based on a specific set of values in a specified column.

The syntax of the IN operator in SQL is as follows:
SELECT column_name(s)
FROM table_name
WHERE column_name IN (value1, value2, ...);

Here is an example to illustrate the use of the IN operator:

Suppose we have a table named "employees" with columns "emp_id", "emp_name", and "emp_dept". To retrieve rows where the "emp_dept" column contains either "Sales" or "Marketing" we would use the following query:

SELECT *
FROM employees
WHERE emp_dept IN ('Sales', 'Marketing');

This query will return all rows where the "emp_dept" column contains either "Sales" or "Marketing". The IN operator allows for more concise and efficient querying of large datasets.

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Could Anyone help me with these two questions?

Could Anyone help me with these two questions?
Could Anyone help me with these two questions?

Answers

Answer:1st is b

2nd is d

Explanation:


i
need this wepsites


websites using e-commerce and what type of business model and
what strategy they are using

Answers

There are numerous websites using e-commerce with various business models and strategies.

The e-commerce landscape is vast and diverse, with countless websites utilizing e-commerce to conduct business. Each website adopts a specific business model and employs various strategies to succeed in the online marketplace.

Some prominent e-commerce websites include Amazon, which operates under a business-to-consumer (B2C) model and focuses on a wide range of products, utilizing strategies like competitive pricing, fast shipping, and personalized recommendations to attract and retain customers.

Another example is Shopify, which offers an e-commerce platform as a service, catering to businesses of all sizes with features such as customizable storefronts, secure payment processing, and marketing tools.

Additionally, there are niche e-commerce websites like Etsy, which follows a business-to-consumer (B2C) model and specializes in handmade and unique products.

Etsy's strategy includes fostering a sense of community among sellers and buyers, emphasizing craftsmanship, and promoting sustainable and ethical practices.

Furthermore, there are direct-to-consumer (D2C) brands like Warby Parker and Glossier, which focus on selling their products directly to customers through their online platforms.

These brands often prioritize customer experience, storytelling, and building strong brand identities.

Overall, e-commerce websites employ different business models and strategies to cater to their target audience, differentiate themselves in the market, and drive sales and customer engagement.

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Help FAST PLS in complete sentences discuss the process used to determine your credit score. Do you think it is fair? Why or why not? Make sure to use complete sentences.

Answers

Answer:

A fair credit score just means that the credit reference agencies think you're doing an okay job of managing your credit history. ... This means lenders could reject you for some of the best credit cards or loans

What should a technician do when solving a problem is beyond their ability?
-Ask the customer for advice
-Disassemble the system and rebuild it from scratch
-Tell the customer that the problem cant be fixed
-Escalate

Answers

Escalate the problem to higher-level technical support or seek assistance from experienced colleagues when it is beyond the technician's ability to solve.

How to handle challenging technical problems?

When confronted with a problem beyond their ability, a technician should follow the best course of action by escalating the issue. Escalation involves seeking assistance from higher-level technical support or experienced colleagues who possess the necessary expertise.

By doing so, the technician ensures that the problem receives attention from individuals who are better equipped to handle it. Simply asking the customer for advice may not yield a satisfactory solution if the technician lacks the necessary knowledge or skills.

Disassembling the system and rebuilding it from scratch without the requisite expertise can lead to further complications or damage. Informing the customer that the problem cannot be fixed without exploring all available options can result in dissatisfaction.

Escalation is a responsible approach that allows for a higher level of technical expertise to be engaged, increasing the likelihood of successfully resolving the problem.

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puung.
f. Differentiate between second and third Generation Computer
IG ANSWER QUESTIONS​

Answers

Answer:

Second generation computers were based on transistors, essentially the same as first generation computers, but with the transistors replacing the vacuum tubes / thermionic valves.

Third generation computers used printed circuit boards to replace much of the wiring between the transistors. This had the advantage that components could be mass produced, reducing the number of errors because of incorrect wiring and making the component boards replacable.

Explanation:

hope it is helpful to you

puung.f. Differentiate between second and third Generation ComputerIG ANSWER QUESTIONS

Which is a screen that shows information from a computer​

Answers

computer monitor is an output device that displays information in pictorial form. A monitor usually comprises the visual display, circuitry, casing, and power supply.

What it job is in charge of a software application development team that develops, designs, and tests software applications?.

Answers

Answer:

Head Applications Developers

After securing your space at the end of the day, you should try to badge back in to ensure it is locked.a. Trueb. False

Answers

Answer:

True

Explanation:

What do you mean by gigo?Explain in breif​

Answers

Answer:

garbage in garbage out

Explanation:

it means bad input gives you also a bad output.

could you mark me as brianlist.

How do i fix this? ((My computer is on))

How do i fix this? ((My computer is on))

Answers

Answer:

the picture is not clear. there could be many reasons of why this is happening. has your computer had any physical damage recently?

Answer:your computer had a Damage by u get it 101 Battery

and if u want to fix it go to laptop shop and tells him to fix this laptop

Explanation:

What are the two main types of software​

Answers

system software and application software

Answer:

System software and application software

Explanation:





The concept of vertical farming allows agriculture to occur when there is not enough___Available .

Answers

Answer:

land

Explanation:

Vertical farming is a modern method of farming or growing crops and vegetation. It allows growing of crops in stacked layers which is vertical. The crops are grown in a well equipment controlled-environment set up.

Vertical farming is done where there is fewer land resources as well as water resources. The main is to increase the crop yield with a very less use of land resources. But it requires more energy than the conventional energy.

A misplacement of punctuation or spacing in a command during programming that causes the program to stop running is most likely which type of error?

Answers

Answer:

Please mark me the brainliest

Explanation:

A misplacement of punctuation or spacing in a programming command that causes the program to stop running is most likely a syntax error.

Some key types of errors in programming include:

• Syntax errors - Mistakes in the structure or order of commands that make the code invalid. This includes things like mismatched brackets, semicolons in the wrong place, incorrect indentations, etc. These prevent the program from running properly.

• Semantic errors - Commands that are syntactically correct but logically wrong. The code runs but produces an incorrect output.

• Logical errors - Bugs in the programmer's logic and reasoning that lead to the program not working as intended.

• Runtime errors - Issues that only appear when the program is running, such as dividing by zero.

• Resource errors - Problems accessing files, memory, databases, etc. that the program needs to function.

• Spelling errors - Simple typos in command names, variable names, function names, etc. These can often be hard to spot but cause the code to break.

Based on the description provided, it is clear that a misplaced punctuation mark or extra/missing space would result in invalid syntax, causing the program to stop running. The code would no longer be properly formatted or structured, resulting in a syntax error.

So in summary, a spacing or punctuation issue leading to a program crash would likely indicate a syntax error, which is one of the most common and frustrating types of errors for programmers to debug.

Please let me know if this helps explain the concept or if you have any other questions!

Edmentum Question- Consumer and Credit Loans

When would someone be restricted from filing for bankruptcy?

A. if the debtor fails the asset test

B. if the debtor fails the income-liability test

C. if the debtor fails the credit-overload test

D. if the debtor fails the means test

Answers

Answer:

D, if the debtor fails the means test

Explanation:

i took the test on platos and got it right

All of the following are key design principles of responsive web design except:
1. A) exible grid-based layouts. 2. B) media queries. 3. C) coding by convention. 4. D) exible images and media.

Answers

The key design principle of responsive web design that is not listed among the options is C) coding by convention.

Responsive web design is an approach to designing and building websites that aim to provide an optimal viewing experience across various devices and screen sizes. It involves adapting the layout, design, and content of a website dynamically based on the characteristics of the device accessing it.

The design principles of responsive web design include:

1. A) Flexible grid-based layouts: This principle involves using fluid grid systems that adjust and scale the layout based on the screen size. It allows content to be displayed proportionally and optimally on different devices.

2. B) Media queries: Media queries enable the website to apply different styles and layout rules based on the characteristics of the device, such as screen size, resolution, and orientation. This ensures that the website adapts and responds to different devices appropriately.

3. D) Flexible images and media: This principle involves using techniques like CSS to make images and media elements flexible and responsive. It ensures that images and media adjust in size and scale proportionally based on the device's screen size.

Therefore, the correct answer is **C) coding by convention**, as it is not a key design principle of responsive web design.

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15 points please help!!!!


David works at a company that provides financial solutions. He wants to create an interactive presentation for his company. Which interactive platforms can David use for this presentation?

David can use an interactive or a for his presentation.

Answers

Answer:

Powerpoint presentation

Explanation:

Powerpoint presentation is a part of Microsoft office that is established by Microsoft. PowerPoint. It is used to present the company visions, missions, key points in a short and in an attractive way by using the various designs, pictures, audio clips, etc

Here David wants to create an interactive presentation so he should use the powerpoint presentations so that he could present the company visions, objectives, etc

Why is special code needed for <?

Answers

The guy above is right!!!

pls help!! which of the following is not a step required to view a web page?

pls help!! which of the following is not a step required to view a web page?

Answers

The first one! It’s not required to view web pages

what is an advantage of a computer billing system related to posting payments

Answers

One advantage of a computer billing system related to posting payments is the automation and efficiency it brings to the process.

An advantage of a computer billing system related to posting payments is the automation and efficiency it offers in the payment processing workflow. With a computerized system, payment information can be electronically captured, recorded, and posted to customer accounts in a streamlined manner.

Here are some key points of explanation:

Automation: A computer billing system automates the payment posting process, eliminating the need for manual entry of payment details. Payment information can be directly imported from various sources, such as electronic payment gateways, bank transactions, or scanned checks. This reduces the chances of human errors that may occur during manual data entry.

Accuracy: Computerized payment posting ensures a higher level of accuracy compared to manual methods. The system can perform validation checks and match payment information against customer accounts, ensuring that payments are accurately allocated. This helps to minimize errors, discrepancies, and potential issues related to incorrect payment postings.

Speed and Efficiency: By leveraging technology, a computer billing system enables faster processing of payments. Payments can be posted in real-time or batched for efficient handling. This reduces the time required to manually process and post payments, allowing billing personnel to focus on other critical tasks. Customers also benefit from faster updating of their account balances and payment records.

Integration and Reporting: A computer billing system can seamlessly integrate with other financial systems and generate comprehensive reports related to payment posting. This enables better financial management and tracking of revenue streams. Detailed reports can be generated, including payment histories, outstanding balances, and reconciliation statements, providing valuable insights for financial analysis and decision-making.

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Other Questions
On a cold winter day, Joel and Duncan brought a container of hot chocolate with them to go sledding. There were 15 ounces of hot chocolate, and they split it evenly. How much hot chocolate did each boy get? Exercise 2: Consider two households, A and B and two goods, and . Overall, there are 10 units of good and 8 units of good that the households A and B can share.The utility that household A gathers when consuming xA units of good and yA units of good is given by A = xA + 4yA 1/2 (yA )^2The utility that household B gathers when consuming xB units of good and yB units of good is given by B = xB + 6yB 1/2 (yB)^2Questions:1. Assume that each household owns some positive initial endowments of the goods such that, overall, they have 10 units of good and 8 units of good . Assume as well that they set up a market where the price of good is 1. Find the equilibrium price for good and the resulting consumption of good for each household. PLEASE ANSWER BOTH PARTS:PART A:Bill buys a single call option with an exercise price of $20 for $3.75 from Simon.What is Simon's profit if the stock price is $0 on the expiration date of the option?What is Simon's profit if the stock price is $50 on the expiration date of the option?What is Simon's profit if the stock price is $100 on the expiration date of the option?PART B:You have bought 1 share of stock for $24.06 and 4 call options on the same stock. Each option has an exercise price of $30, cost $3.99 each, and expires in three months.What is your profit from buying the stock (only) if the stock price is $20 in three months (in $)? Ignore the options for now.What is your profit from buying the options (only) if the stock price is $50 in three months (in $)? Ignore the stock for now.What is your total profit if the stock price is $100 in three months (in $)? Question 6 > A person going to a party was asked to bring 4 different bags of chips. Going to the store, she finds 17 varieties. How many different selections can she make? Question Help: Video Writte Find the greatest common divisor d of 3982 and 29874, express d in the form d = $3982 + t29874, = where s and t are integers and explain how you can find infinitely many pairs of integers (s', t') such that kd = s'3982 + t 29874 = une values of , y and z. 2. The function f is defined, for x > 0, by Inc ka f(3) = k where k is some positive constant. Determine the values of k for which f has critical (or stationary) points. 2+1 F fill in the blank. The ______ component of assertiveness skills concerns knowing where and when not to behave assertively. Question 10 of 20 One of the Union's major advantages during the early years of the Civil War was having: O A. alliances with European countries. B. a more industrialized economy. O C. a highly organized military. O D. few political divisions. All of the following statements are the part of Darwin's theory of natural selection exceptGenetic variation exists among individuals in a population.The size of most populations remains relatively constant, despite the fact that more offspring are produced than are needed to maintain it.Early settlers saved seed only from the most productive crop plants to plant the following year.Disease, competition, and other environmental forces tend to eliminate the individuals in a population that are less adapted to their environment.Individuals that are best adapted to their environment tend to pass on heritable advantageous characteristics to their offspring. Stock price is S0=$50.S0=$50. Only one (discrete) dividend $5$5is going to be paid in 9 months. Continuously compounded risk-freeinterest rate is 12%. Var(FP0,1(S))=0.01Var(F0,1P(S))=0.01 in 1year. Without solving, determine the character of the solutions of the quadratic equation in the complex number system, 3x-3x+1=0 as a 4.4-kg object moves from (2 i 5 j) m to (6 i - 2 j) m, the constant resultant force acting on it is equal to (4 i - 3 j) n. if the speed of the object at the initial position is 4.9 m/s, what is the work done by the force, and what is its kinetic energy at its final position? as your answer in canvas, write the kinetic energy in joules.\ bob produces dvd movies for sale, which requires a building and a macine that copies the original movie onto a dvd Explain (in details) the following two (2) types of secondarysecurities markets:i. organized exchangesii. over the counter market Wilson Company reports the following expenditures related to plant assets for the most recent fiscal year! Replacing worn-out machine gears: $1,125Routine vehicle maintenance: $ 875Replacement engine for delivery van: $2,600Expansion of production facility: $84,500 Painting of office building: $ 1,800 Installation of heating system: $ 6,200 Wilson's accountant records all expenditures as capital expenditures. As a result, net income will be A.understated by $10,000. B understated by $93,300. C. overstated by $3,800. D. overstated by $81,575. Why do people buy stock/invest in Blue Apron Holdings Inc. andApple Inc.?300+ words each please Put the steps in correct order to prove that if n is a perfect square, then n + 2 is not a perfect square.1).Lets assume m 1.2) If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)^2.3) Hence, n + 2 is not a perfect square4) Expand (m + 1)^2 to obtain (m + 1)^2 = m2 + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.5) .Assume n = m2, for some nonnegative integer m Aunt Petra has deposited $33,000 today into an account that will earn 10 percent per year. She plans to leave the funds in this account for seven years earning interest. If the purpose of this deposit is to cover a future obligation of $65,000, what recommendation would you make to Aunt Petra? Is this investment right for you, yes or no? explain. howdo publice pension plans differ in other countries? Hasprivatization worker overseas? The formula for budgeted direct materials purchases is: Multiple Choice Budgeted production units + Ending direct materials inventory Beginning direct materials inventory o Budgeted production units + Beginning direct materials inventory Ending direct materials inventory production unis + Begini Materials needed for production + Ending direct materials inventory Beginning direct materials inventory O Materials needed for production + Beginning direct materials inventory Ending direct materials inventory materials needed for production + Beginning direct materials