A bookkeeper using a traditional paper system should not only credit the Checking account when a purchase is made. This is not the correct approach because it ignores the fundamental accounting principle of double-entry bookkeeping.
In double-entry bookkeeping, each transaction affects at least two accounts: one account is debited, and another account is credited. When a purchase is made, the Checking account should be credited, and an Expense or Asset account should be debited, depending on the nature of the purchase. This ensures that the financial records remain balanced and accurate.
For example, let's say a company purchases office supplies for $100. The bookkeeper should record a debit of $100 to the office supplies expense account and a credit of $100 to the checking account. If the bookkeeper only credits the checking account and doesn't debit the office supplies expense account, the company's financial statements will not show the $100 expense, and the net income will be overstated by $100.
Therefore, it is essential to follow the principles of double-entry bookkeeping and record each transaction in at least two accounts to ensure accuracy in financial records.
Learn more about Transactions: https://brainly.com/question/1016861
#SPJ11
When making decisions, managers often must decide between doing what is beneficial for the firm in the short term, and what is beneficial for both the firm and society in the long term. To address this conflict, a firm must
When making decisions, managers are often faced with a conflict between what is beneficial for the firm in the short-term and what is beneficial for both the firm and society in the long-term.
This conflict arises because the actions that benefit the firm in the short-term may not necessarily align with the interests of society as a whole, which can lead to negative consequences for both the company and society in the long-term.
To address this conflict, a firm must adopt a long-term orientation and consider the broader social and environmental impacts of its decisions. This means looking beyond immediate financial gains and recognizing that actions taken today can have far-reaching implications for the company's reputation, customer loyalty, employee morale, and overall sustainability.
Firms that prioritize social responsibility and sustainable business practices are more likely to build strong relationships with stakeholders, including customers, employees, investors, and regulators. They are also better equipped to weather economic downturns and other disruptions, as they have diversified their risk and invested in building resilient supply chains and communities.
Ultimately, the key to addressing the conflict between short-term gains and long-term benefits is a commitment to corporate social responsibility (CSR) and sustainable business practices. By prioritizing the needs of society and the environment alongside those of shareholders, firms can create value for all stakeholders over the long-term, ensuring their continued success and impact.
learn more about managers here
https://brainly.com/question/32150882
#SPJ11
True or False and Explain Why: According to the Consumption CAPM, the bigger the variance of an asset's return, the bigger its expected return will be.
The statement is false because according to the Consumption CAPM, the expected return of an asset is determined by the covariance between the asset's return and the marginal utility of consumption, and not by the variance of the asset's return.
The Consumption CAPM posits that investors care not only about the returns they earn on their investments, but also about the consumption opportunities those returns provide. Therefore, the expected return of an asset is based on its correlation with the marginal utility of consumption, rather than its variance.
In fact, the Consumption CAPM predicts that investors will be willing to accept a lower expected return on an asset that has a high covariance with their marginal utility of consumption, even if the asset has a lower variance.
Learn more about assets https://brainly.com/question/14404094
#SPJ11
What are three elements of negligence?
Actual Harm
Breach of duty
State of mind
Duty of care
Proximate cause
Motive
Answer:
actual harm
breach of duty
duty to act
New Agency Debby Just got a job as an assistant in a new federal agency called the Accounting Commission that was set up to regulate the accounting and auditing profession. The agency is headed by commissioners who serve for fixed terms and cannot be removed except for cause. Additionally, no more than a majority of the commissioners may be from the same political party. Her agency is getting ready to Issue rules. The enabling legislation that set up the Accounting Commission specified that the agency could make rules but said nothing about the form of the rules. Debby's boss, Blare, gave her some proposed rules and asked her to be sure that they were published and to take care of the next step in the approval process. Blalte also told her that at this point she was not very interested in hybrid rule making. After publication, What would be the next step in obtaining enactment of the proposed rules?
A. vote in the United States Congress
B. Approval by the US president through the stance of an active order
C. Apublic hearing
D. An opportunity for parties to be witten comments
E. Ang before medie lige IAL
Answer:
D. An opportunity for parties to be written comments
Explanation:
New agency is making some new rules for legislation. Blare, the boss of Debby gave her some of the proposed rules and asked her to publish them for the people and prepare for the next approval process.
So for the next step after Debby provides a public notice to its citizens is the opportunity for the common public and the interested parties to study the rules and sends their thoughts and comments on the rules made so that the agency can analyze those comments and consider the positive views in the rules and can also respond to their comments.
Thus the correct option is (D).
use of management accounting to support decision making and tell how management accounting support decision making give examples give me as soon as possible answer write own ideas donot copy paste write 2000 words
Management accounting is a process that is used to evaluate, plan, and control an organization's resources in a way that ensures that all stakeholders' objectives are met. Decision-making, on the other hand, refers to the process of selecting the best alternative from several available options based on a set of criteria and assumptions. In this context, management accounting is critical in providing relevant information that supports decision-making processes within an organization.The use of management accounting to support decision makingManagement accounting is concerned with providing information to managers for use in planning, control, and decision-making. It aids in the collection and analysis of data, as well as the interpretation and reporting of financial information that aids in decision-making.The following are the ways in which management accounting supports decision making:
1. Cost and Profit Analysis: Cost and profit analysis are an essential aspect of management accounting. It is critical to determine the cost and profit of each product, service, or activity. Cost analysis aids in determining the cost of raw materials, labor, overheads, and other expenses incurred during the production process. Profit analysis, on the other hand, helps in determining the net income generated from each product or service. The information gained from these analyses is beneficial in making informed decisions regarding product pricing, volume, and margins.
2. Budgeting: Budgeting is an essential aspect of management accounting. It is the process of planning and controlling future operations by projecting anticipated income, expenses, and cash flows. Budgeting aids in the allocation of resources to different departments or activities, ensuring that all expenses are covered, and identifying areas of wastage. The budget is an important tool for managers to compare actual performance with planned performance and make informed decisions.
3. Performance Evaluation: Management accounting provides tools for evaluating an organization's performance. It is essential to monitor performance and identify areas of weakness and improvement. Various performance metrics such as ROI, EVA, ROCE, etc., are used to evaluate performance. By using these tools, managers can identify areas of weakness and improvement, make necessary changes, and enhance the organization's overall performance.
4. Capital Investment Decisions: Capital investment decisions are significant decisions that have long-term implications. It is essential to assess the feasibility of the investment, expected return, and risk involved. Management accounting provides tools for evaluating capital investment decisions, such as NPV, IRR, Payback period, etc. These tools aid in selecting the best investment opportunity, considering all factors, including risk, return, and time horizon.Examples of how management accounting supports decision making
1. Cost and Profit Analysis: A company that produces multiple products can use management accounting to determine the cost and profit of each product. Based on the information gathered, management can decide to discontinue the production of a low-profit product or increase the price of a high-profit product.
2. Budgeting: A company can use management accounting to create a budget for the upcoming year. Based on the budget, the management can decide to allocate more resources to departments that have higher growth prospects or reduce the resources allocated to departments that are not performing well.
3. Performance Evaluation: Management accounting can be used to evaluate the performance of different departments or divisions of an organization. By using tools like ROI, managers can identify the departments that are performing well and those that need improvement. Based on the information gathered, management can take corrective action to enhance overall performance.
4. Capital Investment Decisions: Management accounting can be used to evaluate different investment opportunities. For example, a company can use NPV to evaluate whether investing in a new product line is viable or not. Based on the results, management can make an informed decision regarding the investment.These are some examples of how management accounting supports decision-making processes within an organization. In conclusion, management accounting is an essential aspect of decision-making as it provides relevant information that aids in evaluating, planning, and controlling an organization's resources. The use of management accounting tools such as cost and profit analysis, budgeting, performance evaluation, and capital investment decisions aid in making informed decisions.
To know more about Management Accounting, click here
brainly.com/question/21597572
#SPJ11
Which career pathways involve high risk due to exposure to dangers?
Firefighters in the Emergency and Fire Management pathway, Correctional Officers in the Corrections pathway, and Detention Officers in the Law Enforcement pathway
Firefighters in the Emergency and Fire Management pathway, Detention Officers in the Corrections pathway, and Intelligence Analysts in the Security and Protective Services pathway
Intelligence Analysts in the Security and Protective Services pathway, Detention Officers in the Corrections pathway, and Police Officers in the Law Enforcement pathway
Firefighters in the Emergency and Fire Management pathway, Detention Officers in the Corrections pathway, and Police Officers in the Law Enforcement pathway
Answer:
Firefighters in the Emergency and Fire Management pathway, Correctional Officers in the Corrections pathway, and Detention Officers in the Law Enforcement pathway.
Explanation:
The career pathways that involve high risk due to exposure to dangers is :
A) Firefighters in the Emergency and Fire Management pathway, Correctional Officers in the Corrections pathway, and Detention Officers in the Law Enforcement pathway.
"Career Pathways"The career pathways that involve high risk due to exposure to dangers is:
Firefighters in the Emergency
Firefighters too give an critical part in teaching the open with respect to fire and security.
Instructing fire anticipation and teaching the open on how to reply in crisis circumstances can offer assistance spare lives.
Fire Management pathway
Candidates require a long time of work encounter in law requirement, fire security, or an crisis administration field.
Crisis administration executives ordinarily require a bachelor's degree
Correctional Officers in the Corrections pathway
Corrections officers may do a few or all of the taking after:
supervise prisoners' day by day schedule, which incorporates feast, work and amusement times. screen, evaluate and oversee the conduct and security of detainees watch jail buildings and grounds.
Detention Officers in the Law Enforcement pathway.
A detainment officer forms prisoners, keeps up imprison security, serves dinners, transports detainees, gets and forms detainees into care of educate, looks detainees, and takes charge of individual property and gives detainees with opportunity to call their lawyer or relative.
A Career Pathway traces the positions, compensation, and preparing required to development in an industry.
Thus, the correct answer is A.
Learn more about "pathways":
https://brainly.com/question/25866470?referrer=searchResults
The branch of economics that examines the economy as a whole is called.
The branch of economics that examines the economy as a whole is called Macroeconomics.
What is macroeconomics?Macroeconomics studies the function of the entire economy of a nation, group of nations, or the world.
Microeconomics deals with individuals, households, organizations, and businesses as they interact within an economic system.
Thus, the branch of economics that examines the economy as a whole is called Macroeconomics.
Learn more about Macroeconomics at https://brainly.com/question/17996535
#SPJ1
Type the correct answer in the box. Spell all words correctly.
What is an example of using a transaction processing system to process data immediately?
transactions are a perfect example of the transaction processing system.
POS systems for inventory management is an example of using a transaction processing system to process data.
Transaction is an agreement, or verbal exchange, between a consumer and seller to trade items, services, or assets for payment. Any transaction entails a change in the popularity of the budget of two or greater groups or individuals. A transaction is a business event that has a economic effect on an entity's economic statements, and is recorded as an entry in its accounting statistics. Examples of transactions are as follows: Paying a provider for services rendered or goods added. Accounting transactions refer to any business pastime that outcomes in a direct impact on the economic repute and monetary statements of the commercial enterprise. Such transactions come in many paperwork, including: income in coins and credit score to customers. Receipt of cash from a patron by means of sending an bill
Learn more about transaction here:https://brainly.com/question/1016861
#SPJ1
when insurance companies take on the risk of loss or injury, it refers to the fact that no one can predict:
when insurance companies take on the risk of loss or injury, it refers to the fact that no one can predict: trouble.
What are the types of risk in insurance?Personal risk, property risk, and liability risk are the three forms of risk that insurance typically covers.Any danger that could jeopardize a person's health or safety, such being sick or getting hurt in an accident, is referred to as personal risk. a variety of categories into which hazards can be divided.Market risk, credit risk, operational risk, strategic risk, liquidity risk, and event risk are a few categories that are frequently utilized.If you are hurt or unwell while traveling, insurance will pay for your medical bills and transportation back home.Personal injury protection and coverage for harm or accidents you cause.coverage for lost or broken goodsTo learn more about Insurance refer,
https://brainly.com/question/28501076
#SPJ4
Claire opened her own Starbucks franchise in her community. She is pleased with how quickly she was able to open her franchise and that she
was able to establish a good customer base from the start because of name recognition. However, since she started this business to be her
own boss, Claire is likely to
A. Invest in his own capital and national and local advertising programs
B. Take sole responsibility for all the decisions in the business
C. Embrace the franchisors restrictions because they lead to a greater chance for success
D. Resent the management training and support the franchiser provides
E. Get frustrated with the restrictions of the franchise
Claire is likely to Embrace the franchisors restrictions because they lead to a greater chance for success option(c) is correct.
Who was Claire?Claire was a person who gradually opened her Starbucks actually in her community she established a good customer base merely of her name in that organization.
As she is her own boss she accordingly embraces the franchisors restrictions which actually lead for more and more success of her.
Therefore Option(c) is correct.
Learn more about Claire here:
brainly.com/question/19558712
#SPJ2
what was part of the monuments of a product of the pax augusta?
To mark his triumphant return from Spain and Gaul, Caesar Augustus erected the massive altar known as the Ara Pacis Augustae in Rome's Campus Martius.
One of the finest examples of Roman art, the altar is composed of an altar on a podium surrounded by walls. It is lavishly decorated with sculpture. One of the best works of sculpture produced during the reign of Augustus is the Ara Pacis, and its degree of preservation is astounding.
High Classical Greek sculpture serves as the primary source of inspiration for the understated, purposefully chilly, and immobile majesty of the Ara Pacis processional reliefs. The reliefs depicting the procession during the dedication of the altar are the first works of Western art to clearly depict recognizable people taking part in a current event.
Learn more about on Ara Pacis Augustae, here:
https://brainly.com/question/32361392
#SPJ4
What is the stock market simple definition?
Answer:
Explanation:
The stock market, also known as the equity market, is a marketplace where publicly traded companies' stocks are bought and sold. It provides a platform for companies to raise capital by selling their stocks to investors, and for investors to buy and sell stocks in publicly traded companies with the aim of earning a return on their investment. The prices of stocks are determined by supply and demand in the market and are influenced by a variety of factors, such as a company's financial performance, industry trends, and global events. The stock market is an important component of the overall economy, as it plays a significant role in the allocation of capital and influences the direction of economic growth.
An accounting firm ensures that the candidate pool for its new graduate program is diverse by recruiting at both public and private colleges and universities throughout 10 states, and posting information on multiple social media sites. This describes which type of affirmative action program?
targeted recruitment
The affirmative action program type described here is one that focuses on targeted recruitment.
What does targeted hiring entail?A predefined method for attracting individuals with certain experience, abilities, or attributes is known as a focused recruitment strategy. A successful focused recruitment plan employs data to monitor ROIs and is highly explicit in its objective and goals. Direct recruiting on college campuses and in career-related programs is one kind of targeted recruitment. Achieving internship as well as cooperative education arrangements with nearby colleges and high schools can assist in directing talented and motivated people toward entry-level roles inside your company.
To know more about recruitment visit:
https://brainly.com/question/28225955
#SPJ4
Marla is a buyer at a major corporation. Although she is authorized to make purchasing decisions on her own, she often seeks the input of trusted colleagues before settling on a decision. What type of buying center does Marla participate in
Answer:
Consultative
Explanation:
I did this question
if a person has atm fees each month of $21 for 8 years, what would be the total cost of those banking fees?
To calculate the total cost of ATM fees over 8 years, we need to multiply the monthly fee by the number of months in 8 years. Given that the person has ATM fees of $21 each month, the total cost can be calculated as follows:
$21 (monthly fee) x 12 (months in a year) x 8 (number of years) = $2,016
If the person incurs ATM fees of $21 each month for 8 years, we need to consider the number of months and multiply it by the monthly fee. There are 12 months in a year, so by multiplying the monthly fee of $21 by 12, we get the annual cost, which is $252. To find the total cost over 8 years, we multiply the annual cost ($252) by the number of years (8), resulting in $2,016. Therefore, the person would incur a total cost of $2,016 in banking fees over the 8-year period.
To learn more about total cost of ATM fees visit: brainly.com/question/28467548
#SPJ11
which budgeting approach requires justification for all expenditures
Answer:
i would love to help you but i dont know the answer
1. Goals of UAE organizations concerned with the Child Protection Law and the reasons for its inception
Answer:
The answer is below
Explanation:
The goals of UAE organizations concerned with the Child Protection Law and the reasons for its inception are the following:
1. No Poverty: as a result of poverty in some rural areas which is affecting children's development in UAE, the government has made it official to eradicate poverty in those areas.
2. Education for All: this is to ensure that children of age 6 to 18 or Grade 12, all have access to quality education, so as to boost literacy level in UAE
3. Social Support: this is to ensure those with the lowest income are able to cater to their children and afford a decent life.
Write any 4 points regarding the nature of target customers, which in the present times has led to the growing importance of ‘Persuasive function of Promotion'? MARKETING
Answer:
A target customer profile is simply a specific group of customers most likely to respond positively to your promotions, products, and services. 4 points regarding the nature of target customers:
What kind of people we’re looking?Where to find them?What our customers want from our brand, to adapt our value proposition so that our brand is relevant to a specific need or problem?How they compare and choose products to adjust marketing campaigns to make our offering seem the most compelling?Digital marketing has led to the growing importance of ‘Persuasive function of Promotion' because customers can learn about promotions from home and even compare the campaigns.
Explanation:
Persuading function of Promotion is to motivate customers to buy products under promotion due to intense competition among different industries producing similar types of products.
Ava has a large inventory of electric generators in a database table. Her boss asked her to create a
table of 100 to 500 kilowatt generators that can also be used during freezing weather. How can Ava
use this table to create a promotion for their customers?
As the existing customer of the company is concern, the list of individual of the database can be incentivized either by sales discount or gift during their next purchase of generator in the company.
What is Promotion in marketing?In marketing, a promotion refers to an form of communication, contact or action aimed at influencing people to buy more of their products or services.
In conclusion, as the existing customer of the company is concern, the list of individual of the database can be incentivized either by discount or gift on their next purpose of generator in the company.
Read more about sales promotion
brainly.com/question/1312782
bakeco, an nyse-listed food company, has decided to split off its cookie-making operation into a separate corporation. current shareholders will receive one share of the new company, bigcookieco, for each share of bakeco they own as of the record date. this action is an example of
This is an example of a corporate spin-off. A corporate spin-off is a type of corporate restructuring in which a company creates a separate business unit by separating a portion of its operations from the parent .
company and distributing it to existing shareholders as a new company.
This type of corporate action occurs when a company wants to focus on a particular business segment or when it wants to unlock the value of a business unit that is not reflected in the overall company’s share price.
In this case, the parent company, Bakeco, is separating its cookie-making operations into a new company, Bigcookieco, and distributing one share of Bigcookieco for each share of Bakeco owned by existing shareholders on the record date.
This action is beneficial to existing shareholders of Bakeco, who will now have shares of both Bakeco and Bigcookieco, allowing them to diversify their investments.
To learn more about investments visit:
https://brainly.com/question/20360874
#SPJ4
QUESTION FOUR [25]
Trendy Limited uses a combination of shares and debt in their capital structure. There are 2 million R1 ordinary shares in issue and the current market price is R2.50 per share. The latest dividend paid was 40 cents and a 9% average growth for the past six years was maintained. The company has 1 000 000 R2, 8% preference shares with a market price of R1.80 per share. Trendy Limited has a public traded debt with a face value of R2 million. The coupon rate of the debenture is 7% and the current yield to maturity of 10%. The debenture has 6 years to maturity They also have a bank overdraft of R600 000 due in 3 years’ time and interest is charged at 15% per annum.
Additional information:
• Trendy Limited has a beta of 2.1, a risk-free rate of 7% and a return on the market of 16%. • Company tax rate is 30%.
Required:
4.1 Calculate the weighted average cost of capital, using the Gordon Growth Model to calculate the cost of equity. (22)
4.2 Calculate the cost of equity, using the Capital Asset Pricing Model. (3)
The weighted average cost of capital (WACC) for Trendy Limited is 13.6%.
The cost of equity for Trendy Limited, using the Capital Asset Pricing Model (CAPM), is 25.9%.
4.1 Calculate the weighted average cost of capital (WACC), using the Gordon Growth Model to calculate the cost of equity:
The Gordon Growth Model formula to calculate the cost of equity is as follows:
Cost of Equity = (Dividend / Current Stock Price) + Growth Rate
Given:
Current market price per share: R2.50
Dividend per share: 40 cents
Growth rate: 9% (expressed as 0.09)
Cost of Equity = (0.40 / 2.50) + 0.09
Cost of Equity = 0.16
To calculate the WACC, we need to determine the weights of equity and debt in the capital structure. Let's assume the weights are as follows:
Equity weight: 60%
Debt weight: 40%
Cost of Debt = Current Yield to Maturity = 10% (expressed as 0.10)
WACC = (Equity Weight * Cost of Equity) + (Debt Weight * Cost of Debt)
WACC = (0.60 * 0.16) + (0.40 * 0.10)
WACC = 0.096 + 0.04
WACC = 0.136 or 13.6%
Therefore, the weighted average cost of capital (WACC) for Trendy Limited is 13.6%.
4.2 Calculate the cost of equity, using the Capital Asset Pricing Model (CAPM):
The Capital Asset Pricing Model formula to calculate the cost of equity is as follows:
Cost of Equity = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
Given:
Risk-Free Rate: 7% (expressed as 0.07)
Beta: 2.1
Market Return: 16% (expressed as 0.16)
Cost of Equity = 0.07 + 2.1 * (0.16 - 0.07)
Cost of Equity = 0.07 + 2.1 * 0.09
Cost of Equity = 0.07 + 0.189
Cost of Equity = 0.259 or 25.9%
Therefore, the cost of equity for Trendy Limited, using the Capital Asset Pricing Model (CAPM), is 25.9%.
learn more about capital here
https://brainly.com/question/32408251
#SPJ11
Is the presentation of raw numerical or verbal descriptions in a form that is useful for a specific purpose.
Information is the presentation of raw numerical or verbal descriptions in a form that is useful for a specific purpose.
What is the importance of information?It should be noted that information simply means the data that has been processed.
In this case, inormation is the presentation of raw numerical or verbal descriptions in a form that is useful for a specific purpose.
Learn more about information on:
brainly.com/question/4231378
#SPJ1
The Bradshaw family has $200,000 of total assets and $140,000 of liabilities. What is their net worth?
Malleable
Measurable
Maintainable
Manageable
Answer: $60,000
Explanation:
The Net worth of a person or people can be calculated by deducting their liabilities from their total assets.
The net worth of the Bradshaw family is therefore;
= 200,000 - 140,000
= $60,000
The options given are not for this question. There is a similar question which asks what the M in the Goal-setting acronym S.M.A.R.T stands for.
The answer to that is Measurable.
what can i do if my total in cash account is not the same in credit and debit side?
Answer:
Consider which items are meant for debit and credit.
Explanation:
The principle of double entry States that for every debit entries, there must be a corresponding credit entries and vice versa. This principle follow suits when preparing ledger accounts and trial balance.
Trial balance is the arithmetrical accuracy of the ledger. Once double entry principle is adhered to, the trial balance must definitely balance.
Where there are differences, check that items which ought to be debited and credited are correctly done. Also check if correct amount is posted like avoiding transposition error.
Buggy Wars Two friends and neighbours arrange to go into business together and then become bitter rivals: This is the story of Bob Bell and Michael Sharpe, who once lived just four houses apart on Oxford Street in Guelph, Ontario. Bell and Sharpe thought they had a good idea for a new business venture—a bicycle trailer—but the good idea turned into a long, sizzling struggle.
The correct answer to this open question is the following.
Unfortunately, the question is incomplete. Indeed, there is no question at all, just a series of statements.
What we can do is to comment on this case.
We are talking about the story of Bob Bell and Michael Sharpe.
Royalties were the main reason for this dispute. Bob Bell was the engineer that invented the bicycle trailer. Michale Sharpe would focus on Marketing the product due to his experience with computers and sales. Sharpe wanted both to share the financial risks but Bell considered it hos invention and wanted more royalties. Things went in the wrong direction, the situation got worse and they both hired lawyers in Toronto, Canada.
After disputes and legal actions, Bell won the case and he could expanse his business nationwide and signed an agreement with a Chinese company to sell the product. On the other hand, Sharpe made a 180-degree turn and started a fitness business.
Boeing's 737 airplane and Hewlett-Packard's printer business are examples of using enhancements and migrations of existing products to build on a ________.
product platform
product dais
product pulpit
product foundation
product template
Answer: product platform
Explanation:
Product platform is simply referred to as the common elements regarding the products of a company. When a new product is introduced into a particular market, the existing elements can be used.
Since Boeing's 737 airplane and Hewlett-Packard's printer business are examples of using enhancements and migrations of existing products, the product platform is attributable here.
Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers. We say that $z \in S$ is a unit if there exists a $w \in S$ such that $zw = 1.$ Find the number of units in $S.$
Answer:
Number of units possible in S are 4.
Explanation:
Given S is a set of complex number of the form \(a+bi\) where a and b are integers.
\(z\in S\) is a unit if \(w\in z\) exists such that \(zw=1\).
To find:
Number of units possible = ?
Solution:
Given that:
\(zw = 1\)
Taking modulus both sides:
\(|zw| = |1|\)
Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.
i.e.
\(|z_1z_2|=|z_1|.|z_2|\)
So,
\(|zw| = |1|\\\Rightarrow |zw| =|z|.|w| =1\\\Rightarrow |z|=\dfrac{1}{|w|}\)......... (1)
Let \(z=a+bi\)
Then modulus of z is \(|z| = \sqrt{a^2+b^2}\)
Given that a and b are integers, so the equation (1) can be true only when \(|z| = |w| =1\) (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:
(a = 1, b = 0) , (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)
So, the possible complex numbers can be:
\(1.\ 1 + 0i = 1\\2.\ -1 + 0i = -1\\3.\ 0+ 1i = i\\4.\ 0 -1i = -i\)
Hence, number of units possible in S are 4.
An entrepreneur is a person who does not undertake a business venture.
True
False
Answer:
false
Explanation:
.........
..
....
............
NEED HELP 100 POINTSThe Harappan civilization had a language with how many symbols attached to it? (Hint: It has never been decoded.)
A. 400 symbols
B. 100 symbols
C. 200 symbols
D. 300 symbols
Answer: A. 400 symbols
Explanation:
Which benefit would a client expect from joining a self-help group after being discharged from a mental health facility
The benefits that a person would expect from joining a self help group would be
reduction of distressReduction of lonelinessless isolatedhave people to talk toWhat is a self help group?These are a groups of people that are known to have common issues so they form informal gatherings that would help them combat their issues.
Joining such a group is going to be very helpful to the recovery process of the patient.
Read more on mental health here: https://brainly.com/question/983672