The two different quantities to measure which school has higher academic performance are :
• Graduation rate / Budget per student
• SAT average / Budget per student
In other to define a quantity which measures academic achievement;
We take the ratio of a related metric or parameter which is a measure of the academic performance of the student in each school and the budget per student for each school.
The parameters which could be used to measure academic achievement are :
• The graduation rate of each school.
• The SAT average of each school.
Hence, defining the quantity to measure academic achievement relative to budget per student could be expressed as :
• Graduation rate / Budget per student
• SAT average / Budget per student
Which is a metric unit?
Metric units are devices primarily based at the meter, gram or second and decimal (electricity of ten) multiples or sub-multiples of these. The maximum widely used examples are the units of the international device of devices (SI).
What are five standard metric devices?
The international system of gadgets (system international dunnites or SI) is the modern-day global popular metric system and is likewise the device maximum broadly used round the arena. It is an extension of Giorgi's MKSA machine – its base devices are the meter, kilogram, 2d, ampere, kelvin, candela and mole.
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A stock with a beta > 1 has returns that are ___________ volatile than the market.
A stock with a beta > 1 has returns that are more volatile than the market.
If beta is more than one, the returns on the enterprise inventory are greater risky than the marketplace go back. An agency inventory with a beta of more than one is referred to as an aggressive stock. If beta is much less than one, the returns on the company inventory are less risky than the market go back.
A stock that swings greater than the market over the years has a beta above 1.0. If a inventory moves much less than the marketplace, the inventory's beta is much less than 1. zero. high-beta shares are purported to be riskier but provide better go back potential; low-beta stocks pose much less threat but additionally decrease returns.
Beta is a statistical measure of the volatility of a inventory versus the general marketplace. A beta above 1 approach a inventory is more volatile than the general market. A beta below 1 way a stock is much less risky than the overall marketplace.
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A shift of the demand curve for thin-crust pizza would not be caused by a change in?
A shift of the demand curve for thin-crust pizza would NOT be caused by a change in the PRICE of thin-crust pizza.
Demand is not determined by price, hence a change in price does not result in a change in demand. Ceteris paribus, if the price of new cars varies, the quantity demanded will change, and the demand curve will alter.
Demand Curve: The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time.
A shift of the demand curve for thin-crust pizza would NOT be caused by a change in the PRICE of thin-crust pizza.
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who has an absolute advantage in coffee production? who has an absolute advantage in nut production?
Based on the amount of coffee that Jody and Benny are able to produce, C. Jody has an absolute advantage in both coffee and nuts.
Who has the absolute advantage?The person with the absolute advantage is the one that is able to produce more coffee or nuts than the other person in the same time period.
Jody can produce 20 pounds of coffee in a week and Benny can only produce 15 pounds.
Jody can produce 40 pounds of nuts in a week and Benny can only produce 20 pounds.
Jodi therefore has an absolute advantage in both the production of nuts and coffee.
Full question is:
Jody and Benny both produce nuts and coffee. They each prefer to consume a diet that is half nuts and half coffee.
Both have access to the same resources If Jody focuses on producing only coffee, she can produce 20 pounds of coffee in a week.
If she only produces nuts, she can produce 40 pounds of nuts in a week Benny can produce a maximum of 15 pounds of coffee in a week.
He could also choose to produce only nuts, in which case he can produce 20 pounds of nuts a week 1st attempt Part 1
Who has an absolute advantage in coffee production? Who has an absolute advantage in nut production?
A. Benny has an absolute advantage in both coffee and nuts. B. Benny has an absolute advantage in coffee, and Jody has an absolute advantage in nuts. C. Jody has an absolute advantage in both coffee and nuts. D. Jody has an absolute advantage in coffee, and Benny has an absolute advantage in nuts.Find out more on absolute advantage at https://brainly.com/question/9067127
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N april 1, the cash account balance was $46,220. during april, cash receipts totaled $248,600 and the april 30 balance was $56,770. determine the cash payments made during april. $fill in the blank 3
The cash payments made during April are $238,050. This is calculated as Opening balance + cash receipts - ending balance.
What is Cash account?Cash is the head of accounting and this represents a complete account. The management of cash is represented in the cash account in the company accounts.
The cash account balance at 1st April was $46,220, the cash receipts for the month of April needs to be added in this opening figure of cash account so the total will be $294,820. However the ending balance on 30 April was $56,770, this is the balance of cash account that is remaining at the end of the month which means the difference of the two would represent the cash payments made during the month of April.
The cash payments made during the month of April is $238,050 ($294,820 - $56,770).
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Suppose a gardener produces both tomatoes and squash in his garden. If he must give up 8 bushels of squash to get 5 bushels of tomatoes, then his opportunity cost of 1 bushel of tomatoes is.
Suppose a gardener produces both tomatoes and squash in his garden. If he must give up 8 bushels of squash to get 5 bushels of tomatoes, then his opportunity cost of 1 bushel of tomatoes is 5/2 bushels of squash.
Opportunity costs are the possible advantages which any person or investor or any company forgoes while deciding between the two options.
Opportunity costs are invisible in nature. An opportunity cost is simply by definition is the difference between the expected returns of each option and this is also the formula for doing so.
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bill wants to reach valuable, relevant audiences and engage with them quickly and often with his ads.
We can actually deduce here that if Bill wants to reach valuable, relevant audiences and engage with them quickly and often with his ads, creating a Display Ads campaign allow him to reach his goal in the following way: It allows him to reach over 90% of global internet users across more than three million apps and websites.
What is advertisement?Advertisement refers to the process of creating awareness for a particular good and service in order to reach the target market.
In our today world of technology, advertisement is evolving and there are different forms that people engage in running advertisement.
The social media platforms are platforms that have become great tools for advertisement.
The complete question is seen below:
Bill wants to reach valuable, relevant audiences and engage with them quickly and often with his ads. How will creating a Display Ads campaign allow him to reach his goal?
A. It allows him to isolate valuable audiences regionally and convert local sales the first time his ad is seen.
B. It allows him to select for new audiences and scale down his advertising to appear on specific websites that he chooses.
C. It allows him to identify valuable audiences and collect statistical usage data from the websites where his ad appears.
D. It allows him to reach over 90% of global internet users across more than three million apps and websites.
Thus, option D is the correct answer.
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credit secrets: 2 books in 1 - blast your credit score through the roof and repair bad credit by having everything you need to know explained in detail pdf drive
Insider's secrets and techniques To Getting our credit score rating Up. The credit restores manual the entirety we want to know to hold,
credit score secrets and techniques 2 books in 1 - blast your credit score rating through the roof and repair bad credit score by having the entirety we need to recognize explained in detail pdf.
a credit score is the capability to borrow money or get admission to items or services with the expertise that you'll pay for later.
credit is a transaction among events wherein one the creditor or lender supplies cash, goods, offerings, or securities in going back for a promised destiny fee by way of the opposite.
An example of credit is the quantity of cash available to spend in a bank price account or the finances added to a bank account. the credit score is described as giving honor to someone or giving money again to an account.
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If the total assets to equity ratio of a company is increasing, it is possible that:
The company is reducing its usage of debt and achieving lower financial leverage.
When the proportion of total assets to equity rises, it indicates that the corporation is less reliant on creditors' loans.
What is the asset-to-equity ratio?
The assets to equity ratio reflects the number of assets earned by a company using loan resources. If this ratio rises, the company's utilisation of debt decreases.
An increase in the assets to equity ratio also implies that the company, bought through debt, is running with very minimal danger of losing money.
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Complete Question
recall chapter 1's opening story about the british sea captains and the convicted felons. instead of paying the sea captains for each prisoner placed on board the ships in great britain, an economist suggested:'
Paying for each prisoner who walked off the ship in Australia.
What is prisoner ?An Australian television soap opera by the name of Prisoner, which aired on Network Ten (formerly The 0-10 Network) from February 1979 to December 1986, ran for eight seasons and 692 episodes. Prisoner is known in the UK and the US as Prisoner: Cell Block H. If you think prison is horrible for a man, consider what it would be like for a woman, read the tagline of this groundbreaking television series.
Reg Watson came up with the idea for the Grundy Organization-produced show, which was shot both on location and in the former Network Ten Melbourne Studios in Nunawading.
The series developed a cult following across the world and was one of the biggest media exports, performing notably well in the United States and Canada.
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When a market is in equilibrium, the quantity of the good that buyers are willing and able to buy ________.
At the equilibrium price, there is no shortage or surplus: The quantity of the good that buyers are willing to buy equals the quantity that sellers are willing to sell.
What is equilibrium price ?
An equilibrium price, also known as a market-clearing price, is the consumer cost given to a product or service at a point where supply and demand are equal or nearly equal. The producer or vendor can sell as many units as they want, and the buyer can buy as many as they want.
Dynamic pricing aims to identify equilibrium prices in response to market changes, modifying prices on the fly when supply and demand fluctuate. Other pricing models, such as value-based pricing, seek to capitalize on intangible attributes or use other strategies to control demand and obtain a bigger profit margin than can be estimated by cost-based pricing.
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If you are a high-status person in a hierarchically organized group, most likely?
In a group that is hierarchically structured, it is likely that a high status individual will initiate more communications than a low status individual.
What features do norms have? What function do secondary groups serve in society?The features of norms are shared by group members (rather than individual beliefs); describe members' thoughts, behaviors, and emotions; establish guidelines for acceptable conduct; frequently ignored by members
Secondary groups are short-term, task-based, transactional, and serve practical demands. They offer a social network where individuals can assess one another. The group members help one another emotionally.
The following are secondary groupings' primary traits:
a physical separation between members.brief in duration.large amount.Members are not intimate with one another.Formal interactions and minimal personality involvement.casualness of the exchange.status-based and impersonal.specific objectives or formational interests.to know more about organized groups visit: https://brainly.com/question/4196949
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Jane is willing to pay $80 for a pair of shoes. the actual price of the shoes is $50. her marginal benefit from the pair of shoes is?
The marginal benefit for Jane is $80. The cost of the shoes is $50 but still Jane is willing to buy them for $80.
The marginal benefit can be described as the maximum amount a person is willing to pay for that additional good or product. The marginal benefit usually reduces with the increase in consumption of the product. Utility can be defined as the satisfaction the person will get by consuming that good or service.
The marginal benefit usually declines when the person buys more of a product. For example, Jane was willing to pay $80 for a pair of shoes. Maybe another pair of shoes of the same kind she will not be willing to spend that much as she already has a pair of shoes. So when the customers keep on buying the same product the marginal benefit will reduce.
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In the b-to-b market, one strategy is to offer a complete solution to a buyer's problems. this is called?
in the B-to-B market, one strategy is to offer a complete solution to a buyer's problems. This is called A. supplier development.
What is supplier development?Supplier development entails collaboration with these partners in order to enhance the capabilities and competitiveness of significant, strategic, and high-potential suppliers for the joint benefit of the customer and the supplier.
In order to improve a supplier's overall performance or a supplier's capabilities particularly, supplier development can be planned and strategic.
Supplier development goes beyond the parameters of the agreements the company now has with its suppliers. Along with cost savings and improved supplier quality, it may also involve joint product creation between client and supplier organizations.
Finding opportunities for improvement is typically done using SPM, or supplier performance management. SPM must incorporate supplier development in order to go from performance management to performance improvement.
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Consider the 5-bit generator g = 10011, and suppose that d has the value 1010101010, what is the value of r? (show your work to get credit)
G is equal to 10011 in the 7-bit generator, whereas D is equal to 1010101010. then R has a value of 0100.
What is Bit Generator?
A BitGenerator is where Generator gets its random values from. The BitGenerators only contain methods for seeding, getting or setting the state, jumping or advancing the state, and accessing low-level wrappers for consumption by code that can effectively access the functions provided, such as number. They do not directly provide random numbers.A stream of random values is offered by a bit generator. BitGenerators support setting their initial state via a seed to produce reproducible streams. Any arbitrary-sized non-negative integer, or a collection of such integers, may be used as the seed by any of the BitGenerators offered. These inputs must be processed by BitGenerators to create a high-quality internal state for the BitGenerator.To know more about Bit Generator visit:
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the primary objective of financial accounting information is to provide useful information about economic activity to:multiple choice
Financial accounting information has the primary objective B. To provide financial statements to help external users analyze and interpret an organization's activities
What is the purpose of financial accounting?Financial accounting allows for the provision of financial statements that give in-depth details about the affairs of a company.
This is made available to external users who are then able to use this information to interpret the activities of the organization and decide on whether to invest or not.
Options include:
A. To serve the decision-making needs of internal usesB. To provide financial statements to help external users analyze and interpret an organization's activitiesC. To monitor and control company activitiesD. To provide information on both the costs and benefits of managing products and servicesE. To know what, when and how much to produceFind out more on financial accounting at https://brainly.com/question/14546386
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What is the terms used to describe the independence and autonomy of the physician in working with the practice manager?
The term that is used to describe the independence and autonomy of the physician in working with a practice manager is d. Medical case manager.
What is a medical case manager?A medical case manager refers to a physician who is working with a practice case manager. This physician is autonomous in their role which means that they have independence and autonomy.
The physician is meant to take care of health care cases independently with the help of the practice manager.
Options for this question:
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If+sales+are+$814,000,+variable+costs+are+65%+of+sales,+and+operating+income+is+$277,000,+what+is+the+contribution+margin+ratio?
35 % is the contribution margin ratio.
Operating income = $ 271,000
Sales = $ 814,000
Variable costs = 65 % of sales
= 814,000 x 65 %
= $ 529,100
Contribution margin = Sales - Variable costs
= 814,000 - 529,100
= $ 284,900
Contribution margin ratio = Contribution margin / Sales
284,900 / 814,000 =
= 35 %.
The contribution margin ratio (CM ratio) of an enterprise is identical to its sales much less all variable costs, divided with the aid of using its sales. It represents the marginal advantage of manufacturing one extra unit.
The contribution margin ratio is the distinction among a company's income and variable costs, expressed as a percentage. This ratio indicates the quantity of cash to be had to cowl constant costs.
The nearer a contribution margin percent, or ratio, is to 100%, the better. The better the ratio, the extra cash is to be had to cowl the enterprise's overhead expenses, or constant costs. However, it is much more likely that the contribution margin ratio is nicely underneath 100%, and in all likelihood underneath 50%.
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Disclaimer: The question is incomplete. Please read below to find the missing content.
If sales are $814,000, variable costs are 55% of sales, and operating income is $277,000, what is the contribution margin ratio?
Defining and adhering to an organizational mission, evaluating ownership and management alternatives, and outlining the goods/service category to be sold are parts of which element of retail strategy?
Defining and adhering to an organizational mission, evaluating ownership and management alternatives, and outlining the goods/service category to be sold are parts of the situation analysis element of retail strategy.
What do you understand by Retail Strategy?The method you employ to create your goods or services and market them to clients is known as a retail strategy. This strategy consists of several components, including location, store, goods/assortment, visual merchandising, personnel, quality, advertising, and price. Frequently, when we visit a retail location, we find items like gum, chocolates, and other items with smaller SKUs that may be picked up while the customer waits at the checkout counters. The main goal of retail strategies is to boost sales and customer satisfaction equally, so a retail store must have a plan to market its products and services and attract a suitable audience.
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Is best described as a set of goal directed actions a firm takes to gain and sustain superior performance relative to?
Strategy is the set of goal-directed actions a firm takes to gain and sustain superior performance relative to competitors. In any competitive situation, therefore, a good strategy enables a firm to achieve superior performance.
The assumed conception or needs of a function are what constitute job performance in the workplace. Contextual and task performances are the two categories of job performances. While contextual performance is based on personality, task performance is based on cognitive ability. Task completion is related to behavioral roles that are mentioned in job descriptions and pay scales. They are directly tied to organizational performance, as opposed to contextual performances, which are value-based and add extra behavioral roles that are not acknowledged in job descriptions and are compensated; these extra roles are related to organizational performance in an indirect manner. The same collection of individual activity and contributions (prosocial organizational behavior) that promote organizational culture is related to citizenship performance, just as it is with contextual performance.
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The figure shows the labor market. As a result of the minimum wage law of $15 per hour, _____ workers are hired and exactly ____ people are unemployed.
The figure shows the labor market. As a result of the minimum wage law of $15 per hour, 50,000 workers are hired and exactly 2,00,000 people are unemployed. The correct answer is option(b).
The labor market, often known as the job market, is defined as the relationship between supply and demand for labor, wherein employees offer the supply and employers provide the demand. Every economy needs it, and it is tightly related to the markets for capital, products, and services.
The labor market is impacted by almost everything that happens in the economy. changes in the population's size, the minimum wage rate, and the demand for products and services. Because having a job is one of the key determinants of overcoming poverty, labor markets are essential in determining the economic and social development of developing countries. The most effective strategy to increase salaries and consumption levels over the long run is to have a reputable, well-paying job that you can count on.
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The question is incomplete. Check below the full question
The figure shows the labor market. As a result of the minimum wage law of 15 per hour, ___ workers are hired and exactly ___ people are unemployed.
A. 50000/0,
B. 50000/200000,
C. 50000/100000,
D. 150000/50000,
kendall corporation purchased $160,000 of barker company’s 7% bonds at par value that mature in 10 months. the bonds pay interest semiannually on june 1 and december 1. kendall plans to hold the bonds until they mature. the journal entry to record kendall’s purchase of the bonds is:
Barker Company issued $160,000 in 7% bonds with a 10-month maturity that was bought at par by Kendall Corporation. Interest on the bonds is paid twice a year, on June 1 and December 1. Kendall intends to keep the bonds on hand until they are due. Kendall's purchase of the bonds is documented by the following journal entry: debit Short-Term Investments—HTM $160,000; credit Cash, $160,000.
A business transaction is documented in the accounting records of the company using a journal entry. Journal entries are typically made in the main ledger, but they can also be entered in a subsidiary ledger and subsequently rolled forward into the general ledger once they have been summarized. After then, the general ledger is used to produce the company's financial statements.
The logic of a journal entry requires that every business transaction be recorded in at least two places (known as double entry accounting). For instance, when you make a cash sale, both the revenue account and the cash account are increased. Alternately, making purchases on credit leads to an increase in the accounts payable and inventory accounts.
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Define a base condition to find the sum of arithmetic progression of the function
Then the method to discover the sum of a mathematics development is Sn = n/2[2a + (n − 1) × d] wherein, a = first term of arithmetic progression, n = variety of phrases within the mathematics progression and d = not unusual difference.
A sequence of numbers is known as an arithmetic progression if the difference among any consecutive terms is usually equal.
There are varieties of mathematics progressions: Finite arithmetic development: The finite arithmetic progression is a series with a finite range of phrases. The primary time period, remaining term, commonplace difference, and the variety of terms may be diagnosed from the collection.
To determine the number of target audience individuals a stadium can preserve. While we take a taxi, we are able to be charged a preliminary cost and then a consistent with mile or kilometer price.
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at a yard sale, reagan calculated that she was willing to pay $200 for a queen bed that was being sold for $100
regan used optimization using total value and $300 is the correct answer.
Reagan estimated that she would be willing to pay $200 for a queen bed at a yard sale that was being offered for $100 (creating a net benefit of $100) and $220 for a king bed that was being sold for $300 (producing a net benefit of $80) optimization using total value is the response. Expense optimization is a business-focused, ongoing discipline that helps to maximize corporate value while driving spending and cost reduction. It contains:
securing the most competitive rates and conditions for all company transactions,Platforms, applications, procedures, and services should be standardized, simplified, and rationalized, automating and digitalizing business and IT processes.To learn more about optimization here
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In the buying center, ryan answers the phones, receives and opens the mail, and monitors the incoming email. He sorts through all the sales solicitations and forwards the most interesting ones to his boss. Which role is he playing in this decision-making unit?.
In the buying center, Ryan does all the work from answering, forwarding, sales solicitations. The role that he is playing here in the decision-making unit is that of a gatekeeper.
A gatekeeper is a person who filters information before it is distributed to various employees of an organization's decision-making. They gather and process all the data that is sent to them before deciding where and to whom to send it. A coordinated effort like this aids in greater comprehension and makes every employee's tasks much simpler.
A group of people who participate in the decision-making process for obtaining goods and services is known as an organization's decision-making unit (DMU). It may also be known as a company's "buying center." The decision-making unit is essential in B2B because it helps businesses focus on the needs of their target market, learn more about their clients, make better decisions, and save time and money. A gatekeeper is exactly what it sounds like—someone who is posted at a gate to keep off unauthorized guests. It is the duty of the person in charge of deciding who may contact the decision-maker to keep the area free of obtrusive visitors and phone calls.
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at one point in the evolution of marketing, the united states entered a buyer's market and the customer became king. which era is being described?
This era is being described as market-oriented. Thus, option D is correct.
What is marketing?Marketing can be defined as the way through which the market transaction is being done, in this case, the customer is being made aware of the product or service that is being given to them.
As in recent times, the competition has increased between the business, and the customer has also been more oriented toward what he was he want. This name that the market is being oriented to be a market-oriented where the more the protection the most profit of form of company can get. Therefore, option D is the correct option.
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The question is incomplete, the complete question will be:
Which era is being described?
Select one:
a. economics-oriented
b. value-based marketing
c. production-oriented
d. market-oriented
e. sales-oriented
you estimate that by the time you retire in 35 years, you will have accumulated savings of $2.7 million.
To help with planning, having a percentage or cash number can be useful, although Story advises against concentrating primarily on it. He advocates trying to build a ballpark annual estimate based on what you live on now and what might change when you retire rather than relying on a general amount because "everyone's lifestyle is different. What they want to do in their retirement years may be extremely different as well."
Social Security will be the main source of retirement income for the majority of Americans. The money in your workplace and personal retirement accounts, pensions, annuities, proceeds from selling your home or business, rental income, or an inheritance are all potential sources of income that may be available to you many years from now. (Even if benefit payments are reduced in the future, Social Security is unlikely to disappear.)
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For a manufacturer, when indirect labor costs are recorded, the debit entry is to ________.
For a manufacturer, when indirect labor costs are recorded, the debit entry is to Work-In-Process Inventory.
The portion of an employee's salary or wage that is attributable to indirect manufacturing costs is referred to as indirect labor cost. This includes all employment overhead costs, such as social security, fringe benefits, and workers' compensation insurance. It also includes employee time spent on activities related to manufacturing but do not directly produce a finished product. Indirect labor costs may include, for example, time spent on quality control inspections and cleaning machines.
Work-in-process items are goods that are only partially completed. These items are also known as goods-in-process. Some people define work-in-process as products that go from raw materials to finished products in a short period of time. Manufactured goods are an example of a work-in-process.
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what type of contract do you have once the seller has accepted the buyer’s offer in writing and the buyer has been notified of the acceptance?
the agreement that results after the seller accepts the buyer's offer in writing and notifies the buyer of the acceptance.
A purchase agreement is what?
An offer is said to be "under contract" for the purchase of real estate if it has been acknowledged in writing and is signed by both parties. A purchase agreement is the name given to this written document.
In a purchase agreement, the following details are provided:
The parties involved are identified (buyer and seller)
Defining the property legally
Financial information
Purchase cost
purchaser financing
Amount of the down payment
Closing expenses (and how those will be split between the buyer and seller)
Terms and conditions of the sale
contingencies
Conveyed items in the sale (appliances, fixtures, etc.)
Timelines
Durations for contingencies
Offer's cutoff time
the deadline
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a student sells his old computer at a computer hardware store and gets $150 for it. he uses this cash to buy computer accessories.
A student sells his old computer at a computer hardware store and gets $150 for it. he uses this cash to buy computer accessories. This is the Physical asset market.
The physical asset market also called the cash market or the bodily market, the spot market is in which properties are offered for cash and introduced right now. A monetary asset marketplace is a vicinity in which a contractual proper to a certain form of wealth is sold and bought.
An intangible asset is an asset that isn't bodily in nature. Goodwill, emblem reputation, and intellectual belongings, together with patents, emblems, and copyrights, are all intangible assets. Intangible asset exists in opposition to tangible belongings, which encompass land, motors, gadget, and stock.
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Disclaimer:- your question is incomplete, please see below for the complete question.
A student sells his old computer at a computer hardware store and gets $150 for it. He uses this cash to buy computer accessories.
What kind of market is this?
at mike’s first meeting with other business unit managers, his boss, jim, goes through the latest production data. mike finds that over the last several months, vendors have complained about problems with some of the yogurt from his line. how should mike respond to this news?
Before making a decision on what to do, Mike should verify these reports to get a better idea of this issue.
Decision makingWe must make decisions every day, and while they might be simple or complex, they are a necessary part of life. But how can we make choices that produce the best results? With an ever-increasing body of research on the subject, decision-making is becoming into a science that can be very helpful in providing direction. The implementation of such research, while unquestionably valuable in some situations, greatly depends on the type of judgments being made, particularly in the corporate world.
There are evident limitations, and the majority of decision-making research to date only pertains to one particular form of decision, which is not the type that managers find to be the most difficult.
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