design a greedy algorithm for making change consisting of quarters, dimes, nickels, and pennies. (a)provide the pseudocode. (b)write down the running time of your

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Answer 1

Design a greedy algorithm for making change consisting of quarters, dimes, nickels, and pennies.

(a) Here is the pseudocode for the greedy algorithm:

```
function makeChange(cents)
   quarters = 0
   dimes = 0
   nickels = 0
   pennies = 0

   while cents >= 25
       cents = cents - 25
       quarters = quarters + 1
   endwhile

   while cents >= 10
       cents = cents - 10
       dimes = dimes + 1
   endwhile

   while cents >= 5
       cents = cents - 5
       nickels = nickels + 1
   endwhile

   pennies = cents

   return quarters, dimes, nickels, pennies
endfunction
```

(b) The running time of this greedy algorithm depends on the input size (number of cents), but its time complexity is O(cents). Since the while loops run a number of times proportional to the amount of cents, the algorithm's running time will increase linearly with the number of cents. In practice, the algorithm is relatively fast, as the number of iterations is limited by the coin denominations.

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Related Questions

Internal control procedures for cash disbursements (other than small disbursements from petty cash) should include that:_______.

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Internal control procedures for cash disbursements (other than small disbursements from petty cash) should include that Segregate duties and Review authorized signors.

Internal control is a procedure implemented by a company's management, board of directors, and other staff members and is intended to give reasonable assurance that the information is accurate, timely, and reliable. of adherence to relevant laws, rules, agreements, policies, and procedures.

Internal control is a procedure for ensuring that an organization's objectives in operational effectiveness and efficiency, accurate financial reporting, and compliance with laws, rules, and policies are met, according to the definitions of accounting and auditing.

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Britney is selling her bungalow via an installment contract. The buyer made payments dutifully for five years, but has not made any payments for more than a year. Which of the following is true

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"Britney is selling her bungalow via an installment contract. The buyer made payments dutifully for five years, but has not made any payments for more than a year." This is further explained below.

What is an installment contract.?

Generally, A contract known as an installment purchase agreement is one that facilitates the financing of the purchase of assets.

In conclusion, Britney has the right to retain the whole of the money that was received and to reclaim the property.

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In order to win a contract from Mexico, QVB Autos Manufacturing must make 65% of the component parts for their automobiles in Mexico. This is an example of a Blank______.Multiple choice question.local distribution requirementlocal content requirementinternational content requirementlocal supplier requirement

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The correct answer is Option B.

In order to win a contract from Mexico, QVB Autos Manufacturing must make 65% of the component parts for their automobiles in Mexico. This is an example of local content requirement.

What is Local Content Requirement?Government rules known as "local content standards" force businesses to function in economies that rely on domestically produced goods and services. The usage of these indicators has significantly increased in recent years as governments attempt to accomplish a number of policy goals that focus on employment, industrial, and technological development goals. LCRs still play a considerable role in policy today despite the long-standing and overwhelmingly unfavorable evidence of their effects on economic development and trade.

More than 340 localization initiatives, including over 145 new local content mandates, have been implemented by governments since the financial crisis a decade ago, primarily in an effort to boost domestic employment and industrial performance.

Therefore, the situation given in the question is an example of local content requirement.

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XYZ Development has just purchased a large tract of land that it plans to develop into 50 one-acre building lots. To have the ability to sell off individual lots before paying off the entire balance due, the developer will need to obtain

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To have the ability to sell off individual lots before paying off the entire balance due, the developer will need to obtain a blanket mortgage.

What is a blanket mortgage?A blanket mortgage is a single mortgage that covers many properties and serves as security for the loan. Real estate developers and larger investors frequently purchase multiple properties at once, thus a blanket mortgage allows them to consolidate such deals into a single loan.Consider the money you'd save on closing fees, both for the original mortgage and any subsequent refinances. Refinancing from numerous loans to a single blanket mortgage may also result in lower monthly payments, which may increase your cash flow.

Therefore, to have the ability to sell off individual lots before paying off the entire balance due, the developer will need to obtain a blanket mortgage.

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An investment project costs $10,000 and has annual cash flows of $2,860 for six years. What is the discounted payback period if the discount rate is zero percent

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The Discount rate is : Zero percent: payback in 3.49 years.

What is Discounted Payback Period?

The discounted payback period (DPP) is a method applied in the capital budgeting process to determine the number of periods an investor has to wait to be compensated the initial cost of a project from the projected cash inflows. DPP recognizes the time value of money theory hence it is classified as a discounting method of capital budgeting. The future cash inflows are discounted to their present worth before the discounted payback period is computed.

Given:

Costs = $10,000

Annual cash flows = $2,860

n =6 years.

r =0%

Solution-

Discount rate is zero we are doing the payback period

[tex]Payback in Year =\frac{investment}{cash flow per year}[/tex]

[tex]10,000 / 2860 Per Year = 3.4965[/tex]

Therefore, we can conclude that The Discount rate is : Zero percent: payback in 3.49 years.

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Shen Company reports the costs incurred below for the month ended May 31. The company has no beginning Work in Process Inventory. Overhead is applied using a predetermined overhead rate of 120% of direct materials costs. Job 4 was completed and Job 5 is still in process at month-end. Prepare a schedule of cost of goods manufactured for the month.

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Based on the costs incurred by Shen Company, the schedule of costs of goods sold for manufactured goods is:

                                                                                 Total

Direct materials used                                            $6,300

Direct labor                                                             $4,390

Manufacturing overhead                                      $7,560

Total cost                                                               $18,250

Beginning WIP                                                            $0

Add: Cost during year                                           $18,250

Total manufacturing cost                                      $18,250

Less; Ending WIP                                                   $(6,770)

Cost of goods manufactured                               $11,480

What goes into the schedule of cost of goods manufactured?

Direct materials:

= 3,400 + 2,900

= $6,300

Direct labor:

= 4,000 + 390

= $4,390

Manufacturing overhead:

= 6,300 x 1.2

= $7,560

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The schedule of Cost of Goods Manufactured for May by Shen Company is as follows:

Cost of Goods Manufactured:

Direct materials       $3,400

Direct labor               4,000

Overhead applied    4,080 ($3,400 x 120%)

Total costs            $11,480

What is the Cost of Goods Manufactured?

The cost of goods manufactured includes the costs of direct materials, direct labor, and overhead applied.

The cost of goods manufactured is only for Job 4 and does not include the costs incurred for Job 5 which is still in process at month-end.  Instead, the costs of Job 5 will be recorded as ending work in process.

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Large dam projects are extremely costly and often benefit the wealth who invest in their construction, but they also create a lot of energy

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Large dam projects are extremely costly and often benefit the wealth who invest in their construction, but they also create a lot of energy electricity, power, or energy that is carbon free.

What is Energy?Energy is referred to by scientists as the capacity for work. People have figured out how to transform energy from one form to another and then use it to accomplish tasks, making modern civilization possible. Walking and bicycling, driving cars on roads and boats through water, cooking meals on stoves, making ice in freezers, lighting our homes and workplaces, producing goods, and sending astronauts into space all require the usage of energy. Energy is capable of changing its forms. For instance, a person's body stores chemical energy from the food they consume until they may use it as kinetic energy when working or playing.

When an energy source is designated as carbon-free, it means that it was created using a resource that emits no carbon dioxide, like nuclear power or huge hydropower plants.

Therefore, Large dams create a lot of energy electricity, power, or energy that is carbon free.

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A borrower is purchasing a three-family, owner-occupied rental property. Rental income will be $2,000 (verified only by leases). The PITIA on the property is $2,350. The borrower has a gross monthly income of $5,760 and monthly debt payments of $625. What are the ratios for this loan

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LTV= principal amount/ market value of your property.

what is a Loan ratio - Financial institutions utilize the Loan-to-Value Ratio (LTV) to determine the lending risk before approving a mortgage for the purchase of real estate.
26:10
Rental income will be $2,000 (verified only by leases)
The PITIA on the property is $2,350
The borrower has a gross monthly income of $5,760
monthly debt payments of $625.
Pitia refers to the following items: principal, interest, taxes, insurance, including hazard and flood insurance, as well as homeowners' association or condominium dues, although it excludes mortgage insurance charges.
Debt payment is the action of returning money you have borrowed. m making debt payments is difficult and a lot of people struggle to make their debt payments.
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With regard to business definition, railroads may have lost business because they:

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With regard to business definition, railroads may have lost business because they defined their business too narrowly.

Railways are a safe land transport system whilst in comparison to different kinds of shipping. Railway transport is capable of excessive stages of passenger and load usage and strength performance however are frequently less flexible and more capital-intensive than avenue delivery when decreased site visitor levels are taken into consideration.

The Railroad become the first advanced in top-notch Britain. a person named George Stephenson efficaciously implemented the steam technology of the day and created the world's first hit locomotive.

The primary engines used in the United States of America had been bought from Stephenson Works in England.

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Determine the effective hourly cost, the total annual cost, and the labor burden markup for the Superintendent with the following wage and benefit information

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Given the following information, calculate the hourly cost and labor burden markup percentage of a project manager

Base Salary: 880.000 annually

Total Labor Burden: $ 22.000 annually worked hours per week: 40 worked weeks per year: 52

Paid Vacation: 2 weeks per year ($1.600 for.

the hourly cost and labor burden markup percentage of a project manager.

Answer - (A) $53.05 per hour. 40% labor burden markup.

The total cost formula combines the variable and fixed costs of product offerings into one sum. The formula is Total cost = (average fixed cost x average variable cost) x number of units produced.

The total annual cost is the sum of the normal cost and the additional annual cost.

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Marginal productivity theory assumes that a worker’s income is a function of the contribution of that worker to the value of the output. in business this is called the ""______________"" approach .

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Marginal productivity theory assumes that a worker’s income is a function of the contribution of that worker to the value of the output. in business, this is called the "value-added" approach.

There is a correct theory called marginal productivity theory. Wages are paid at a level equal to the marginal revenue product of labor, the MRP (value of the marginal product of labor). MRP is the increase in income caused by the increase in output produced by the last employed worker.

The marginal productivity theory of income distribution proposes that each individual should receive income based on their contribution to total output. The marginal productivity theory of income distribution has been criticized for the following reasons. Income from inheritance is inconsistent with the theory.

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Winn Co. signs a 60 day note payable for a $15,000 copy machine with an interest rate of 8%. Winn will record total interest expense of Multiple choice question. $1,200 $15,000 $15,200 $200

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Winn will record a total interest expense of $200.

15,000 x .08 x (60/360)

= 200.

Interest expense is a non-operating expense recognized in the income statement. It represents interest paid on borrowings such as bonds, loans, convertible bonds, or lines of credit. This is basically calculated as the interest rate multiplied by the principal amount of the debt.

The simplest way to calculate interest expense is to multiply the company's total debt by the average interest rate on the debt. If a company has an average interest rate of 5% and he has a debt of $100 million, the interest expense will be $100 million multiplied by 0.05, or $5 million.

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In gathering audit evidence, the accessibility of information may be a factor thereby influencing which judgment trigger

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The answer is availability

What process uses warehousing to add value to a product through component​ modification, repair,​ labeling, and​ packaging?.

Answers

Answer:

Customizing

Hope this helps :)

Which of the following statements is true of comparative negligence? Group of answer choices It allows a plaintiff to claim damages without establishing proximate causation and causation in fact. It requires a plaintiff and a defendant to settle their dispute through arbitration. It allows a plaintiff to claim only punitive damages but not actual damages. It compares a plaintiff's fault with a defendant's and reduces the damage award proportionally. It completely bars a plaintiff from recovering any damages.

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The inference illustrates that the true statement about comparative intelligence is that it compares a plantiffs fault with a defendant's and reduces the damage award proportionally.

What is an inference?

It should be noted that an inference simply means the conclusion that can be deduced from the information given.

In this case, the inference illustrates that the true statement about comparative intelligence is that it compares a plantiffs fault with a defendant's and reduces the damage award proportionally.

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The true statement about comparative negligence is D. It compares a plaintiff's fault with a defendant's and reduces the damage award proportionally.

What is comparative negligence?

Comparative negligence is an attempt to distribute the liability arising from an incident between the plaintiff and the defendant according to their contributions.

This implies that the fault or negligence of each party involved is compared so that the liability arising thereon is based upon their respective contributions.

Thus, the true statement about comparative negligence is D. It compares a plaintiff's fault with a defendant's and reduces the damage award proportionally.

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Urst Ammunition Inc., a firm controlled and managed by the government of Urst, is the only company that has the license to produce defense arms in the country. Which of the following industry competitive structures does this best illustrate

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The fact that Urst Ammunition Inc is the only company in Urst that is allowed to produce defense arms means that the industry competitive structure it uses is a Monopoly.

What is a monopoly?

This refers to a company that either has the overwhelming majority market share in an industry, or is the only company  that is allowed to operate in that industry.

There are several ways that this can happen and one way is by government regulations. Urst Ammunition Inc. is the only company that is allowed to make weapons and arms so this is a monopoly.

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The accounting concept that requires every business to be accounted for separately from other business entities, including its owner or owners is known as the:

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Answer: Business entity assumption.

Explanation: assume enitities

The accounting concept that requires every business to be accounted for separately from other business entities, including its owner or owners is known as the business entity assumption.

What is business?

An economic activity that involves the exchange of goods and services with the help of buying and selling with the objective to gain some profit is called Business.

The accounting concept helps improve the recording of the income and position statement of business mainly referred to as financial statements  and provides better accuracy of transactions which helps in easy interpretation.

The business entity assumption focused on the individual entity of any business separate from another business entity which makes it unique and distinguishable from others.

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What are the best ways that a firm can reduce the threat of imitation?

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A firm can reduce the threat of imitation by following the Principles of defensive strategies.

Defensive strategies includes the courage to attack our potentials by asking questions again and again and eliminating the old ones to introduce new options.

Defensive strategies also include an initial investment. Defensive strategies consist of amassing the greatest skills nd strengths of the attacker. The firm must also manage the speed of the action taken by it.

Imitation could also be reduced by increasing the strategic complexity and creating a threat of retaliation.

Meaning of imitation is the act of un authorized copying of the competitor's technology.

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The purpose of a responsibility accounting system is to provide information to: (Check all that apply.)

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The purpose of a responsibility accounting system is to provide information to:

Evaluate a manager's performanceAssign cost and expenses to the manager's responsible for controlling them

Responsible accounting is a type of management accounting that is responsible for the overall management, budgeting, and internal accounting of a company. The main goal of this accounting system is to support all planning, calculation, and responsibility centers of the company.

Therefore, accountability is based on the basic principle that managers are only responsible for the actions they control. Responsible accounting follows the basic principles of cost management systems such as budget control and standard costing.

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All terms and conditions the client authorizes must be specified and included in an offer to sell or buy. when is it acceptable to offer the property under other terms?

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It is properly necessary to accept to offer the property under other terms at the acceptance stage of a offered service.

What is a terms and condition?

This refers to the document that is governing the contractual relationship between the provider of a service and its user.

In order word, these are the legal agreements between a service provider and a person that wants to use that service.

The practice is that such person must agree to abide by the terms of service in order to use the offered service.

Therefore, It is properly necessary to accept to offer the property under other terms at the acceptance stage of a offered service.

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If the two countries were to specialize and trade with one another, which country would import airplanes?

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The country that should import airplanes is country A.

Which country should import airplanes?

The country that should import airplanes is the country that does not have a comparative advantage in the production of airplanes. A country has comparative advantage in production if it produces at a lower opportunity cost when compared to other countries.

A country has a lower opportunity cost if it forgoes less quantity of an alternative product when producing another product.

Opportunity cost of country A in the production of airplanes: 8 million / 8 = 1 million

Opportunity cost of country B in the production of airplanes: 4 million / 6 = 670,000

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Answer:

A

Explanation:

its correct

An employee concerned primarily with the seniority system, insurance plan, and retirement policy is motivated by:

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An employee concerned primarily with the seniority system, insurance plan, and retirement policy is motivated by security needs.

A retirement policy is designed to help you manage your retirement and live a stress-free life. One such type is a retirement plan that helps you grow your money and provide a steady income for life.Such plans help secure retirement money while you are still working. increase.

A retirement benefit is a monetary or another incentive that a person collects after the termination of employment. Develop a payout plan while you are employed and collect a portion of your salary and contributions from your employer on a regular basis until retirement.

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If a nondiscriminating imperfectly competitive firm is selling its 80th unit of output for $40, its marginal revenue:_____.

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   If a nondiscriminating imperfectly competitive firm is selling its 80th unit of output for $40, its marginal revenue:   will be less than $40

To calculate the marginal revenue, a corporation divides the trade in its general sales via the trade of its total output amount. Marginal sales are equal to the selling rate of an unmarried additional object that becomes bought. beneath is the marginal sales formula: Marginal sales = trade in revenue/alternate in amount.

The marginal price of production and marginal revenue are economic measures used to decide the amount of output and the charge in line with a unit of a product that will maximize earnings

Marginal revenue is the additional profits generated from the sale of 1 extra unit of a great or provider. it can be calculated by evaluating the full revenue generated from a given wide variety of income (e.g. 11 devices), and the total sales generated from selling one more unit (i.e. 12 gadgets)

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A manufacturer's raw-material purchasing department would likely be classified as a: Select one: a. investment center. b. cost center. c. profit center. d. contribution center. e. revenue center.

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b. cost center

The department responsible for buying raw materials for a manufacturing would probably be categorized as a cost center.

What are cost centers and how do they differ?

There are primarily two categories of cost centers: centers for production costs, where goods are made or processed. An assembly area is an illustration of this. Cost centers for services, where goods and services are delivered to other cost centers. The canteen or the personnel office are two examples of this.

What sort of thing would be a cost center?

The accounting, human resources, IT, maintenance, and research and development departments are a few examples of cost centers. In comparison to a department, a cost center can be defined at a lower level. It might have to do with a certain machine, manufacturing line, or work role.

Why is a cost center created?

Cost centers' main duty is to maintain a record of the costs incurred. The managers or other high-level officials are tasked with keeping expenditures in line with the allotted budget; they are not responsible for the use of the earnings that are earned.

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After a share exchange, one corporation (the _____ corporation) owns all the shares of the other corporation (the _____ corporation).

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After a share exchange, one corporation (the parent corporation) owns all the shares of the other corporation (the subsidiary corporation).

A share exchange is where one or more shareholders exchange shares they hold in one company for shares in another company. So after a share exchange, one corporation suppose, the parent corporation owns all the shares of the other corporation, called the subsidiary corporation.

A parent corporation has subsidiaries, which are wholly or partially owned separate businesses controlled by the parent. On the other hand, a subsidiary corporation is a business that is owned by another corporation, either partially or entirely.

Hence, after a share exchange, one corporation owns all the shares of the other corporation.

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Data that has been collected for some other purpose than to answer the question at hand is called?

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Data that has been collected for some other purpose than to answer the question at hand is called secondary data.

Secondary data is  data collected for research that has  been gathered previously and can be accessed by researchers.

The term also contrasts with primary data means the data which is data collected directly from its source.

Secondary data is always used to increase the sampling size of research studies.

Secondary data is also chosen for its efficiency and the  speed that comes with using an already existing resource.

Secondary data helps in large research projects, in which different research groups work in teams to collect secondary data. The main researcher is then focuses on primary research or particular areas of interest.

Common sources of  secondary data includes data collected by government public services departments, different  libraries, websites over the internet  and censuses.

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Ensuring land is put to the use for which it is best suited while also protecting livability of a community and property values is achieved through ______.

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Ensuring that land is put to the use for which it is best suited, while protecting a community's livability and property values are achieved through zoning.

What is zoning?

It is an important instrument for urban planning, being used to regulate land use, respecting local, safety and protection characteristics, so that the availability of land use happens legally.

Therefore, zoning is essential for the maintenance of urban space in a structured and controlled way by the government, for the purposes of environmental protection and organization.

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The merger of media enterprises into powerful, synergistic combinations that can cross-market content on many different platforms is referred to as?

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The merger of media enterprises into powerful, synergistic combinations that can cross-market content on many different platforms is referred to as industry convergence.

Industry convergence is based on the digital business principles. It represents the most fundamental opportunity of the growth for the organizations. Industry boundaries are redefined by the industry convergence as it shifts the focus from the single product to cross industry value experiences.

Industry convergence is such a powerful code which has been cracked by the world's most powerful companies.

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A monopolistically competitive firm is one:

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A monopolistically competitive firm is one of many firms that produce slightly different but very similar goods

Exclusive competition occurs when there are many companies offering products that are similar but not identical to the industry. Unlike monopolies, these companies have little power to curb supply or raise prices to increase profits.

There are no barriers to entry in monopoly competition. Therefore, the market is competitive in the long run and companies make normal profits. In monopoly competition, companies are not price takers (fully elastic demand) because they produce differentiated products. Demand is inelastic.

In essence, a monopolistical competitive market is so called because while companies compete to some extent for the same customer group, each company's products are slightly different from all other companies products.

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Company A, a public company, is planning to make a tender offer to acquire all of the shares of Company B, another public company, for cash. Company A is planning to offer a 30% premium to the market price of B's shares, based on the expected synergies of the deal. Why would Company A's board want to obtain a fairness opinion

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"Company A, a public company, is planning to make a tender offer to acquire all of the shares of Company B, another public company, for cash. Company A is planning to..." Company A's board wants to obtain a fair opinion because the expected synergies in corporate combinations are hard-to-measure

This is further explained below.

What is a fair opinion?

Generally, An evaluation of the facts surrounding a merger, acquisition, carve-out, spin-off, repurchase, or another sort of corporate transaction is called a fairness opinion.

In conclusion, "In order to buy all of Business B's shares for cash, Company A, a public company, plans to launch a tender offer. Company A intends to take action to..." The Board of Directors of Company A seeks a balanced view since the anticipated synergies of business mergers are difficult to quantify

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A data value is considered _______ if its z-score is less than 2 or greater than 2. You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area A traditional epic usually involves some type of quest, which is a riddle that has more than one answer. True False Why does the crystal merchant say maktub multiple times in the book The alchemist When testing the tonicity of potato strips, why is the amount of wait time after adding the potato strip an important factor in the experiment? Vessels and Nephron Components Place each label in the correct box, indicating whether it is a component of a nephron or a component of the renal vasculature. Which factor could influence an employer to increase an employee's wages?An economic downturnO High worker productivityO Increase in insurance costsO Low demand for the company's goods All of the following statements are true for exothermic chemical reactions EXCEPT _______.Exothermic reactions may give off heatExothermic reactions may give off lightExothermic reactions may increase the temperature of the surroundingsExothermic reactions may decrease the temperature of the surroundings what technique is illustrated in this diagram microbiology What is the primary purpose of practicing and improving your style of speech delivery? Destiny bags 3 grocery bags a minute. how long will it take her to bag 150 bags? \You earn $1,300 working at a summer job. You decide to put it into an account and leave it there for four years while you are in college. The principal will earn 1.5% simple interest. How much will you have in your account at the end of four years You apply a force on an object that is 100 times its mass. The acceleration of the object will be 100m/s^2. After a while, it perpendicularly hits another object with a mass 10 times smaller than the first object. When they collide, in theory, the momentum of the first object will all get transferred into the small object. And that means, the heavy object will completely be at rest, while the smaller object will have a force applied to it by the big object equal to ma. In real life, it seems that when two objects collide, the bigger object doesnt completely stop and just pushes the smaller or the same massed object. In real life, it seems that when the collision happens, the first object continues moving towards the other object, and doesnt completely get at rest right after the collision. Why is that? The water park charges a $45 fee plus $5 per student for a field trip. Thebowling alley charges a $35 fee plus $7 per student. The lines in the graphrepresent the cost of each field trip.For what number of students will the total cost of each field trip be the same,and what will that cost be?Cost ($)100908070605040302010Field Trip Costsy = 35+ 7xy = 45 + 5x1 2 3 4 5 6 7 8 9 10Number of students Several items are omitted from the income statement and cost of goods manufactured statement data for two different companies for the month of December: Siskiyou, inc. Has total current assets of $1,200,000; total current liabilities of $500,000; and long term assets of $800,000. How much is the firm's total liabilities & equity? Which economic system is characterized by public ownership of the means of production, the pursuit of collective goals (rather than market-oriented production), and centralized decision making The stemplot below represents the number of bite-size snacks grabbed by 10 students in an activity for a statistics class. A stemplot titled number of snacks. The stems are 1, 2, 3, 4. The first column of leaves is 5, 0, 2, 2. Column 2 is 6, 1, blank, blank, Column 3 is 6, 3, blank, blank. Column 4 is 7, blank, blank, blank, Column 5 is 9, blank, blank, blank. Key 2 slash 4 is a student who grabbed 24 snacks. What is the correct set of data for the stemplot? 15, 16, 17, 19, 20, 21, 23, 32, 42 15, 16, 16, 17, 19, 21, 23, 32, 42 15, 16, 16, 17, 19, 20, 21, 23, 32, 42 15, 15, 16, 17, 19, 20, 21, 23, 32, 42 Suppose a and b are independent events. if p(a) = .5 and p(b) = 0.45 what is p(a^b) The probability of picking an ace at random out of adeck of 52 cards is What would be the probabil-13ity of picking an ace at random if 2 aces wereremoved from the deck?