Use Laplace transform to solve the following initial value problems:
(a) y'- 2y + 2y = cost, y(0) = 1, y'(0) = 0.
(b) y)-y=0, y(0)=2, (0) = -2, (0)=0, "(0) = 0.
(c) y + y(t) = '(0) = 0. 0 1≤t<5 otherwise, y(0) 0,

Answers

Answer 1

The given initial value problems involve differential equations that can be solved using Laplace transforms.

In problem (a), the Laplace transform will be used to find the solution for the given equation and initial conditions. In problem (b), the Laplace transform will be applied to solve a different equation with specific initial conditions. Lastly, problem (c) requires applying the Laplace transform to find the solution for a differential equation with a piecewise function and initial condition.

(a) To solve the initial value problem y' - 2y + 2y = cost, y(0) = 1, y'(0) = 0, we first take the Laplace transform of both sides of the equation, substitute the initial conditions, and then solve for Y(s). After finding Y(s), we take the inverse Laplace transform to obtain the solution y(t).

(b) For the initial value problem y" - y = 0, y(0) = 2, y'(0) = -2, y''(0) = 0, we again take the Laplace transform of the given equation and apply the initial conditions. This will give us the transformed equation in terms of the Laplace variables. By solving for Y(s), we can then use the inverse Laplace transform to find the solution y(t).

(c) In the initial value problem y' + y(t) = '(0) = 0, 0 ≤ t < 5, and y(0) = 0, we encounter a piecewise function. We will apply the Laplace transform to the equation, taking into account the different intervals. By considering the initial condition and solving for Y(s), we can obtain the inverse Laplace transform to find the solution y(t) for the given differential equation.

Using Laplace transforms allows us to solve these initial value problems and find the solutions to the respective differential equations with their specific initial conditions.

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Related Questions

Gross investment minus depreciation is equal to:
a. the change in capital stock.
b. the value of durable goods.
c. gross national product.
d. non-residential investment

Answers

Gross investment minus depreciation is equal to the change in capital stock. Option a is correct.

Gross investment refers to the total amount of investment in an economy, including both the purchase of new capital goods and the replacement of depreciated capital goods. Depreciation, on the other hand, represents the decline in the value of existing capital goods over time. When we subtract depreciation from gross investment, we are essentially accounting for the reduction in the value of capital due to wear and tear or obsolescence.

The result of subtracting depreciation from gross investment gives us the net investment, which represents the change in the capital stock of an economy. The capital stock refers to the total amount of physical capital, such as machinery, equipment, and buildings, available in an economy at a given point in time. Therefore, the change in capital stock reflects the net addition or subtraction of capital goods from the existing stock due to investment and depreciation.

Options b, c, and d are not accurate in this context. The value of durable goods refers to the worth of long-lasting consumer goods, while gross national product (GNP) is a measure of the total economic output of a country, including consumption, investment, government spending, and net exports. Non-residential investment specifically refers to investment in capital goods by businesses, but it does not capture the concept of net investment or the change in capital stock. Therefore, the correct answer is option a: the change in capital stock.

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Subject: Business process reengineering
Q#1: Need to make control chart against electricity crisis in Karachi? (Need proper authentic chart with data)
Q#2: Need control plan of electricity crisis for Karachi? (need proper control plan)
(Note: please do not copy paste previous answer, need proper answer with charts)

Answers

Business process reengineering is an important aspect of management that deals with the analysis and optimization of existing business processes. It aims to improve efficiency, effectiveness, and productivity in order to achieve business objectives.



A control chart can be used to monitor the performance of a process and identify any variations that may be present. To make a control chart against electricity crisis in Karachi, the following steps can be taken:

1. Collect data on electricity supply and demand in Karachi for a specific period of time (e.g. one year).

2. Plot the data on a graph, with time on the horizontal axis and electricity supply/demand on the vertical axis.

3. Calculate the mean and standard deviation of the data.

4. Draw upper and lower control limits on the graph based on the mean and standard deviation.

5. Plot the data on the graph and monitor for any variations that fall outside the control limits.

6. Investigate any variations and take corrective action as necessary.

Q#2: Control plan of electricity crisis for Karachi

A control plan is a document that outlines the steps that will be taken to ensure that a process is under control and meeting the required specifications. To create a control plan for electricity crisis in Karachi, the following steps can be taken:

1. Define the problem: Clearly define the problem of electricity crisis in Karachi, including the specific issues that need to be addressed.

2. Identify the root cause: Identify the root cause of the problem, including any underlying factors that may be contributing to the crisis.

3. Develop a solution: Develop a solution to address the root cause of the problem, including specific actions that need to be taken to improve the situation.

4. Implement the solution: Implement the solution and monitor its effectiveness, making any necessary adjustments as needed.

5. Establish a control plan: Establish a control plan to ensure that the solution remains effective over time. This includes defining the process, setting performance targets, and monitoring progress against those targets.

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Question 3[5 marks]: Consider the given slicing structure matrix: 0 1 10 0 0 0 0 1 3 0 1 0 1 0 1 2 574 1 1 1 1 1 6 8 0 1 1 a) [2 points) Draw the slicing structure tree diagram for the given slicing structure matrix. b) [2 points] Draw the layout for the given slicing structure matrix. c) [1 point] Construct an alternative slicing structure matrix. (neighborhood)

Answers

a) Slicing Structure Tree Diagram:

The slicing structure tree diagram represents the hierarchy of the slicing structure matrix. Each row in the matrix represents a level in the hierarchy, and the numbers in each row indicate the connections between the slices.

Here is the slicing structure tree diagram based on the given matrix:

       Level 1       Level 2     Level 3    Level 4

          0             1           10

          |             |

          0             1

          |

          1

          |

          0

          |

          0

          |

          0

          |

          1

          |

          3

          |

          0

          |

          1

          |

          2

          |

         574

          |

     1    1    1    1    1

      \   |   |   |   |   /

       6  8   0   1   1

                      |

                      0

                      |

                      1

b) Layout:

The layout represents the physical arrangement of slices based on the slicing structure matrix. Each number in the matrix represents a separate slice, and the connections between the slices determine their arrangement.

Here is the layout based on the given slicing structure matrix:

         Slice 1           Slice 2         Slice 3

         +-----+           +-----+         +-----+

         |     |           |     |         |     |

         |  10 |           |  1  |         |  1  |

         |     |           |     |         |     |

         +-----+           +-----+         +-----+

            |                 |

         +-----+           +-----+

         |     |           |     |

         |  1  |           |  3  |

         |     |           |     |

         +-----+           +-----+

            |

         +-----+

         |     |

         |  2  |

         |     |

         +-----+

            |

         +-----+

         |     |

         | 574 |

         |     |

         +-----+

            |

         +-----+-----+-----+-----+-----+

         |     |     |     |     |     |

         |  1  |  1  |  1  |  1  |  1  |

         |     |     |     |     |     |

         +-----+-----+-----+-----+-----+

            |     |     |     |

            6     8     0     1

                            |

                            1

                            |

                            0

                            |

                            1

c) Alternative Slicing Structure Matrix (Neighborhood):

Constructing an alternative slicing structure matrix (neighborhood) requires specific guidelines or criteria to determine the connections between slices. Without additional information or guidelines, it is not possible to construct a specific alternative slicing structure matrix based on the given matrix.

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When it comes to trainee reactions, instructor style is more
important than perceived organizational support for training? Group
of answer choices True False

Answers

False is the answer to the given question. It has been argued by experts that the instructor style is more important when it comes to trainee reactions rather than perceived organizational support for training.

In other words, it's not just the organizational support that matters, but the instructor's behavior and approach to training also play a crucial role.According to researches, instructor style is an important factor that influences trainees' reactions. Trainees may react differently to different instructors based on their teaching style. A study by Colquitt et al. (2000) demonstrated that instructor style accounts for approximately 25% of the variance in trainee reactions. Instructor style refers to the way the instructor presents the course material, how he/she interacts with the trainees, the feedback provided to the trainees, and the tone of the training session.In contrast, while perceived organizational support is also an important factor, its impact on trainee reactions is relatively lower. Perceived organizational support can be defined as the extent to which employees believe that their organization values their contributions and cares about their well-being. Therefore, the instructor style is more important when it comes to trainee reactions than perceived organizational support for training.

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as a global company, electra bikes sells its products to other countries. this process is referred to as

Answers

As a global company, Electra Bikes sells its products to other countries. This process is referred to as Exporting.

Exporting refers to the sale of goods and services produced in one country to customers in another country. It is one of the easiest and most effective ways for companies to expand globally because it allows them to start small and slowly build a business relationship with foreign customers. In addition, exporting enables companies to reduce their reliance on a single market and expand their customer base, which can help mitigate the risks associated with doing business domestically. In this case, Electra Bikes sells its products to other countries, which is a form of exporting. This implies that the business is looking to expand globally by identifying other potential markets where they can sell their bikes.

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The statement of financial position of Michael Limited at 31 December, 2017 and 2018 were as follows: Notes 31/12/2017 31/12/2018 GH₂000 GH 000 Non-current assets Tangible assets Investment at cost 1 730 1,100 100 50 830 1.150 Current assets 80 110 Inventory Receivables 110 180 Cash at banks 20 30 210 320 1,040 1,470 Equity Stated capital Capital surplus 500 680 100 200 Income surplus 200 190 800 1,070 Non-current liabilities 10% loan notes 3 100 150 900 1,220 Current liabilities Trade payables 100 120 Bank overdraft 40 130 140 250 1,040 1,470 Notes 1. Tangible assets: During the year tangible assets with a net book value of GHe 80,000 were sold for GH 60,000. The depreciation charge for the year on all tangible assets held at the end of the year was GHe 100,000. 2. Investments: Investments which cost GH50,000 were sold during the year for GH$40,000. 3. 10% Loan notes: GHe 50,000 of 10% loan notes were issued on 1 January 2018. All interest to 31" December has been paid. 4. Stated capital: The Company's stated capital at 31 December 2017 consisted of GH 500,000 of ordinary shares. Another 80,000 shares were issued during the year at a price of GH2.25 per share. 5. Capital surplus: The freehold land and buildings were revalued upwards by GHe 100,000 during the year. Required: Prepare the company's statement of cash flows for the year ended 31 December 2018 complying with IAS 7 Statements of cash flows. Ignore taxation.

Answers

The statement of cash flows for the year ended 31 December 2018 shows cash from operating activities of GH 250,000, cash used in investing activities of GH 80,000, and cash used in financing activities of GH 90,000. The net increase in cash for the year is GH 80,000.

To prepare the statement of cash flows, we need to analyze the changes in cash flows from operating, investing, and financing activities. Operating Activities: Cash inflow from receivables: GH 70,000 (Increase from GH 110,000 to GH 180,000) Cash inflow from inventory: GH 30,000 (Increase from GH 80,000 to GH 110,000) Cash outflow for trade payables: GH 20,000 (Increase from GH 100,000 to GH 120,000) Net cash from operating activities: GH 80,000 (GH 70,000 + GH 30,000 - GH 20,000)Therefore, the net increase in cash for the year ended 31 December 2018 is GH 80,000.

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Case Study
The Malaysian economy is in equilibrium. Changes began to happen
in the economy. Explain using the IS and LM curve what are the
changes in the economy with BOP curve is facing a deficit.
2.

Answers

When the Malaysian economy experiences changes, particularly a deficit in the balance of payments (BOP), it can be analyzed using the IS-LM framework to understand the impact on the economy.

The IS curve represents the equilibrium in the goods market, showing the relationship between output (Y) and the interest rate (r). A BOP deficit implies that the country is importing more than it is exporting, resulting in a leakage from the domestic economy. This leads to a decrease in output and a leftward shift of the IS curve. As a result, the equilibrium level of output decreases, leading to a contraction in the economy.

The LM curve represents the equilibrium in the money market, showing the relationship between the interest rate and the level of income (Y). With a BOP deficit, the outflow of funds increases, leading to a decrease in the money supply. Consequently, the LM curve shifts upward, indicating a higher interest rate is required to achieve equilibrium in the money market.

Combining the IS and LM curves, the new equilibrium point is determined where the two curves intersect. This point represents the lower output level and higher interest rate resulting from the BOP deficit. The decrease in output and the higher interest rate negatively impact investment and consumption, leading to a slowdown in economic activity.

To address the BOP deficit and stimulate the economy, policymakers may implement measures such as fiscal policies (e.g., reducing government spending or increasing exports) and monetary policies (e.g., lowering interest rates or implementing exchange rate adjustments) to restore equilibrium in the goods and money markets.

Overall, a BOP deficit in the Malaysian economy would lead to a contraction in output and an increase in the interest rate, as depicted by the shifts in the IS and LM curves. Policymakers would need to undertake appropriate measures to restore equilibrium and foster economic growth.

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The concept of public opinion played a central role in
the work this thinker (Hegel). Write a paragraph on the concept of
public opinion as developed by any Hegel

Answers

As developed by Hegel, the public opinion is a key aspect of the modern state. Public opinion serves as a vital link between the state and the people.

According to Hegel, public opinion represents the collective views, beliefs, and values of a society. It is shaped by the various social, cultural, and political forces that operate within a given society. Hegel believed that public opinion was a crucial factor in shaping the direction and trajectory of the state.

He argued that public opinion could influence the policies and decisions of the state by exerting pressure on the ruling elites. Hegel believed that public opinion was a key factor in the process of social and political change. He argued that the state had to take into account the views and opinions of the people if it wanted to maintain its legitimacy and authority.

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HLTAHA001 HLTAHA003 HLTAHA005 HLTAR 4e. List three manual handling tasks that you may need to perform as an AHA and explain how you can control the risk factors of each. 5. Explain how you obtain a client's consent prior to commencing a program with them. 6. A policy and procedure that a gym or physical therapy studio has in place is for every participant to sign an informed consent. What is the purpose of such a document?

Answers

4e. Three manual handling tasks that may be required of an AHA include: Assisting clients who may have difficulty in moving: For such individuals, the AHA may have to help them out of their beds or chairs and into other positions.

AHA can control the risk factors of such activities by using assistive equipment, such as a hoist or a mechanical lift, to support the client. Transferring clients from one location to another: To move patients from one place to another, such as from a bed to a wheelchair or to the bathroom, an AHA may require assistance. They can control the risk factors of such activities by properly positioning themselves when lifting or transferring the patient, as well as by using assistive equipment to aid in the transfer. Assisting patients with walking: In some cases, AHAs may be required to assist patients in standing and walking, particularly those who are elderly or disabled. To control the risk factors of such activities, they should use proper techniques to support the patient, such as using gait belts or other assistive devices.  

To obtain a client's consent before commencing a program with them, AHAs must do the following: Identify themselves as a service provider to the client, Describe the program or service that they intend to provide to the client, Explain the potential risks, benefits, and alternatives of the program, Get the client's consent in writing, and Keep a copy of the written consent in the client's file.

An informed consent document is a form that gym or physical therapy studio participants are required to sign. The document is intended to ensure that the participants are aware of the risks and benefits of the program or services they are signing up for, as well as the risks involved in physical activity. The document protects the facility in the event that a participant sustains an injury while participating in the program or services by proving that the participant was aware of the risks associated with physical activity and had given their informed consent to participate.

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please help
art 2 of 2 ants ellook Print 2. In industries that process joint products, the costs of the raw materials inputs and the sales values of intermediate and final products are often volatile. Change the

Answers

In industries that process joint products, the costs of the raw materials inputs and the sales values of intermediate and final products are often volatile. Thus, the method of allocating joint costs to the different products produced becomes an important and often controversial issue.

Industries that process joint products face a problem while calculating the costs of raw materials inputs and sales values of intermediate and final products. Joint cost allocation is the process of dividing joint production costs, such as rent, electricity, and machinery, into individual products based on the value of each product. However, joint cost allocation becomes a significant and often contentious problem due to the volatility of the costs and sales values of the different products produced. Joint cost allocation is done to estimate the profitability of the different products produced. Although several methods have been developed to assign joint costs, each method has its advantages and disadvantages. As a result, it is important for industries that process joint products to choose a joint cost allocation method that is suitable for their business operations.

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Steel Co.'s cash balance according to the general ledger was $13,260 on February 28th, 2021. According to the bank staten Time left 1:22:04 the balance in Steel Co.'s bank account on February 28th was $13,310. The following cash related transaction for the month ended February 28, 2021 occurred: 1. The last deposit of the month, for $1,000, was made as a night deposit on February 28th by the company's owner for the services he rendered during the month of February. 2. One of Steel Co.'s customers paid its account by making an $600 EFT. 3. The bank subtracted a service charge of $40 from the company's bank account for February. Outstanding cheques totaled $1,200 at the end of February. 4. 5. The bank deducted $650 from Steel Co.'s account for payment of loan principal 6. The bank returned a $150 cheque marked NSF that a customer used to pay off their account 7. The bank statement showed that cheque number 004 (which Steel Co, had issued to pay for utilities expense) was recorded by the bank as $785, which is the correct amount for the invoice, while the company incorrectly recorded this cheque as $875. Required: Prepare the bank reconciliation for February 28, 2021. (8 marks) 2 What is the amount which Steel Co. should report on its statement of financial position on February 28th, 20217 (1 mark) 1 A BIG PART 1) BANK RECONCILIATION Bank Reconciliation

Answers

Bank reconciliation is the process of comparing the balance in a company's cash account with the balance on the bank statement.  The amount which Steel Co. should report on its statement of financial position on February 28th, 2021 is $13,260

The purpose of bank reconciliation is to identify and reconcile any differences between the two balances. In this case, the bank reconciliation for February 28, 2021 is as follows:Bank Reconciliation for Steel Co. as of February 28, 2021Balance per bank statement: $13,310Add:EFT from customer: $600Last deposit made on February 28th: $1,000Total: $14,910Deduct:Service charge: $40NSF cheque: $150Cheque #004 - utilities: $90 (the difference between the amount on the bank statement and the amount recorded by the company)Loan principal: $650Total: $930Adjusted balance: $13,980Balance per general ledger: $13,260Add: Deposit in transit: $1,000Less: Outstanding cheques: $1,200Adjusted balance: $13,060The adjusted balance per bank statement and adjusted balance per general ledger do not match. The difference is $920 ($13,980 - $13,060). This difference is due to the bank service charge, NSF cheque, and the difference in the recording of cheque #004.2. The amount which Steel Co. should report on its statement of financial position on February 28th, 2021 is $13,260, which is the balance per general ledger.

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Achart (mph) is a graph for proportions. True or False?

Answers

The statement "Achart (mph) is a graph for proportions" is False.

An Achart is not a graph for proportions, rather, it is a graphical representation of the acceleration of an object with respect to time. Achart is a type of motion graph that is often used to represent the movement of an object undergoing constant acceleration. It shows the change in velocity over time.

A proportion is a statement that two ratios are equal. For instance, in a statement like 2/4 = 4/8, the ratios on each side of the equal sign are equal, so the statement is a proportion. Proportions are widely used in mathematics and other disciplines, and they are used to solve a variety of problems.

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Problem 1 (Specific Factors Model). Canada and U.S. trade two products with each other - Cars (C) and Textile (7). Denote all US variables with *. Each product is produced using labour only but there are two types of workers in each industry: low- skilled workers (L) and high-skilled ones (H). Low-skilled workers can easily change occupation and move from one industry to another if they can earn more there. Skilled workers, however, cannot change occupation because their skills are specific to the industry in which they work. Denote with L low-skilled labor, so that Lc and LT are employment of low-skilled workers in auto and textile industries and Lc+LT = L is the full employment condition for unskilled labor, with Ī being the total number of unskilled workers. For skilled labor, employment levels are given exogenosuly by Hc and HT. Production technologies in the two industries are the same in both coun- tries and are given by the following production functions: Yc LOHC YT = LT + HT Consumers in both countries have the where Yo and Yr are output levels. same preferences given by utility function U = CECT where Ce and CT are consumption levels of the two goods. Also suppose that Canada has more skilled workers in auto industry but less in textiles than US: Hc> Hc; HT

Answers

Based on the information provided, Canada has more skilled workers in the auto industry compared to the US, but fewer skilled workers in the textile industry.

In the specific factors model, the employment levels of low-skilled workers in the auto and textile industries are denoted by Lc and LT, respectively, while the employment levels of skilled workers are given exogenously by Hc and HT.

The production technologies in both countries are the same, with the output of cars denoted as Yc and the output of textiles denoted as YT. The production functions for both industries are Yc = LOHc and YT = LT + HT.

Consumers in both countries have the same utility function, U = [tex]U = C^{e} \cdot T^{CT}[/tex], where Ce and CT represent the consumption levels of cars and textiles, respectively.

Based on the information given, Canada has a higher number of skilled workers in the auto industry compared to the US (Hc > Hc), indicating a comparative advantage for Canada in the production of cars. On the other hand, Canada has fewer skilled workers in the textile industry compared to the US (HT < HT), suggesting a comparative disadvantage for Canada in the production of textiles.

These differences in skilled labor distribution between the two countries can have implications for trade patterns and specialization. Canada is likely to export cars to the US and import textiles from the US, reflecting its comparative advantage in the auto industry and comparative disadvantage in the textile industry.

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Cost of capital is often used as the hurdle rate or maximum
acceptable rate of return when evaluating investment projects.
Group of answer choices
True
False

Answers

The cost of capital is often used as the hurdle rate or maximum is a false statement. The cost of capital is the cost incurred by a business to fund its operations. It can be used as a benchmark to assess the potential profitability of an investment.

The cost of capital is the return required by investors to provide funds to a company. In other words, it is the cost of financing a company's operations through equity or debt. The cost of capital is an important metric used by investors and analysts to evaluate a company's potential returns. A hurdle rate, on the other hand, is the minimum rate of return required by an investor or project sponsor to invest in a project. It is used to assess the feasibility of a project by comparing it to the expected rate of return. The hurdle rate is usually set higher than the cost of capital to compensate for the risks involved in the investment.
In conclusion, the cost of capital and the hurdle rate are two distinct concepts used in finance. While the cost of capital is the cost incurred by a business to fund its operations, the hurdle rate is the minimum rate of return required by an investor or project sponsor to invest in a project. Hence, the statement that the cost of capital is often used as the hurdle rate or maximum is false.

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Shown below is information relating to the stockholders' equity of Grant Corporation at December 31, Year 1:
5.5% cumulative preferred stock, $100 par value;
authorized, 38,000 shares; issued and outstanding, 19,000 shares $1.900.000

Common stock, $5 par value; authorized, 540,000 shares; issued and outstanding, 324,000 shares : $ 1,620,000

Additional paid-in capital: preferred stock $ 190,000
Additional paid-in capital: common stock $ 2,500,000
Retained earnings $ 1,020,000

Dividends have been declared and paid for Year 1.
The average issue price per share of Grant's preferred stock was:
A) $105.50. B) $55.00 C) $100.00. D) $110.00.

Answers

The average issue price per share of Grant Corporation's preferred stock is (C) $100.00.

To calculate the average issue price per share of Grant Corporation's preferred stock, we divide the total amount of preferred stock issued by the number of shares issued. The information provided states that the preferred stock has a par value of $100, and 19,000 shares were issued and outstanding. The par value represents the initial value assigned to each share of preferred stock.

To calculate the total amount of preferred stock issued, we multiply the par value by the number of shares issued:

$100 (par value) * 19,000 (shares issued) = $1,900,000. Since the total amount of preferred stock issued is $1,900,000 and the number of shares issued is 19,000, the average issue price per share of the preferred stock is:

$1,900,000 (total amount issued) / 19,000 (shares issued) = $100.00

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Question 10 [CLO-1] If there is an ethical conflict concerning your direct supervisor, you may contact board of directors local media IMA Ethics Counselor O attomey Moving to another question will save this response. MacBook Air

Answers

If there is an ethical conflict concerning your direct supervisor, you may contact the IMA Ethics Counselor.

When confronted with an ethical conflict involving your direct supervisor, it is crucial to take appropriate steps to address the situation. One effective course of action is to contact the IMA Ethics Counselor. The IMA, as a professional organization, recognizes the importance of maintaining ethical conduct in the workplace. They have established an Ethics Counselor to provide guidance and support to members facing ethical dilemmas. By reaching out to the Ethics Counselor, you can seek expert advice on how to navigate the situation while upholding ethical standards and ensuring your concerns are addressed.

Engaging with the IMA Ethics Counselor demonstrates your commitment to maintaining professional integrity and upholding the ethical principles outlined in the organization's Standards of Ethical Conduct. The Ethics Counselor serves as a resource to help you understand your rights and responsibilities in challenging situations. Their expertise and guidance can assist you in resolving the conflict effectively, protecting your professional reputation, and contributing to a culture of ethics within your organization. By taking this step, you can demonstrate your dedication to ethical behavior and contribute to the ethical well-being of your workplace.

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American Eagle Distributing Co. (AEDC) is a regional distributor of Budweiser beer. Ross Hopkins, 41, who works for the company, ordered a Budweiser beer from a local bar after his shift on a Saturday evening. By the way, he drank Coors beer because he wanted to drink it quickly, because a competitor's beer, Coors, came to him by mistake by the clerk. The bar that was finished at that time was attended by the son-in-law of the AEDC major shareholder.
The following Monday, Hopkins was fired. The reason was that he failed to meet his obligations of conflicts of interest. Accordingly, Hopkins filed a lawsuit invalidating the dismissal, arguing that the company had no authority to order what beer to drink outside of working hours.
Reference:
Joseph DesJardins, J. (2020), An Introduction to Business Ethics (6th Ed.) McGraw-Hill
Filed an invalidation lawsuit against a man fired for drinking beer from a competitor (Herald, 2005. 5. 18) Question
1. Is it morally wrong for a company to fire someone for behavior outside of Hopkins working hours (drinking a competitor's beer)? isn't there? (Think in terms of what you have learned, such as the duty of good faith, trust and loyalty, and conflicts of interest among members of the organization.)
2. If you are a manager, how would you respond to organizational members who use a competitor's products/services? Why?

Answers

a. No, it is not morally wrong for a company to fire someone for behavior outside of working hours if that behavior creates a conflict of interest or violates the duty of good faith, trust, and loyalty towards the organization.

In this case, Ross Hopkins, an employee of American Eagle Distributing Co., ordered and consumed a competitor's beer while representing the company. This behavior raises concerns about conflicts of interest and loyalty, as well as the potential impact on the company's reputation. Organizations have a legitimate interest in ensuring that their employees maintain a level of integrity and avoid actions that could undermine the company's interests.

b. As a manager, it is important to address situations where organizational members use a competitor's products/services. First, I would establish clear policies and guidelines regarding conflicts of interest and loyalty. This would include educating employees about the potential consequences of actions that could create conflicts or harm the organization's reputation. Open communication channels would be encouraged, allowing employees to raise concerns or seek guidance. In cases where conflicts of interest arise, it may be necessary to evaluate the nature and severity of the conflict on a case-by-case basis. Transparency and fairness are key in handling such situations, ensuring that decisions are made in the best interest of the organization while also respecting the rights and well-being of employees. By promoting a culture of ethical behavior and addressing conflicts of interest proactively, the organization can maintain trust, integrity, and a focus on its mission and goals.

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The company depreciates motor vehicles on a straight-line basis.
Their expected useful life is six years.Each motor vehicle has a residual value of $5000.
For tax purposes, the motor vehicles depreciate at 20% per annum on a straight-line basis.
Accounting profit before tax (PBT) for the years 2015 to 2020 is $60000 per annum.
The tax rate is 12.5%.
Required
a. Calculations of current and deferred tax (5 marks)
b. Related figures to be included in the financial statements for the years 2015 to 2020 (5 marks)

Answers

a) Deferred tax liability = (Tax depreciation charge - Annual depreciation charge) x Tax rate = ($6,000 - $4,166.67) x 12.5% = $229.17

b) Balance sheet:

Deferred tax liability = $229.17 (to be carried forward from the previous year)

a. Calculation of current and deferred tax:

Year 2015:

Depreciation calculation:

Cost of motor vehicle = $30,000

Residual value = $5,000

Depreciable amount = Cost - Residual Value = $25,000

Annual depreciation charge = Depreciable amount / Useful life = $4,166.67

Tax depreciation rate = 20%

Tax depreciation charge = Cost x Tax depreciation rate = $30,000 x 20% = $6,000

Accounting profit before tax = $60,000

Taxable profit = Accounting profit before tax - Tax depreciation charge = $60,000 - $6,000 = $54,000

Current tax liability = Taxable profit x Tax rate = $54,000 x 12.5% = $6,750

Deferred tax liability = (Tax depreciation charge - Annual depreciation charge) x Tax rate = ($6,000 - $4,166.67) x 12.5% = $229.17

Year 2016 to 2020:

The same calculations can be applied to each year as follows:

Accounting profit before tax = $60,000

Taxable profit = Accounting profit before tax - Tax depreciation charge = $60,000 - $6,000 = $54,000

Current tax liability = Taxable profit x Tax rate = $54,000 x 12.5% = $6,750

Deferred tax liability = (Tax depreciation charge - Annual depreciation charge) x Tax rate = ($6,000 - $4,166.67) x 12.5% = $229.17

b. Related figures to be included in the financial statements for the years 2015 to 2020:

Year 2015:

Income statement:

Profit before tax = $60,000

Tax expense:

Current tax = $6,750

Deferred tax = $229.17 Net profit after tax = $52,020.83

Balance sheet:

Deferred tax liability = $229.17

Year 2016 to 2020:

Income statement:

Profit before tax = $60,000

Tax expense:

Current tax = $6,750

Deferred tax = $229.17 Net profit after tax = $52,020.83

Balance sheet:

Deferred tax liability = $229.17 (to be carried forward from the previous year)

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In economics, as a result of scarcity: Consumers face tradeoffs regarding what they want to purchase and consume. Producers face tradeoffs regarding what they are able to supply. It may not be possible to fulfill all possible wants and needs among all individuals in the economy. All of the above.

Answers

The correct answer is "All of the above." Scarcity, which refers to the limited availability of resources in relation to unlimited wants and needs, impacts both consumers and producers in the economy.

Consumers face tradeoffs because they have limited income and resources to allocate towards different goods and services. They must make choices about what they want to purchase and consume, weighing the benefits and costs of different options. For example, a consumer may have to choose between buying a new car or going on a vacation due to limited financial resources.

Producers also face tradeoffs as they have limited resources and production capabilities. They must decide what goods and services to produce given these constraints. Allocating resources towards producing one good means sacrificing the production of another. For instance, a company may need to choose between producing more of one product or investing in research and development for future innovations.

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Long-Run Competitive Equilibrium Market demand is given by D(p) = 100 – ½p, all firms in the market have the following long-run cost function C'(y) = y² +9. a) Find the firm's supply function, yż(p). b) Find the equilibrium price, p*. c) Find the equilibrium firm and market quantity, yž, and y*. d) Find the equilibrium number of firms, n*.

Answers

a) The firm's supply function is yż(p) = p/2.

b) The equilibrium price is p* = 40.

c) The firm's quantity is 20 and the market quantity is y* = n * yż = n * (p*/2).

d) The equilibrium number of firms (n*) in the market is 3.

a) To find the firm's supply function, we need to equate marginal cost (MC) to price (p). In the long run, a competitive firm will choose the quantity that minimizes its cost for a given price. The firm's cost function is given as C'(y) = y² + 9.

First, we need to find the marginal cost function (MC). Taking the derivative of the cost function with respect to quantity (y), we get:

MC = dC/dy = 2y.

Setting MC equal to price (p), we have:

2y = p.

Solving for y, we get the firm's supply function:

yż(p) = p/2.

b) To find the equilibrium price (p*), we need to equate market demand (D) to market supply. Market demand is given by D(p) = 100 - ½p, and the firm's supply function is yż(p) = p/2.

Setting D(p) equal to the total supply (n*yż(p)), where n is the number of firms in the market, we have:

100 - ½p = n * (p/2).

Simplifying the equation, we get:

100 - ½p = np/2.

Solving for p, we find the equilibrium price:

p* = 40.

c) To find the equilibrium firm quantity (yż) and market quantity (y*), we substitute the equilibrium price (p*) into the firm's supply function (yż(p)) and the market demand function (D(p)).

For the firm's quantity:

yż = yż(p*) = p*/2 = 40/2 = 20.

For the market quantity:

y* = n * yż = n * (p*/2).

d) To find the equilibrium number of firms (n*), we can substitute the equilibrium price (p*) and equilibrium firm quantity (yż) into the market quantity equation:

y* = n * (p*/2).

Given that y* = 100 - ½p*, we have:

100 - ½p* = n * (p*/2).

Substituting the value of p* and solving for n, we find:

100 - ½(40) = n * (40/2).

60 = 20n.

n* = 3.

Therefore, the equilibrium number of firms (n*) in the market is 3.

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The Machine Shop is a retailer of tools for carpenters. Their top selling product is a revolutionary saw, which sells for €999. However, they are short on cash and try to hold the storage as short as possible. A customer interested in the saw buys with a probability of 0.8 if the saw is in the shop. If he has to wait for a day, he will buy and come back with a probability of 0.6. If the customer has to wait for two days, he will buy with a probability of 0.6, and if he has to wait for more than that, the customer will choose another saw. The owner thinks about offering discounts to customers willing to wait: 5% for one day waiting, 10% for two days waiting, and 15% for more than two days of waiting. Then he believes that the probability of a customer buying will go up to 0.8 for one day waiting, 0.6 for two days waiting, and 0.4 for more than two days of waiting. The owner can buy the saw for €450 and choose express freight (€80 for one day delivery), ordinary delivery (€40 for two days delivery), and snail delivery (free of charge, the tool will come when it comes). What decisions should be made? TY show and game "Who Wants to be a ings for each ques-

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Machine Shop is a retailer of tools for carpenters. Their top selling product is a revolutionary saw, which sells for €999. However, they are short on cash and try to hold the storage as short as possible. A customer interested in the saw buys with a probability of 0.8 if the saw is in the shop. If he has to wait for a day, he will buy and come back with a probability of 0.6. If the customer has to wait for two days, he will buy with a probability of 0.6, and if he has to wait for more than that, the customer will choose another saw. The owner can buy the saw for €450 and choose express freight (€80 for one day delivery), ordinary delivery (€40 for two days delivery), and snail delivery (free of charge, the tool will come when it comes).

The owner thinks about offering discounts to customers willing to wait: 5% for one day waiting, 10% for two days waiting, and 15% for more than two days of waiting. Then he believes that the probability of a customer buying will go up to 0.8 for one day waiting, 0.6 for two days waiting, and 0.4 for more than two days of waiting.The owner can buy the saw for €450 and choose express freight (€80 for one day delivery), ordinary delivery (€40 for two days delivery), and snail delivery (free of charge, the tool will come when it comes).Let us consider the expected net profit for the Machine Shop in each of the following cases:

Case 1: The saw is available in the shop Expected demand if the saw is available is 0.8. Expected net profit = Expected revenue - Expected cost Expected revenue = Selling price = €999 Expected cost = Purchase price + Delivery cost = €450 + €0 (Snail delivery) = €450 Expected net profit = €999 - €450 = €549

Case 2: The saw is not available in the shop, but it will arrive in one day The probability that a customer will wait for a day is 1 - 0.8 = 0.2 Expected demand if the saw will arrive in one day is 0.6Expected net profit = Expected revenue - Expected cost Expected revenue = Selling price - 5% = €999 - (5/100) × €999 = €949.05Expected cost = Purchase price + Delivery cost = €450 + €80 (Express freight) = €530 Expected net profit = €949.05 - €530 = €419.05

Case 3: The saw is not available in the shop, but it will arrive in two days The probability that a customer will wait for two days is 1 - 0.8 - 0.2 = 0 Expected demand if the saw will arrive in two days is 0.6Expected net profit = Expected revenue - Expected cost Expected revenue = Selling price - 10% = €999 - (10/100) × €999 = €899.1Expected cost = Purchase price + Delivery cost = €450 + €40 (Ordinary delivery) = €490 Expected net profit = €899.1 - €490 = €409.1

Case 4: The saw is not available in the shop, and it will take more than two days to arrive The probability that a customer will wait for more than two days is 1 - 0.8 - 0.2 - 0 = 0 Expected demand if the saw will arrive in more than two days is 0.4Expected net profit = Expected revenue - Expected cost Expected revenue = Selling price - 15% = €999 - (15/100) × €999 = €849.15Expected cost = Purchase price + Delivery cost = €450 + €0 (Snail delivery) = €450 Expected net profit = €849.15 - €450 = €399.15The best decision for the Machine Shop is to stock the saw in the shop as the expected net profit (€549) is higher than the expected net profit for other cases.

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Bess company shows the following unit costs for its product

Direct materials $70
Direct labour 50
Variable overhead 5
Fixed overhead 8

What is the unit product cost using variable costing?
A.None of the given answers
B.$120
C.$125
D.$133

Answers

The unit product cost using variable costing for Bess Company's product is (C) $125.In the given scenario, Bess Company has provided the unit costs for its product.

Variable costing excludes fixed manufacturing overhead costs because these costs are not directly tied to the production volume or the number of units produced. Fixed overhead costs remain constant regardless of the level of production or sales.

Given the following unit costs:

Direct materials: $70

Direct labor: $50

Variable overhead: $5

To calculate the unit product cost using variable costing, we add the variable costs together:

$70 (direct materials) + $50 (direct labor) + $5 (variable overhead) = $125

Therefore, the unit product cost using variable costing for Bess Company's product is $125.This cost represents the direct costs directly associated with producing each unit of the product, while excluding the fixed overhead costs. Therefore, option C, which states that the unit product cost is $125, is the correct answer.

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The Academy of Nutrition and Dietetics suggests all of the following actions for parents of children with peanut allergies EXCEPT:
read food labels carefully.
consider consulting with a registered dietitian to develop an eating plan that avoids allergens.
educate family members and caregivers about managing the allergy.
avoid talking to the child about the food allergy so he or she does not feel stigmatized.
discuss the peanut allergy with teachers.

Answers

The Academy of Nutrition and Dietetics suggests all of the following actions for parents of children with peanut allergies EXCEPT avoiding talking to the child about the food allergy so he or she does not feel stigmatized.

The Academy of Nutrition and Dietetics recommends that parents of children with peanut allergies should read food labels carefully, consider consulting with a registered dietitian to develop an eating plan that avoids allergens, educate family members and caregivers about managing the allergy, and discuss the peanut allergy with teachers. However, they do not recommend avoiding talking to the child about the food allergy as this can lead to feelings of isolation and make it more difficult for the child to manage the allergy.

Peanut allergies can be serious and potentially life-threatening, so it is important for parents of children with this allergy to take appropriate steps to manage it. The Academy of Nutrition and Dietetics provides several recommendations for parents of children with peanut allergies, including reading food labels carefully to identify any potential allergens, considering consulting with a registered dietitian to develop an eating plan that avoids allergens, and educating family members and caregivers about managing the allergy. Additionally, the Academy recommends discussing the peanut allergy with teachers to ensure that appropriate accommodations can be made in school settings. This may include things like providing alternative snacks for the child, having an emergency plan in place, and educating other students about the allergy.

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A researcher is testing the hypothesis that the average monthly income in the population is 20,000 AD. Using the formula for testing a hypothesis about the mean,
the researcher calculates the Z value to be 2.06. If the researcher is using 9596 confidence level, what should the researcher do next?

Answers

Based on the calculated z-value and the 95% confidence level, the researcher should reject the null hypothesis that the average monthly Income in the population is 20,000 ad.

To determine the next step, we need to refer to the critical value table for the standard normal distribution. since the researcher is using a 95% confidence level, we need to find the critical value corresponding to an alpha level of 0.05 (1 - 0.95).

the critical value for a two-tailed test at a 95% confidence level is approximately 1.96. since the researcher's calculated z-value of 2.06 is greater than the critical value of 1.96, it falls in the rejection region. the evidence suggests that the average monthly income is significantly different from 20,000 ad.

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A company forecast to have negative economic value added (EVA) forever, will be trading at EV/Capital ratio that is smaller than one. (All else equal.) True False Next Previous 4 pts Question 11 6 pts Sprung Verlag's is currently trading at a PE ratio of 10 and has a return on equity (ROE) equal to 20% and net prot margin (NPM) equal to 10%. Given this information what are Sprung Verlag's PB and PS ratios? OPB-1 and PS-1 OPB-1 and PS-20 PB-2 and PS-1 PB-2 and PS-2 it is impossible to determine PB and PS from the information provided

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False. The EV/Capital ratio being smaller than one does not necessarily mean that a company will have negative Economic Value Added (EVA) forever.

The EV/Capital ratio compares the enterprise value (EV) of a company to its invested capital, and a ratio smaller than one indicates that the market value of the company is lower than its invested capital. Economic Value Added (EVA) measures the company's profitability and value creation by subtracting the cost of capital from its net operating profit after taxes (NOPAT). It is a measure of how much value the company generates above its cost of capital.

While a company with an EV/Capital ratio smaller than one may face challenges in generating positive EVA, it does not guarantee that it will have negative EVA forever. Factors such as operational improvements, cost reductions, and strategic changes can impact a company's future profitability and EVA.

Therefore, the relationship between the EV/Capital ratio and EVA is not straightforward, and it cannot be concluded that a company with an EV/Capital ratio smaller than one will have a negative EVA forever.

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Consider a project with a life of 8 years with the following information: initial fixed asset investment = $490,000; straight-line depreciation to zero over the 8-year life; zero salvage value; price = $31; variable costs = $16; fixed costs = $181,300; quantity sold = 96,089 units; tax rate = 22 percent. How sensitive is OCF to changes in quantity sold?
a) $8.31
b) 15.09
c) 11.70
d) 0.09

Answers

The answer is (b) 15.09.

The sensitivity of OCF to changes in quantity sold is calculated as follows:

Sensitivity = (P - VC) x (1 - Tax Rate) / Quantity Sold

In this case, the sensitivity is:

Sensitivity = ($31 - $16) x (1 - 0.22) / 96,089 units

= $15.09

This means that a 1 unit change in quantity sold results in a $15.09 change in OCF.

The sensitivity of OCF to changes in quantity sold is important because it can help us to understand how much risk is associated with the project. A high sensitivity indicates that the project is more sensitive to changes in quantity sold, and therefore more risky.

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Short Continuous Assessment. 1: Define global leadership and identify any four great global leaders you know 2: Enumerate the opportunities and challenges of global leaders. 3: As a global leader, identify and develop your own global talent pool. Lecture Day 3 Class exercise & discussion

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Global leadership refers to the ability to lead and inspire individuals, teams, and organizations to achieve goals on a global scale. It requires a combination of interpersonal skills, strategic thinking, cultural awareness, and adaptability to navigate complex and diverse environments.


Global leaders face both opportunities and challenges in their roles. Some opportunities include access to a wider talent pool, diverse perspectives and ideas, and the potential for greater innovation and growth. However, they also face challenges such as cultural differences, language barriers, and varying political and economic environments.

To identify and develop their own global talent pool, global leaders need to focus on attracting and retaining top talent from different parts of the world, building strong relationships with local stakeholders, and creating a culture of collaboration and innovation.

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You have recently joined Blue Bob Inc. as a project manager. There is currently a Management Information System (MIS) development project in-progress that is still at the planning stage. A business case was submitted for the project by the previous project manager and the project was subsequently approved with a commitment of funds and other available resources (inclusive of project team members with key skills) by the Project Evaluation Board. Your first responsibility as the project manager together with your project team, is to design the scope management plan for this project. Keep in mind that the quality of your plan will be benchmarked against the successes of the previous project manager (even with scope creep regularly rearing its head on many projects). The scope management plan for this project should therefore be all encompassing, illustrating every finite aspect of scope management planning and should simultaneously be explicit to all relevant stakeholders.
Define the scope of the project. (5 Marks)

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The scope of the project refers to the boundaries and deliverables of the Management Information System (MIS) development project. It defines the work that needs to be accomplished to achieve the project objectives and deliver the desired outcomes.

In the case of Blue Bob Inc.'s MIS development project, the scope will encompass the following aspects:

1. Objective: The project aims to develop a robust and user-friendly MIS system that enhances data management, reporting, and decision-making processes within the organization.

2. Deliverables: The project will deliver a fully functional MIS system, including modules for data capture, storage, analysis, reporting, and integration with existing systems.

3. Boundaries: The scope will define the limitations of the project, such as specific functionalities and features to be included, target user groups, and any constraints, such as budget and timeline.

4. Exclusions: The scope will explicitly state what is not included in the project, such as integration with external systems beyond the defined scope, hardware infrastructure upgrades, or training activities for end-users.

5. Assumptions: The scope will outline any assumptions made during the planning stage, such as the availability of key resources, existing data sources, and necessary support from stakeholders.

By clearly defining the scope of the project, all stakeholders, including the project team, management, and users, will have a shared understanding of what will be delivered and what is beyond the project's boundaries.  The scope includes both what is included in the project as well as what is excluded. This will help manage expectations, control scope creep, and ensure the successful completion of the MIS development project.

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Which of the following is true about defined contribution plans?
They are preferred more in smaller companies than larger ones.
They shift the investment risk to the employer.
They promise a specific benefit level for employees upon retirement.
They present greater administrative challenges to employers.
They have become less

Answers

C). Defined contribution plans are retirement plans that specify the amount of money that an employer will contribute to an employee's account during their working years. The employee then chooses how to invest those funds, and the account balance grows over time. Upon retirement, the employee receives the accumulated balance, which depends on investment performance.


Out of the given options, the statement that is true about defined contribution plans is that they present greater administrative challenges to employers. This is because employers are responsible for choosing and managing the investment options available to employees, as well as ensuring that the plan meets legal requirements.
Defined contribution plans are not preferred more in smaller companies than larger ones, as they can be implemented by companies of any size. They do not promise a specific benefit level for employees upon retirement, as the final amount depends on investment performance. Additionally, they do not shift investment risk to the employer, as this risk is borne by the employee.


Overall, defined contribution plans have become more popular in recent years, as they provide more flexibility for employees and employers alike. However, they do require careful management to ensure that they provide adequate retirement benefits while remaining financially sustainable.

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i want a full research on the DATA ANALYSIS (METHODOLOGY) to
social media for customer engagement (

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An interaction between a customer and an organization via various online or social media channels is referred to as customer engagement.

Social media customer involvement benefits a business because consumers enjoy reading about and sharing positive encounters between companies and real people. Better social media involvement translates to clients who are more engaged with the brand. It offers more chances to boost sales and cultivate loyalty.

The following are advantages of client interaction on social media.

Expanding my audience.

Belief in a brand.

Direct interaction.

We receive insightful input.

Possibilities for social listening.

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Units Unit Cost January 1, 2021 (beginning inventory) 600 $8.00 Purchases: 1,100 9.00 1,300 10.00 January 5, 2021 January 25, 2021 February 16, 2021 March 26, 2021 800 11.00 600 12.00 A physical inventory on March 31, 2021, shows 1,500 units on hand. Instructions. Prepare schedules to compute the ending inventory at March 31, 2021, under each of the following inventory methods. (a) FIFO. (b) LIFO. (c) Weighted average. Consider logistic difference equation xn + 1 = rxn( 1 - xn) = f(x), 0 < = xn< = 1. Show that expression f(f(x))-x = 0 can be factorized into rx- (1+r) x + 1+r/r) = 0 Show that x1 = 1 + r + {1 + r)(r - 3)/ 2r x2 = 1 + r - (1+ r)(r - 3)/2 rare a two-cycle solution to Eq. (1). before forming strategic alls c. Governance Risk. Explain the methods by which MNEs can tackle issues of governance as they expand into new nations. d. Host Goverment Investment Duties. Host govemment Consider the following sample data values. 7 4 6 12 8 15 1 9 13 a) Calculate the range. b) Calculate the sample variance. c) Calculate the sample standard deviation. a) The range is 14 b) The sample variance is (Round to two decimal places as needed.) c) The sample standard deviation is (Round to two decimal places as needed.) fe(clo4)3(s) 6h2o(l)fe(h2o)3 6(aq) 3clo4(aq) lewis acid is fe(clo4)3 6h2o The 20 august 2017, you receive a invoice of 10 000$ for school taxes covering the period from july 1st 2017 to june 30th 2018. The payment is made the 30 september 2018. Register all the journal entryaugust :September : 1. What is a null matrix with order 2?2. What is a null matrix with order 3? Is this matrix applicablefor a Leontief input-output model (economy)? The conditional pdf of X given Y = y is given by (0 (y))" fxy(x|y) = -0(y)xpn-1 X>0 r(n) where 0 (y) is a function of y (a) Find E(X Y = y) 1 (b) For given E(X | Y = y) = -- and fy (y) = Be-By, y> 0 y AREAS OF EVALUATION 1. Risk Management Planning 2. Understanding and Assessing the Current Situation 3. Setting Objectives for Managing Risk 4. Risk Strategy 5. Risk Response Plan 6. Implementing the Risk Plan RISK MANAGEMENT PLAN (OUTCOME) SUMMARY OF FINDINGS, PATTERNS AND TRENDS Under this column summarize your findings in the Areas of Evaluation List down your suggested improvements or remarks, if any. REMARKS AND RECOMMEDATIONS Give your comments on the overall doability of the Risk Management Plan. What will you recommend to the Risk Management team of the organization. FILL IN THE BLANK. On December 30, 2021, Whitney sold a piece of property for $365,600. Her basis in the property was $164,520, and she incurred $3,656 in selling expenses. The buyer paid $18,280 down with the balance payable in $34,732 installments over the next ten years. In addition, the buyer assumed a $54,840 mortgage on the property. Under the installment sales method, what is the total contract price, the total gain on the sale, and the amount of gain reported in 2021? Round any division to two decimal places, and use that amount in subsequent computations. If required, round your final answer to the nearest dollar. Under the installment sales method, the total contract price is $_______ the total gain on the sale is $______ and the amount of gain reported in 2021 is $_____