nicolas barrens conspired with his manager to steal nearly $6,000 over 2 months from the grocery store where they worked. each time nicolas rang up a customer at the register, he asked the customer if he'd like a receipt. when a customer said no, nicolas pretended to discard the receipt in the trash, but actually slipped the receipt into his pocket. at the end of his shift, he filled out a void slip for each of these sales and submitted them to his supervisor for approval. with the original receipt and the approved void slip, nicolas removed cash from the register in the amount of the voided sales and split the proceeds with his supervisor. nicolas committed what type of fraud scheme?
Answers
Nicolas committed a cash theft fraud scheme by conspiring with his supervisor to steal nearly $6,000 over two months from the grocery store where they worked. He achieved this by pretending to discard receipts in the trash when customers declined them and then filling out void slips for these sales at the end of his shift.
The void slips were then submitted to his supervisor for approval, and with the original receipt and the approved void slip, Nicolas removed cash from the register in the amount of the voided sales and split the proceeds with his supervisor.This type of fraud scheme is also known as a skimming fraud scheme, where a customer's payment is received by an employee, but the transaction is not recorded in the company's accounting system. Instead, the cash is pocketed by the employee, allowing them to steal funds without detection.It is important for businesses to implement internal controls, such as regular audits and segregation of duties, to prevent and detect fraud schemes like this. Employees should also be trained on the importance of honesty and integrity in the workplace and the severe consequences of engaging in fraudulent behavior. Ultimately, the customer should always be the top priority, and any dishonest behavior that harms them or the company's financial health should never be tolerated.
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Basics Test - English EXIT PREVIOUS Paul is setting up a marketing/sales event at a community center where he is going to discuss UnitedHealthcare Medicare Advantage plans. He has placed a UnitedHealthcare logo pen ($3 value), Clarity consumer workbook, and an Enrollment Guide at each seat. What, if anything, has Paul done wrong
Answers
Answer:
What Paul has done wrong is to place these marketing materials on seats. He should devised a plan to give out these materials at the registration point where participants would be registered and then they would collect the items. By placing them on the seats, some of the participants could collect more than one, especially the valuable pen that is worth $3 each.
Explanation:
Marketing materials cost the entity some funds to produce. They should not be wasted. In addition, the number of participants with some details like names and contact information should be captured for future marketing efforts. Allowing participants to have free access to the marketing materials that cost so much without driving any potential customer list is not prudent.
Which of the following exemplifies a pure competitive market?A) a market where many buyers and sellers trade over a range of prices rather than a single market priceB) a market where a single firm controls the larger fraction of the market shareC) a market where a few powerful firms control the larger fraction of the market shareD) a market characterized by only a few large sellersE) a market where many buyers and sellers trade in a uniform commodity
Answers
A purely competitive market is characterized by a large number of buyers and sellers who engage in the trading of a standardized or uniform commodity. The correct answer that exemplifies a purely competitive market is E) a market where many buyers and sellers trade in a uniform commodity.
In this type of market, no individual buyer or seller has significant control over the market price or quantity. All participants in the market have perfect information about prices and product quality, and there are no barriers to entry or exit for new firms.
The presence of many buyers and sellers ensures that no single entity can exert significant influence on the market. This results in a competitive environment where prices are determined by market forces of supply and demand.
Therefore, the correct answer that exemplifies a purely competitive market is E) a market where many buyers and sellers trade in a uniform commodity.
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Option E, a market where many buyers and sellers trade in a uniform commodity, exemplifies a pure competitive market.
A pure competitive market is a market structure where there are many buyers and sellers trading in a uniform commodity. In this type of market, no single buyer or seller has control over the market price. The prices are determined by the forces of supply and demand.
In the given options, option E exemplifies a pure competitive market. Option E states that it is a market where many buyers and sellers trade in a uniform commodity, which aligns with the characteristics of a pure competitive market.
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Why do you think it is important to understand GDP?
Answers
jordan moved from the united states and took a job at a company based in china. he was always trying to get his co-workers in china to discuss their personal feelings regarding corporate decisions, but they were reluctant to do so because such conversations were not typical of their culture. jordan's behavior is an example of
Answers
Jordan moved from the United States and took a job at a company based in China. He was always trying to get his co-workers in China to discuss their personal feelings regarding corporate decisions but they were reluctant to do so because such conversations were not typical of their culture. Jordan's behavior is an example of Emotional Intelligence.
In the Emotional Intelligence, the worker perform their work at company with keep in mind some aspects which are ability to understand, and manage their own emotion in positive way.
He was reluctant to discuss their personal feelings regarding corporate decisions because he didn't want co-workers feel low due to such conversations were not typical of their culture but he was also tried to get company performed good by his decision.
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How does the increasing water scarcity in Egypt affect prices and even the availability of some goods and services?
Answers
Answer:
because input price increases the out put price also increases
Explanation:
the law of supply
"Bronson Manufacturing is planning to issue $12 million in bonds. Based on a poll of potential investors, they have the highest chance of raising the funds they need with one of four sets of bond characteristics. Which option would cost them the MOST in total interest over the life of the bond
Answers
Answer:
C.eight-year bond with 5.5% annual interest rate
Explanation:
The computation of the total options under each option is as follows:
As we assume the par value be $1,000
For Option A
Total interest
= 9.5% × $1,000 × 3 years
= $285
For Option B
Total interest is
= 7.25% × $1,000 × 4 years
= $290
For Option C
Total interest is
= 5.5% × $1,000 × 8 years
= $440
For Option D
Total interest is
= 6% × $1,000 × 6 years
= $360
As we can see that the option C contains high value of the total interest. So the same is to be selected
Refer to this income statement to answer the question below.
Forks Gym
Income Statement
From the Month Ended January 31, xxxx
Revenue:
Membership Fees Revenue, 15,000.00
Rental Revenue, 8,000.00
Instruction Revenue, 5,000.00
Total Revenue = 28,000.00
Expenses:
Advertising Expense, 2,000.00
Rent Expense, 1,000.00
Salaries Expense, 3,000.00
Utilities Expense, 1,000.00
Total Expenses = 7,000.00
Net Income - 21,000.00
Forks Gym has a net loss.
- True
- False
Answers
Answer:
The answer is False
Explanation:
Just making it easier for ppl to see
___________ refers to the short distance movement that usually takes place within the confines of a building such as a plant or distribution center and between a building and a transportation service provider.
a. physical distribution.
b. materials management.
c. warehousing.
d. materials handling.
Answers
Answer:
d. materials handling.
Explanation:
That's the correct answer. Hope that helps
Materials handling refers to the short-distance movement that takes place within the confines of a building such as a plant distribution centre and between a building and a transportation service provider. The correct option is d.
What are materials handling?Materials handling can be understood as a short-distance movement within the confines of a building or between a building and a vehicle. It uses a wide range of manual, semi-automated, and automated equipment and includes consideration of the protection, storage, and control of materials throughout their manufacturing, warehousing, distribution, consumption, and disposal.
Material handling can be used to create time and place utility through the handling, storage, and control of waste, as distinct from manufacturing, which creates form utility by changing the shape, form, and makeup of the material. Almost every item of physical commerce has been transported on a lift truck or another type of material handling equipment in manufacturing plants, warehouses, and retail stores.
Therefore material handling plays an important role in manufacturing and logistics.
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What is something that quantitative research won't tell you?
A. A company's annual earnings
B. A company's stock performance over the past five years
C. How happy a company's employees are
D. When a company went public
Answers
The findings that quantitative research won't tell you is "When a company went public."
This is because quantitative research measures the situation in value using numbers analysis
Usually, quantitative research analyzes numerical data to conclude.
Options A, B, and C can be measured on numerical scales, in which the conclusion can be reached.
However, option D is just a date; it cannot be analyzed with quantitative research analysis.
Hence, in this case, it is concluded that the correct answer is option D. "When a company went public."
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Answer:
c
Explanation:
took the test
In the chapter about owning versus leasing, one set of examples compares the cost of owning versus the cost of leasing for Southside Clinic, a not-for-profift organization. The net advantage to owning (versus leasing) for Southside amounted to $676. The difference between the two methods of financing: A) is so small that it might be disregarded. B) may be considered as a nearly neutral comparison between the two methods. C) is so small that it might be disregarded and may be considered as a nearly neutral comparison between the two methods. D) None of these is correct
Answers
Answer:
The correct answer is D) None of the above options are correct.
Explanation:
In making a decision about whether to own or lease a property, if the cost of ownership is only slightly higher than leasing, financial intelligence requires that the company, or business or entity or person checks to see if the property is an income is generating one.
If yes, then it's should be considered for purchase
If the asset is not income-generating but plugs a cost leakage, it can also be considered if the value can appreciate in value.
It only becomes advisable to lease the assets if:
the cost of purchasing the property far outweighs the cost of leasing as well as the current capacity of the Clinic;It's an assets that is non-income generatingIf it's a non-income generating asset that attracts lots of taxes etc.Cheers
When the outcome of an event is uncertain and information is costly, we can never arrive at a Pareto-optimal negotiated outcome to reduce externalities.
a.True
b. false
Answers
The following statement is true: When the outcome of an event is uncertain and information is costly, we can never arrive at a Pareto-optimal negotiated outcome to reduce externalities.
The optimal outcomes of an economic system, also known as Pareto efficiency or Pareto optimality, are those in which no one can be better off without making someone else worse off. An allocation of resources in which every person is better off is referred to as a Pareto improvement. A negotiated outcome to minimize externalities is always a Pareto-optimal one if and only if the benefits of the activity are equal to the costs, since only then would there be no net welfare impact.
Externalities are indirect impacts that an economic activity has on parties that are not involved in it. They may be beneficial or detrimental and are frequently ignored in private transactions since they are not explicitly accounted for in the cost-benefit calculations. As a result, externalities might lead to suboptimal outcomes since they are not accounted for in market activity.
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Suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow. The demand for wine is given by p = $480 – 0.2Q where p is the price and Q is the total quantity sold. The industry consists of just the two Cournot duopolists, Grinch and Grubb. Imports are prohibited. Grinch has constant marginal costs of $ 60 and Grubb has marginal costs of $45. How much is Grinch's output in equilibrium?
Answers
The value of q1, we need to solve the above two equations for q1. Solving the equations, we get:q1 = 160q2 = 128. Thus, the optimal output of Grinch is q1 = 160 units.
Cournot duopoly is a market situation where a small number of firms compete against one another. These firms offer differentiated or homogeneous goods and services. Cournot's solution explains the output levels and equilibrium prices under oligopoly.
In the given problem, Grinch and Grubb go into the wine business in a small country where wine is difficult to grow. It has been given that the demand for wine is given by p = $480 – 0.2Q, where p is the price and Q is the total quantity sold.
The total quantity sold is given by: Q = q1 + q2where, q1 is the output of Grinch and q2 is the output of Grubb.
The marginal cost (MC) of Grinch is $60, and the marginal cost of Grubb is $45. The marginal cost is the additional cost that the firms incur in producing one extra unit of the good. Therefore, the total cost (TC) of producing a given quantity of the output is given by:TC1 = 60q1 andTC2 = 45q2In the Cournot duopoly, each firm maximizes its profit by considering the output decision of its competitor.
The output decision of Grinch, q1, depends on the output decision of Grubb, q2. Thus, the optimal output decisions of Grinch and Grubb can be expressed as:q1 = (a – b.q2) / 2q2 = (a – b.q1) / 2 where, a = 480 and b = 0.2Substituting the values of a and b, we get:q1 = (480 – 0.2q2) / 2q2 = (480 – 0.2q1) / 2
Multiplying both sides by 2, we get:2q1 = 480 – 0.2q22q2 = 480 – 0.2q1. Simplifying the above two equations, we get:q1 = 144 – 0.1q2q2 = 144 – 0.1q1 .
Therefore, to find the value of q1, we need to solve the above two equations for q1.
Solving the equations, we get:q1 = 160 q 2 = 128. Thus, the optimal output of Grinch is q1 = 160 units.
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Contribution margin is first used to cover expenses. Once the break-even point has been reached, contribution margin becomes:.
Answers
It should be noted that the contribution margin is first used to cover fixed expenses.
What is contribution margin?
The contribution margin simply shows you the aggregate amount of revenue that is available after variable costs to cover fixed expenses.
Contribution margin is first used to cover fixed expenses. Once the break-even point has been reached, the contribution margin becomes profit.
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Competitive firms will always try to earn more than a normal profit by doing the following, except
A. Adopting better production technology
B. Improving their business organization and operation
C. Developing new products
D. Raising the prices of their existing products
Answers
competitive firms adopt various strategies to earn more than a normal profit, such as adopting better production technology, improving their business organization and operation, and developing new products. However, raising the prices of their existing products is not always a viable strategy and can backfire if not executed correctly.
Competitive firms are always striving to earn profits, and this is essential for their survival and growth in the market. However, in a competitive market, earning more than a normal profit can be challenging as there are several players competing for the same customers. In such a scenario, firms have to adopt various strategies to gain an edge over their rivals.One such strategy is to adopt better production technology. By using advanced technology, firms can produce goods at a lower cost, which can help them increase their profit margins. For instance, if a firm uses automated machinery to produce its products, it can reduce its labor costs and increase efficiency, which can help it earn more profits.Another strategy is to improve their business organization and operation. By streamlining their operations, firms can reduce their overhead costs and increase their efficiency, which can help them earn more profits. For instance, if a firm implements better inventory management practices, it can reduce its inventory costs and increase its profitability.
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3. Of the following provisions that might be found in a bond indenture, which would tend to reduce the coupon interest rate on the bond in question?
a
A subordination clause in a debenture.
b
A call provision.
c
A convertible feature.
d
Having relatively few restrictive covenants.
e.
All of the above.
Answers
The bond in question's coupon interest rate would typically be reduced by a convertible feature.
Define the term "convertible feature"?An asset that can be changed by the shareholder into common stock is known as a convertible, which can be a bond, preference share, or other type of financial instrument. Convertible securities aren't considered to be either debt or equity; rather, they're viewed as a cross between the two groups because they have the cash flow characteristics of both bonds and stocks.
What distinguishes a convertible bond from other bonds?An investment that may be converted into a predetermined number of shares of common stock is known as a convertible bond. It pays fixed-income interest payments. During the bond's term, the bond can be converted into stock at precise points at the bondholder's option.
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JohnBoy Industries has a cash balance of $54,000, accounts payable of $134,000, inventory of $184,000, accounts receivable of $219,000, notes payable of $129,000, and accrued wages and taxes of $41,500. How much net working capital does the firm need to fund?
Answers
Answer:Net working capital = $152,500
Explanation:
Net working capital = CA– CL
Where CA= Current Assets = Cash + Inventory + Accounts Receivable
and CL= Current Liabilities= Account payable + Notes payable + accrued wages and taxes
CA=$54, 000 + $184,000 + $ 219,000 =$457,000
Current liabilities = Account payable + Notes payable + accrued wages and taxes
CL = $134,000 + $129,000 + $41,500 = $304,500
Net working capital = Current assets – Current liabilities
Net working capital = $457,000 – $304,500= $152,500
Net working capital = $152,500
Item 2
Which of the following is NOT an example of a servant?
A graphic designer in a marketing firm
A manager in a paint store
A chef in a restaurant
A real estate broker who is hired to sell land
Answers
A real estate broker hired to sell land does not correspond to an example of a servant, who is a professional assigned to perform functions for the employer.
What are the functions of a broker?They are licensed professionals who have the essential training requirements to provide real estate service, and can work independently or with the hiring of other professionals for the job.
Therefore, the real estate broker is a professional capable of working independently, but must be licensed and comply with the code of ethics of the National Association of Realtors.
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identify two example of how products might be promoted directly to customer using the internet
Answers
Answer: ads while watching tv
Explanation:
Allen Technical Institute (ATI), a school owned by Susan Allen, provides training to individuals who pay Juition directly to the school. ATI also offers training to groups in off-site locations. Its unadjusted trial balance as of December 31,2022 , is found on the trial balance tab. ATI initially records prepaid expenses and unearned revenues in balance sheet accounts. Descriptions of items a through h that require adjusting entries on December 31 follow. a. An analysis of ATI's insurance policies shows that $2,650 of coverage has expired. b. An inventory count shows that teaching supplies costing $3,440 are available at year-end. c. Annual depreciation on the equipment is $6,400. d. Annual depreciation on the professional library is $12,200. e. On November 1, ATI agreed to do a special six-month course (starting immediately) for a client. The contract calls for a monthly fee of $2,600, and the client paid the first five months' fees in advance. When the cash was received, the Unearned Training Fees account was credited. f. On October 15. ATI agreed to teach a four-month class (beginning immediately) for an executive with payment due at the end of the class. At December 31,$3,400 of the tuition has been earned by ATI. 9. ATi's two employees are paid weekly. As of the end of the year, two days' salaries have accrued at the rate of $220 per day for each employee. h. The balance in the Prepaid Rent account represents rent for December. For each adjustment, indicate the income statement and balance sheet account affected, and the impact on net income. If an adjustment caused net income to decrease, enter the amount as a negative value. Net income before adjustments can be found on the income statement tab. (Hint: Select unadjusted on the drop-down.)
Answers
a. Insurance expense will increase, and prepaid insurance will decrease, reducing net income by $2,650.
b. Teaching supplies expenses will increase, and inventory will decrease, reducing net income by $3,440.
c. Depreciation expense will increase, and accumulated depreciation will increase, reducing net income by $6,400.
d. Depreciation expense will increase, and accumulated depreciation will increase, reducing net income by $12,200.
e. Unearned revenue will decrease, and earned revenue will increase, increasing net income by $10,400.
f. Accounts receivable will increase, and tuition revenue will increase, increasing net income by $3,400.
g. No adjustment is needed. The salary expense has been recorded and the salaries payable account shows what is owed to the employees at year-end.
h. Rent expense will increase, and prepaid rent will decrease, reducing net income by $8,000.
Note: The sum of all the adjustments will result in a decrease in net income of $6,900 ($2,650 - $3,440 - $6,400 - $12,200 + $10,400 + $3,400 - $8,000 = -6,900).
The impact on the income statement and balance sheet accounts and the impact on net income for each adjustment is provided in the answer above.
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*
Every year,
large public corporations commit fraud.
3 out of 7
5 out of 7
O
1 out of 7
4 out of 7
Answers
The best description of cash inflow is money
A. received from different sources, such as salary and interest earned on bank accounts.
B. spent for items that must be included in a budget, such as rent and utilities.
C. invested in financial products, such as stocks and bonds.
D. left after paying for items included in a financial plan.
Answers
Answer:
A, received from different sources, such as salary and interest earned on bank accounts.
The best description of cash inflow is money received from different sources, such as salary and interest earned on bank accounts.
I hope this helped at all.
What will be the end result for the taxpayer who filed his federal income tax
return using the 1040EZ form shown below?
Answers
Answer:
I got " He Will Owe $180
Explanation:
A P E X
Answer: he will owe 250
Explanation:
Financial reports are used by a.management b.creditors c.investors d.All of these choices are correct.
Answers
Financial reports are used by management, creditors, and investors. Thus the correct option is D.
What is the objective of financial reports?The financial report is the statement or description of the income and expenses that took place in the organization. This report is prepared to analyze the financial position of any organization.
This helps to understand whether the organization is achieving profitability or not. These help investors to know about the current position of the organization in the market.
It helps management to estimate the turnover along with profitability to determine the assets and liabilities records in the financial year.
It helps creditors to assess the company's creditworthiness and ability to make payments on its debt in a timely manner.
Therefore, in option D all of the above, creditors, investors, and management used financial reports.
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United Artist Inc. a Maryland corporation sponsored a defined benefit pension plan administered by United Pension Plan. United Pension was controlled by a board of trustees. For a period of 9 years, seven members of the board made loans to themselves from the pension assets. The loans were made without reference to the ability of the borrowers to repay, the period in which repayment would be made, or the provision of collateral for the loans. The trustees were charged less than the market rate of interest. None of the loans were repaid in full and the plan suffered substantial losses. Did the board of trustees violate ERISA and what, if any, is their liability? Explain.
Answers
The board of trustees likely violated ERISA through their self-dealing loans from the pension assets. They may be held personally liable for the losses suffered by the plan.
The board of trustees of United Pension Plan likely violated the Employee Retirement Income Security Act (ERISA) through their actions. ERISA imposes fiduciary duties on pension plan trustees, including the duty to act prudently and solely in the interest of plan participants.
The board's decision to make loans to themselves without considering repayment ability, repayment period, or collateral provision raises concerns about prudence and loyalty to the plan participants.
By charging themselves interest rates lower than the market rate, the trustees may have also breached their fiduciary duty to act solely in the interest of the plan participants. This action could be seen as self-dealing and a misuse of plan assets.
As a result of the board's actions, the plan suffered substantial losses, indicating a failure to fulfill their fiduciary duties. The board members may be personally liable for these losses and could be required to restore any losses caused by their actions to the plan.
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If the nominal gross domestic product (GDP) of the nation of Hypothetica increased in 2007 relative to the previous year, it must be true that in Hypothetica in 2007:_____.
a. the price level and/or the real GDP has increased
b. no
Answers
If the nominal gross domestic product (GDP) of the nation of Hypothetical increased in 2007 relative to the previous year, it must be true that in Hypothetical in 2007 the price level and/or the real GDP has increased.
Hypothetical realism is a vulnerable shape of realism based totally on the principle of the growth of know-how recommend by way of evolutionary epistemology. The basic assumption is that human cognitive capacity has developed through interaction with the outside world.
Other similar terms to respond to hypotheticals may consist of, “properly, it truly is within the destiny, however, what I will inform you are”, or “I do not need to speculate on that. What's essential proper now is” it's in which the “live inside the present” rule is so important.
A hypothetical query is one based totally on supposition, not statistics. They may be commonly used to elicit critiques and beliefs approximately imagined conditions or conditions that don't exist.
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Interest payable, income tax payable and salary payable are all examples of _______.
Answers
Those are all examples of liabilities. To be more specific, they are current liabilities. Interest payable, income tax payable, and salary payable are obligations that must be paid of within one operational cycle, thus they are just current liabilities.
Current liabilities are debts that must be paid off within a year or one operational cycle, whichever comes first. They can also be paid off using current assets or generate new current liabilities.
Analysts, accountants, and investors assess a firm's payables to determine how effectively it can fulfill its short-term financial obligations thus, the firm basically needs to generate sufficient profits and money in the immediate term to meet its debt commitments.
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Consider an American call option on a stock. The stock price is $70, the time to maturity is eight months, the risk-free rate of interest is 10% per annum, the exercise price is $65, and the volatility is 32%. A dividend of $1 is expected after three months and again after six months. Use Blackâs approximation, calculate the option price.
Answers
To calculate the option price using Black's approximation, we can use the following formula:\(C = S_0N(d_1) - Xe^(-rT)*N(d_2)\). The final answer is the option price using Black's approximation is $11.23.
S_0 = current stock price = $70
X = exercise price = $65
r = risk-free rate of interest = 10% per annum = 0.10
T = time to maturity = 8/12 = 0.6667 years
\(d_1 = [ln(S_0/X) + (r + σ^2/2)T] / [σ√T]\)
\(d_2 = d_1 - σ√T\)
σ = volatility = 32%
N() = standard normal cumulative distribution function
First, we need to calculate d_1 and d_2:
\(d_1 = [ln(70/65) + (0.1 + 0.32^2/2)0.6667] / [0.32√0.6667] = 0.7971\)
\(d_2 = 0.7971 - 0.32*√0.6667 = 0.5512\)
Next, we can calculate the option price:
\(C = 70N(0.7971) - 65e^(-0.1*0.6667)*N(0.5512) = $11.23\)
Therefore, the option price using Black's approximation is $11.23.
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How are squared top balusters used
Answers
Initially, the handrail would not be possible without the balusters. Balusters also fill in the spaces between the posts, making the railing safer by reducing the number of potential entry points for a person to fall over. Finally, balusters are an apparent way to give your railing some more flare in terms of both design and structure.
This is further explained below.
What are balusters?Generally, Staircases, parapets, and other architectural elements often feature balusters, which are vertical molded shafts, squares, or lathe-turned forms. Its primary use is as a spindle in the assembly of furniture. Wood, stone, and metal or ceramic are typical building materials.
In conclusion, To start, the railing is held up by balusters. To further enhance safety, balusters fill up the spaces between the posts. Lastly, balusters are an apparent way to give your railing some more flare in terms of both design and structure.
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Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers. We say that $z \in S$ is a unit if there exists a $w \in S$ such that $zw = 1.$ Find the number of units in $S.$
Answers
Answer:
Number of units possible in S are 4.
Explanation:
Given S is a set of complex number of the form \(a+bi\) where a and b are integers.
\(z\in S\) is a unit if \(w\in z\) exists such that \(zw=1\).
To find:
Number of units possible = ?
Solution:
Given that:
\(zw = 1\)
Taking modulus both sides:
\(|zw| = |1|\)
Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.
i.e.
\(|z_1z_2|=|z_1|.|z_2|\)
So,
\(|zw| = |1|\\\Rightarrow |zw| =|z|.|w| =1\\\Rightarrow |z|=\dfrac{1}{|w|}\)......... (1)
Let \(z=a+bi\)
Then modulus of z is \(|z| = \sqrt{a^2+b^2}\)
Given that a and b are integers, so the equation (1) can be true only when \(|z| = |w| =1\) (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:
(a = 1, b = 0) , (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)
So, the possible complex numbers can be:
\(1.\ 1 + 0i = 1\\2.\ -1 + 0i = -1\\3.\ 0+ 1i = i\\4.\ 0 -1i = -i\)
Hence, number of units possible in S are 4.
The class trip is going to cost each of the fifty
students $130.00. If tax is 5%, what is the total
cost for the entire class?
Answers
Answer:
$6,825.00
Explanation:
50x$130=$6,500.00
$6,500 × 5% = $325.00
$325.+$6,500=6,825.00