Consider a bond with maturity 2 year, 100 face value, coupon 4. 60%, and yield 7. 0%. Compute a dollar duration numerically using a dy =0. 1%. Report you result with two digits decimal accuracy and the correct sign. Example: -185. 95

Answers

Answer 1

The dollar duration for a bond with maturity 2 year, 100 face value, coupon 4.60%, and yield at 7% is - 0.00174785.

What is dollar duration?

It measures the dollar change in bond's value to a change in the market interest rate. The dollar duration is used by professional bond fund managers as a way of approximating the portfolio's interest rate risk.

Now, let's calculate the dollar duration of this bond.

Bond price at yield 7% = (coupon rate / 1 + yield rate) + (coupon rate + 100) / (1 + yield rate) ^2

= 4.6 / 1.07 + 4.6 + 100 / 1.07^2

= 4.29906542 + 91.36169098

= 95.6607564

note : with dy = 0.001%, new yield = 7.001%

New bond price with new yield 7.001%

= (coupon rate / 1 + new yield rate) + (coupon rate + 100) / (1 + new yield rate) ^2

= 4.6 / 1.07001 + (4.6 + 100) / 1.07001^2

= 4.29902524 + 91.35998331

= 95.65900855

Therefore, the dollar duration for this bond is = 95.65900855 - 95.6607564

= - 0.00174785

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Related Questions

Tony is the head of a company that develops cutting edge technology. His team is working on their next big thing and they are close to a breakthrough. As his team works, Tony spends a good portion of his time making sure each part of his team has what they need to produce their best work. Tony also spends some of his time making sure any potential obstacles to his team are taken care of and coaching his team through some of their challenges.

What type of leadership is Tony practicing here?

A. Laissez-faire
B. Democratic
C. Servant Leader
D. Directing

Answers

The answer is B - Democratic

Answer:

D- Directing

Explanation:

It can't be laissez-faire because that literally makes zero sense at all. It's not democratic because that would mean that he would have had his team take a vote at some point in time, but this question says nothing about that. It is not servant leader because literally wth is that. It would have to be directing because Tony is giving his team some direction to help them keep moving forward.

Who typically reviews and approves the guidelines for running a corporation, which are also known as
corporate governance policies?
A. The investors
B. The shareholders
C. The management team
D. The board of directors

Answers

The board of directors typically reviews and approves the guidelines for running a corporation, also known as corporate governance policies. The board of directors consists of elected individuals who are responsible for establishing and overseeing the general policies and strategic direction of the corporation.

What is the board of directions responsible for?

The board of directors is responsible for overseeing the management of a corporation and ensuring that the corporation is being run in a way that is consistent with the guidelines set forth in the corporate governance policies.

These policies are designed to ensure that the corporation is being run in a way that is fair, transparent, and accountable to its stakeholders, including shareholders, employees, and customers.

The board of directors typically reviews and approves these policies to ensure that they are being followed and that the corporation is operating in a way that is consistent with its mission and values.

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Generally unfavorable evidence on purchasing power parity (PPP) suggests thata. transportation costs can make it difficult to directly compare commodity pricesb. Efficiency of the internal market of large multinational corporations fail to overcome any barriers to international commodity marketc. Countries should adjust GDP for the PPP value to make comparison of standards of living between countries more meaningfuld. the range of goods and services considered for price level comparison across countries is not wide enoughe. the global foreign exchange market is very efficient

Answers

The answer to the question is a. transportation costs can make it difficult to directly compare commodity prices. This is because PPP is based on the idea that the same goods and services should have the same price across different countries, but transportation costs can significantly affect the prices of goods in different countries.

The answer to the question is a. transportation costs can make it difficult to directly compare commodity prices. This is because PPP is based on the idea that the same goods and services should have the same price across different countries, but transportation costs can significantly affect the prices of goods in different countries. Therefore, it is difficult to directly compare commodity prices between countries. However, it is important to note that PPP is still a useful concept for adjusting GDP and making comparisons of standards of living between countries more meaningful. The efficiency of the internal market of large multinational corporations may also play a role in overcoming barriers to international commodity markets, but it is not directly related to the limitations of PPP.

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QUESTION 4 of 10: A clothing designer is looking for a job that can cover her living expenses of $5,000 per month. If she plans on working
forty hours a week, with four weeks a month, what's the minimum hourly wage she needs?

Answers

Answer:

$31.25

Explanation:

40 hours a week x 4 weeks a month = 160 hours of work per month

$5,000 divided by 160 = $31.25

ou are to receive an annuity of $1,000 per year for 10 years. you will receive the first payment two years from today. at a discount rate of 10%, what is the present value of this annuity?

Answers

ou are to receive an annuity of $1,000 per year for 10 years. you will receive the first payment two years from today. at a discount rate of 10% The present value of an annuity of $1,000 per year for 10 years at a discount rate of 10% is $614

Present Value = Annuity Payment / (1 + Discount Rate)n

Annuity Payment = $1,000

Discount Rate = 10% = 0.1

n = 10 years

Present Value = $1,000 / (1 + 0.1)10

Present Value = $1,000 / 3.59

Present Value = $7,029.71

Present value = Payment per period × [1 – (1 + r)-n / r]

Payment per period = $1,000

r = Discount rate = 10% = 0.1

n = Total number of periods = 10 years

Present value = $614.

Therefore, the present value of the given annuity is $614.

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If you are trying to establish a credit history, would you use credit to make a purchase even if you could pay cash? Why?

Answers

Answer:

By using credit, you're building up your overall score. Cash purchases go unnoticed by companies and your bank.

Explanation:

Managing the international environment (Connect, Perform) Kirin Brewery, Japan's largest producer of beer, allows the Charles Wells Brewery in England to manufacture beer to Kirin's specifications and market the beer as Kirin Beer. Kirin Brewery earns a royalty on the beer sold in England. What type of international business is this an example of? O Franchising Licensing O Exporting Importing Disney invested approximately $4 billion to construct a Disney theme park and resort near Shanghai, China.

Answers

In the given situation international business is an example of the (B) licensing business.

What is licensing business?

A business arrangement whereby one firm authorizes another company to produce its goods in exchange for a certain fee.

Leasing out your patents, trademarks, copyrights, designs, and other intellectual property to third parties is one of the fastest and most profitable methods to expand your firm.

Normally, a company's economic activity and physical location (address) decide whether licenses are required to operate lawfully.

The number of employees and the type of organization, such as sole proprietorship or corporation, may also be deciding considerations.

A company operating without the necessary business permits may be fined or shut down by government organizations.

Therefore, in the given situation international business is an example of the (B) licensing business.

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Correct question:
Kirin Brewery, Japan's largest producer of beer, allows the Charles Wells Brewery in England to manufacture beer to Kirin's specifications and market the beer as Kirin Beer. Kirin Brewery earns a royalty on the beer sold in England. What type of international business is this an example of?

A. Franchising

B. Licensing

C. Exporting

D. Importing

In Section 2, you learned about costs and profit. Now, you'll apply what you learned.

1. Choose a real or made up example of a company, and describe at least three variable costs the company has. (1-3 sentences. 1.5 points)


2. Choose a real or made up example of a company, and describe at least three fixed costs the company has. (1-3 sentences. 1.5 points)


3. Is gross profit or net profit more important to consider when you're deciding how successful and profitable a company is? Why? Explain. (1-3 sentences. 2.0 points)


4. If you were running a company, describe at least two things you would do to improve its productivity. (1-4 sentences. 2.0 points)


5. Describe at least two advantages a large company has over a smaller company. (1-4 sentences. 2.0 points)


6. Choose a good you are familiar with, and analyze its economic utility, using the questions below. NOTE: Choose a good for this exercise, not a service.

a. What type of good did you choose? (1 sentence. 1.0 points)



b. Describe the form utility of the product you chose. What makes its form useful? Can you think of any improvements that could be made to its form utility? (1-3 sentences. 2.0 points)


c. Describe the place utility of the product. Can you think of any improvements that could be made to its place utility? (1-3 sentences. 2.0 points)


d. Describe the time utility of the product. Can it be improved at all? (1-3 sentences. 2.0 points)


e. Describe the possession utility of the product. Can it be improved at all? (1-3 sentences. 2.0 points)


f. Describe the information utility of the product. Can it be improved at all? (1-3 sentences. 2.0 points)

Answers

A company which makes custom-fitted sweaters for cats has three variable costs. The cat sweater designer only does home visits, so for each customer, the designer will have to drive to the house to measure the cat. Each cat’s shape and measurements differ, so the yarn to make their sweaters will vary for each cat. The time spent knitting the sweaters will vary for each cat depending on the style their owner wants and the cat’s size and shape. For this company, the variable costs would be gas, the yarn, and staff wages for how much time each sweater takes.

What does a corporation mean?

A group of people can come together to legally form a corporation to do business and run a commercial or industrial venture. Depending on its jurisdiction's corporate legislation, a corporation may be set up in a variety of ways for tax and financial liability reasons.

What is the difference between a company and a business?

Although a corporation might conceivably be managed by a single person, a company by definition needs to have numerous owners. One might employ a few members of their family to work at a small carwash, for instance. As a business, that would qualify.

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An investor whose highest priority is getting the largest gains possible, even if
it requires a lot of risk, would most likely invest in ________.
A. Hedge funds
B. Bonds
C. Mutual funds
D. Saving accounts

Answers

The investor whose highest priority is getting the largest gains possible would invest in hedge funds. (option A)

What are hedge funds?

Hedge funds are alternative investments that pool the financial resources of different high net worth people together in order to invest in different ventures. Hedge funds are known to invest in different risky and illiquid investments. This increases the rate of their returns relative to other options.

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What are four influences that typically affect consumer buying behavior?.

Answers

There’s:
- Cultural
- Personal
- Social
- Psychological

I’d also say motivation as a fifth but those are the actual 4

Deena works at a small brewery. She is the only person trained in changing out the labels on the automatic bottling machine. The brewery has high dependency on deena because she has low.

Answers

Deena is employed by a tiny brewery. The automatic bottling machine's labels can only be changed by her because she has received special training. Due to Deena's low substitutability, the brewery is highly dependent on her.

What is substitute?

A replacement is someone or something that steps in for the original. To substitute as a verb is to implement such a change.

Although the word substitute is used in many other settings, it is probably most often connected to substitute teachers and athletes who step in to play in place of another player in a team sport.

By virtue of being replaceable, substitutability is interchangeability.

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Please help in this question asap

Please help in this question asap

Answers

Answer:

All of these

Explanation:

do I need to explain lol?? :]

The correct answer is D, all of these.

What are the 3 reasons for the Wealth Gap?

Answers

Answer:

(iii) Growth in technology widens income gap. Growth in technology arguably renders joblessness at all skill levels [3].  

(iv) Gender does matter. In many countries, there is a gender income gap in the labor market [3].

(v) Personal factors.  

(ii) Globalization.

Explanation:

mark brainliest

Which of the following best completes the table?

Table listing kinds of trade barriers with examples of each. Regulation, clothing made using child labor. Tariff, foreign steel. Embargo, diamonds from Zimabawe.

What is an example of local content requirement?

Customs duties paid on cloth made in India

Imported apples exceeding a percentage of domestic production

Inexpensive sugar grown in the Caribbean

Oil from a Middle Eastern country that is considered hostile

Answers

Answer:

1. The best that completes the table is:

Oil from a Middle Eastern country that is considered hostile.

2. An example of local content requirement is:

Imported apples exceeding a percentage of domestic production.

Explanation:

Many countries of the world impose free-trade restrictions.  For example, tariffs raise the prices of imported goods relative to domestic goods (good produced at home), thereby making imports more expensive.  Some governments provide subsidies to their domestic industries, thereby making the domestic goods cheaper than their foreign counterpart and discouraging free trade. Local content requirements are another means to restrict free trade.  These requirements demand that part of the production process for imported goods be completed domestically.

Answer:

C. inexpensive sugar grown in the Caribbean

Explanation:

just took the quiz

Which career pathways involve high risk due to exposure to dangers?

Firefighters in the Emergency and Fire Management pathway, Correctional Officers in the Corrections pathway, and Detention Officers in the Law Enforcement pathway
Firefighters in the Emergency and Fire Management pathway, Detention Officers in the Corrections pathway, and Intelligence Analysts in the Security and Protective Services pathway
Intelligence Analysts in the Security and Protective Services pathway, Detention Officers in the Corrections pathway, and Police Officers in the Law Enforcement pathway
Firefighters in the Emergency and Fire Management pathway, Detention Officers in the Corrections pathway, and Police Officers in the Law Enforcement pathway

Answers

Answer:

Firefighters in the Emergency and Fire Management pathway, Correctional Officers in the Corrections pathway, and Detention Officers in the Law Enforcement pathway.

Explanation:

The career pathways that  involve high risk due to exposure to dangers is :

A) Firefighters in the Emergency and Fire Management pathway, Correctional Officers in the Corrections pathway, and Detention Officers in the Law Enforcement pathway.

"Career Pathways"

The career pathways that involve high risk due to exposure to dangers is:

Firefighters in the Emergency

Firefighters too give an critical part in teaching the open with respect to fire and security.

Instructing fire anticipation and teaching the open on how to reply in crisis circumstances can offer assistance spare lives.

Fire Management pathway

Candidates require a long time of work encounter in law requirement, fire security, or an crisis administration field.

Crisis administration executives ordinarily require a bachelor's degree

Correctional Officers in the Corrections pathway

Corrections officers may do a few or all of the taking after:

supervise prisoners' day by day schedule, which incorporates feast, work and amusement times. screen, evaluate and oversee the conduct and security of detainees watch jail buildings and grounds.

Detention Officers in the Law Enforcement pathway.

A detainment officer forms prisoners, keeps up imprison security, serves dinners, transports detainees, gets and forms detainees into care of educate, looks detainees, and takes charge of individual property and gives detainees with opportunity to call their lawyer or relative.

A Career Pathway traces the positions, compensation, and preparing required to development in an industry.

Thus, the correct answer is A.

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Use the drop-down menus to explain how to create a subreport. 1. Open the table in view. 2. On the Design tab, click Min Grouping & Totals. 3. Select "with a footer section" from a drop-down menu in a pane below. 4. Next, choose Subform/Subreport from the command group. 5. Place the cursor at an insertion point. Then, to create a space. 6. In the Subreport Wizard, choose what you want to include in the subreport from the main table. 7. Once you are satisfied, create a name for the subreport, and click Finish. DO NOT PUT ANY FILES JUST THE ANSWER.​

Answers

Answer:

design

group and sort

control

click and drag

Explanation:

gg

25. what would you do if the expectations of your job were having a severely negative impact on your personal relationships?

Answers

The balance between a relationship and a career is important. If your partner dislikes your work and wants you to find something better, go for it even if you enjoy yours.

How could issues in personal connections affect interactions in the workplace?

Personal issues between the pair may lead to tension, communication issues at work, or allegations of stalking or harassment. Employees may "take sides" in response to a public break-up, which could lead to stress throughout the entire organisation. By concentrating on employee work performance, these issues can be avoided.

What goals do you have for this position?

My objectives for the company are for it to have a working environment where I can contribute to the team, get credit for my work, and provide

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Which of the following is not an example of professional behavior
?

Answers

What are the answers?

The triple bottom line "people/social" and it's relationship with social responsibility

Answers

Answer:

TBL was proposed by Elkington. But there is difficulty in measuring social and environmental bottom line.

Explanation:

Triple bottom Line (TBL)  in economics is the line that focus on the relationship on social and environmental concern. In TBL there are three bottom line that is people, profit, and planet. This term Triple Bottom Line was coined by John Elkington in 1994.

His main aim was to measure the performance of people in America. According to this idea it is possible to maintain both economy and environment. It can improve the lives of people as well can save the environment. It can be called a full time cost business. It is like Planet + People = Environmental responsibility + Social.

According to TBL if a company does not pay attention on how to interact socially but only focuses on business, it will not account full business.

The triple bottom line is a concept that states that rather than firms to focus on making profit as sole of operation, they should also commit their impact to the social and environment sphere.

The triple bottom line is divided into 3 according to importance to be given:

People / Social impactPlanet / Environmental impactProfit / Financial impact.

In conclusion, the business concept posit that firms should ensures that its impact are felt in any social and environmental circle around the world.

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The Morrit Corporation has $1,080,000 of debt outstanding, and it pays an interest rate of 11% annually. Morrit's annual sales are $6 million, its average tax rate is 25%, and its net profit margin on sales is 3%. If the company does not maintain a TIE ratio of at least 6 to 1, then its bank will refuse to renew the loan, and bankruptcy will result. What is Morrit's TIE ratio?

Answers

Answer:

3.020

Explanation:

Morrit Corporation

interest amount = $1,080,000*.11 = $118,800

Net profit = 3% *$6,000,000= $180,000

Net profit + tax = profit before tax =

180000/.75 = 240000

Profit before tax + Interest = Earning before interest and tax

= $240,000+$118,800 = $358,800

TIE ratio= EBIT/Interest = $358,800/118,800

= 3.020

Therefore the TIE ratio is 3.020

Implementing and executing strategy successfully requires Implementing and executing strategy successfully requires:______________

A. the same kinds of creative management talent and innovative thinking capabilities as crafting strategy.

B. a financially driven process aimed at squeezing the most profit out of conducting daily operations.

C. the efforts of a company's whole management team, not just a few senior managers

D. a high caliber CEO that possesses the business vision, industry and competitive analysis skills, and entrepreneurial creativity needed to navigate the competitive landscape.

E. less managerial expertise and effort to perform well, at least in comparison with crafting a winning strategy.

Answers

Answer: C. . the efforts of a company's whole management team, not just a few senior managers

Explanation:

Planning, implementing and carrying out strategies requires a careful, collective and calculative decision to be made by all head of department and the board of an organization, because the decision taken will rub off through these departments for implementation. The decision or choice of decision should not be left to a few persons in the organization because when the ideas and plans are arranged the execution may fail as all the respective department were not involved by their heads.

How can you avoid spending more than what is in your bank account?
1. Check your bank statement once a month.
2. Ask your financial institution to notify you when you are close to $0 in your account.
3. Keep your own records to compare with your financial institution's records.
4. None of the above

Answers

Its mostly likely 1 or 3 im not sure which one though .....

The Hartford Symphony Guild is planning its annual dinner-dance. The dinner-dance committee has assembled the following expected costs for the event. The committee members would like to charge 35 per person for the evening's activities.
(b) Assume that last year only 300 persons attended the dinner-dance. If the same number attend this year, what price per ticket must be charged in order to break even?

Answers

$40 price per ticket must be charged in order to break even.

Giving the following information:

2) Q= 300    P=?

300=6000/(P-20)

300*(P-20)= 6000

300P=12000

P=$40.

The break-even point is the point at which total costs equal total revenue. In other words, there is no loss and no profit for SMEs. This means that we have reached a stage of production where the cost of production equals the revenue of the product.

To calculate the break-even point in units, use the following formula: Break-even point (units) = fixed cost ÷ (selling price per unit – variable cost per unit) or in sales dollars, using the following formula: break-even point - points (sales) = fixed costs ÷ contribution margin.

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Art teacher Monica earns time and a half for the number of hours she works over 40 hours. One week she worked 48 hours. How many hours of overtime did she work?

Answers

Answer:

8 hours

Explanation:

Here, we want to know the number of overtime hours worked.

From the question, we are told that the pay is slightly different and higher if she worked for some hours over 40 hours

What this means is that the regular number of hours is 40; then the number of hours in this case 8 over 40 is her over time

Choose an advertisement that you found to be especially memorable. Describe the
advertisement and explain how effective it is. Discuss the techniques you would have
used to make it more effective.

Answers

Answer:

use the droritos commuecials those were good

Explanation:

Match the job titles with the job descriptions.
federal aid coordinatoi
corrections officer
Assist an attorney in research and administrative tasks
Evaluate student applications for financial aid
Supervise the management of a prison facility.
paralegal

Answers

The correct matching of the jobs given is shown below:

The Job Matchings

A federal aid coordinator is responsible for administering and distributing federal aid to individuals or organizations in need.

A corrections officer is responsible for overseeing and maintaining security within a prison facility.

A paralegal assists attorneys in legal research, drafting legal documents, and providing administrative support.

And finally, a financial aid evaluator reviews student applications and determines eligibility for financial aid.

These job titles and descriptions vary widely in their responsibilities and required skills. Federal aid coordinators must have strong organizational and communication skills to manage the distribution of funds effectively.

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Answer:

corrections officer-Supervise the management of a prison facility

financial aid evaluator-Evaluate student applications for financial aid

federal aid coordinator-administering and distributing federal aid to individuals/organizations that need help

authority is defined as the multiple choice assignment of a task that an employee is supposed to carry out. expectation that employees will perform a job and report the status of their performance. assignment of additional responsibility to a subordinate at a lower level. legitimate right to make decisions and to tell people what to do. narration of a set of predicted future conditions.

Answers

Authority is defined as the multiple choice assignment of a task that an employee is supposed to carry out legitimate right to make decisions and to tell people what to do.

What is importance of authority?

Any organisation or system must have authority in order to establish a clear chain of command and make decisions. It enables individuals or groups to decide on and take actions that are consistent with the goals and objectives of the organisation. Having authority helps to ensure that tasks are completed effectively and efficiently by providing structure and order. Additionally, it aids in ensuring that people are held accountable for their deeds and obligations. A positive work culture can be cultivated and increased trust and respect among coworkers by having clear authority within an organisation. In conclusion, authority is crucial because it promotes good decision-making, accountability, and direction.

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if the actual rate of unemployment equals the natural rate of unemployment, then select one: a. potential output equals real gdp. b. potential output is less than real gdp. c. potential output is greater than real gdp. d. there is a recessionary gap.

Answers

If the actual rate of unemployment equals the natural rate of unemployment, then potential output equals real GDP. Thus, the correct answer is option A.

What is natural rate of unemployment?

The natural rate of unemployment is the rate of unemployment caused by all factors other than changes in aggregate demand. Potential GDP estimates are based on the long-term natural rate.

At full employment equilibrium, the actual and natural rates of unemployment are equal. At this point, all resources have been fully utilized to produce output.  As a result, potential output will equal real GDP.

Therefore, at full employment, there will be no recessionary or inflationary gap, and potential output equals real GDP.

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What are benefits of 2023 leaf’s available hybrid heater system?.

Answers

The benefits of 2022 Nissan LEAF's available hybrid heater system are:

increases driving range Enhances the efficiency of the coil.

Why is the 2022 Nissan LEAF's available hybrid heater system better?

The hybrid heater is so special because if its efficiency unlike the previous model of the heater.

Therefore, when the heater is on, the driving range usually goes up.

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Which of these are benefits of a job as the term is used in this lesson? (1
O a high hourly wage
O an office in a great neighborhood
O working for a good cause
O a 401(k) plan

Answers

Answer:

high Hourly wage

Explanation:

Answer:

D. a 401(k) plan

Explanation:

Other Questions
select the correctly ordered list of psychological theorists, with the earliest theorist listed first. A satellite is in circular orbit at a height of 5.0x 10^5 m above the earths surface. The radius of the earth is 6.38x10^6m and the mass of earth is 5.98x10^24kg. a) Find the speed of the satellite. b) Find the gravitational field strength at this altitude Part B Which value is closest to the product 0.04 8.01? A. 32 B. 3.2 C. 0.032 D. 0.32 pls help 60 points! How did the Roman Empire's vast geographic expanse become a serious disadvantage in the third century? What was the effect of this disadvantage? * through the process of escheat the deceased's property passes to What are the different philosophies between Imperialists and Progressives how does the time of fall relate to the weight (mg) of the coffee filters (drag force)? if one filter falls in time, t, how long would it take four filters to fall, assuming the filters are always moving at terminal velocity? verify your results with experimental data. Find the equation of the line that contains the point P(4, 1) and is perpendicular to the graph of y = 4/5x 4. a keyboard access key is assigned to a button using the button control's ________ property. Music: Madison can you help with this, is the second one If 2 pounds of apples cost $2.90 how much would 3 pounds cost In at least 3 sentences, explain how you see your identity, based on the discussion from the Power Point. Then explain how Kit sees her identity. Pleases solve this problem for me:((( 78.4 divided by 0.56 What does a high boiling point temperature indicate about a substance?A. Little heat has been added to the system.B. Intermolecular forces are hard to overcome.C. Chemical bond energy is very high.D. The pressure over the liquid is very low. Lena buys candy that costs $7 per pound. She will buy less than 12 pounds of candy. What are the possible amounts she will spend on candy As a high net worth individual, Aria searches for developing companies in need of additional funding to achieve their goals. In return for this __________, she expects to give up some percentage of ownership in the business. Multiple Choiceanalysisventure capitalsecurities investmentcorporate loan Find synonyms for each of the phrasal verbs below:Phrasal verbsSynonyms1. pass down 2. live on 3. deal with 4. close down 5. face up to 6. get on with 7. come back 8. turn down 9. find out 10. bring out 11. look forward to 12. look through solve the following equation using the addition property of equality 7p+3=12+6p Why do quarterbacks throw the football with significant spin about its long axis? choose the correct explanation.