if astd is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by astd

Answers

Answer 1

The initial condition satisfied by A(t) is: A(0) = e^C

In continuous compounding, the amount of an investment at time t (denoted by A(t)) can be described by the following differential equation:

dA(t)/dt = r * A(t)

where r represents the continuous interest rate.

To write this in a more explicit form, we can solve the differential equation using separation of variables. Let's assume that A(0) is the initial amount of the investment at time t=0. Integrating both sides of the equation gives:

∫(1/A(t)) dA(t) = ∫r dt

ln|A(t)| = rt + C

where C is the constant of integration.

By taking the exponential of both sides, we get:

A(t) = e^(rt + C)

Since A(0) represents the initial condition satisfied by A(t), we substitute t = 0 into the equation to find the value of C:

A(0) = e^(r*0 + C)

A(0) = e^C

Therefore, the initial condition satisfied by A(t) is:

A(0) = e^C

The specific value of A(0) will depend on the given initial investment amount.

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Related Questions

After making a payment of $5,000 for an automobile, Molly paid $565 per month for 60 months with interest charged at 4.8% per year compounded monthly on the unpaid balance.
How much did Molly pay towards the principal of the loan on the car?
What was the original cost of the car (in dollars)?
What is the total amount that Molly paid for the car (in dollars)?
How much of Molly's total car payments went toward interest charges (in dollars)?

Answers

Molly paid $2,400 towards the principal of the loan on the car. The original cost of the car was $7,400. Molly paid a total of $33,900 for the car, with $26,500 going towards interest charges.

Step 1: Calculating the principal payment

To find out how much Molly paid towards the principal of the loan, we need to subtract the total interest paid from the total payments made. The total interest paid can be calculated using the formula for compound interest:

Total interest = Total payments - Principal

Molly paid $565 per month for 60 months, resulting in a total payment of $565 * 60 = $33,900. Since the interest is charged on the unpaid balance, we can subtract the original payment of $5,000 from the total payments to find the principal payment:

Principal payment = Total payments - Original payment = $33,900 - $5,000 = $28,900

However, this amount includes the interest. To find the actual principal payment, we need to subtract the interest charges.

Step 2: Calculating the interest charges

The interest is charged at a rate of 4.8% per year, compounded monthly. We can use the formula for compound interest to calculate the total interest charges:

Total interest = Principal * (1 + (rate / n))^(n*t) - Principal

Where:

- Principal is the initial loan amount

- Rate is the interest rate per period (in this case, per month)

- n is the number of compounding periods per year (12, since it's compounded monthly)

- t is the total number of periods (60 months)

By substituting the given values into the formula, we can calculate the total interest charges:

$28,900 = $28,900 * (1 + (0.048 / 12))^(12*5) - Principal

Principal = $28,900 - $23,500 = $5,400

Thus, Molly paid $2,400 towards the principal of the loan on the car.

Step 3: Calculating the original cost and total payments

To determine the original cost of the car, we add the principal payment to the original payment made:

Original cost = Principal + Original payment = $5,400 + $5,000 = $10,400

Therefore, the original cost of the car was $10,400.

To calculate the total amount Molly paid for the car, we add the total interest charges to the original cost:

Total amount paid = Original cost + Total interest = $10,400 + $23,500 = $33,900

Hence, Molly paid a total of $33,900 for the car.

Finally, to determine how much of Molly's total car payments went towards interest charges, we subtract the principal payment from the total payments:

Interest charges = Total payments - Principal payment = $33,900 - $2,400 = $31,500

Thus, $26,500 of Molly's total car payments went towards interest charges.

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Suppose the short-run production function is q = 10L2. Suppose that the wage rate is $110 per unit of labor. What is the marginal cost at q = 253? Your Answer:

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The marginal cost at q = 253 is approximately $1.09. To find the marginal cost at q = 253, we need to calculate the derivative of the cost function with respect to quantity.

Given the short-run production function: q = 10L^2

We can calculate the total cost function as the product of the quantity and the wage rate:

TC = wL

where TC is total cost, w is the wage rate, and L is the quantity of labor.

Taking the derivative of the total cost function with respect to quantity, we can find the marginal cost:

MC = d(TC)/dq = dwL/dq = w(dL/dq)

Since q = 10L^2, we can differentiate this equation to find dL/dq:

dL/dq = 1/(20L)

Substituting this back into the marginal cost equation:

MC = w(1/(20L))

Given that the wage rate w = $110 and q = 253, we can calculate the marginal cost:

MC = $110 * (1/(20L))

At q = 253, we need to find the corresponding value of L:

253 = 10L^2

L^2 = 25.3

L ≈ 5.03

Substituting L = 5.03 into the marginal cost equation:

MC = $110 * (1/(20*5.03))

MC ≈ $1.09

Therefore, the marginal cost at q = 253 is approximately $1.09.

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how did the industrial revolution affect economic relationships among nations?

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The Industrial Revolution had a profound effect on the economic relations between nations. Some of the ways this relationship affects include:

Expansion of trade: The growth of manufacturing and the emergence of new industries led to an increase in international trade and the exchange of goods and services between countries.Creation of new markets: The expansion of trade creates new markets for goods, which allows countries to specialize in the production of certain products and increases their economic competitiveness.Rise of colonialism: The Industrial Revolution also led to the expansion of European colonial empires as countries sought new markets and sources of raw materials.Changes in labor patterns: The Industrial Revolution brought about significant changes in the way work was organized and performed, leading to new forms of labor exploitation and growth of the wage workforce.Development of financial systems: The growth in international trade and investment led to the development of new financial systems, such as banks and stock exchanges, which allowed cross-border capital flows.

Overall, the Industrial Revolution changed economic relations between countries, leading to increased globalization and the establishment of new economic systems and patterns of trade and investment.

The Industrial Revolution was a period of rapid economic and social change that occurred between the late 18th and early 19th centuries. It is characterized by a shift from manual labour-intensive production methods to machine-based manufacturing processes and the widespread use of new technologies and innovations.

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https://padlet.com/ItsOniiSama/rx8veyhelyfcu68i

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I don’t get that but u could write the question down so I could help u answer

Answer:

?

Explanation:

why

What situation helped cause the stock market crash of 1929 ?

Answers

The stock market crash of 1929 was caused by a combination of factors, including excessive speculation, market overvaluation, and weak economic fundamentals.

The stock market crash of 1929 was a result of a combination of several factors. Firstly, investors were engaging in excessive speculation, which means buying stocks with borrowed money in hopes of quickly selling them at a higher price.

As the market became more and more overvalued, investors began to worry that stocks were too expensive and that the stock market had reached its peak. This caused many investors to sell their stocks, which further decreased the market’s value.

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a copayment is a percentage of the fee for services provided that the patient pays. a set amount that each patient pays for each office visit. a portion of the fee that the physician must write off. a capitation payment.

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Capitation payments are used by managed care organizations to regulate healthcare costs. Capitation payments control the amount of healthcare consumed by putting the doctor's finances at risk for patient care.

Describe capitation.

Capitation is one way to pay for medical services. It pays a fixed amount for each enrolled individual assigned to them during a specific time period regardless of whether that person seeks care. Public insurance payments are used by managed care organizations to regulate healthcare costs. Capitation payments control the amount of healthcare consumed by putting the doctor's finances at risk for patient care. An example of capitation would be a 5,000 patient IPA, a type of HMO. The IPA must ensure that its patients will have insurance for the upcoming session. 

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Which assumption would a lender most likely make about a person with a credit score around 800?
O that the person has invested a great deal of money in the stock market
O that the person has had very few delinquent payments in the past
O that the person has lived in the same city for a long time
O that the person has avoided using credit cards

Answers

The correct answer would be the 2nd option.

Empathy involves _____.


feeling pity

active listening

feeling sorry

written communication

Answers

Answer:

active listening

Explanation:

Empathy involves making every effort to understand others FROM THEIR POINT OF VIEW. It means communicating an understanding of how THAT PERSON feels in a situation, NOT how YOU would feel in that situation.

Empathy is defined as “the feeling that you understand and share another person's experiences and emotions” or “the ability to share someone else's feelings”. Feeling sorry for a person automatically generates feelings of pity, which is not helpful in situations where people are in pain.

I hope this helps! :)

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why is it important to examine demand relationships

Answers

Answer:

together they determine the prices and quantities of most goods and services available in a given market.

Explanation:

Supply and demand have an important relationship because together they determine the prices and quantities of most goods and services available in a given market. According to the principles of a market economy, the relationship between supply and demand balances out at a point in the future.

What annual growth rate is indicative of a thriving and expansive industry—one that creates niches for new entrants?
a. 5 to 10 percent
b. 10 to 20 percent
c. 30 to 50 percent
d. 10 to 25 percent

Answers

The annual growth rate that is indicative of a thriving and expansive industry—one that creates niches for new entrants is 10 to 25 percent. (Option D)

Industries that are expanding and thriving typically have an annual growth rate of at least 10 percent. This level of growth allows for new entrants to enter the market and create new niches, as there is ample opportunity for growth and innovation.

A growth rate of 5 to 10 percent may indicate a stable industry, but it may not be expansive enough to create new niches for entrants. A growth rate of 30 to 50 percent may be indicative of a rapidly growing industry, but it may also be unsustainable and could potentially lead to a market crash. Therefore, an annual growth rate of 10 to 25 percent is generally considered to be indicative of a thriving and expansive industry.

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i have a brainlest for anybody if the can tell me who won the wwe champoinship in 1996

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I’m pretty sure it was Shawn Michaels or Bret hart

What system strives to improve access to preventative health care services?

Answers

Answer:

Managed care systems

Define net taxes as taxes minus transfers. Suppose country a had net taxes of $30 million and government expenditures of $35 million. In addition, household saving in country a totaled $5 million while consumption was $80 million. The government of country a is running a budget ________ and national saving is ________ million.

Answers

The government of country a is running a budget deficit and national saving is $0 million.

The income of a government is derived from the taxes it has collected. The money that the government makes is used for subsidies, salaries, and other expenses.

Taxes are subtracted from transfer payments to determine net taxes. On the government's credit side is where the net taxes are located. Government expenditures or spending are on the debit side. The gap between net taxes and spending on the government called the budget.

If net taxes are higher than spending by the government, there is money left over in the budget.

In this scenario, the government is saving money. This is due to the fact that when net taxes are higher than spending, the government saves money since it makes more money than it spends.

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The purpose of this assignment is to enhance students' understanding on the various sources of funds that firms can use to finance their operation. REQUIREMENT You are required to answer Assignment 1 by referring to the attached rubrics. You have to submit the assignment only ONCE in a single file. Assignment 1: Students are required to: 1. Discuss various sources available to firms in financing their operation. 2. Discuss the benefits of using debts. 3. Discuss the benefits of using equity. 4. Summary.

Answers

1. Firms have access to various sources of funds to finance their operations. These sources can be categorized into two main types: internal and external sources. Internal sources include retained earnings, where profits are reinvested back into the firm, and depreciation funds generated from the firm's assets. External sources encompass debt and equity financing. Debt financing involves borrowing funds from external parties, such as banks or bondholders, which must be repaid over time with interest. Equity financing, on the other hand, involves selling ownership stakes in the firm to investors in exchange for capital. This can be done through initial public offerings (IPOs) or private placements.

2. Debt financing offers several benefits to firms. Firstly, it allows them to leverage their operations and acquire funds without diluting ownership control. Additionally, the interest payments on debt are tax-deductible, reducing the firm's tax burden. Debt financing also enables firms to take advantage of financial leverage, potentially increasing their return on investment (ROI). However, excessive debt can lead to financial distress, higher interest payments, and reduced flexibility in managing operations.

3. Equity financing provides several advantages to firms. It allows them to raise capital without incurring debt or interest obligations. Equity investors share in the risks and rewards of the firm, aligning their interests with the company's success. Equity financing also provides a long-term funding source that doesn't require repayment. Moreover, equity funding can attract investors who bring valuable expertise, networks, and strategic guidance to the firm. However, equity financing can dilute ownership and control, as shareholders have voting rights and may influence major decisions.

4. In summary, firms have multiple sources of financing available to them, including internal funds, debt, and equity. Debt financing offers benefits such as leveraging operations, tax advantages, and increased ROI potential. Equity financing provides advantages like capital without debt obligations, shared risks and rewards, and access to valuable expertise. Firms must carefully evaluate the costs, risks, and trade-offs associated with each source to determine the most suitable financing mix for their specific needs and goals.

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Net present value: Select one: is the best method of analyzing mutually exclusive projects. is less useful than the internal rate of return when comparing different-sized projects. s the easiest method of evaluation for nonfinancial managers. is the easiest method of evaluation for nonfinancial managers. cannot be applied when comparing mutually exclusive projects. is very similar in its methodology to the average accounting return.

Answers

Answer:

is the best method of analyzing mutually exclusive projects

Explanation:

Net present value is the present value of after-tax cash flows from an investment less the amount invested.  

Only projects with a positive NPV should be accepted. A project with a negative NPV should not be chosen because it isn't profitable.  

When choosing between positive NPV projects, choose the project with the highest NPV first because it is the most profitable.

Internal rate of return is the discount rate that equates the after-tax cash flows from an investment to the amount invested

Accounting rate of return = Average net income / Average book value  

Average book value = (cost of equipment - salvage value) / 2

NPV is more preferred to IRR for projects with multiple negative cash flows during the project live .

Discuss whether or not growth of an industry will increase the profit earned by the firms in the industry.

Answers

Answer: Definitely, the larger the market, the larger the demand, the higher the profit. In some cases where the market is large, the producers may not meet up on some occasions, this make other producers to actually increase their profit margin based on they have to increase production.

Explanation:

Industries have their various activities, competition, customers (both prospective and existing). A growth in industry would mean that there is a larger demand for what is been sold in that industry, and when the demand is high, their would be lack, which would create that gap and allow marketers or producers get more profit, based on the high demand now. Definitely, the larger the market, the larger the demand, the higher the profit. In some cases where the market is large, the producers may not meet up on some occasions, this make other producers to actually increase their profit margin based on they have to increase production.

A country has a current account deficit if the sum of net exports, net income from abroad, and net unilateral transfers is positive. the sum of net exports, net income from abroad, and net unilateral transfers is positive. it receives more income from foreign assets than it pays to foreigners for foreign-owned domestic assets. its capital inflows (sales of US assets to foreigners) exceed its capital outflows (US purchases of foreign assets). In an open economy, private savings funds all of the following EXCEPT domestic investment O the current account domestic absorption O government debt

Answers

The statement that is NOT funded by private savings in an open economy is government debt.

In an open economy, private savings funds all of the following EXCEPT government debt. An open economy is an economy that has an active participation in international trade. In an open economy, the private savings of the individuals in the country go into domestic investments, current account, and domestic absorption. Domestic investment is the capital invested within the country while current account deficit refers to the difference between the imports and exports of a country.The private savings of individuals in the economy are responsible for funding the investments.

The current account deficit of a country occurs when the sum of net exports, net income from abroad, and net unilateral transfers is positive. Hence, the statement that is NOT funded by private savings in an open economy is government debt.

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What's the main reason to use a personal budget?
O A. To keep costs below benefits
O B. To stay out of debt
C. To appropriate discretionary funds
O D. To maximize investment returns

Answers

Answer: B, stay out of debt

Explanation: A budget reveals areas where you're spending too much money so you can refocus on your most important goals. A budget can keep you out of debt or help you get out of debt. A budget actually creates extra money for you to do use on things that matter to you.

B because the whole point of having a budget is to make sure you don’t over spend and to make sure your spending enough money on everything you need

Suppose a small group of manufacturers in the auto parts industry currently enjoy considerable monopoly power. How would you expect monopoly power in this industry to change in the long​ run?.

Answers

The demand curve that each firm must deal with will become more elastic as the industry's number of businesses increases. Therefore, monopoly power will gradually wane.

What is monopolistic power defined as?A firm's demand curve will evolve in a monopolistic competitive market over time until it becomes parallel to the firm's average total cost curve. As a result, the business will only be able to break even rather than make an economic profit.An attempt to raise prices above the level of competition may result in enough new competitors even in the absence of an existing rival, making the price increase unprofitable. In that case, even though the corporation may currently have a dominant market share, it lacks monopoly power.    

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Select the correct answer. Under which market structure does the action of one company have a spillover effect on other companies’ decisions?

A. oligopoly
B. perfect competition
C. monopoly
D. monopolistic competition

Answers

Answer:

A. oligopoly

Explanation:

a state of limited competition, in which a market is shared by a small number of producers or sellers.

Under oligopoly, the action of one company has a spillover effect on other companies’ decisions. Thus, option A is the correct option.

What is a company?

A company can be defined as an institution who makes a product or service and sells it or endorse it in the market to earn revenue.

When there is any change or shift in the market with respect to any sort of commodity than that effect goes on to another product which can be considered as a substitutional product is called as oligopoly.

For example, in the case of a cold drink if one cold drinks prices increases or the demand decreases then people start to prefer to another call ring that can be considered as it substitute product this system can be referred to as an oligopoly. Therefore, option A is the correct option.

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list your personal interest​

Answers

Answer:

my interest is to reach conqueror in pubg mobile

Match the academic requirements with the careers.

-training -Ph.D. -bachelor’s degree


-anthropologist

-telecommunications technician

-network administrator

Answers

The academic requirements as well as the training required has been grouped below:

anthropologist: Ph.Dtelecommunications technician: trainingnetwork administrator: bachelor’s degree

What is a work requirement?

This is the term that has to do with the job requirement that is needed for specific disciplines. That is the amount of training and the level of training that is required to be experts in the careers that have been chosen by the specialists.

Hence we can say that The academic requirements as well as the training required has been grouped below:

anthropologist: Ph.Dtelecommunications technician: trainingnetwork administrator: bachelor’s degree

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A new parent-focused website is adding a blog to attract readers. Which of the following elements are likely to be discussed at the project plan approval meeting?

a.)
The editing guidelines document for the new blog

b.)
Preferred methods for communicating schedule changes

c.)
A list of topics that will be covered each week in the new blog

d.)
A review of the number of days assigned to testing the changes to the website

Answers

Answer: d

Explanation: :()

Hawaiian food would be an example of what type of cuisine?
A
Classic cuisine
B
Regional cuisine
С
Nouvelle cuisine
D
National cuisine

Answers

Nouvelle cuisine



Hope it helps


Pls mark as brainlist

Nouvelle cuisine is the type of cuisine. As it is an example of Hawaiian food. Hence, option C is correct.

What is Nouvelle cuisine?

Nouvelle cuisine, which translates to "new cuisine," is a diverse international cooking style that first appeared in France in the 1960s and 1970s. It emphasized freshness, lightness, and clarity of flavour while also influencing new culinary trends across the globe.

Roger Verge, a pioneer of nouvelle cuisine, developed a Provençal cuisine he named "the meal of the sun" at his renowned restaurant Le Moulin de Mougins near Cannes, France. On Friday, Roger Verge passed away in his Mougins residence.

Nouvelle cuisine is still relevant today. Many chefs throughout the world are advocating the idea of using the freshest and locally produced ingredients, stressing plating as well, to obtain a good explosion of flavour in every dish.

Thus, option C is correct.

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If you buy a burger and fries at your favorite fast food restaurant, Group of answer choices then neither GDP nor consumption will be affected because you would have eaten at home had you not bought the meal at the restaurant. then GDP will be higher, but consumption spending will be unchanged. then GDP will be unchanged, but consumption spending will be higher. then both GDP and consumption spending will be higher.

Answers

Answer:

d. then both GDP and consumption spending will be higher

Explanation:

In case when the consumer purchased a burger and the fries to the favorite of his fast-food restaurant than it leads to an increase in the spending of the consumer and the Gross domestic product

As if the consumer spends his money so automatically his consumer spending risen also leads to the increase in gross domestic product.

Therefore the last option is correct

why isn’t full employment the same as zero unemployment?

Answers

The full employment isn't same as zero unemployment due to the fact that there are several forms of unemployment, some of which are inevitable or even necessary for a healthy labour market, full employment is not the same as zero unemployment.

There are various sorts of unemployment, some of which cannot be avoided or even eliminated, hence full employment is not the same as zero unemployment required for a thriving labour market. Jobs are constantly being produced and destroyed as industries change, and the transition from one employment to another is not smooth.

For instance, frictional unemployment develops when workers leave their jobs or get fired and often do not take the first new position that comes their way.

The majority of people take the time to choose a job that is a good fit for their skills, unless they are under intense pressure to make up for missed revenue. Due to this lag, a portion of the workforce is perpetually looking for work and is labelled as unemployed.

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write command to list of available database on your pc

Answers

show tables;

Explanation:

[ db name ];

about 88% of the increase in global food production has come from using high-input industrialized agriculture to increase yields called (the) .

Answers

The high-input industrialized agriculture to increase yields called the Green Revolution.

What is the Green Revolution?

The Green Revolution, also known as the Third Agricultural Revolution (the first two being the Neolithic and British Agricultural Revolutions), is a series of research and technology transfer initiatives that took place between 1950 and the late 1960s and significantly increased agricultural production in various parts of the world, with the late 1960s showing the greatest impact. The initiatives led to the adoption of high-yielding varieties (HYVs) of grains, particularly dwarf wheat and rice. It was linked to newer techniques for farming, such as mechanization, controlled water supply (typically involving irrigation), chemical fertilizers, and agrochemicals. Collectively, these were viewed as a "package of practices" that should replace "Traditional" technology and be adopted as a whole.

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What does indigenous technology mean?​

Answers

Answer: I hope this is helpful mark brainlist if right then no if wrong

Explanation:

Indigenous technology is used by the native inhabitants of a country or region and it constitutes an important part of its cultural heritage. Characteristically, indigenous technologies: Are recognized as animate, imbued with the breath of life and they live in form and function.Technologies employed by the native inhabitants of a country and which constitute an important part of its cultural heritage and should therefore be protected against exploitation by industrialized countries; the problem of indigenous knowledge has been discussed during the Rio Conference but it does not receive much ...Types of indigenous technology in India are; (i) Generic Drugs. (ii) Thorium based Nuclear Reactors. (iii) Plastic RoadsIndigenous Technology is created within a sensory environment that builds on our sense of relationship, meaning, balance, feeling, memory and place as well as sight, sound, smell, taste and touchIndigenization is the process by which Indigenous ways of knowing, being, doing and relating are incorporated into educational, organizational, cultural and social structures of the institution.One example of Indigenous Technologies in action today can be witnessed in differential approaches to medicine. Medical technologies in the Western Scientific sense of the term might conjure images of biomedical research labs, electromagnetic monitors or imaging systems such as CT or MRI scans.Indigenous technology is used by the native inhabitants of a country or region and it constitutes an important part of its cultural heritage. Characteristically, indigenous technologies: Are recognized as animate, imbued with the breath of life and they live in form and function.

Click this link to view O*NET’s Tasks section for Municipal Firefighters. Note that common tasks are listed toward the top, and less common tasks are listed toward the bottom. According to O*NET, what are some common tasks performed by Municipal Firefighters? Check all that apply. directing traffic at accident sites analyzing evidence of criminal activity guarding crime suspects until they can be arrested searching burning buildings to locate victims rescuing victims from burning buildings and accident sites administering first aid and cardiopulmonary resuscitation to help injured people

Answers

Answer:

it's D E F

Explanation:

Click this link to view O*NETs Tasks section for Municipal Firefighters. Note that common tasks are listed

Answer:

i got abd on edg

Explanation:

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