Find the consumer's surplus if the demand for an item is given by D(x)=72-x^2, assuming supply and demand are in equilibrium at x=6. (Hint: Find D(6), then find the appropriate integral of D(x)-D(6).)

Answers

Answer 1

The demand for a good is given by D(x) = [tex]72-x^2[/tex]. The consumer surplus in this scenario is 144.

To find the consumer surplus, we first need to understand what it represents. Consumer surplus is a measure of the economic benefit or value that consumers derive from purchasing a good at a price lower than the maximum price they are willing to pay.

In this case, the demand for the item is given by the function [tex]D(x) = 72 - x^2[/tex], where x represents the quantity demanded. We are given that supply and demand are in equilibrium at x = 6, which means that the quantity supplied is equal to the quantity demanded.

To find the consumer surplus, we need to find the maximum price that consumers are willing to pay for the item at the equilibrium quantity of x = 6. We can calculate this by evaluating D(6), which gives us [tex]D(6) = 72 - 6^2 = 72 - 36 = 36[/tex].

The consumer surplus is the area between the demand curve and the equilibrium price. In this case, it is the integral of the difference between the demand function D(x) and D(6) over the range from x = 0 to x = 6. Mathematically, it can be expressed as:

Consumer's Surplus = ∫[0 to 6] (D(x) - D(6)) dx

Integrating the given demand function, [tex]D(x) = 72 - x^2[/tex], we get:

Consumer's Surplus = ∫[0 to 6] (72 - [tex]x^2[/tex] - 36) dx

= ∫[0 to 6] (36 - [tex]x^2[/tex]) dx

Evaluating this integral gives us:

Consumer's Surplus = [36x - ([tex]x^3[/tex])/3] evaluated from 0 to 6

= [(36 * 6 - ([tex]6^3[/tex])/3) - (36 * 0 - ([tex]0^3[/tex])/3)]

= [216 - 72] - [0 - 0]

= 144

Therefore, the consumer surplus in this scenario is 144.

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Related Questions

Explain how the ability to manage intrapersonal conflict may help you deal better with interpersonal conflict amongst your friends​

Answers

The correct answer to this open question is the following.

Although there are no options attached we can say the following.

The ability to manage intrapersonal conflict may help you deal better with interpersonal conflict amongst your friends​ because you will have the character to understand what the situation is, will be able to comprehend the nature of the problem, knowing what was your responsibility and was whatnot, and try to have an open line of communication to discuss teh situation not to win an argument but to get to a mutual understanding with the other person and resolve the issue in an amicable way.

Let's remember that interpersonal conflict is the kind of conflict we have with another individual or other persons. Do not confuse it with another similar term; intrapersonal conflict. This intrapersonal conflict means internal conflicts with yourself.

Do the Tigris and the Euphrates both run through Iraq ?

Answers

Answer:

yes

Explanation:

which of the following is used to begin a routine request when using the direct approach?

Answers

The correct way to begin a routine request when using the direct approach is present a straightforward question. The correct option is C. This approach immediately engages the recipient, communicates the purpose of the request, and saves time by eliminating unnecessary background information.

When using the direct approach to begin a routine request, one of the most effective strategies is to present a straightforward question.

Option C, "Present a straightforward question," is the appropriate choice.

This approach focuses on getting straight to the point and clearly articulating the request.

By starting with a straightforward question, you immediately engage the recipient and communicate the purpose of your request.

This approach saves time and eliminates unnecessary background information that might distract from the main objective. It also shows respect for the recipient's time by cutting to the chase and allowing them to quickly assess the request.

While the other options (A, B, D, E, F, and G) are important elements that can be included in a routine request, they are not specifically used to begin the request when using the direct approach.

These elements may be incorporated after the initial straightforward question to provide additional context, explain the purpose in more detail, or highlight the desired outcome.

In summary, when using the direct approach, starting with a straightforward question is the recommended way to begin a routine request.

This approach immediately captures the recipient's attention and sets the tone for a concise and efficient communication exchange.

Hence, the correct option is C: Present a straightforward question.

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Complete question:

A: State the purpose of the request.

B: Provide a brief background/context.

C: Present a straightforward question.

D: Highlight the urgency of the request.

E: State the desired outcome.

F: Emphasize the recipient's expertise or authority.

G: Reference a previous interaction or event.

Two ways by which people are related as family​

Answers

Well......
1. Obviously if your born into a family.
2. If you marry into a family.
3. If your adopted.
Hope this helps!

Answer:

QUESTION:

Two ways by which people are related as family​

ANSWER:

Here is three ways. But I know that you only need two so you can pick which ones that you wanna use.

~ Nuclear family: This is also known as the conjugal family or family of procreation.

~ Extended family: The extended family is the most common type of family in the world.

~ Joint family: Joint families are composed of sets of siblings, their spouses, and their dependent children.

Explanation:

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How has bank made our lives easier?Explain.

Answers

Explanation:

Giving loans. Help in storing money. Helping us buy things in installments. Giving credit and debit cards of different credibility

Which of the Following is a Sacrament in the Catholic Church
a. death
b. birth
c. communion
d. resurrections

Answers

Answer:

The correct answer is Choice A.

(death)

Explanation:

Hope this helps!

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Name the THREE mountains located in the western hemisphere.

Answers

The three major mountain ranges of the US are the Appalachian Mountains, the Rocky Mountains, and the Sierra Nevada. The Rocky Mountains, commonly known as the Rockies, are a major mountain range in western United States.

Explanation:

Describe at least two examples of responsible and appropriate wildlife viewing practices that a tour operator should implement, in order to avoid negatively impacting the animals and their habitats. Suggest two distinctive approaches. Please use two examples that have different/distinctive approaches

Answers

The term "wildlife" originally referred to undomesticated animal species, but it has since expanded to encompass any plants, fungi, and other living things that are native to a place and have not been introduced by people.

Wildlife is a collective term for a population of local or indigenous creatures. Wildlife is important because it keeps the natural components in balance and ensures the survival of food chains. A sizable gene pool is provided by wildlife. It helps with species conservation in a given area.

Wildlife originally referred to undomesticated animal species, but it has now expanded to include all living things that develop naturally or exist in the wild without human intervention. Game, which included the birds and mammals that were shot for sport, was sometimes referred to as wildlife. There is wildlife in every habitat.

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Why did the students think it was important to include item #12 in their constitution?

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They thought that next year's club members would want to create their own constitution.
They felt it would allow them to deal with any important issues that were not already mentioned in the constitution.

Frankl states that "man’s search for meaning is the primary motivation in his life and not a "secondary rationalization" of instinctual drives. This meaning is unique and specific in that it must and can be fulfilled by him alone; only then does it achieve a significance which will satisfy his own will to meaning." So, my question is do you think that man’s search for meaning can change over time if it "satisfy his own will to meaning?

Answers

" This mean-ing is unique & specific in th-at it mu-st & should be sati-sfied by him-self; only also do-es it attain a significance wh-ich will sati-sfy his own wi-ll to meaning."

There are many pens who contend that meanings & values are ‘ nothing but defense mechanisms, response conformations & sublimations. ’ But as for my-self, I would not be will-ing to live simply for the sake of my ‘ defense mechan-isms, ’ nor would I be re-ady to die simply for the sake of my ‘ response conformations. ’ Man, still, is suitable to live & indeed to die for the sake of his ideals & values! “

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If the government saw that consumer confidence was low, what step can it take to shift the AD to the right? Congress can pass tax cuts. The local government could cut social programs The Federal Reserve can increase interest rates O Government can decrease its spending

Answers

If the government saw that consumer confidence was low,Congress can pass tax cut when the government wanted to increase.

Buyer certainty implies that purchasers were excessively hopeful about the economy, One such step would be for Congress to curtail government expenditure rates, which would diminish extra cash and in this way decline customer spending.

Another step would be for the Central bank to increment financing costs, which would make getting more costly and subsequently decline venture and shopper spending. Also, the public authority could diminish its own spending, which would diminish in general interest in the economy.

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do you think the compromise of 1850 was more fair to pro-slavery or anti-slavery?

Answers

Answer:

Permitted slavery in Washington, D.C., but outlawed the slave trade.

Explanation:

1. describe the main characteristics of this organization’s culture. provide examples to support your answer. as part of your answer, explain how tracy lawrence’s leadership helped shape the culture.

Answers

The organization’s culture is the unique set of beliefs, values, and practices that shape how work gets done within the organization. Tracy Lawrence’s leadership was a crucial factor in shaping the culture of the organization.

Main characteristics of this organization’s culture:

There are various characteristics of organizational culture. Here are some of the main characteristics of this organization’s culture:

1. Clear communication: The organization has a culture of open and transparent communication, which promotes collaboration and fosters innovation.

2. Emphasis on learning and development: The organization places a high value on learning and development, providing employees with training and development opportunities to enhance their skills and knowledge.

3. Respect and trust: The organization values respect and trust, which is reflected in the way employees interact with each other.

4. Diversity and inclusion: The organization is committed to diversity and inclusion, and promotes a workplace that is free from discrimination and bias.

5. Work-life balance: The organization values work-life balance, providing employees with flexible work arrangements to help them manage their work and personal responsibilities.

6. Customer focus: The organization places a high emphasis on meeting the needs of its customers, and focuses on delivering high-quality products and services.

Examples to support your answer:
Here are some examples that illustrate the characteristics of this organization’s culture:
1. Clear communication: The organization holds regular meetings to ensure that all employees are informed about important updates and changes.

2. Emphasis on learning and development: The organization provides employees with opportunities to attend conferences and training sessions to enhance their skills and knowledge.

3. Respect and trust: The organization encourages employees to share their opinions and ideas, and takes them into account when making decisions.

4. Diversity and inclusion: The organization has a diversity and inclusion committee that ensures that the workplace is free from discrimination and bias.

5. Work-life balance: The organization provides employees with flexible work arrangements, such as telecommuting and flexible schedules, to help them manage their work and personal responsibilities.

6. Customer focus: The organization conducts regular surveys to gather feedback from customers, and uses the information to improve its products and services.

How Tracy Lawrence’s leadership helped shape the culture:
Tracy Lawrence’s leadership was a crucial factor in shaping the culture of the organization. Here are some ways in which her leadership helped shape the culture:

1. Leading by example: Tracy Lawrence led by example, setting the tone for the rest of the organization to follow.

2. Empowering employees: Tracy Lawrence empowered employees, giving them the freedom and flexibility to make decisions and take risks.

3. Fostering collaboration: Tracy Lawrence fostered a culture of collaboration, encouraging employees to work together to achieve common goals.

4. Creating a sense of purpose: Tracy Lawrence created a sense of purpose, helping employees understand how their work contributed to the overall success of the organization.

5. Encouraging innovation: Tracy Lawrence encouraged innovation, creating an environment where employees were free to experiment and come up with new ideas.

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The country that people are most likely to consider an example of socialism is (a) Canada (b) Norway (c) Cuba (d) North Korea.

Answers

Answer:

B

Explanation:

I live in Canada. I would say that you could argue that it is close to being a socialist country -- especially our health care system and pretty much universal education.

I think however, the answer you want is Norway.

Cuba is a communist country and North Korea is even more communist.

women were pre-occupied with body consciousness and the fitness craze as represented by ___________________.

Answers

Women were pre-occupied with body consciousness and the fitness craze as represented by the rise of fitness magazines, diet programs, and the popularity of exercise equipment.

During certain periods, women's preoccupation with body consciousness and the fitness craze has been reflected in various cultural phenomena. One of these manifestations is the rise of fitness magazines that promote exercise routines, healthy lifestyles, and beauty ideals. These publications provide guidance on workouts, nutrition, and overall wellness, catering to women's desire for a fit and attractive physique.

Additionally, diet programs have gained popularity as women sought to achieve their desired body shapes. These programs often focus on specific dietary guidelines and weight loss strategies to meet societal standards of beauty and fitness.

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1.2 Why did President Washington refuse to support either of the political parties?

Answers

Answer:

Explanation:

He argues that every government has recognized political parties as an enemy and has sought to repress them because of their tendency to seek more power than other groups and to take revenge on .

Washington recognizes that it is natural for people to organize and operate within groups such as political parties, but he also argues that every government has recognized political parties as an enemy and has sought to repress them because of their tendency to seek

How did Franklin D. Roosevelt handle the banking crisis of the Great Depression? He turned control of the Fed over to Congress, which then created the FDIC to oversee the banking system. He closed all banks for four days so their viability could be checked by government officials and so the public’s confidence in the banks could be restored. He established the Federal Reserve System, which gave the country a strong central bank capable of weathering financial storms. He commanded the Treasury Department to forgive the debts of borrowers whose savings had been depleted because of the financial crisis.

Answers

Answer:

CORRECT ANSWER: Following his inauguration on March 4, 1933, President Franklin Roosevelt set out to rebuild confidence in the nation's banking system and to stabilize America's banking system. On March 6 he declared a four-day national banking holiday that kept all banks shut until Congress could act.

Franklin D. Roosevelt established the Federal Reserve System, which gave the country a strong central bank capable of weathering financial storms. Thus, option C is correct.

Who is Franklin D. Roosevelt?

Franklin Delano Roosevelt, normally known as FDR, was an American legislator and political pioneer who filled in as the president

Following his introduction on Walk 4, 1933, President Franklin Roosevelt set off to revamp trust in the country's financial framework and to balance out America's financial framework.

On Walk, he proclaimed a four-day public financial occasion that kept all banks shut until Congress could act. The Roosevelt Organization was a period of incredible development of the National Government, including the arrangement of new Branches of Business and Work.

Therefore, option C is correct.

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which theory views crime as the outcome of an imbalance between impulses toward criminal activity and the social or physical controls that deter it?

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The theory that views crime as the result of an imbalance between impulses toward criminal activity and the social or physical controls that deter it is the social control theory.

According to this theory, individuals with weak social ties to conventional individuals and institutions are more likely to engage in criminal activity. The theory assumes that people are motivated to engage in crime and that they would do so if they were not prevented by social controls. This theory believes that people are not inherently good or bad, but rather are influenced by their environment.

The lack of social control can create an environment that is conducive to criminal activity. Social control theory states that socialization is the process by which people learn the norms, values, and beliefs of their culture. Individuals who have been socialized effectively are more likely to conform to social norms and to avoid criminal behavior. In conclusion, the social control theory views crime as the outcome of an imbalance between impulses toward criminal activity and the social or physical controls that deter it.

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Sandy and Will are the parents of two sons, William, age 15, and Thomas, age 14. The boys have to call one of their parents as soon as they get home from school, and they are not allowed to do anything but homework or reading until their parents get home. They are only allowed to socialize with teens whose parents are friends of Sandy and Will. They can attend school dances only when Sandy or Will chaperones. Sandy and Will are using which type of parenting strategy

Answers

Answer: Cocooning

Explanation:

Cocooning could be described as a method of training that revolve around protection from harm which is not really known, i.e a form of preventive measures taken in place to protect from the unknown. Sandy and Will are training their children with the method of Cocooning, where they limited their movement and activities around themselves, their parents.

which therapy technique requires a patient to monitor multiple aspects of their daily functioning to aid in relief of symptoms?

Answers

The therapy technique that requires a patient to monitor multiple aspects of their daily functioning to aid in the relief of symptoms is Cognitive Behavioral Therapy (CBT).

What is Cognitive Behavioral Therapy (CBT)?Cognitive Behavioral Therapy (CBT) is a short-term, problem-focused therapy method that has been proven to be effective in treating a wide range of mental health problems. The goal of CBT is to alter patterns of thought or behavior that underlie an individual's difficulties in order to assist them in adjusting their emotional responses and behaviors.

CBT therapists employ a number of strategies and techniques in their therapy sessions, one of which is monitoring one's daily functioning to aid in the relief of symptoms. A therapist may, for example, ask their patient to keep a diary or record of their mood, thoughts, and behaviors throughout the day and reflect on these experiences during subsequent therapy sessions. This helps the patient recognize patterns and negative thought processes that contribute to their problems, and work with the therapist to develop alternative and more adaptive ways of thinking and behaving.

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Question Mode Multiple Choice Question As a young child, Gregory began demonstrating aggressive behavior. He would physically attack his siblings and peers, and often destroyed others' property. By middle school, Gregory had been suspended from school at least 10 times for theft, fighting, and disrespect toward his teachers. He started drinking at the age of 10 and graduated to cocaine by age 13. At age 15, he spent over 6 months in a residential treatment center after he stole a car and crashed it while under the influence. These characteristics indicate ______.

Answers

Answer:

disinhibition.

Explanation:

What services are provided by state programs?​

Answers

Answer:

Medical care or financial assistance for medical care, health insurance, prescription assistance, medical supplies, medical equipment, disease screening, respite care, or others.

How does each society determine who will consume what is produced ?

Answers

Answer:

its unique combination of social values and goals. Households own the factors of production and consume goods and services.

Explanation

*NO COPY RIGHT OR PLAGIRISM*

100 PONITS!!!!!!! PLZZ

What are the best ways to support a political party? Check all that apply.

campaigning for candidates
allocating your taxes to that party
writing letters of support
raising campaign funds
volunteer for an opposing party

Answers

Hey! The answers are:
campaigning for candidates
writing letters of support
raising campaign funds

Answer:

campaigning for candidates

writing letters of support

raising campaign funds

Explanation:

Adolescent egocentrism includes which of the following? (check all that apply)

A). Imaginary audience
B). Cautiousness
C). Personal fable
D). Reduced self-consciousness
E). Risk taking

Answers

The options A, C, and E are the ones that align with the concept of adolescent egocentrism.

Which of the following are components of adolescent egocentrism?

The options that are included in adolescent egocentrism are:

Imaginary audience Personal fableRisk taking

Explanation:

Adolescent egocentrism refers to a cognitive phenomenon where teenagers have a heightened self-focus and an altered perception of themselves and their social interactions. It involves several components, some of which are listed below:

Imaginary audience: This refers to the belief that one is constantly being watched, judged, or evaluated by others, even in situations where this may not be the case. Adolescents may feel self-conscious and believe that everyone is focused on their appearance, behavior, or actions.

Personal fable: The personal fable is a belief held by adolescents that they are unique, exceptional, and invulnerable. They may believe that their experiences and feelings are entirely unique, leading to a sense of being special or different from others. This can contribute to a sense of invincibility and a disregard for potential consequences.

Risk taking: Adolescents often engage in higher levels of risk-taking behavior compared to other age groups. This can include engaging in dangerous activities, experimenting with substances, or seeking out novel experiences. The sense of invincibility and the belief that negative consequences won't apply to them can contribute to increased risk-taking behavior during adolescence.

B) Cautiousness and D) Reduced self-consciousness are not typically considered components of adolescent egocentrism. Cautiousness generally involves being careful or hesitant, which is not a characteristic commonly associated with adolescent egocentrism.

Reduced self-consciousness, on the other hand, is not a typical characteristic of adolescence, as teenagers often experience heightened self-consciousness due to increased self-awareness and social evaluations.

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What did historian Tom Garner find in the Pensacola Bay area? Bead earrings Deer hides Piece of a jar from a Spanish colony Journals from early explorers

Answers

Piece of a jar is that better

duh i mean if this is history then don't you think it is about people against people like really

QUESTION 1

a. What did you do for
Spring Break ?

b. What is a perfect spring break in your eyes? If you could go anywhere and do anything, what would that be ??

COMPLETE SENTENCES!!

Answers

For spring I went to a picnic with my friends.
A perfect spring break in eye is that having fun with your friends and taking your time don’t worry about school so much and enjoy your spring break:D
The answer is B I know this because I took the quiz and went back to look at all my correct answers and this was 1 of them


Explain the difference between Earth's rotation and Earth's revolution​

Answers

The earths rotation could be known as a day or 24 hours and the earths revolution is known as a year or 365 days

I hope this helps!

Sample Response: Rotation occurs when an object spins about its own axis. Revolution occurs when one object moves around another object.

Explanation:

Sampling method is commonly used to pretest a questionnaire? a. stratification b. quota c. snowball d. purposive

Answers

The most appropriate answer is d. purposive Sampling method is commonly used to pretest a questionnaire

What is Purposive sampling

Purposive sampling is commonly used to pretest a questionnaire. In purposive sampling, individuals are deliberately selected based on specific criteria that align with the research objectives.

For pretesting a questionnaire, researchers may select individuals who possess the desired characteristics, such as knowledge of the topic or experience with the subject matter.

Purposive sampling allows researchers to gather valuable feedback on the questionnaire's clarity, relevance, and effectiveness before conducting the actual study.

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which societies have a migrating food supply? pastoral societies hunting and gathering societies fishing societies horticultural societies

Answers

The societies that have a migrating food supply are pastoral societies. Option a is correct.

Pastoral societies rely on the herding and raising of animals as their primary food source. These societies typically move their livestock to different grazing areas as a way to ensure a steady food supply for their community. The movement of the animals allows them to access fresh grazing lands and maintain the health and growth of their herds.

In contrast, hunting and gathering societies rely on hunting wild game and gathering wild plant resources, fishing societies depend on fishing as a food source, and horticultural societies cultivate crops in a fixed location rather than relying on migrating food sources.

Therefore, a is correct.

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Which of the following must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s? (Check all that apply.) (You must provide an answer before moving to the next part.) Check All That Apply the inclusion-exclusion principle the sum rule the product rule the division rule. Review the public traded company- Microsoft's most recent statement of cash flows. Be prepared to discuss. Review the companys operating, investing, and financing activities. Suggest at least two items from each activity that creditors should analyze when deciding whether to lend money to the company. Justify your response. The approximation of 1 = Lo cos (x2 + 5) dx using simple Simpson's rule is: -0.93669 -0.65314 N This option This option -1.57923 0.54869 true or false: if wage contracts have short duration, it would make the recession induced by contractionary monetary policy more severe. Which Act is being violated when you post the private infomation of someone on social media? (1x1) (1) elaborate mr. t has a gold chain with a mass of 100 grams. the density of gold is 19.3 g/cm3. in liters, what is the volume of mr. ts gold chain? As a general rule, there is no legal obligation for retailers to honor incorrectly advertised prices. Federal law does not penalize businesses for honest mistakes in advertising. Typing errors, communication errors and other unexpected glitches can cause commodities to be offered at heavy discounts. To be subject to current laws, in concern to the false or misleading advertisements, the advertiser must intend to deceive the customer. If the company can demonstrate that it made an error in showcasing its prices, it is exempt from legal action for false advertising. So according to me, If Sackett's can prove that they advertised the wrong price by mistake, then they have the right to not sell that machine to Martens at that advertised price. Although Martens is free to take legal action, but will not be benefited from it. So, there is no breach of contract. are young managers (age < 40) more motivated than senior managers (age > 40)? a randomly selected group of each were administered the sarnoff survey of attitudes toward life (ssatl), which measures motivation for upward mobility. the ssatl scores are summarized below. judging from the way the data were collected, which test would likely be most appropriate to employ? on a certain portion of an experiment, a stastical test result yielded a p-value of 0.21 How many of the following expenses are likely to be allocated in a nursing departments operating budget?A. DietaryB. Community relationsC. Human resourcesD. Medical recordsE. A & BF. C & DG. B & CH. All of the above What are the coordinates of the terminal point determined by t = 1177? A (-4) B. (-.-)OC (1)OD. (1.) PLEASE ANSWER QUICK!!!! 35 POINTS RIGHT ANSWERS ONLY!!!!!!!How much energy does the water in this experiment absorb according to the calorimeter data? A candle company would like to ship out 9 candles per box. The candles are 6 inches in height and have a diameter of 6 inches. The candles are placed inside the box in a 3 3 1 formation. If the boxes have 1 inch of padding on all sides of the box and 1 inch of padding between each of the candles, what are the dimensions of the box? Select the correctly punctuated absolute phrase from the drop-down menu to add it to the sentence. Seora Alvarez choose...a. Waited excitedly for her guests to arrive.b. Waited, excitedly, for her guests to arrive.c. Waited excitedly, for her guests to arrive.d. Waited, excitedly for her guests to arrive. .Find the value of each of the following quantities:C(11,1)=C(7,7)=C(8,3)=C(12,6)=C(5,4)=C(12,2)= rue or false: when a tax is imposed on sellers, demand remains the same because the tax does not change any of the non-price determinants of demand. 1990s Internet Stock Boom According to an article, 21.5% of Internet stocks that entered the market in 1999 ended up trading below their initial offering prices. If you were an investor who purchased three Internet stocks at their initial offering prices, what was the probability that at least two of them would end up trading at or above their initial offering price? (Round your answer to four decimal places.)P(X 2) = native americansall these answers are correct.can now teach children exclusively in their native language in schools run by the bureau of indian affairs.today number more than 2 million.are less than half as likely to finish college as other americans.have a far higher infant mortality rate than the national average. Which connection must have transformers that use two secondary windings that provide equal voltages? a.zig-zag connection b.six-phase connectionc. double-wye connection d. double-delta connection Explain Why The Facts Of Brown V. Board Of Education Led To A Similar Holding In United States V. Scotland Neck City School Board