What irish king died leading his men to victory over the vikings in the decisive 1014 battle of contarf?.

Answers

Answer 1

The Irish king who died leading his men to victory over the Vikings in the decisive 1014 Battle of Clontarf was Brian Boru.

He was one of the most significant and influential Irish kings, known for his military prowess and political achievements.Brian Boru was born in Munster, Ireland in 941 CE. He became the king of Munster in 978 CE and later became the high king of Ireland in 1002 CE.

He is also known for his role in the unification of Ireland. Brian Boru fought against the Vikings in many battles, including the Battle of Sulcoit and the Battle of Glen Mama.

However, his most notable victory was the Battle of Clontarf in 1014 CE, where he led his troops against a Viking and Irish force. Though Brian Boru and his army won the battle, he was killed in the process, and his death led to a political vacuum in Ireland.

The Battle of Clontarf is considered a turning point in Irish history, and Brian Boru is revered as a national hero. He is often depicted in art and literature as a powerful warrior-king who fought to unite Ireland and free it from foreign rule.

His legacy lives on in Irish culture, and his memory is honored every year on the anniversary of his death.

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Related Questions

What is propaganda. What was the effect of government propaganda on nearly every nation at war in 1914.

Answers

Answer: Propaganda is communication primarily meant to persuade or influence the audience to advance an agenda. The effect of propaganda on every nation at war in 1914 was inciting national national hatred prior to the war.

Explanation:

Drag the tiles to the boxes to form correct pairs.
Match the type of local government with its primary function.
school district
municipality
special district
provides one function or service
serves as the administrative arm of the state government
provides local services around a population center
provides public education services
county

Answers

A local government with its primary function are as follows: school: provides public education services county, district: serves as the administrative arm of the state government, municipality: provides local services around a population center, special district: serves as the administrative arm of the state government.

A variety of essential services for residents and companies in certain areas are handled by the local government. There are well-known ones like social services, education, housing, planning, and waste collection among them, as well as less well-known ones like pest treatment, business support, licensing, and registrar services. Across a variety of various types of authority, more than one million people in England are employed in local government, offering more than 800 distinct services to local communities. The majority of local authorities are local councils, which are composed of council members chosen by the general population during local elections.

To establish and carry out local goals, council members collaborate with residents and partners, including neighborhood businesses and other organizations.

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A local government with its primary function are as follows: school: provides public education services county, district: serves as the administrative arm of the state government, municipality: provides local services around a population center, special district: serves as the administrative arm of the state government.

A variety of essential services for residents and companies in certain areas are handled by the local government. There are well-known ones like social services, education, housing, planning, and waste collection among them, as well as less well-known ones like pest treatment, business support, licensing, and registrar services. Across a variety of various types of authority, more than one million people in England are employed in local government, offering more than 800 distinct services to local communities. The majority of local authorities are local councils, which are composed of council members chosen by the general population during local elections.

To establish and carry out local goals, council members collaborate with residents and partners, including neighborhood businesses and other

why might people support long plan over the new deal

Answers

Answer:

Because long did not impose a high tax burden to the citizens.

Explanation:

Both Huey Long's plan and the New Deal consist of several public programs that were aimed to increase the general welfare of the citizens.

There's one distinct difference between the two of them.

The New Deal which proposed by President Roosevelt acquired the funds for the programs by increasing the tax rate that must be paid by the citizens. Huey Long's plan on the other hand, acquired the funds for the programs by only taxing big businesses.

This made Huey Long's plan became much more popular among the citizens.

who really benefits from globalization? write a short paragraph arguing who benefits from globalization *13 POINTS*

Answers

World leaders via presidents etc...

Explanation:

Select the correct answer. Why did activists cross the Edmund Pettus Bridge near Selma, Alabama, in 1965

Answers

The reason why activists crossed the Edmund Pettus Bridge near Selma, Alabama was to demand voting rights.

Why was there a protest at Edmund Pettus Bridge?

The South had come up with ways to deny African Americans voting rights since the end of Reconstruction.

The protest at Edmund Pettus Bridge where protesters crossed the bridge, was one of several ways that activists tried to get the right for African Americans to vote.

Did Selma forget about Pettus Bridge?

Alabama senator Edmund Winston Pettus served in the late 19th century. He was also a former commander of the Confederacy and the Grand Dragon of the Alabama chapter of the Ku Klux Klan. Did Selma simply forget about the contentious past, then?

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One of the achievements of Spanish exploration was __________. A. mapping the coast of Africa B. claiming Brazil for Spain C. finding large amounts of gold in Africa D. proving the existence of the Americas

Answers

Answer:One of the achievements of Spanish exploration was .

Explanation:B claiming Brazil for Spain

what religon is anasazi

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Answer: Scholars believe that the Anasazi practiced an animistic, nature-based religion emphasizing honor and care of the Earth as a religious duty. It is thought that the Anasazi were polytheists, worshiping several different spirits and deities including a rain deity, a sun deity, and an apocalyptic earth deity.

Explanation:

what were the key events in japan’s unification and isolation

Answers

Answer:

Explanation:

Tokugawa Ieyasu was one of Hideyoshi's strongest daimyo allies, and he completed the unification of Japan.This victory earned him the loyalty of daimyo throughout Japan. Years later, Ieyasu became the only ruler or the shogun. So, he moved Japan's capital to his power base at Edo, which later became the city of Tokyo.

Answer:

By the time he was assassinated, Nobunaga had succeeded in unifying almost all of Japan. Following this, Nobunaga’s successor; Toyotomi Hideyoshi, killed Nobunaga’s assassinator and became the military dictator of Japan. Hideyoshi finished what Nobunaga began and defeated opposing Daimyo, thus unifying Japan.

In a wealthy ________ family in ________, the body of a deceased relative stays at the family home until it is time for cremation. Before cremation, the body will be washed by family members.A.) Jewish; IsraelB.) Catholic; RomaniaC.) Lutheran; AustriaD.) Hindu; India

Answers

Answer:

D- Hindu; India

Explanation:

What is the relative importance of the causes of the civil war in the period from 1830 to 1861?

Answers

The relative importance of the causes of civil war are disagreements caused due to slavery existed in the United States. This is the main reason for the disunion and subsequent war. In the mid-19th century, most of the top countries such as the United States were experiencing rapid growth in each sector and variations in their economic plans.

              Strategies that were established in each sector such as in industries, agriculture, small-scale companies, and large-scale industries. This has brought major differences in the same country but different regions such as southern and northern regions in the United States. When it comes to the northern region only a few industries mostly depend on small-scale farming which is mostly limited, whereas in the southern region mostly developed in a rapid way in large scale faming to huge industries which brought economical differences between northern and southern region, in the southern region people enslaved blacks to grow certain crops such as tobacco and cotton so the existence of slavery in America, which became the backbone of their economy was in the most danger.

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TRUE/FALSE. after their conquest of northern india, muslim rulers agreed to recognize the traditional use of alcohol among the hindu population.

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After their conquest of northern india, muslim rulers agreed to recognize the traditional use of alcohol among the hindu population. Is a False statement.

Did Hinduism went before the foundation of Brahmanism in India?

Hinduism went before the foundation of Brahmanism in India. Yet again bodhisattvas were those people who neglected to arrive at illumination and in this way nirvana and needed to get back to the pattern of rebirth.

What is the conviction of Mahayana and Theravada?

While Theravada Buddhists endeavour to become Arhats and gain independence from the pattern of samsara, Mahayana Buddhists might decide to remain in the pattern of samsara out of sympathy for other people.

Who presented the rank framework and began Hinduism in India?

As per one long-held hypothesis about the beginnings of South Asia's rank framework, Aryans from focal Asia attacked South Asia and presented the standing framework for of controlling the nearby populaces. The Aryans characterized key jobs in the public arena, then, at that point, appointed gatherings to them.

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What are 5 facts about the indian removal act and trail of tears?

Answers

Answer:

Interesting Facts about the Trail of Tears

The persecution of Native Americans didn't end with the removal to Oklahoma. ...

The Cherokee were given money to buy food along the way. ...

John Ridge, a Cherokee leader who agreed with the removal treaty, was later assassinated by Cherokee men who survived the march.

In 2-3 sentences explain the impact of Plessy V Ferguson differed from that of Brown v Board of Educational of Topeka.

Answers

Answer:

In 1896, the Supreme Court ruled in Plessy v. Ferguson (1896) that separate accommodations based on race was constitutional. 58 years later in Brown v. The Board of Education of Topeka (1954) the court ruled that separate accommodations based on race were inherently unequal and so unconstitutional, also the Supreme Court decision that overturned the Plessy vs. Ferguson's decision Ferguson elision (1896); led by Chief Justice Earl Warren, the Court ruled that "separate but equal" schools for blacks were inherently unequal and thus unconstitutional. The decision energized the Civil Rights Movement in the 1950s and 1960s.

hich statement best explains a result of slave codes during the colonial era? slave codes increased the rights of enslaved people. slave codes eliminated the rights of enslaved people. slave codes ensured that enslaved people were treated fairly. slave codes ensured that slaveholders could not free e

Answers

The argument best describes the effect of slave codes during the colonial era Slave codes eliminated the rights of enslaved people. Thus, option b is correct.

Slave codes were laws passed in colonial America that described the lawful group of enslaved people and set the ownership of slave owners. The principles were altered by territory but typically limited the rights of enslaved people and refused their basic human rights.

While slave codes did not totally destroy the society of enslaved people, they did select a legal framework that robbed them of multiple of their rights and freedoms. This lawful status donated to the perpetuation of the club of slavery and made it hard for enslaved people to flee.

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The complete question is-

which statement best explains the result of slave codes during the colonial era?

a. slave codes increased the rights of enslaved people.

b. slave codes eliminated the rights of enslaved people.

c. slave codes ensured that enslaved people were treated fairly.

d.slave codes ensured that slaveholders could not free

Which did the Mothers of the Plaza de Mayo do? Select three responses. Increase populist programs support the government campaign for human rights challenge government power fight for truth and democracy

Answers

Answer:

C, D, and E.

Explanation:

campaign for human rights

challenge government power

fight for truth and democracy

Mothers of the Plaza de Mayo helped to:

Campaign for human rights.Challenge government power.Fight for truth and democracy.

Who are the mothers of Plaza de Mayo?

In Buenos Aires, the Mothers of the Plaza de Mayo is known too be the union of women who were said to have lost their children or their grandchildren as a result of the Dirty War.

Note that due to their campaign that was said to have called on international attention to see the plight of the disappeared persons, they were able to get some justices.

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Select the correct answer.
What of these is referred to as the "third rail" of American politics?
A.
the aging of the population
B.
Medicaid
OC.
Medicare
D.
Social Security

Answers

Answer:

Social Security

Explanation:

A third rail is referred to as a topic of discussion that leads to disaster. I believe social security fits this term the best.

is the proctection of endangered species a biblically mandadted responsibility for chrisitans

Answers

Yes, according to the Christian's teachings of stewardship the protection of endangered species a biblically mandated responsibility for Christians.

The question of whether the protection of endangered species is a biblically mandated responsibility for Christians is a complex one, and there are differing views among Christian theologians and scholars.

Some Christians argue that the protection of endangered species is consistent with biblical teachings on stewardship, which emphasize the responsibility of human beings to care for and protect the natural world.

They point to passages in the Bible, such as Genesis 1:28, which instructs humans to "be fruitful and multiply, and fill the earth and subdue it," as evidence that God has given humans a mandate to care for and manage the natural world.

Others argue that while the Bible does emphasize the importance of caring for the natural world, it does not provide a specific mandate to protect individual species. They note that the Bible focuses more broadly on the need to care for the earth as a whole and to be good stewards of God's creation.

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The activity depicted in the maps represents which of the following changes with respect to slavery between 1450 and 1750?

The direction of the slave trade changed as the movement of indigenous American populations decreased.
Africans reluctantly became involved with the international slave trade.
The volume of the slave trade increased as slavery increasingly became a non-inherited status.
The slave trade became more focused on traffic to the Americas as traffic to the Old World declined.

The activity depicted in the maps represents which of the following changes with respect to slavery between
The activity depicted in the maps represents which of the following changes with respect to slavery between

Answers

Answer:

D

Explanation:

The maps clearly show the expansion of routes traveling to the New World, and decrease in routes going to the Old World.

Answer:

D.The slave trade became more focused on traffic to the Americas as traffic to the Old World declined.

Explanation:

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What overriding political belief informed the creation of the Articles of Confederation by its drafters in the Second Continental Congress?

Answers

The overriding political belief that informed the creation of the Articles of Confederation by its drafters in the Second Continental Congress was a deep-seated distrust of centralized authority and a desire to protect the sovereignty.

The Founding Fathers were deeply influenced by the political philosophy of classical republicanism, which emphasized the importance of civic virtue, the common good, and the diffusion of power among different branches of government. They believed that a strong central government posed a threat to individual liberties and could easily become tyrannical. As a result, they sought to create a system of government that would balance the need for collective action with the preservation of individual freedom.

The Articles of Confederation, adopted in 1781, created a loose confederation of 13 independent states with a weak central government. Under the Articles, the national government had limited powers and could not tax or regulate commerce. Instead, each state retained its sovereignty and autonomy, and decisions were made by a unicameral Congress in which each state had one vote.

While the Articles of Confederation provided a framework for national governance during the early years of the United States, they proved to be inadequate in many ways. The lack of a strong central government made it difficult to regulate commerce, enforce laws, and defend the nation against foreign threats. These weaknesses ultimately led to the adoption of the Constitution in 1787, which established a stronger central government with a separation of powers and checks and balances to prevent abuses of power.

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When the Stamp Act Resolves (Virginia Resolves) passed, Governor Fauquier ________ the House of Burgesses.

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When the Stamp Act Resolves passed, Governor Fauquier dissolved the House of Burgesses.

The Stamp Act Resolves were a series of resolutions passed by the Virginia House of Burgesses in response to the Stamp Act, which was passed by the British Parliament in 1765. The Stamp Act required colonists to pay a tax on all printed materials, including newspapers, legal documents, and playing cards. The Virginia Resolves declared that only the Virginia Assembly had the right to tax Virginia citizens, and that any attempt to tax Virginians without their consent was a violation of their rights as Englishmen.

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What are the four pillars of the church

Answers

Creed, Prayer, Sacraments, and Morality.
The four pillars of the Church typically refer to the four essential elements or core components that uphold and guide the life and mission of the Church. These pillars are:

1. Creed: The Creed represents the foundational beliefs and teachings of the Church. It is a summary of the essential doctrines and truths of the Christian faith, including beliefs about God, Jesus Christ, the Holy Spirit, salvation, and the Church itself. The Nicene Creed and the Apostles' Creed are two well-known examples of creeds used in Christian worship.

2. Sacraments: The Sacraments are visible signs or rituals instituted by Jesus Christ through which God's grace is communicated to believers. The Catholic Church recognizes seven sacraments: Baptism, Eucharist (or Holy Communion), Confirmation, Reconciliation (or Confession), Anointing of the Sick, Holy Orders, and Matrimony. These sacraments are considered central to the life of the Church and play a vital role in the spiritual growth and nourishment of believers.

3. Moral Life: The moral life refers to the ethical teachings and principles that guide the behavior and actions of believers. It involves living according to the teachings of Jesus Christ and striving to follow the moral precepts outlined in Scripture and the Church's teachings. The moral life includes virtues such as love, justice, honesty, humility, and compassion, as well as adherence to the Ten Commandments and other ethical teachings of the Church.

4. Prayer: Prayer is the communication and relationship between believers and God. It is an essential pillar of the Church's life, enabling individuals to deepen their spiritual connection with God, seek guidance, express gratitude, and intercede for others. Prayer can take various forms, including personal prayer, communal worship, liturgical prayers, devotional practices, and contemplative prayer.

These four pillars represent the foundational aspects that support the beliefs, practices, and mission of the Church, providing a framework for Christian faith and living. While the specific terminology may vary among different Christian traditions, the concepts behind these pillars remain central to the Christian understanding of the Church's identity and purpose.

11. What was Poland's military like ?

Answers

Poland never officially capitulated....the army was recreated in west and as well as in East........
They were not industrialized.

Summarize the Japanese approach to the great depression.

I have to turn this in tomorrow, please answer soon.

Answers

Answer:

Since Japan didn'thave many natural resources,they were hit harder than othernations by the Depression. Brieflysummarize theJapaneseapproach:The crash of the Stock Exchange caused the whole world into adepression. Japan was effected one of the hardest since theydidn't have many natural resources.

Japan achieved an early recovery from the Great Depression. A veteran finance minister, Takahashi Korekiyo, managed to stage the recovery by prescribing a combination of expansionary fiscal, exchange rate, and monetary policies

what is the main difference between the social structures of the Spanish colonies in America and the English colonies?

Answers

The Spanish colonies were characterized by a highly centralized and rigid social structure, whereas the English colonies were more diverse and decentralized, with greater social mobility

The social structures of the Spanish colonies in America and the English colonies were significantly different due to various factors, such as the goals of colonization, demographics of settlers, and the economic systems they established.

Spanish colonization aimed to extract wealth from the New World and transfer it back to Spain, resulting in a highly centralized and hierarchical social structure. The Spanish Crown granted extensive land holdings, called encomiendas, to Spanish nobles and soldiers, who then forced the native population to work the land or mine for resources. The Spanish social hierarchy was organized in a strict caste system, with peninsulares (Spanish-born settlers) at the top, followed by criollos (American-born descendants of Spanish settlers), mestizos (mixed-race individuals), and indigenous people at the bottom.

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rapid rail construction after the civil war was possible because

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Rapid rail construction after the civil war was possible because the federal and state governments offered crucial initiatives. The right answer is c.

Railway building in the United States greatly surged starting in the early 1870s. The federal government provided aid through land grants for the construction of four of the five transcontinental railroads. Congress provided the railroads with millions of acres of public land, ensuring they would have both land on which to build their tracks and land to sell, the profits that helped the corporations finance the construction of their railroads.

However, not all railroads received government funding for construction. Small railroads had to buy the land from private landowners, some of whom protested to the railroads and declined to provide rights of way, in order to build their tracks there.

The correct answer is option c.

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The question seems incomplete. The complete question is:

Rapid rail construction after the civil war was possible because:

a. there was little competition between the builders

b. private companies were ready to fund

c. federal and state governments provided important activities.

By the end of the nineteenth century, married middle-class women were expected to a. not work outside of the home. b. work part time. c. work full time.

Answers

C.

Reason:
In Victorian England, most working-class women had no choice but to work in order to support their families. They worked in factories, domestic service for wealthy families, or in family businesses. Many women also worked at home, such as finishing garments and shoes for factories, doing laundry, or preparing snacks to sell in markets or on the streets.

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What does this quote mean? Give a short summary.
“The atonement made in giving back their independence to the Phillippine islands might purge the united states from that treason of democracy into which it has been betrayed and from which it had suffered at home by the reaction of foreign imperialism.”

Answers

This quote suggests that restoring independence to the Philippines could help the United States regain its reputation for being a democratic country, after being betrayed by foreign imperialism. It suggests that the act of atonement for this betrayal and suffering could be giving back the Philippines' independence.

An article was recently published concerning the evidence of cardiac death attributable to the earthquake in Los Angeles County on January 17, 1994. In the week before the earthquake, there were on average of 15.6 cardiac deaths per day in Los Angeles County. On the day of the earthquake, there were 51 cardiac deaths. Is the occurrence of 51 deaths an unusual occurrence?

Answers

Yes, the occurrence of 51 cardiac deaths on the day of the earthquake is an unusual occurrence.

An article was recently published concerning the evidence of cardiac death attributable to the earthquake in Los Angeles County on January 17, 1994. In the week before the earthquake, there were on average 15.6 cardiac deaths per day in Los Angeles County. On the day of the earthquake, there were 51 cardiac deaths which is a significant rise in the daily average in the given week. The hypothesis test can be conducted to verify the results obtained from the given data.

The null hypothesis, H0: μ=15.6 cardiac deaths per day

The alternative hypothesis, Ha: μ>15.6 cardiac deaths per day.

The level of significance, α=0.05Z = (51 - 15.6) / [(15.6 / 7)^0.5]≈ 21.86.

It can be concluded that the occurrence of 51 cardiac deaths on the day of the earthquake is an unusual occurrence.

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which were technological causes of the age of exploration

Answers

Answer: There were several technological advances that facilitated and enabled the Age of Exploration. Some of these technological causes include:The development of the compass: The compass allowed sailors to navigate more accurately and safely across vast stretches of open water.The construction of larger, more seaworthy ships: Ships such as the caravel and the galleon were built with stronger, more durable hulls and were equipped with multiple masts and sails, which made them more capable of sailing long distances and facing rough seas.Improvements in navigation and cartography: Advances in cartography, or mapmaking, allowed explorers to create more accurate maps of the world, and new navigation techniques such as the use of the astrolabe and quadrant allowed sailors to more accurately determine their position at sea.The development of gunpowder and firearms: The introduction of gunpowder and firearms gave European explorers an advantage over native peoples they encountered in the New World, allowing them to conquer and colonize these regions more easily.These technological advances allowed European explorers to embark on long voyages of discovery and expansion, leading to the establishment of European colonies and trade routes in the Americas, Africa, and Asia.

Explanation:

Why were indentured servants needed in Virginia?

because growing tobacco required a large number of workers

because the colonists did not know how to grow tobacco

because slavery was not allowed in the colony

Answers

Answer:

a

Explanation:

Tobacco was in high demand in England and it required a lot of workers. Settlers had to use a lot of land because tobacco would drain the nutrients. A large number of servants had to pick the tobacco.

The indentured servants needed in Old Dominion (V) are because growing tobacco required a large number of workers. Thus, option (a) is correct.

What is workers?

The term workers refer to the work in the industries and the agriculture sectors. The workers are the provided the services with the exchange of the wages. The workers are the main work to the manufacture the product and the cutting the crops. The worker are the important part of the economy.

The state was known as Old Dominion (V), and its principal crops were cotton and tobacco. Tobacco was in high demand in England, and it required numerous workers. Settlers had to use a lot of land since tobacco depleted the nutrients. Tobacco had to be picked by numerous servants.

As a result, Old Dominion (V) growing tobacco required a large number of workers. Therefore, option (a) is correct.

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Solve for x: 2(x + 3) = 2x 6 NEED HELP PLZ:(A: 0 B: 3 C:All real numbers D:No solution Slope intercept form of an equation of the line with slope 3 and passes through the points (-1,-2) A group of 10 students participate in chess club, karate club, or neither.Let event A = The student is in chess club.Let event B = The student is in karate club.WallyXanderCHESSCLUBKARATECLUBZoeQuinYolandaRobVikiSamTuanUyenOne of these students is randomly selected. What is P(ALB)? During the Whiskey Rebellion, what did the rebels do to the farmers and distillers who paid the whiskey tax?A. They tarred and feathered them.B. They burned down their barns.C. They arrested and interrogated them.D. They executed them. helpppppppplwaseeee what other differences do you notice in the selection from the declaration of independence Find the expected value of the winningsfrom a game that has the following payoutprobability distribution:Payout ($) 0 1 3 9 27Probability 0.67 0.22 0.07 0.03 0.01Expected Value = [?]Round to the nearest hundredth.Enter which of the following auditing techniques would be the most appropriate for a retail business with a large volume of transactions to address emerging risk proactively? __________ / __________ psychology is concerned with the relationship between people and their work environments. which salt would you expect to dissolve more readily in acidic solution, strontium phosphate or strontium sulfate? 5 dogs had long hair out of the 8 dogs at the park. What percent of the dogs had long hair? Round your answer to the nearest whole percent. a. intel corporation had assets equal to $65,586 million and liabilities equal to $13,756 million for a recent year-end. what was the total equity for intel's business at year-end? to provide a comparison for evaluating the effects of a specific treatment, experimenters make use of a(n) In Class #15 we talked about two types of advertising message appeals - cognitive and emotional.Which type of messages do you find (a) more memorable and (b) more persuasive? Does it depend on the product category or the advertising medium used? Please illustrate with examples. Which word has the same vowel sound as a bold word? Create an argument to answer the question: What were the priorities for education in the 19th century? Your argument should: clearly state your claim. include evidence from multiple sources. provide explanations for how the evidence supports the claim. use words, phrases, and clauses to create cohesion. create cohesion among claims, counterclaims, reasons, and evidence. establish and maintain a formal style. produce a concluding statement or section that follows from and supports your argument. Which organelle stores water, sugar, and waste products in plant cells?vacuolesthe cell wallchloroplastsribosomes QUESTION 40.5 poLead contamination has been found in some brands of calcium supplements.O True.O False. Questions1. What is tempo?A.B.C.D.2. What dynamics were used?A..C.D.3. What is the texture?A.B.C.D.4. Describe the melody.A.B.C.D.5. Is this music familiar to you? Where did you first hear it?..C.D. Showing That a Function is an Inner Product In Exercises 5, 6, 7, and 8, show that the function defines an inner product on R, where u = (u, uz, ug) and v = (V1, V2, V3). 5. (u, v) = 2u1 V1 + 3u202 + U3 V3