How many digits are in the repeating cycle of 1727

39 answers

To find the repeating cycle of the decimal representation of 1727, we can divide 1 by 1727:

1 ÷ 1727 = 0.00057907...

The decimal representation of 1 divided by 1727 is a non-repeating decimal, and therefore does not have a repeating cycle.
How many digits are in the repeating cycle of 17/27
To find the repeating cycle of the fraction 17/27, we can perform long division:

____0. (no repeating part here)
27 | 17. (decimal part starts here)
-16
10
- 9
1

The decimal representation of 17/27 is approximately 0.629629629..., where the digits 6, 2, and 9 form the repeating cycle. Thus, the repeating cycle of 17/27 contains 3 digits.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses

by putting them in parentheses
by putting them in parentheses

by printing them in italics
by printing them in italics

by putting a bar over them
by putting a bar over them

by underlining them
The correct answer is:

by putting a bar over them
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
Responses

any finite length
any finite length

infinitely long
infinitely long

up to six digits long
up to six digits long

up to seven digits long
If the denominator of a rational number is 7, then the repeating cycle of the corresponding repeating decimal can be up to six digits long.

This is because when we divide a number by 7, the remainder can be any number from 0 to 6. So, the repeating cycle can consist of at most six different digits.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can set it up as an algebraic equation.

Let x = 0.27¯¯¯¯¯.

We can multiply both sides of the equation by 100 to eliminate the repeating decimal:

100x = 27.¯¯¯¯¯

Next, we can subtract the original equation from the multiplied equation:

100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯

This simplifies to:

99x = 27

Now we can solve for x:

x = 27/99

To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:

x = (27/9) / (99/9)
x = 3/11

Therefore, the rational number equivalent to the repeating decimal 0.27¯¯¯¯¯ in simplest form is 3/11.
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000.

Multiplying both sides of the equation by 1000 would eliminate the repeating decimal, as it would shift the decimal point three places to the right. This is because there are three digits repeating in the decimal part.
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
Responses

10
10

100
100

1,000
1,000

999
999
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 100.

Multiplying both sides of the equation by 100 would eliminate the repeating decimal, as it would shift the decimal point two places to the right. This is because there are two digits repeating in the decimal part.
What is the largest integer whose square root is an irrational number between 3 and 4?
The largest integer whose square root is an irrational number between 3 and 4 is 3.

If we calculate the square root of 3, it is approximately 1.73205080757, which is an irrational number. However, if we calculate the square root of 4, it is exactly 2, which is a rational number. Therefore, 3 is the largest integer whose square root falls within the given range and is an irrational number.
Show an example of an irrational number between 9 and 11.(1 point)
Responses

100−−−√
start root 100 end root

99−−√
start root 99 end root

20−−√
start root 20 end root

10−−√
An example of an irrational number between 9 and 11 is √10 (square root of 10).
The square root of 10 is approximately 3.16227766017, which is an irrational number.
Why did colonists oppose writs of assistance?
(1 point)
Responses

They thought it limited their access to land.
They thought it limited their access to land.

They thought it violated their rights.
They thought it violated their rights.

They thought it unfairly taxed goods and services they produced.
They thought it unfairly taxed goods and services they produced.

They thought it gave Native Americans an advantage over trade.
The correct answer is:

They thought it violated their rights.

Colonists opposed writs of assistance because they believed it violated their rights, particularly their right to privacy and protection against unreasonable searches and seizures. Writs of assistance were general search warrants that allowed British officials to search any location at any time without specifically stating what they were searching for. This practice was seen as a violation of individual liberties and a threat to their personal property and belongings.
Why did the British want to expand control into the Ohio Valley in the mid-1700s?
(1 point)
Responses

to force the French out of North America
to force the French out of North America

to put French settlers there under English rule
to put French settlers there under English rule

to demonstrate Britain’s strength to France and Spain
to demonstrate Britain’s strength to France and Spain

to gain access to the region’s natural resources
The correct answer is:

to gain access to the region’s natural resources.

The British wanted to expand control into the Ohio Valley in the mid-1700s because they saw it as a valuable territory with abundant natural resources. They sought to exploit these resources for economic gain, including valuable fur trade and potential agricultural opportunities. Control over the Ohio Valley would also allow the British to expand their influence and trade routes in North America, as well as establish dominance over French and Native American populations already present in the region.
What was the significance of the battle at Fort Necessity?
(1 point)
Responses

British defeated the French and went on to claim Fort Duquesne.
British defeated the French and went on to claim Fort Duquesne.

The battle ended the French and Indian War.
The battle ended the French and Indian War.

The battle ended in a stalemate but with heavy losses on both sides.
The battle ended in a stalemate but with heavy losses on both sides.

It was one of the first battles of the French and Indian War.
The correct answer is:

It was one of the first battles of the French and Indian War.

The battle at Fort Necessity was one of the initial engagements of the French and Indian War. It took place in 1754 at Fort Necessity, which was located in present-day Pennsylvania. The conflict arose from territorial disputes between the French and British forces in the Ohio River Valley. In this battle, the inexperienced British forces, led by a young George Washington, were defeated by the French and their Native American allies. The significance of this battle lies in the fact that it marked the beginning of a long and costly war between the British and French in North America.
Why did the Algonquins become allies with the French? Select all that apply.
(1 point)
Responses

They were afraid that the French would take their land.
They were afraid that the French would take their land.

They wanted to maintain their strong fur trading relationship.
They wanted to maintain their strong fur trading relationship.

They wanted to help the French secure land east of the Mississippi.
They wanted to help the French secure land east of the Mississippi.

The French respected Native American land and did not destroy their hunting grounds.
The French respected Native American land and did not destroy their hunting grounds.
The correct answers are:

- They wanted to maintain their strong fur trading relationship.
- The French respected Native American land and did not destroy their hunting grounds.

The Algonquins became allies with the French primarily because they wanted to maintain their strong fur trading relationship. The French had established a profitable fur trade network in North America, and the Algonquins benefited from this economic relationship.

Additionally, the French respected Native American land and did not destroy their hunting grounds. Unlike some other European powers, the French had a more cooperative and respectful approach towards Native American tribes. This approach appealed to many Native American groups, including the Algonquins, who saw the French as potential allies in protecting their land and way of life.
In the text you read this about the aftermath of the Boston Massacre: The soldiers were arrested and tried in court. John Adams agreed to defend them, saying that they deserved a fair trial. He wanted to show the world that the colonists believed in justice, even if the British government did not. At the trial, Adams argued that the crowd had provoked the soldiers. His arguments convinced the jury. In the end, the heaviest punishment any soldier received was a branding on the hand.
Question
Use the excerpt to answer the question.
How could John Adams defend the British soldiers but still be seen as a Patriot?
(1 point)
Responses

Adams knew that many Patriots wanted the British soldiers to be set free.
Adams knew that many Patriots wanted the British soldiers to be set free.

Adams defended the soldiers because many Patriots asked him to.
Adams defended the soldiers because many Patriots asked him to.

Adams defended the soldiers while defending the Patriots' belief in justice.
Adams defended the soldiers while defending the Patriots' belief in justice.

Adams defended the soldiers because he thought it would make the British pity the Patriot cause.
Adams defended the soldiers because he thought it would make the British pity the Patriot cause.
The correct answer is:

Adams defended the soldiers while defending the Patriots' belief in justice.

John Adams defended the British soldiers in court because he believed in the principles of justice and wanted to show the world, including the British government, that the colonists upheld these principles. By providing the soldiers with a fair trial and arguing that the crowd had provoked them, Adams ensured that justice was served. This act demonstrated the Patriots' commitment to justice and the rule of law, even in the face of a tense and volatile situation with the British government. Defending the soldiers did not mean Adams was siding with the British, but rather that he was upholding the principles of justice for all parties involved.
“Our Colonies must be the biggest Beggars in the World, if such small Duties appear to be intolerable Burdens in their Eyes.”

—“Pacificus,” Maryland Gazette, March 20, 1766
Question
Use the excerpt to answer the question.
This excerpt is from a citizen in England in response to the colonial outrage toward the Stamp Act. What central argument of the American colonists against the Stamp Act is not understood by the writer?
(1 point)
Responses

that trade was heavily restricted due to the taxes, which made it difficult for the colonists to make enough money to live let alone pay the taxes
that trade was heavily restricted due to the taxes, which made it difficult for the colonists to make enough money to live let alone pay the taxes

that although the tax is small, it is the idea that the colonists have to repay the British government for a war they did not support that is unjust
that although the tax is small, it is the idea that the colonists have to repay the British government for a war they did not support that is unjust

that it is not the amount of tax that is the problem but rather the fact that the colonists were not involved in passing the tax
that it is not the amount of tax that is the problem but rather the fact that the colonists were not involved in passing the tax

that the tax may seem small to those in England but for the American colonists it is a very large amount of money
The correct answer is:

that it is not the amount of tax that is the problem but rather the fact that the colonists were not involved in passing the tax.

The central argument of the American colonists against the Stamp Act that is not understood by the writer is that it is not the amount of tax that is the problem. Instead, the colonists were primarily concerned with the lack of representation and their inability to have a say in the passage of taxes that affected them. The colonists believed in the principle of "no taxation without representation" and felt that they should have a voice in the decisions that affected their lives and livelihoods. The excerpt reflects a misunderstanding or skepticism regarding this argument and instead focuses on the perceived smallness of the tax burden.
Why did the British feel justified imposing the Stamp Act on the colonists? Select all that apply.
(1 point)
Responses

British citizens living in England faced increased taxes due to wars in the colonies.
British citizens living in England faced increased taxes due to wars in the colonies.

The taxes protected colonists living in the Ohio River valley from Native Americans.
The taxes protected colonists living in the Ohio River valley from Native Americans.

Britain had spent money protecting colonists from the French.
Britain had spent money protecting colonists from the French.

The taxes were being used to raise money for more supplies for the colonists.
The correct answers are:

- British citizens living in England faced increased taxes due to wars in the colonies.
- Britain had spent money protecting colonists from the French.

The British felt justified imposing the Stamp Act on the colonists because British citizens living in England faced increased taxes due to wars fought in the colonies. The British government needed to raise revenue to cover the expenses incurred in defending and protecting the colonies, and imposing taxes on the colonists was seen as a means to achieve this. Additionally, Britain had spent significant amounts of money protecting the colonists from French threats and believed that the colonists should contribute to the costs of their own defense.
What was the purpose of the Olive Branch Petition?
(1 point)
Responses

to declare war on England
to declare war on England

to raise a colonial army
to raise a colonial army

to declare allegiance to the King of England
to declare allegiance to the King of England

to convince France to enter the war
The purpose of the Olive Branch Petition was to declare allegiance to the King of England.

The Olive Branch Petition was a final attempt by the colonists to avoid a full-blown armed conflict with England during the American Revolutionary War. It was sent to King George III in July 1775 and expressed the colonists' desire for peace and a return to their previous harmonious relationship with Britain. The petition declared the colonists' allegiance to the king and sought a peaceful resolution of their grievances. However, the olive branch was rejected by the king, and shortly after, the Declaration of Independence was drafted, leading to the formal separation of the American colonies from Britain.
What was the purpose of the Olive Branch Petition?
(1 point)
Responses

to declare war on England
to declare war on England

to raise a colonial army
to raise a colonial army

to declare allegiance to the King of England
to declare allegiance to the King of England

to convince France to enter the war
The purpose of the Olive Branch Petition was to convince King George III of England to negotiate a peaceful resolution to the conflicts with the American colonies. It was not to declare war on England, raise a colonial army, or to convince France to enter the war. Instead, it aimed to affirm the colonists' loyalty to the British crown and express their desire for a peaceful settlement of their grievances.
Why were colonial minutemen so prepared for the arrival of the British in Concord? Select all that apply.
(1 point)
Responses

When Washington saw the British, he fired three canon shots sending a warning signal.
When Washington saw the British, he fired three canon shots sending a warning signal.

Paul Revere had warned villages that the redcoats were coming.
Paul Revere had warned villages that the redcoats were coming.

The Green Mountain Boys hid in the bushes and warned the Continental Army.
The Green Mountain Boys hid in the bushes and warned the Continental Army.

When the British headed out, Americans hung two lamps as a warning signal.
The correct answers are:

- Paul Revere had warned villages that the redcoats were coming.
- The Green Mountain Boys hid in the bushes and warned the Continental Army.

The colonial minutemen in Concord were so prepared for the arrival of the British because they had received prior warnings. Paul Revere famously rode through the countryside warning the villagers that the British troops were approaching. This allowed the local militias and minutemen to get prepared for the impending conflict. Additionally, the Green Mountain Boys, a militia group from Vermont, had positioned themselves in the area and were able to observe the British movements. They provided valuable intelligence and warnings to the Continental Army, contributing to their preparedness for the confrontation.
How did Washington gain control of Boston?
(1 point)
Responses

He sent 16,000 troops to launch a surprise attack on the British fort protecting Boston.
He sent 16,000 troops to launch a surprise attack on the British fort protecting Boston.

He surrounded the harbor, giving them no option other than to surrender.
He surrounded the harbor, giving them no option other than to surrender.

He strategically placed cannons overlooking the harbor which forced out the British.
He strategically placed cannons overlooking the harbor which forced out the British.

He gained the trust of Native Americans who led a deadly attack on the British.
The correct answer is:

He strategically placed cannons overlooking the harbor which forced out the British.

George Washington gained control of Boston by placing cannons on Dorchester Heights overlooking the harbor. This strategic move compelled the British forces to evacuate the city. Recognizing the vulnerability of their position and the threat posed by the American cannons, the British made the decision to retreat from Boston rather than engage in a potentially costly conflict. This action effectively gave Washington and the Continental Army control of the city.