How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?
The repeating cycle of a decimal with denominator 7 can have at most 6 digits.
This is because when we divide any number by 7, the remainder can only range from 0 to 6 (since 7 divides evenly into 7 once with a remainder of 0).
So, when we have a fraction with denominator 7, the decimal representation will repeat at most every 6 digits.
Convert 0.27¯¯¯¯¯ to a rational number in simplest form
To convert the recurring decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we let x = 0.27¯¯¯¯¯ and then subtract the non-recurring part of the decimal to eliminate the repetition.
Let's multiply both sides of the equation x = 0.27¯¯¯¯¯ by 100 to shift the decimal point two spots to the right:
100x = 27.27¯¯¯¯¯
Now, let's subtract the original equation from the new one:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯
This simplifies to:
99x = 27 (since the recurring parts cancel out: 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯ = 27)
Now, to get x by itself, we divide both sides of the equation by 99:
x = 27/99
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (27 ÷ 9) / (99 ÷ 9)
x = 3/11
Therefore, 0.27¯¯¯¯¯ is equal to the rational number 3/11 in simplest form.
Which of the following is the role of supporting details in a text?
The role of supporting details in a text is to provide evidence or examples that strengthen or clarify the main ideas or claims being made. Supporting details help to support the main points of the text and provide additional information or explanation to ensure that the reader understands the author's message or argument. These details may include facts, statistics, anecdotes, examples, or expert opinions that help to reinforce the main ideas and make the text more informative and persuasive.
Use the paragraph to answer the question.
One impressive cave system is the lava tube caves of Lava Beds National Monument. The caves provide a safe habitat for millions of bats. In order to visit the caves, visitors must first be screened for white-nose syndrome. It is a disease that is fatal to bats.
Which option best identifies the central idea of the paragraph?
The central idea of the paragraph is the lava tube caves of Lava Beds National Monument and their importance as a safe habitat for millions of bats, while also highlighting the need to screen visitors for white-nose syndrome, a disease that is fatal to bats.
When you tell the most important part of a text, what are you identifying?
When you identify the most important part of a text, you are typically identifying the main idea or central idea of the text. This is the overriding theme or message that the author is trying to convey to the reader. The main idea encapsulates the primary focus or purpose of the text and serves as a guide for understanding the supporting details and arguments presented by the author.
Use the paragraph to answer the question.
About 1.5 million species of fungi exist on Earth. They act as nature’s decomposers. These organisms break down matter and release enzymes and acids that unlock nutrients for plants and soil organisms. You may be familiar with macrofungi, a type of fungus that includes mushrooms. But for the most part, fungi exist as mycelia, tiny threads that snake underground in billions of interconnected threads. They twist and twine with tree root systems, helping tress obtain crucial nutrients. Mycologists call these networks of mycelia "Earth’s nervous system."
Which statement best identifies the central idea of the paragraph?
The central idea of the paragraph is the importance of fungi as nature's decomposers and their role in unlocking nutrients for plants and soil organisms, as well as their symbiotic relationship with trees through mycelia networks.
When writing a summary, what does it mean to be objective?
To be objective in writing a summary means to present information or content in an unbiased and neutral manner, without personal opinions or subjective interpretations. An objective summary focuses solely on the facts, main points, and key details of the text, avoiding any personal bias or emotional response. It accurately represents the original text's content without introducing any personal judgments or perspectives. The goal of an objective summary is to provide an impartial overview of the text's main ideas, allowing readers to form their own opinions based on the presented information.
Use the paragraph to answer the question.
The platypus is an Australian mammal that does not fall neatly into a classification. It is one of only two mammals (the other being the echidna) that bear young by laying eggs. In some respects, the platypus resembles a duck; both have webbed feet and bills. The platypus has a tail like a beaver’s and a furry body similar to an otter’s. Its unusual hybrid of body parts makes it well-suited for its largely aquatic life. The platypus uses its webbed feet to paddle through water, and its tail serves as a kind of rudder for steering. While underwater, the platypus uses its bill to scoop up bits of food, such as insects and shellfish, from the water’s bottom. The platypus also scoops up bits of gravel, which grind up the food, as the platypus is toothless. The platypus stores the food and gravel in its cheeks until it reaches the water’s surface. Once the platypus surfaces, it consumes its meal.
Which idea from the paragraph is important to include in a summary?
An important idea to include in a summary of the paragraph is the unique physical characteristics and adaptations of the platypus that make it well-suited for its aquatic lifestyle. These include its webbed feet for swimming, tail for steering, bill for catching food underwater, and the method of storing and consuming food.
What should summaries always include?
Summaries should always include the most important information from the original text. This includes the main ideas, key points, and crucial details. Summaries should effectively condense the content while retaining the overall meaning and message of the original text. It is important to present the information in a clear, concise, and coherent manner. Additionally, summaries should be written in the writer's own words and should not include personal opinions or interpretations.
Use the paragraph to answer the question.
While the invention of the steamboat is often attributed to American inventor Robert Fulton, credit should really go to John Fitch. Fitch built four steamboats in the late eighteenth century. These boats traveled successfully on lakes and rivers and proved that steam could be used to propel boats. Fitch’s boats included more traditional elements as well, such as paddle wheels and screw propellers. By blending tried and true methods of propulsion with new technology, Fitch created functioning steamboats. He forfeited his place in American memory due not to any mechanical failings, but to financial ones. His production and operating costs were too high to make steam travel economically feasible. As a result, many people have forgotten his role in the invention of the steamboat. It wasn’t until after his death that Robert Fulton created a commercially successful steamboat and became known as “the father of steam navigation.”
Which of the following sentences should be included in a summary of the text?
The sentence that should be included in a summary of the text is: "Fitch built four steamboats in the late eighteenth century, proving that steam could be used to propel boats."
Which of the following made the first villages possible?
I'm sorry, but you haven't provided a list of options. Please provide the options so that I can assist you further.
what made the first villages possible?
The development of agriculture made the first villages possible. When humans transitioned from a nomadic lifestyle to settled agriculture, they began to cultivate crops and raise animals. This allowed for a more reliable food supply and led to the establishment of permanent settlements, which eventually evolved into the first villages. With the ability to grow their own food, people no longer needed to constantly move in search of resources, and they could establish permanent communities where they could live and farm.
A food surplus is a benefit of farming. Which of the following is a food surplus?
(1 point)
Responses
when extra food spoils
when extra food spoils
when people wait in line for food
when people wait in line for food
when families have extra food
when families have extra food
when not enough rain falls to grow food