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Place the following numbers in order from lowest to highest:
⁵⁄₆ ⁷⁄₁₂ 0.8 ¹¹⁄₂₀ ⁹⁄₄
Correct!
Wrong
Wrong
Wrong
Let's break this down step by step:
We have five numbers in different forms: three fractions (⁵⁄₆ ⁷⁄₁₂ ¹¹⁄₂₀), one decimal (0.8), and one improper fraction (⁹⁄₄). To compare them accurately, we need to convert them all to the same form.
First, let's convert 0.8 to a fraction: 0.8 = 8/10 = 4/5 (simplified by dividing both numerator and denominator by 2)
Now we have: ⁵⁄₆ ⁷⁄₁₂ ¹¹⁄₂₀ ⁴⁄₅ and ⁹⁄₄
To compare these fractions, we need a common denominator. Let's find the least common multiple of 6, 12, 20, 5, and 4.
The denominators are: 6, 12, 20, 5, 4
The LCM = 2² × 3 × 5 = 60
Now we can easily compare by looking at the numerators:
Therefore, the order from lowest to highest is: ¹¹⁄₂₀ ⁷⁄₁₂ 0.8 ⁵⁄₆ ⁹⁄₄
Answer (A) is correct.
Answer (B) is incorrect because it places ⁷⁄₁₂ before ¹¹⁄₂₀. When converted to common denominators, ⁷⁄₁₂ = ³⁵⁄₆₀ and ¹¹⁄₂₀ = ³³⁄₆₀. Since 33 < 35, ¹¹⁄₂₀ should come before ⁷⁄₁₂.
Answer (C) is incorrect because it places 0.8 before ⁷⁄₁₂. When converted, 0.8 = ⁴⁸⁄₆₀ and ⁷⁄₁₂ = ³⁵⁄₆₀. Since 35 < 48, ⁷⁄₁₂ should come before 0.8.
Answer (D) is incorrect because it places ⁵⁄₆ before 0.8. When converted, ⁵⁄₆ = ⁵⁰⁄₆₀ and 0.8 = ⁴⁸⁄₆₀. Since 48 < 50, 0.8 should come before ⁵⁄₆.
How frequently, as we navigate our daily routines, do we pause to contemplate the provenance of the quotidian objects that populate our surroundings? Among these indispensable contrivances is the flat-bottomed paper bag, a utility so thoroughly assimilated into contemporary life that its very existence is often taken for granted, yet in the 1860s, its configuration was a concept utterly unheralded.
Margaret Eloise Knight, whose birth in Maine was registered in 1838, found her childhood trajectory abruptly altered following her father’s demise, necessitating a familial relocation to New Hampshire. Consequently, Margaret and her siblings were compelled to truncate their formal education prematurely to seek employment at a local cotton mill. At the precocious age of twelve, Knight bore witness to a catastrophic mill accident wherein a fellow laborer sustained serious injury due to the machinery. Within a fortnight of this harrowing event, she had ingeniously engineered a novel safety apparatus for the mill equipment, a device subsequently adopted by manufacturing concerns throughout the municipality.
In 1867, Knight migrated to Massachusetts and commenced her tenure with the Columbia Paper Bag Company. The ensuing year marked a pivotal achievement: she conceptualized and fabricated a sophisticated machine capable of the automated folding and adhesion of paper to yield the now-familiar flat-bottomed bags. Regrettably, the blueprint for this groundbreaking mechanism was purloined by an individual privy to its construction, who then fraudulently secured the patent under his own name. This brazen act of intellectual property theft threatened to divest Knight of any remunerative royalties accruing from her own ingenuity. Undeterred, she initiated a protracted litigation against the perpetrator and ultimately prevailed, an achievement that cemented her status as the first woman to be formally issued a U.S. patent. Following this landmark victory, she established the Eastern Paper Bag Co. and proceeded to amass a portfolio of eighty-six additional patents, encompassing diverse innovations such as lid-removing pliers, an advanced window frame and sash system, and several specialized components related to rotary engines.
Knight, who remained unmarried throughout her life, passed away in 1914. Posthumously, her contributions were acknowledged by her 2006 induction into the National Inventors Hall of Fame. Notably, several of her inventions, the seminal paper bag foremost among them, remain in widespread and indispensable utilization globally even today.
The text states that Margaret E. Knight's invention was a "contrivance" whose configuration was "unheralded" in the 1860s.
Based on the context of the entire passage, what is the most precise interpretation of the word "unheralded" in this specific sentence?
Wrong
Wrong
Correct!
Wrong
Let's break this down step by step:
The key concepts required to solve this question are:
"...yet in the 1860s, its configuration was a concept utterly unheralded." The passage discusses the flat-bottomed paper bag, an object now common but completely new in the 1860s.
The root word is "herald," which means to announce, proclaim, or signal the arrival of something. Therefore, "unheralded" means "not announced" or "without prior notice or precedent."
The invention being discussed is the flat-bottomed paper bag. If its configuration was "utterly unheralded," it suggests that this specific design was a breakthrough, meaning it hadn't been seen or introduced before. It was a completely new idea.
Answer (A) is incorrect because "unheralded" refers to the concept's lack of prior existence or recognition, not a deliberate action of secrecy by the inventor. The preceding phrase, "completely unheard of," strongly supports the idea of non-existence or novelty, not concealment.
Answer (B) is incorrect because it misinterprets "unheralded" as a comment on the reception or success of the invention. While it may not have been immediately celebrated, the word's primary meaning in this context highlights its newness or unprecedented design, not a lack of public approval.
Answer (C) is correct because it aligns perfectly with the idea that the design was "unheard of" and had no announcement or prior example ("unheralded") in that era. A "novel" design is a new one.
Answer (D) is incorrect because the patenting issue is a legal consequence of the invention's existence, not the definition of its "unheralded" status. An invention is unheralded because it is new, irrespective of whether the patent has been filed yet.
Read the sentence:
Known for her groundbreaking studies in neuroscience, the committee awarded Dr. Ramos the university’s highest research honor.
Which revision corrects the error in sentence structure while keeping the meaning clear and formal?
Wrong
Correct!
Wrong
Wrong
Let's break this down step by step:
“Known for her groundbreaking studies in neuroscience, the committee awarded Dr. Ramos the university’s highest research honor.”
Who did the groundbreaking studies? Dr. Ramos.
Who gave the award? the committee.
A modifier is a word or group of words that gives extra information about something else in a sentence. When that describing part is too far away from the word it’s supposed to describe, or next to the wrong word, the meaning becomes confusing. That’s called a misplaced modifier.
The phrase “Known for her groundbreaking studies in neuroscience” is a description about Dr. Ramos, but in this sentence it’s placed right before the committee.
That makes it sound like the committee did the studies which is not true.
The phrase “Known for her groundbreaking studies in neuroscience” uses the possessive pronoun “her,” so it must describe a female person (Dr. Ramos), not the committee.
But right now, this phrase sits right before the committee, making it sound like the committee is the one known for “her” studies. That doesn’t make sense.
To fix it, place the describing part right beside Dr. Ramos so it clearly connects to her.
Because the phrase “known for her groundbreaking studies in neuroscience” simply adds extra information about Dr. Ramos, something that could be removed without changing the main, it needs two commas around it.
That gives you:
Dr. Ramos, known for her groundbreaking studies in neuroscience, was awarded the university’s highest research honor by the committee.
Therefore, answer (B) is correct.
Answer (A) is incorrect because it still makes it sound like the committee is the one known for its groundbreaking studies in neuroscience. This changes the intended meaning of the sentence. The description was meant to tell us something about Dr. Ramos, not the committee, so the information is attached to the wrong noun. Even though the punctuation is correct, the meaning is inaccurate as the modifier is still misplaced.
Answer (C) is incorrect because it contains a comma splice where two complete sentences are joined only by a comma.
Using just a comma between them is grammatically incorrect. To fix it, the writer could:
Answer (D) is incorrect because, although the description is now placed correctly beside Dr. Ramos, the sentence structure is awkward. The wording “was awarded by the committee the university’s highest research honor” splits the verb and its object in an unnatural way, making the sentence sound disjointed and informal.
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