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The operation $$\diamond$$ is defined by $$x \diamond y=3x+5y$$ for all positive integers $$x$$ and $$y$$. If $$a$$ and $$b$$ are positive integers and $$a \diamond b=b \diamond a$$, what is the ratio of a to $$b$$?
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The effects of sea-level rise that followed the last ice age were not _____________ since they were dependent on local and regional tectonic and other geological effects.
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Archaeologists agree that corn agriculture, first developed by Native American peoples of what is now Mexico, was adopted by Native Americans of what is now the southwestern United States during the Late Archaic period, but the extent of these Late Archaic peoples' dependence on corn agriculture is debated. Some archaeologists infer from the presence of houses storage pits, and large quantities of corn kernels at Late Archaic sites that the inhabitants, once nomadic hunter gatherers, had become settled farmers who, although they lacked the ceramic vessel-making technology typically associated with agriculture, grew and depended on corn. But other evidence strongly suggests that while Late Archaic people grew considerable quantities of corn, it was not their dietary mainstay. Food-processing equipment found at the sites indicates that Late Archaic people continued to rely heavily on wild plant foods. Corn is not a particularly nutritious food. People whose diets are heavily dependent on corn today soak it in limewater and grind it to prepare mush, processes that increase corn's nutritional value; these steps would have been difficult to accomplish without ceramic vessels.
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The passage suggests that prior to the Late Archaic period, southwestern Native Americans
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The author of the passage mentions the nutritional value of corn primarily in order to
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In his history of algebra, John Derbyshire asserts that when Descartes chose the letter X to represent the principal unknown, he did so for the printer' s convenience, because X is used less often in French than Y or Z. In fact, according to cryptography texts, X is used more often than Y in French. Derbyshire's source for his assertion is Classic Math, whose author, Art Johnson, gives no footnote for the claim but who may have misunderstood a conjecture made in 1905 - almost 300 years after Descartes - by Gustav Eneström and mentioned in a book included in Johnson' s Bibliography. Eneström supposed that X was chosen because it occurs more often than Y and Z, and printers therefore would have had more X's available.
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It can be inferred that the author of the passage would agree with which of the following statements about the relationship between Eneström's conjecture and Derbyshire?
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The highlighted text serves primarily to
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The fact that certain musical qualities were shared by African American and White jazz musicians in the mid-1950s was sometimes explained by claiming that jazz was "color-blind." Yet a look at how the discourse of color blindness was deployed in 1950s jazz periodicals helps explain why many African American jazz musicians began to emphasize differences, rather than similarities, between the aesthetic styles of Black and White Musicians. The discourse of “color blindness" tended to exaggerate the permeability of racial boundaries by failing to address the power relationships involved in a social climate where evasiveness about race was often used to silence African American perspectives on the meaning of jazz. While the expression of color-blind sentiments was not necessarily disingenuous, structural racial stratification remained powerful beyond the bandstand.
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The passage suggests that some authors writing in 1950s jazz periodicals
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The author mentions "power relationships” primarily to
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It's hard to envision jazz flourishing without Thomas Edison' s roughly contemporaneous invention of sound recording technology, which enabled the preservation and dissemination of the genre's hallmark musical improvisations for the first time in history. But the same technology also significantly altered jazz's evolution. Before the rise of jazz, African American composers worked extensively with more complex forms. Most of Scott Joplin's ragtime pieces included four sections, each with a distinctive melody and chords, and many early jazz musicians continued in this vein. But early recordings, which limited songs to three minutes, could rarely accommodate such structures and still leave time for improvised solos. With a few exceptions, such as Duke Ellington, most jazz musicians embraced simpler tunes once they began recording their work.
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The function of the highlighted sentence is primarily to
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The passage suggests that Duke Ellington' s early recorded jazz works
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Geologists can determine the ages of rocks and fossils by using natural clocks, including the natural decay of unstable, radioactive atoms into stable forms. The element uranium occurs in minute concentrations in seawater, and certain types of organisms, particularly corals, absorb it as they grow. One isotope of uranium, 238U, decays through a series of steps to 230Th, an isotope of thorium. As a coral grows, it adds tiny amounts of 238U to its skeleton. Over time, this 238U steadily transforms into 230Th. The proportion of the two isotopes changes in a predictable way over time, allowing us to calculate the ages of fossil corals in marine terraces back as far as five hundred thousand years.
A drawback of uranium-thorium dating is that it doesn't work on most fossils. Shells of molluscs like clams and snails are common in marine terrace deposits, but molluscs don't take up uranium from Seawater. Here, though, we have another trick: amino acid racemization. The proteins of living creatures contain amino acids in a specific molecular shape known as the L-configuration. Upon death, some of these amino acids begin shape-shifting to a new arrangement called the D-configuration-a process called racemization. Molluscs are particularly useful for amino acid dating because they live practically everywhere in shallow ocean habitats and because their shells are bound together with matrixes of amino acid-rich proteins. By measuring the ratio of the two types of amino acids in mollusc shell proteins, we can estimate the time since death.
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The author of the passage would most likely agree with which of the following statements about 238U?
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The highlighted sentence serves primarily to
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The passage implies which of the following about differences between fossil molluscs and fossil corals?
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