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$$x^2 = (x-1)^2$$

Quantity A

$$x$$

Quantity B

$$\frac{1}{4}$$




The circle is inscribed in the square.

Quantity A

The ratio of the area of the circular region to the area of the square region

Quantity B

$$\frac{3}{4}$$




Quantity A

The sum of the distances $$PQ$$ and $$RS$$

Quantity B

$$3x$$


A class of $$20$$ students is divided into $$4$$ groups, and each group has at least $$3$$ students. Which of the following statements must be true?
Indicate all such statements.
$$\frac{1}{5} \lt x \lt \frac{2}{5}$$
$$\frac{2}{5} \lt y \lt \frac{4}{5}$$
Which of the following could be the value of $$\frac{x}{y}$$?
For which of the five zoos was the ratio of the annual budget to the annual attendance the least in 2003?
The current number of acres at Zoo $$D$$ is approximately what percent less than what the total number of acres will be after the zoo completes its planned acquisition?
$$c\times10^k + d\times10^{(k+1)}=$$
Due to the importance they accorded roads, railways, rivers, and bridges, the French Impressionist painters were able to create a new iconography of landscape for the industrial age. Most contemporaries saw nothing in these paintings but trivial subjects and retained only the visual shock of the Impressionists' completely new technique and style. The Impressionist canvases were, however, much more complex than their apparent simplicity indicated: Impressionist landscapes balanced traditional images of France with elements representing industrial progress and thereby introduced modernity into painting. While retaining a part of the heritage they had received from their artistic predecessors, who had painted virgin forests and quaint old mills and farms, the Impressionists did not hesitate to place these traditional motifs next to factories and other signs of modernity in order to give as complete a vision as possible of their land. In their own way they were helping to celebrate the reconstruction of France that followed the Franco-Prussian War.
Which of the following does the passage imply about the nineteenth-century reaction to French Impressionist landscape paintings?
The passage suggests which of the following about French Impressionist painters of landscapes?(Consider each of the choices separately and select all that apply.)
In the context in which it appears "retained" most nearly means
The meteorite Monahans 1998 is an ordinary chondrite, a class of meteorites that astronomers have believed contain little or no water. But Monahans 1998 contains water locked inside salt crystals that date from the solar system's formation. The water is presumed to be of the same vintage-the first time that water of primordial origin has been detected. The water could have come from a water- rich comet that plowed into the meteorite's parent asteroid after its formation. But if the water was incorporated into the asteroid as it first coalesced, scientists may have to revise their thinking about conditions at the solar system's formation under which chondrites formed. To carry a concentrated salt solution today, Monahans 1998 must have once been in contact with several times more water than what now remains.
The passage mentions the concentration of the salt solution in Monahans 1998 primarily in order to
Which of the following can be inferred about the explanation offered in the highlighted sentence?
From a purely evolutionary standpoint, pet keeping is an anomalous activity. It is easy to explain, for example, why people keep chickens, pigs, or sheep: these animals are worth at least their own weight in eggs, meat, hide, or fiber. But what could possibly be the adaptive value of keeping Siamese cats or miniature schnauzers? A common response to this evolutionary puzzle, and one that keeps being regurgitated in the literature, is the idea that pets are simply social parasites who have perfected the art of releasing and exploiting our innate parental instincts-called "cute response." Parallels are sometimes drawn with the phenomenon of brood parasitism in birds, in which the parasite' s nestling seems to exaggerate many of the care-soliciting aspects of the host' s, thus insuring that it is fed assiduously to the detriment of its foster parents and siblings. The superficially infantile appearance of some lapdogs lends support to this idea, but it should be emphasized that a key difference between people and songbirds is that the latter are presumably unaware that they are feeding and caring for a nonconspecific intruder. People may indeed find puppies or pug dogs cute, but they are certainly never in any doubt concerning their true provenance.
The author mentions the "infantile appearance of some lapdogs" primarily in order to
The author mentions a "key difference" primarily in order to
It can be inferred that the author would be most likely to agree with which of the following claims about pet keeping?

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