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Ready4	<p style="text-align: center;">p><p>In the triangle above, does $a^{2}+b^{2}=c^{2}$ ?p> <p>(1) $a=b$ p> <p>(2) $x=47$ p>
Ready4	<p style="text-align: center;">p><p>In the figure shown, $w=90$ . Are lines $n$ and $<font color='#FE8080'>p</font>$ parallel?p> <p>(1) $x=w$ p> <p>(2) $y=180-z$ p>
	While the most abundant and dominant species within a particular ecosystem is often crucial in perpetuating the ecosystem, a "keystone" species, here defined as one whose effects are much larger than would be predicted from its abundance, can also play a vital role. But because complex species interactions may be involved, identifying a keystone species by removing the species and observing changes in the ecosystem is problematic. It might seem that certain traits would clearly define a species as a keystone species; for example, Pisaster ochraceus is often a keystone predator because it consumes and suppresses mussel populations, which in the absence of this starfish can be a dominant species. But such predation on a dominant or potentially dominant species occurs in systems that do as well as in systems that do not have species that play keystone roles. Moreover, whereas P. ochraceus occupies an unambiguous keystone role on wave-exposed rocky headlands, in more wave-sheltered habitats the impact of P. ochraceus predation is weak or nonexistent, and at certain sites sand burial is responsible for eliminating mussels. Keystone status appears to depend on context, whether of particular geography or of such factors as community diversity (for example, a reduction in species diversity may thrust more of the remaining species into keystone roles) and length of species interaction (since newly arrived species in particular may dramatically affect ecosystems).
Ready4	<p style="text-align: center;">p><p>Is the triangle above a right triangle?p> <p>(1) In an $xy$ -plane, $L$ and $N$ have the same $y$ -coordinates.p> <p>(2) In an $xy$ -plane, $M$ has coordinates $(-1,6)$ .p>
	In most earthquakes the Earth's crust cracks like porcelain, Stress builds up until a fracture forms at a line depth of a few kilometers and the crust slips to relieve the stress. Some earthquakes, however, take place hundreds of kilometers down in the Earth's mantle, where high pressure makes rock so ductile that it flows instead of cracking, even under stress severe enough to deform it like [hl:6]putty[/hl:6]. How can there be earthquakes at such depths?That such deep events do occur has been accepted only since 1927. when the seismologist Kiyoo Wadati convincingly demonstrated their existence. Instead of comparing the arrival times of seismic waves at different locations, as earlier researchers had done, Wadati relied on a time difference between the arrival of primary(P) waves and the slower secondary(S) waves. Because P and S waves travel at different but fairly constant speeds, the interval between their arrivals increases in proportion to the distance from the earthquake focus, or initial rupture point.For most earthquakes, Wadati discovered, the interval was quite short near the epicenter; the point on the surface where shaking is strongest. For a few events, however, the delay was long even at the epicenter. Wadati saw a similar pattern when he analyzed data on the intensity of shaking. Most earthquakes had a small area of intense shaking, which weakened rapidly with increasing distance from the epicenter. but others were characterized by a lower peak intensity, felt over a broader area. Both the P-S intervals and the intensity patterns suggested two kinds of earthquakes: the more common shallow events, in which the focus lay just under the epicenter, and deep events, with a focus several hundred kilometers down.The question remained: how can such quakes occur, given that mantle rock at a depth of more than 50 kilometers is too ductile to store enough stress to fracture? Wadati's work suggested that deep events occur in areas (now called Wadati-Benioff zones) where one crustal plate is forced under another and descends into the mantle. The descending rock is substantially cooler than the surrounding mantle and hence is less ductile and much more liable to fracture.
Ready4	<p style="text-align: center;">p><p>In the $xy$ -plane shown, the shaded region consists of all points that lie above the graph of $y=x^2+8x$ and below the $x$ -axis. Does the point $(s,t)$ (not shown) lie in the shaded region if $t < 0$ ?p> <p>(1) $t=s^2+8s$ p> <p>(2) $-8 < s < 0$ p>
	A computer generates paths along the vertices of the parallelogram above. It moves in such a way that its path always consists of a side, a diagonal, and then a side and it never ends at the same vertex it begins with, i.e., PQ → QOS → SR. For each vertex on a path, the computer generates a random number. The sum of the numbers on one diagonal is equal to the sum on the other. For a given path, what is the number generated for vertex P?1. The sum of Q and R is always 15 and S carries number 4.2. The intersection of the diagonals, O,carries number 2.
Ready4	<p style="text-align: center;">p><p>In the $xy$ -plane shown, the shaded region consists of all points that lie below the graph of $y=6x-x^2$ and above the $x$ -axis. Does the point $(h,k)$ (not shown) lie in the shaded region if $k > 0$ ?p> <p>(1) $h=3$ p> <p>(2) $k > 6h-h^2$ p>
Ready4	<p class="ng-scope"> A myth in the ongoing debate about minimum wages is that raising minimum wages will necessarily increase a country's unemployment rate. While there are cases in which a marginal increase in wage rates might impact the operations of a company dramatically enough for the company to change its operations, in most companies, the cost increases of higher wages will tend to affect a company's bottom line without altering its staffing structure. For example, if a particular fast-food location operates at a particular time window with a staff of five people, then five must be the minimum staffing level for that business to achieve optimal results. In the case of a national fast-food chain, especially, these operational questions in general will already have been optimized. Even before rates are raised, managers of these locations have asked themselves whether they can afford to cut jobs and whether they are staffed at optimal levels (in this case, five people). A more specific calculation is needed. In this example, the precise question is how a marginal increase in staffing costs would compare to the decrease in business that would result in decreasing the staff level from five to four and serving food less quickly. The results of this analysis would not necessarily be consistent across industries, or even across markets and companies within an industry. p>
Ready4	<p class="ng-scope"> The works of two nineteenth century thinkers promote conflicting theories of the locus of responsibility for the course of historical events. Thomas Carlyle, in his 1841 treatise On Heroes, Hero-Worship, and the Heroic in History, places little emphasis on the events or conditions that produce major figures or the environments that allow them to rise to prominence. Instead, Carlyle posits that the extraordinary charisma, intelligence, wisdom, or political skill of individual “great” figures, invariably men, are the primary means by which social progress is effected. Herbert Spencer (1820–1903), though, writes not only that social environments are responsible for any great figures societies produce, but that Carlyle's approach is puerile and “unscientific” in the vein of many popular sociological works of the era. Although both thinkers promote a theory attempting to isolate the “mechanisms” of history vis-à-vis individual figures, only Spencer's has survived recent criticism largely intact. He emphasizes the lesser-understood contingencies of progress that comprise the immense majority of sociohistorical phenomena. He concludes that while major figures often take credit for the causal chain of significant events, the individuals themselves are less directly responsible for them than is commonly believed. This generality demonstrates how Spencer laid the foundation for twentieth-century historical scholarship, which holds to the belief that historical events, even those led by “heroes,” follow from multitudinous and sometimes untraceable social preconditions.p>
Ready4 OG2022	<p>p> <p>In the figure above, points A, B, C, D, E, and F lie on a line perpendicular to the square's sides. If point A lies on the square, point B lies on the circle, point C bisects AF, point D is the center of the circle, point E bisects DF, and point F lies on the circle and on the square, what is the difference in area between the square and the circle?p> $A B = 6$ and $B C = 4$ . $A B = 6$ and $E F = 3.5$ .
Ready4	<p class="ng-scope"> Two historians of the First World War both depict women as taking up roles previously reserved for men, but they differ slightly in the significance they ascribe to these unprecedented but temporary wartime duties. Gail Braybon describes the war as a liberating experience for many women. Although women working in munitions factories were subject to new dangers, such as explosions and trinitrotoluene poisoning, they were mindful of and proud of supporting the war effort, whether or not they considered the broader significance of their actions. Joshua Goldstein too describes a sense of freedom in women but emphasizes that it was short-lived. Although the war bent gender roles, it did not lessen hostility to women in traditionally male jobs, increase compensation for female labor, or uproot the notion that home life was a strictly female responsibility. Braybon might reply by noting that, while other changes were slower in coming, some women suffragists supported the war and women's role in it to further their cause, and this may indeed have contributed to the advent of women's right to vote after the war, even by Goldstein's account. Perhaps more central to Braybon's position is that the liberation that women experienced during the war was one of sentiment and therefore made no less real by the lack of accompanying widespread reform. Furthermore, even though the spirit of liberation must have faded with the end of the war, it might have lived on in a latent form and ultimately contributed to the formation of the women's movement. p>
Ready4	<p class="ng-scope"> One strain of historical thought that achieved popularity in the 1950s forwarded the notion that immigration - more than the frontier experience, or any other specific event or factor - had been and continued to be the defining element of United States history. In this depiction, the 30 million immigrants who entered the country between 1820 and 1900 had common experiences regardless of their national, religion, or race: namely, in experiencing hardship and alienation, they themselves changed, but they also carried on the development of the nation itself. Both casual and formal students of history should, however, be careful in equating the experiences of different groups of immigrants, especially under the somewhat blurring concept of "hardship." The description that all immigrants experienced hardship and immigration fails to account properly for the fact that in the 17th and 18th century millions of Africans were forcibly shipped to the United States and sold into slavery. While this group of people should not be excluded from any full reckoning of the nation's migrants, its alienation and hardship was of a substantially different character from that of the other populations, who migrated more willingly and independently and who arrived under and lived in vastly different conditions. If it is, indeed, the degree of hardship and alienation experienced by the different groups of our nation's migrants that have above all shaped both themselves and their nation, then to ignore these distinctions would be to distort an important element of what our nation has been shaped to be. p>
Ready4	<p class="ng-scope" zoompage-fontsize="14"> Among the axioms mistaken for fact by the revenue managers of most airlines is the idea that changes in fuel prices affect all competitors in a given market equally. In fact, prices—and therefore profits—fluctuate unpredictably, offering competitive advantages for some airlines and disadvantages for others. For example, a more well-established airline with an aging fleet will experience lower fuel efficiency per mile than a newer company that has invested in the latest technology, meaning fuel represents a larger percentage of the established airline's operating costs. Moreover, airlines that negotiate and lock in fuel prices with suppliers in advance enjoy stabilized expenses and efficient planning; at the same time, they may lose cost savings when market rates drop unexpectedly during the contract period. In addition, the advantages of low fuel prices are greater for those airlines whose business models focus on minimizing costs than for those with high operating budgets and higher prices for consumers. Carriers with highly efficient logistics and operations, for example, may find that falling fuel costs allow them to profitably fly routes that were previously not cost-effective, such as short routes between small cities, generating low profit margins but also increasing the size of their markets. By understanding that they have multiple options and that not all airlines experience the same effects of the volatile fuel market, airline revenue managers can offer their companies an optimized operating strategy by familiarizing themselves with the fuel market and adapting their fuel procurement plans to their business models.p>
Ready4	<p class="ng-scope"> Researchers have attempted to explain the withdrawal of many healthy adult men from the American workforce through traditional economics frameworks, such as overseas competition and increased automation of traditional blue-collar jobs, which are often cheaper options for companies looking to save money on labor. However, detailed investigation indicates that increased offshoring and automation fail to fully explain this drop in labor participation. Instead, this investigation yields data that suggest only a multiplicity of causes can wholly account for widespread male retreat from the workforce. One cause is criminal records: nearly one in eight American men possesses a criminal history, and that disqualifies candidates in the eyes of most potential employers. Another cause is low educational attainment, which diminishes access to an increasingly technical and information-based economy. In light of this investigation, which indicates that multiple social forces have converged to exclude a major swath of the potential working population of the United States, the government should take action to improve poor outcomes for these “missing men.” Legislators should take action to lessen the stigma of criminal convictions, advocate programs proven to reduce recidivism, increase financial support for young people looking to pursue higher education, and provide specialized training for young men who express an interest in the technology-driven fields of the new economy.p>
C13	<p class="ng-scope"> It has been estimated that over 20% of the annual gross domestic product in the United States is the result of innovation backed at some point by venture capital investors. But what is innovation? One traditional view of innovation is that it is a systematic business process occurring within an organization required to secure ongoing financial growth. But much of the most acclaimed and influential innovation has started with an individual's idea and only somewhat later followed with an organization to execute on that idea, so the organizational definition is of limited relevance. A more practical definition of innovation is that it is the creation of anything new intended to be commercialized. Under such a definition, the efforts of a lone individual developing a radical idea and those of a department within a large company to explore a new adjacent market are both examples of innovation. This somewhat loose definition, however, fails to address explicitly what makes an innovation truly new, successful, or authentic, although it may imply that all innovation is equally valid in a sense. Otherwise, the oft-repeated challenge to uses of the term innovation may put too little emphasis on the activity and too much on its results. Quite possibly, 80% of the value of innovation has been contributed by 20% of the activity, but whether that 20% of activity could have manifested itself without a culture and economy to support the whole is less clear. In this regard, policy- and strategy-oriented attempts to refine this loose definition of innovation further are without merit. p>
Ready4	<p class="ng-scope"> M31, M32, and M33 are members of the Local Group, an assemblage of more than 54 galaxies in the neighborhood of the Milky Way, the galaxy which contains our solar system. Like the Milky Way, M31 and M33 are spiral galaxies, whereas M32 is a dwarf elliptical galaxy. Of the three, M31, also known as the Andromeda Galaxy, is the largest, with a mass that has been estimated in recent studies to be equal to or greater than that of the Milky Way. Comprised primarily of older faint stars, M32 is a substantially smaller galaxy and a satellite of Andromeda. M33, known as the Triangulum Galaxy, is more distant and less massive than Andromeda and is believed to have collided with that galaxy in the past. The attributes of these four galaxies may reflect their past interactions and are likely to shape future encounters. For example, astronomers are not currently sure how M32's compact ellipsoid shape took form, but they suspect that M32 may have had a spiral shape earlier that was transformed by a tidal field from Andromeda into its current elliptical shape. Meanwhile, Triangulum and Andromeda are connected by a stream of hydrogen and stars, which is evidence that the two galaxies have interacted in the past between 2 and 8 billion years ago. Finally, among the trio M31, M33 and the Milky, every pair is potentially on a collision course compelled by gravity. Triangulum might be ripped apart and absorbed by M31, it might collide with the Milky Way before the latter has any violent interaction with Andromeda, or it might participate in the collision between the Milky Way and the Andromeda Galaxy, which is expected to occur in about 4 billion years. p>
C13	<p class="ng-scope"> Two historians of the First World War both depict women as taking up roles previously reserved for men, but they differ slightly in the significance they ascribe to these unprecedented but temporary wartime duties. Gail Braybon describes the war as a liberating experience for many women. Although women working in munitions factories were subject to new dangers, such as explosions and trinitrotoluene poisoning, they were mindful of and proud of supporting the war effort, whether or not they considered the broader significance of their actions. Joshua Goldstein too describes a sense of freedom in women but emphasizes that it was short-lived. Although the war bent gender roles, it did not lessen hostility to women in traditionally male jobs, increase compensation for female labor, or uproot the notion that home life was a strictly female responsibility. Braybon might reply by noting that, while other changes were slower in coming, some women suffragists supported the war and women's role in it to further their cause, and this may indeed have contributed to the advent of women's right to vote after the war, even by Goldstein's account. Perhaps more central to Braybon's position is that the liberation that women experienced during the war was one of sentiment and therefore made no less real by the lack of accompanying widespread reform. Furthermore, even though the spirit of liberation must have faded with the end of the war, it might have lived on in a latent form and ultimately contributed to the formation of the women's movement. p>
Ready4	<p>The circle with center $C$ shown above is tangent to the $x$ -axis. The $x$ -coordinate of $C$ is three times its $y$ -coordinate. If the distance from $O$ to $C$ is equal to $n$ , what is the radius of the circle, in terms of $n$ ?p>
Ready4	<p>For any integers n and m, $\ddot{m} (n, m)$ and $\dot{m} (n, m)$ denote the minimum and the maximum of n and m, respectively. For example, $\ddot{m} (4, 3) = 3$ and $\dot{m} (4, 3) = 4$ . For the integer m, what is the value of $\ddot{m} (100, m)$ ?p> $m = \dot{m} (100, n)$ for some integer n. $m = \dot{m} (100, m)$