Finding the Break-Even Point (Substitution Method)

Equivalent Expressions & Rational Functions

Create multiple choice questions using the following information: In November, Mrs. Baker has Holling read The Tempest. Despite his preconceptions, Holling is captivated by all the "good stuff" in the play, especially the cussing, which he decides to learn by heart. He figures that Mrs. Baker could not have read the play herself; if she had, she certainly would not have let him have it. Holling is amazed when he discovers that his teacher not only has read the play, but she knows the bad parts as well. Mrs. Baker gives Holling a one-hundred-and-fifty question test on The Tempest, and assigns him to read the play again, telling him "there is a lot more to (it) than a list of colorful curses." The deadline set by Holling's classmates for him to bring them cream puffs arrives, but although Holling's father's company has won the Baker's Sporting Emporium contract, he refuses to extend an advance on his son's allowance. Desperate, Holling goes to Goldman's Best Bakery, offering to work for the money he lacks to buy the cream puffs. Coincidentally, Mr. Goldman, who is active in Long Island's Shakespeare Company, needs a boy to perform in their upcoming Extravaganza, and because of his work with Mrs. Baker, Holling fits the bill. Mr. Goldman gives Holling the required number of cream puffs in exchange, but sadly, while the students are at recess, Caliban and Sycorax, the escaped rats who inhabit the classroom walls and ceiling, come out and decimate the treats. Somehow, the disaster is blamed on Holling; he must clean up the mess, and his classmates decree that he still owes them cream puffs. The next Wednesday, Holling brings five cream puffs to school, which is all he can afford. In addition to facing his classmates' ire, he has to deal with the fact that, in the Shakespeare Company Holiday Extravaganza, he must play the part of Ariel, who is a fairy, and wear yellow tights with white feathers on an unmentionable part of his anatomy; "not a good thing for a boy from Camillo Junior High." To Holling's surprise, just when things are at their darkest, Mrs. Baker comes through for him, bringing cream puffs for the students on his behalf. That afternoon, Mrs. Baker and Holling discuss The Tempest, and whether or not Caliban, the "monster," deserves a happy ending. Holling argues that, as the antagonist, he does not, but Mrs. Baker muses whether Shakespeare might have shown, even in a monster, the capacity of humankind to use defeat to grow. Mrs. Bigio stumbles into the classroom at this point, emitting sounds of indescribable sadness; she has just learned that her husband has been killed in a futile reconnaissance mission in Vietnam. Two nights after his funeral, the Catholic Relief Agency, which houses Vietnamese refugees, including Holling's classmate Mai Thi, is the target of a hate crime. Holling reflects that Shakespeare, with his happy endings for nearly everyone in The Tempest, is wrong. He says, "sometimes, there isn't a Prospero to make everything fine...and...the quality of mercy is strained." In December, Camillo Junior High is awash in "signs of the season." Mrs. Baker, however, does not share the holiday spirit, but Holling is too absorbed with his problems with the Shakespeare Holiday Extravaganza to wonder why. As always, Holling seeks help from his family, but to no avail; his mother comments insipidly that his embarrassing costume is cute, his father tells him to wear it to please Mr. Goldman, who might one day need an architect, and his sister warns him that if news of his role gets to the high school, no one better find out they are related. The only thing that prevents December from being a total disaster is Mrs. Baker's announcement that Mickey Mantle will be signing autographs at the Baker Sporting Emporium. Unfortunately, Mrs. Baker also tells the class about Holling and the Shakespeare Extravaganza, and encourages the students to attend both events. Holling's classmates are intensely curious about his role as Ariel, whom he euphemistically describes as "a warrior." Mr. Goldman tells Mrs. Baker that Holling needs "some practice on interpretation", and she practices with him, playing the part of Prospero. Mrs. Baker is a terrific reader, and when she and Holling rehearse the part where Prospero releases Ariel from bondage, Holling is inspired, realizing what it means to be free "to create his own happy ending." On the night of the performance, Mrs. Baker, Mrs. Bigio, Danny Hupfer and his parents, Meryl Lee, and Mai Thi are in the audience to support Holling, unlike his own parents, who do not want to miss the Bing Crosby Christmas Special on television. Holling executes his part with such passion that his classmates are moved to tears, and do not even notice what he is wearing. When the show is over, Holling, finding the dressing room locked, rushes outside, still in costume, where his father is supposed to be waiting to take him to Baker's Sporting Emporium to see Mickey Mantle. Typically, his father is not there, and Holling, frantic, flags down a bus and begs the driver to take him to the Emporium. The driver takes pity on him and complies, getting him to the Emporium just in time, but when Holling approaches Mickey Mantle for an autograph, the famous player looks derisively at his costume and snaps rudely, "I don't sign baseballs for kids in yellow tights." Danny Hupfer witnesses this snub, and loyally returns his own autographed baseball to Mickey Mantle, saying, "I guess I don't need this after all." Holling and Danny leave together in silence, smarting because "when gods die, they die hard." During the days remaining until holiday break, Mrs. Bigio is especially cantankerous; her cafeteria cooking is unappetizing at best, and her comments to the students are impatient and unkind. Holling, remembering Mrs. Bigio's sadness when she received the news of her husband's death, does not complain, but he is bewildered at the sheer desolation he witnesses when Mrs. Bigio bitterly tells Mai Thi that she "shouldn't even be here...a queen in a refugee home while American boys are sitting in swamps on Christmas Day." After school on the last day before break, Mrs. Baker gives Holling, Danny Hupfer, and Doug Swieteck each a new baseball and mitt, and sends them to the gym, where, to their delight, they meet Joe Pepitone and Horace Clark in their Yankee uniforms, and receive tickets to Opening Day at the Stadium. Mrs. Baker's family knows what happened with Mickey Mantle, and wants to make it up to the boys. The next day, President Johnson declares a Christmas ceasefire in Vietnam, and the holiday season begins in earnest.

Continental Drift Theory. From the discussion of the rock cycle, it has been pointed out that through Earth's external and internal processes. Earth's surface is constantly changing. However, this idea of a changing environment did not conform with the belief of earlier scientists. Rather, they thought that the geographic positions of ocean basins and continents have been static since the beginning of time. It was around the 1500s when Leonardo da Vinci, upon his discovery of fossil seashells found at the high mountains of Italy, first thought of the idea that the areas where mountains are located may have been oceans in the past. Through time, other fossils of marine organisms found far above the current sea level further supported the idea that mountains were uplifted and weathering wore them down. At around the 1800s, most scientists have accepted the idea that Earth's crust is undergoing large vertical movements or uplifting. There was also evidence of possible horizontal movements, but the scientists then were not convinced about it. Alfred Wegener showed evidence of horizontal or lateral movement of the continents in his continental drift theory. According to him, the continents have drifted around the world and have once formed a giant landmass or supercontinent called Pangaea. To support his theory, Alfred Wegener presented a set of geographical, biological, and climatic evidence.Wegener's geographical evidence included the jigsaw puzzle fit of the current continents. He pointed out that the coastlines of South America and Africa seem to fit together. He also pointed the presence of mountain ranges having similar rock types and age but separated by vast oceans, like that of the folded rocks of the Caledonian mountains. The same folded rocks run through West Africa, North America, Newfoundland, Ireland, Wales, Scotland, Greenland, and Norway, all of which are now separated by the Atlantic Ocean. A geographical evidence on the similar rock types in West Africa, North America, Greenland, and Europe is found. The biological evidence came in the discovery of similar plant and animal fossils in different continents separated by oceans. The animal fossils of Mesosaurus and Lystrosaurus indicate that they were not capable of crossing the oceans to reach the other continents. If they were, the fossils should have been more widely distributed Africa, Australia, India, and South America were too large to be carried by wind. This indicates that the areas where the fossils were found were closely linked. It has also been found out that the plant only grew in areas with subpolar climate, which would indicate that the landmasses were located near the South Pole.Lastly, for his climatic evidence, Wegener discovered that a glacial period occurred during the late Paleozoic era in Southern Africa, South America, Australia, and India. The initial explanation for this event was global cooling, but it was rejected because large tropical swamps with so much vegetation were found at the same time in the Northern Hemisphere. This further supported the idea that the supercontinent was indeed near the South Pole, and the continents in Northern Hemisphere were once near the equator. The glacial period also left glacial striations, or the scratches glaciers make as they move across on the underlying bedrock, on the aforementioned continents. For such an event to happen, the continents would have to be connected. SCIENCE PIONEER. Alfred Wegener (1880-1930). Alfred Wegener was a German polar researcher, geophysicist, and meteorologist. He was known for his work on the continental drift theory. In his effort to defend his work, he went to the Greenland ice sheet where he died.Even with all the compelling evidence, the continental drift theory hardly convinced the scientific community at that time because Wegener was unable to identify a credible mechanism that drives the continental drift. He was unable to clearly explain how the continents moved and how the larger continents broke through the ocean floor. Eventually, critics of the continental drift began to accept the theory when new evidence supporting the theory was discovered. The new evidence led to a more encompassing theory the theory of plate tectonics. This theory provided a more convincing explanation as to how the continents moved. The evidence that paved the way for the theory of plate tectonics was the idea of wandering poles. Scientists began studying volcanic rocks to determine the location of the magnetic poles. When volcanic rocks crystallize, the minerals with magnetic properties align themselves parallel to Earth's magnetic field at the time the minerals were formed. This finding allowed scientists to determine the polarity of Earth's magnetic field and the magnetic inclination that showed the location of the poles. Upon studying the paleomagnetism of the rocks, geophysicists found out that rocks from various locations point to different magnetic north poles, suggesting that the poles have wandered. Since movement of magnetic poles is very unlikely, scientists have accepted the idea that the continents are indeed moving. And if the continents are moving, scientists thought that maybe the ocean basins are moving too. They also discovered that some rocks showed magnetic reversals, which led them to believe that the magnetic north pole now was not always the magnetic north pole. Seafloor Spreading. After World War II, exploration on the ocean floor became the focus of many geologic studies. It was only then that the ocean ridge system was discovered. A geologist in Princeton University named Harry Hess, along with other scientists, studied this ocean ridge system and hypothesized that the oceanic crust was moving away from the ridge. His hypothesis, known as seafloor spreading, showed that the ocean floor is split along the ridge where the magma rises to form the new ocean floor.Because of this, rocks located near the ridge are younger than those that are located magnetic polarity of Earth is also preserved in those rocks. Withe ridge scientists were able to see the magnetic reversals in the ocean floor, and they were able to make use of information to determine that the ocean floor is moving at a rate of about 10 cm per year. Plate Tectonics. Confirmation of the seafloor spreading hypothesis proved that continents are not moving above the ocean floor. Rather, it is the fragments of the lithosphere. The lithosphere is the rigid layer that is composed of the uppermost mantle and the crust that carry the continents and the ocean basins along. These fragments of the lithosphere are called plates. Underneath the lithosphere is a weaker region in the mantle known as asthenosphere that behaves like a fluid. Thus, the lithosphere floats above the asthenosphere, making it detached and free to move. This became the basis of the theory of plate tectonics. Now that it has been made clear that it is the plates which are moving, the question as to how they move remained. Sir Arthur Holmes proposed the driving force for this plate movement in 1919. He suggested that the movement in the mantle carries the plates along. It was previously discussed that Earth's interior is very hot due to the heat produced by radioactive decay. Convection takes place in the mantle, keeping the asthenosphere hot and weak. The convection currents produced in the asthenosphere are the ones carrying the lithospheric plates and making them move. However, convection currents are not enough. Mechanisms such as ridge push and slab pull aid the convection currents to slowly move the lithospheric plates. Ridge push occurs at mid ocean ridges which are higher in elevation than the surrounding trenches and abyssal plains. The new ocean floor from the ridge is hot and relatively thin. As it moves away from the ridge, it cools down and gets denser, heavier, and thicker. Below this cooling ocean floor is the asthenosphere, which is less dense. This area becomes a massive shear zone and the new ocean floor will effectively slide down the slope of the asthenosphere. When the plate collides with another plate with lesser density, the denser plate sinks and a subduction zone is formed. When the subducting plate sinks, it pulls on the rest of the plate behind it. These mechanisms explain the movement of the plates.Earth has seven major lithospheric plates that account for 94% of Earth's surface. These are the North American Plate, South American Plate, Pacific Plate, African Plate, Eurasian Plate, Indo-Australian Plate, and Antarctic Plate. These plates are constantly moving relative to the other plates. Thus, the interaction of plates occurs mostly along the boundaries. These movements are plotted using information from earthquakes and volcanic activities. There are three main types of plate boundaries: convergent, divergent, and transform boundaries Convergent boundaries are boundaries where two plates move towards each other A convergent boundary is also known as destructive margin since this is where the collision between two plates occhins. There are three types of convergence-oceanic oceanic, oceanic-continental, and continental-continental. Trenches are features of the ocean floor that are present in both oceanic-oceanic boundary and oceanic-continental boundary. Subduction occurs at the trenches, therefore, these are characterized as the deepest parts of Earth. A divergent boundary is the opposite of convergent boundary: two plates move away from each other. Divergent boundaries create new crust; thus, they are also known as constructive margins. The ocean ridge system is a divergent boundary where new ocean floor is produced as magma rises, pushing the older rocks aside.Transform boundary is also known as conservative plate margin since two plates just move past one another, neither creating nor destroying land. Earthquake epicenters are usually detected at transform boundaries because the rocks tend to break and not fold or sink, like in convergent boundaries. Evolution of the Ocean Basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins.Continents do not immediately end at the point where the ocean meets the land. They may extend slightly into the oceans. The portion of the continent that is submerged is called continental margin. There are two types of continental margin: passive margin and active margin. A passive continental margin consists of a continental shelf, continental slope, and continental rise. It is not associated with plate boundaries; thus, there are very little tectonic activities. An active continental margin only has a continental shelf and a continental slope. It is associated with plate boundaries; thus, a main feature of this boundary is a trench. The different features of a continental margin are the following: 1. The continental shelf is the gently-sloping submerged portion of the continent. 2. The continental slope is the steep slope after the continental shelf. It is still part of the continent. 3. The continental rise is the gently-sloping area after the continental slope and before the ocean floor. 4. The trenches are the deepest parts of the ocean. These are narrow depressions caused by the subduction of the ocean floor along the convergent boundaries. 5. The mid-oceanic ridge is the mountain range system in the ocean. It is responsible for the production of new ocean floor. This is the region where new magma constantly emerges from. SCIENCE CAREER. A scientific illustrator uses art to inform and communicate complex details and concepts of science. He/She makes use of scientifically informed observations and research along with his/her technical art and aesthetic skills to make accurate representations. In Natural History, the scientific illustrators recreate how the extinct species look like by working with scientists and fossil records. Moreover, with the advances in technology, illustrators are now into 3D modelling, animation, and video making. Earth's History. All the processes that have been discussed require long periods of time to create a noticeable change on Earth's surface. You can just imagine how long it would take to create an oceanas vast as the Pacific Ocean if the ocean floor moves only at about 10 cm/year. It is then important to know the history of Earth to learn the complexities of its past and be able to use it to understand the present. Just like learning the history of a country that requires one to read a lot of books, learning the history of Earth involves studying a lot of rocks. Rocks, especially sedimentary rocks, contain a lot of information about Earth's past. It holds the key to most of the geologic processes that happened on Earth and the key to uncovering how life on Earth evolved. But these discoveries are worthless if there is no time perspective. Thus, one of the most important contributions of geologists to mankind is the geologic time scale, which holds a history that is exceedingly long.

Reading Passage: The Anatomy of a Kill Chain In the lexicon of modern warfare, the term "kill chain" describes the end-to-end process of a military attack, from the initial identification of a target to its eventual destruction and the subsequent evaluation of the strike's effectiveness. Conceptually, the kill chain is a structural model used to understand and optimize the speed and precision of military operations. The fundamental principle of this model is that an attack functions as a sequence of interdependent stages; if any single link in the chain is broken, the entire operation fails. For strategic planners, this creates a dual objective: to accelerate one's own kill chain while simultaneously finding ways to disrupt the adversary's. Strategic Concept: The Kinetic Model (F2T2EA) The traditional military kill chain is often summarized by the acronym F2T2EA, representing a continuous cycle of find, fix, track, target, engage, and assess. The kinetic kill chain begins with Find, the reconnaissance phase where intelligence assets identify a potential target within a theater of operations. Once found, the process moves to Fix, which involves pinning down the target's specific location and ensuring it can be distinguished from friendly forces or non-combatants. Track follows, maintaining a persistent watch on the target's movements to prevent its escape. In the Target phase, commanders select the appropriate weapon system and verify the legality and strategic value of the strike. Engage is the kinetic moment—the actual deployment of ordnance against the objective. Finally, Assess involves battle damage assessment (BDA) to determine if the desired effects were achieved or if further engagement is required. This model emphasizes "compressing the sensor-to-shooter timeline," meaning the faster a military can move through these steps, the more lethal it becomes. The Evolution: The Cyber Kill Chain® As warfare expanded into the digital domain, Lockheed Martin adapted the kinetic model into the Cyber Kill Chain. This framework assists defenders in identifying and stopping Advanced Persistent Threats (APTs). Unlike a physical missile, a cyberattack often unfolds over weeks or months, but the sequential logic remains the same. The model consists of seven distinct stages: Stage Description of Attacker Activity 1. Reconnaissance The harvesting of information. Attackers research targets via social media, public records, and technical scanning to find vulnerabilities. 2. Weaponization Coupling a remote access trojan with an exploit into a deliverable payload (e.g., a malicious PDF or Microsoft Office document). 3. Delivery Transmission of the weapon to the target environment. Common vectors include email attachments, malicious websites, or USB drives. 4. Exploitation The weapon triggers. The code executes on the victim's system, typically by taking advantage of a software or operating system vulnerability. 5. Installation The attacker installs a persistent backdoor or malware on the victim's system, allowing them to maintain access even after a reboot. 6. Command & Control (C2) The compromised system opens a communication channel back to the attacker's server, allowing the intruder to give manual instructions. 7. Actions on Objective The final stage where the attacker achieves their goal, such as data exfiltration, encryption for ransom, or destruction of critical infrastructure. Strategic Implications for Defense The strategic value of the Cyber Kill Chain lies in its ability to provide a roadmap for "proactive defense." By understanding the sequence, security professionals can implement controls at every stage. For instance, robust email filtering can break the chain at the Delivery stage, while endpoint detection can stop the Installation phase. Crucially, the earlier a defender breaks the chain, the lower the cost of mitigation and the lower the risk of damage. If an attacker is stopped during Reconnaissance, they have gained nothing. If they are stopped during Actions on Objective, the damage may already be catastrophic. In both kinetic and cyber environments, the goal is the same: to create a "defensive depth" that makes the cost of a successful attack prohibitively high for the adversary.

Related quizzes

Related quizzes