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If x, y, and z are integers with x ≤ y and y > z, which of the following could x, y, and z represent (respectively)?

⁻3, ⁻2, ⁻3
3, 2, 3
1, 2, 3
3, 2, 1

Explanation

Answer: A - x = ⁻3, y = ⁻2, z = ⁻3. ⁻3 is less than or equal to ⁻2, and ⁻2 is greater than ⁻3.

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Completed by Leonardo da Vinci in 1506, the Mona Lisa is one of the most recognized images in the world. Over the centuries several theories have been proposed regarding the identity of the enigmatic subject of this portrait. While current scholars tend to agree that she is Lisa del Giocondo, the young wife of a wealthy Florence merchant, some dissenters argue that del Giocondo was, in fact, the subject of an earlier portrait, and not the smiling visage of the Mona Lisa. Scholars who reject the del Giocondo identification have proffered several alternative identities. Some scholars believe Mona Lisa was the Duchess of Milan, Isabella of Aragon. Da Vinci was the Aragon family painter for more than a decade and would have had the time and opportunity to create a portrait of the Duchess. Other scholars have theorized that Mona Lisa is the portrait of a mistress of Giuliano de’ Medici, the ruler of Florence in the early 1500s. More recently, scholars using digital analysis have determined that the Mona Lisa is da Vinci himself, painted as a woman. Digital analysis and comparisons of da Vinci’s facial features and those of the woman in the painting show almost perfect alignment of their features. However, other researchers have pointed out that, since the only images of da Vinci are paintings, primarily self-portraits, this alignment might be attributed to the artist, and not the subjects of the painting.Using modern scientific analysis to identify artists and their subjects has become more popular in the last few decades. In addition, the availability of laboratories using specialized equipment has increased for laypeople, or those who are not professional scientists. The internet provides a wealth of information for anyone interested in researching art, and communicating the findings of art historians is easier than ever due to the online publishing of academic journals. 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Vinceti’s Cavaggio investigation was not, however, without controversy. Another art historian, Tomaso Montanari, claimed that Vinceti’s interest in identifying Caravaggio was prurient and morbid, and intended only to attract tourists, rather than to shed light on the tragic life of the artist. He pointed out that violating the artist’s grave yielded little new information about the artist, nor was there any discernible upsurge in interest in Caravaggio’s work. Consistently critical of Vinceti’s projects, Montanari has predicted that the Mona Lisa project will be a failure, and questions the researcher’s motives. Montanari is among a small, but vocal group of highly-regarded art scholars who reject these types of investigations and the value they bring to the study of art. Nevertheless, Vinceti has achieved a significant first step in his research. In August of 2013, he and his team opened and entered a crypt in Florence that has been sealed for over 300 years. 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Even if the remains are confirmed to be those of Lisa del Giocondo, there is no guarantee Vinceti will be able to confirm anything more than the identity of a nearly 500-year-old skeleton. If the skull is not intact, digital scanning of the remains and a simulated reconstruction will be impossible and there will be no way to match the remains to da Vinci’s portrait.Despite these many hurdles Vinceti remains undaunted in his quest to, once and for all, confirm the identity of the most famous face in the world.In the fifth paragraph, the author notes that Tomaso Montanari has characterized Vinceti’s work as “prurient and morbid.” What is the definition of “prurient” as it is used in this sentence?
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Was Hamlet a Hero?Hamlet is a literary work that people from all facets of life have at least heard of. This seventeenth century play encompasses the life of Hamlet, the prince of Denmark. His dramatic life is narrated throughout the pages of William Shakespeare’s play. In creating such a work, Shakespeare created a character that had the potential, power, and authority to serve as a hero among his people; nonetheless, this contradictory man seems too distraught to truly embellish and illustrate the definition of a true hero. In brief, Hamlet signifies a persona that is quite different from the typical hero. Rather than being a noble and courageous man, this prince of Denmark is unrepresentative of the admirable qualities that heroes typically reflect. Hamlet’s internal conflicts, selfish behaviors, absence of courage, and eventual surrender to death make him arguably a simple man, unworthy of the title of hero. Hamlet struggles with immense internal conflicts that create overwhelming and unbearable pain. This madness is displayed in Hamlet’s cruel response to Ophelia, a woman that he has once loved: “I have heard of your paintings well enough / God hath given you one face, / and you make yourselves another, you jig, / you amble, and you lisp,” (III, i ,144-148). Prior to this Hamlet had intentionally pursued Ophelia, but his inability to move beyond his father’s death leaves him struggling to maintain any degree of stability. Throughout the play, others seek to encourage Hamlet, but he maintains distance from those around him, brooding on the past. It is this reluctance to move beyond his father’s death that causes Hamlet to remain entrapped in a sea of internal despair that hinders the role as the hero that his ancestry intended for him to be. Rather than a hero, Hamlet is a man tortured by internal desolation. Equally important, Hamlet displays inconsistent behaviors that are contradictory to heroism. He hates partying, drinking, and dancing, as he recognizes that these attributes lead to inaction, and says to his friend Horatio: “They clepe us drunkards, and with swinish phrase, /Soil our addition, and indeed it takes, / From our achievements, though perform’d at height,/ The pith and marrow of our attribute,” (I, iv, 19-22). Certainly, the recognition that such actions do hinder progress depicts Hamlet as a wise hero, but this illustration is short-lived when Hamlet uses his strong anger towards his mother (who married his uncle Claudius soon after his father’s demise) as an excuse to reject and deny his lover Ophelia. While there are brief glimmers of heroism revealed in the behaviors of Hamlet, most actions are reflective of his inner turmoil and his inability to truly behave as a hero to those around him. Compared to the true hero, Hamlet lacks the courage needed to perform selfless actions. Instead, Hamlet is the opposite of courageous, seeking excuses to delay his killing of Claudius, even though he is taunted by reminders of his late father, who appears as a ghost to urge him to avenge his death. While Hamlet reaches the point of hating anything that defines Claudius, he never attains the courage needed to destroy the man that has symbolically destroyed him. If Hamlet were truly a hero, he would find a way to vindicate his father by following the wishes of the ghost that visits him. Instead, Hamlet remains a captive of the murder that he wants to commit but cannot find the courage to do. This is certainly representative of his non-heroic state. Similarly, Hamlet surrenders in a way that is not indicative of heroism. He feels compelled to surrender his life to destiny. While Hamlet’s ultimate recognition that he has no real control of his own life allows him to gain some resemblance of peace, it is evidence of weakness that does not embody the heroic mindset. Heroes strive for control and supremacy, which is quite the opposite of his inability to act in response to his father’s death. Rather than seeking to reflect knowledge and legacy, he allows himself to be reduced to an individual lacking the knowledge to lead and protect others. It is this absence of knowledge that makes him unable to claim the title of hero. It is Hamlet’s ultimate surrender to the world around him that leads readers to see the extent of how contrary he is to heroism. In looking at the life of Hamlet, one sees the reflection of a man that has the ancestry, the placement, and the ability to be a hero to his people. Unfortunately, he is encapsulated in a life of internal conflict that leaves him struggling to merely live, yet alone be there for others. In his quest for peace, he finds surrender to be his one confidante and friend. In examining the question, “is Hamlet a hero?” the answer lies in the conflict that remains within his inner core, his egotistical ways, the absence of bravery and his surrendering to destiny, which makes him far from heroic.What is an example that shows Hamlet’s absence of courage?
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