# Binomial coefficient

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Triangle, time ranging from 2nd century BC to 18th century AD. Among all the academic works by ancient mathematicians, I’m going to focus on Jiu Zhang Suan Shu [Nine Chapters on the Mathematical Art] composed by Chinese scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After that, I will introduce Jade Mirror of the Four Unknowns written by Zhu Shijie around 14th century AD. My focus will be his idea of using the “four unknowns” to convert a problem into a mathematical system of polynomial equations. Later on, I will also…

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HD is the exact number of “S” in a sample. Calculations were the earliest use; and I use the same example as above. According to scientists, “the representation H (x; n, M, N) is the proper way to show this distribution. In contrast, NBD is the amount of failures per each random trial, with successes being fixed. Today, measurement, counting, and data are some of the ways they are used. The number of students that a tutor helped to receive either a pass or fail is my example. Nb (x; r, p)…

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Question 1 The globalisation process has had significant impact on the overall economic performance of the nation. This is when South Africa re-joined the scene of international economies in the 1990’s during which time globalisation had begun to gain prominence. Its move from a socialist socialist movement to a democratic system in 1994 has been a major key towards its gain in economic performance during the globalisation period. This is as the first democratically elected president, Nelson…

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Boldly stated within a viral video titled "Wealth Inequality in America" is that "[most people] certainly don 't have to go as far as Socialism to find something that is fair for hardworking Americans," a statement that colorfully highlights one of the largest issues in America today: the wealth gap. Using statistics, the creator of the video proves that the saying “While the rich get richer, the poor get poorer” is true; as the rich are given an excess of opportunities to gain more money, the…

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America prides itself on being a democratic government and a land of equal opportunity, but does it live up to those standards? Incoming inequality is growing in American society, and the effectiveness of democracy is being threatened by this increasing inequality. While America has claimed to make strides toward racial and gender inequality there is a growing gap between the haves and have nots. This income gap is increasing rapidly between the rich and the middle class and the middle class is…

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Inequality will be produced between states, but also within states among different classes. First, this paper will examine inequality within state borders. The Gini coefficient is a tool used to measure the income distribution within the country. A Gini coefficient of 0 means equal distribution of income, while a Gini coefficient of 1 is the most unequal distribution. When the income data is examined in quintiles, one will see inequality rising. The interesting factor being income inequality…

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“As I often say, we have come a long way from the days of slavery, but in 2014, discrimination and inequality still saturate out society in modern ways. Though racism may be less blatant now in many cases, its existence is undeniable” (Al Sharpton). Not only has racism been a key factor in the inequality and social stratification in today’s society, but gender and income has also played a key role as well. Social stratification involves hierarchical differences not only in economic positions,…

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I shall compare the different national economies using the criteria of economic inequality. Next, I will attempt to establish the correlation between inequality and the role of the government through redistributive fiscal policies. These statistical findings will eventually be tied to some of the key concepts from the class readings, particularly on the comparison of national systems of political economy. Methodology For data sampling, I have selected four developed countries and two emerging…

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policies set by Russia and China and patron-clientelism are no exception. Fiscal policies dictate how much the government spends and how much it taxes. A key difference between a capitalist state and a communist state is that a communist state holds more control over its economy through more government spending and taxation. China’s current economy relies on exports and construction, both areas that the government has great control over. Russia current economy relies on oil and mineral exports,…

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Introduction On November 19, 1863, President Lincoln delivered a speech during the dedication of the battlefield cemetery at Gettysburg, which hit every main point in less then two minutes. One line in particular, Lincoln states, “It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced.” (Burns, 2012). Inequality had brought on the civil war, with the issues of slavery and central power which had divided the United…

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