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In the groups Z/nZ introduced above, the element 1 is primitive, so these groups are cyclic. Indeed, each element is expressible as a sum all of whose terms are 1. Any cyclic group with n elements is isomorphic to this group. A second example for cyclic groups is the group of n-th complex roots of unity, given by complex numbers z satisfying zn = 1. These numbers can be visualized as the vertices on a regular n-gon, as shown in blue at the right for n = 6. The group operation is multiplication of complex numbers. In the picture, multiplying with z corresponds to a counter-clockwise rotation by 60°. Using some field theory, the group Fp× can be shown to be cyclic: for example, if p = 5, 3 is a generator since 31 = 3, 32 = 9 ≡ 4, 33 ≡ 2, and 34 ≡ 1.
What example of cyclic group satisfies the express of zn = 1?
A: the group of n-th complex roots of unity

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North Carolina consists of three main geographic sections: the Atlantic Coastal Plain, which occupies the eastern 45% of the state; the Piedmont region, which contains the middle 35%; and the Appalachian Mountains and foothills. The extreme eastern section of the state contains the Outer Banks, a string of sandy, narrow barrier islands between the Atlantic Ocean and two inland waterways or "sounds": Albemarle Sound in the north and Pamlico Sound in the south. They are the two largest landlocked sounds in the United States.
What section of North carolina makes up 45% of the state?
A: Atlantic Coastal Plain

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The debate on a new delimitation of the German territory started in 1919 as part of discussions about the new constitution. Hugo Preuss, the father of the Weimar Constitution, drafted a plan to divide the German Reich into 14 roughly equal-sized states. His proposal was turned down due to opposition of the states and concerns of the government. Article 18 of the constitution enabled a new delimitation of the German territory but set high hurdles: Three fifth of the votes handed in, and at least the majority of the population are necessary to decide on the alteration of territory. In fact, until 1933 there were only four changes in the configuration of the German states: The 7 Thuringian states were merged in 1920, whereby Coburg opted for Bavaria, Pyrmont joined Prussia in 1922, and Waldeck did so in 1929. Any later plans to break up the dominating Prussia into smaller states failed because political circumstances were not favorable to state reforms.
How many states was the German Reich to divided into?
A: 14

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In an essay on Sephardi Jewry, Daniel Elazar at the Jerusalem Center for Public Affairs summarized the demographic history of Ashkenazi Jews in the last thousand years, noting that at the end of the 11th century, 97% of world Jewry was Sephardic and 3% Ashkenazi; by the end of XVI century, the: 'Treaty on the redemption of captives', by Gracian of the God's Mother, Mercy Priest, who was imprisoned by Turks, cites a Tunisian Hebrew, made captive when arriving to Gaeta, who aided others with money, named: 'Simon Escanasi', in the mid-17th century, "Sephardim still outnumbered Ashkenazim three to two", but by the end of the 18th century, "Ashkenazim outnumbered Sephardim three to two, the result of improved living conditions in Christian Europe versus the Ottoman Muslim world." By 1931, Ashkenazi Jews accounted for nearly 92% of world Jewry. These factors are sheer demography showing the migration patterns of Jews from Southern and Western Europe to Central and Eastern Europe.
According to Daniel Elazar at the Jerusalem Center for Public Affairs, at the end of the 11th century, what percentage of the world's Jewry was Sephardic?
A:
97%