Problem: Please answer a question about the following article about Group (mathematics):
Some topological spaces may be endowed with a group law. In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g h, and g1 must not vary wildly if g and h vary only little. Such groups are called topological groups, and they are the group objects in the category of topological spaces. The most basic examples are the reals R under addition, (R {0}, ), and similarly with any other topological field such as the complex numbers or p-adic numbers. All of these groups are locally compact, so they have Haar measures and can be studied via harmonic analysis. The former offer an abstract formalism of invariant integrals. Invariance means, in the case of real numbers for example:
What variables do locally compact groups share that can be studied by harmonic analysis?
A: Haar measures
Problem: Please answer a question about the following article about United States dollar:
Unlike the Spanish milled dollar the U.S. dollar is based upon a decimal system of values. In addition to the dollar the coinage act officially established monetary units of mill or one-thousandth of a dollar (symbol ), cent or one-hundredth of a dollar (symbol ), dime or one-tenth of a dollar, and eagle or ten dollars, with prescribed weights and composition of gold, silver, or copper for each. It was proposed in the mid-1800s that one hundred dollars be known as a union, but no union coins were ever struck and only patterns for the $50 half union exist. However, only cents are in everyday use as divisions of the dollar; "dime" is used solely as the name of the coin with the value of 10, while "eagle" and "mill" are largely unknown to the general public, though mills are sometimes used in matters of tax levies, and gasoline prices are usually in the form of $X.XX9 per gallon, e.g., $3.599, sometimes written as $3.59910. When currently issued in circulating form, denominations equal to or less than a dollar are emitted as U.S. coins while denominations equal to or greater than a dollar are emitted as Federal Reserve notes (with the exception of gold, silver and platinum coins valued up to $100 as legal tender, but worth far more as bullion). Both one-dollar coins and notes are produced today, although the note form is significantly more common. In the past, "paper money" was occasionally issued in denominations less than a dollar (fractional currency) and gold coins were issued for circulation up to the value of $20 (known as the "double eagle", discontinued in the 1930s). The term eagle was used in the Coinage Act of 1792 for the denomination of ten dollars, and subsequently was used in naming gold coins. Paper currency less than one dollar in denomination, known as "fractional currency", was also sometimes pejoratively referred to as "shinplasters". In 1854, James Guthrie, then Secretary of the Treasury, proposed creating $100, $50 and $25 gold coins, which were referred to as a "Union", "Half Union", and "Quarter Union", thus implying a denomination of 1 Union = $100.
How much monetary value does a dime hold?
A: one-tenth of a dollar
Problem: Please answer a question about the following article about Sexual orientation:
A third concern with the Kinsey scale is that it inappropriately measures heterosexuality and homosexuality on the same scale, making one a tradeoff of the other. Research in the 1970s on masculinity and femininity found that concepts of masculinity and femininity are more appropriately measured as independent concepts on a separate scale rather than as a single continuum, with each end representing opposite extremes. When compared on the same scale, they act as tradeoffs such, whereby to be more feminine one had to be less masculine and vice versa. However, if they are considered as separate dimensions one can be simultaneously very masculine and very feminine. Similarly, considering heterosexuality and homosexuality on separate scales would allow one to be both very heterosexual and very homosexual or not very much of either. When they are measured independently, the degree of heterosexual and homosexual can be independently determined, rather than the balance between heterosexual and homosexual as determined using the Kinsey Scale.
What is another benefit of measuring sexuality on two scaless verses just the Kinsey scale?
A: the degree of heterosexual and homosexual can be independently determined,
Problem: Please answer a question about the following article about Windows 8:
On August 1, 2012, Windows 8 (build 9200) was released to manufacturing with the build number 6.2.9200.16384 . Microsoft planned to hold a launch event on October 25, 2012 and release Windows 8 for general availability on the next day. However, only a day after its release to manufacturing, a copy of the final version of Windows 8 Enterprise N (a version for European markets lacking bundled media players to comply with a court ruling) leaked online, followed by leaks of the final versions of Windows 8 Pro and Enterprise a few days later. On August 15, 2012, Windows 8 was made available to download for MSDN and TechNet subscribers. Windows 8 was made available to Software Assurance customers on August 16, 2012. Windows 8 was made available for students with a DreamSpark Premium subscription on August 22, 2012, earlier than advertised.
What was the final build Microsoft decided to manufacture?
A:
9200