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OG19-数学分册 The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to $$\frac{p}{q}$$?
OG19-数学分册 A school club plans to package and sell dried fruit to raise money. The club purchased 12 containers of dried fruit, each containing $$16\frac{3}{4}$$ pounds. What is the maximum number of individual bags of dried fruit, each containing $$\frac{1}{4}$$ pounds, that can be sold from the dried fruit the club purchased?
OG19-数学分册 The sequence $$a_{1}$$, $$a_{2}$$, $$a_{3}$$, $$a_{4}$$,$$a_{5}$$ is such that $$a_{n}=a_{n-1}+5$$ for $$2\leq n\leq 5$$. If$$ a_{5} = 31$$, what is the value of $$a_{1}$$ ?
OG19-数学分册 If S = {0, 4, 5, 2, 11, 8), how much greater than the median of the numbers in S is the mean of the numbers in S ?
OG19-数学分册 A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?
OG19-数学分册 List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?
OG19-数学分册 $$\frac{(39,897)(0.0096)}{198.76}$$ is approximately
OG19-数学分册 The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example, the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 + 2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?
OG19-数学分册 When a subscription to a new magazine was purchased for m months, the publisher offered a discount of 75 percent off the regular monthly price of the magazine. If the total value of the discount was equivalent to buying the magazine at its regular monthly price for 27 months, what was the value of m ?
OG19-数学分册 At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?
OG19-数学分册 In a certain sequence, each term after the first term is one-half the previous term. If the tenth term of the sequence is between 0.0001 and 0.001, then the twelfth term of the sequence is between
OG19-数学分册 A certain drive-in movie theater has a total of 1 7 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?
OG19-数学分册 The average (arithmetic mean) of the positive integers x, y, and z is 3. If x < y < z, what is the greatest possible value of z?
OG19-数学分册 The product of 3,305 and the 1-digit integer xis a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?
OG19-数学分册 What is the largest integer n such that $$\frac{1}{2^{n}}> 0.01$$ ?
OG19-数学分册 What is the least integer z for which $$(0.000125)(0.0025)(0.00000125) \times 10^{z}$$ is an integer?
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Ready4

One of the most asked questions has always been: How was the universe created? Many once believed that the universe had no beginning or end and was truly infinite. With the advent of the Big Bang theory, however , no longer could the universe be confidently considered infinite. The universe was forced to take on the properties of a finite phenomenon, possessing a history and a beginning. However, over the decades, there have been multiple interpretations of the Big Bang. In the standard interpretation of the Big Bang, which took shape in the 1960s, the formative event was not an explosion that occurred at some point in space and time — it was an explosion of space and time. In this view, time did not exist beforehand. Even for many researchers in the field, this was a bitter pill to swallow. It is hard to imagine time just starting: How does a universe decide when it is time to pop into existence?

In 2004 Sean Carroll and a graduate student of his, Jennifer Chen, came up with a much different answer to the problem of "before." In his view time's arrow, or time`s flow in only one direction, and time's beginning cannot be treated separately and are in fact cyclical: There is no way to address what came before the Big Bang until we understand why the before precedes the after. “Our universe has been evolving for 13 billion years,” Carroll says, “so it clearly did not start in equilibrium.” Rather, all the matter, energy, space, and even time in the universe must have started in a state of extraordinarily low entropy. That is the only way we could begin with a Big Bang and end up with the wonderfully diverse cosmos of today. Understand how that happened, Carroll argues, and you will understand the bigger process that brought our universe into being. In Carroll and Chen's theory, fluctuations in the dark-energy background trigger a crop of pocket universes from empty space which eventually go back to becoming empty spaces.

Yet another theory is put forth by rebel physicist Julian Barbour. According to Barbour in his 1999 book "The End of All Time," all possible configurations of the universe, every possible location of every atom, exist simultaneously. There is no past moment that flows into a future moment; the question of what came before the Big Bang never arises because Barbour's cosmology has no time. The Big Bang is not an event in the distant past; it is just one special place in a vast universe.

Ready4

     It has been estimated that over 20% of the annual gross domestic product in the United States is the result of innovation backed at some point by venture capital investors. But what is innovation? One traditional view of innovation is that it is a systematic business process occurring within an organization required to secure ongoing financial growth. But much of the most acclaimed and influential innovation has started with an individual's idea and only somewhat later followed with an organization to execute on that idea, so the organizational definition is of limited relevance.      A more practical definition of innovation is that it is the creation of anything new intended to be commercialized. Under such a definition, the efforts of a lone individual developing a radical idea and those of a department within a large company to explore a new adjacent market are both examples of innovation. This somewhat loose definition, however, fails to address explicitly what makes an innovation truly new, successful, or authentic, although it may imply that all innovation is equally valid in a sense. Otherwise, the oft-repeated challenge to uses of the term innovation may put too little emphasis on the activity and too much on its results. Quite possibly, 80% of the value of innovation has been contributed by 20% of the activity, but whether that 20% of activity could have manifested itself without a culture and economy to support the whole is less clear. In this regard, policy- and strategy-oriented attempts to refine this loose definition of innovation further are without merit.    

Ready4

     In 1905, the Supreme Court of the United States decided on the case Lochner v. New York, and in doing so overturned the Bakeshop Act, which limited the number of hours that a baker could work per day to ten. The Court ruled that the Act removed a person's right to enter freely into contracts, which it construed as provided for by the Fourteenth Amendment. The Court had previously determined through multiple rulings that the Due Process Clause, found in both the Fifth and Fourteenth Amendments, was not merely a procedural guarantee, but also a substantive limitation on the type of control the government may exercise over individuals. Lochner set a precedent against the established federal and state laws regulating working hours and wages. For example, in Adkins v. Children's Hospital, in 1923, the Court ruled that federal minimum wage legislation for women was an unconstitutional infringement of liberty of contract, as protected by due process.      Some subsequent development of human rights evolved on the basis of Lochner; for example, Adkins was a significant point in the women's rights movement in the U.S., as the legislature and justice department for decades debated whether to establish absolute equality of women or provide only special protections and regulations for them. Nevertheless, the Court overturned Adkins and undermined Lochner in deciding West Coast Hotel v. Parrish, in 1937. That ruling repudiated the idea that freedom of contract should be unrestricted and echoed, after the fact, the dissenting opinion of Justice Holmes in Adkins that there were plenty of constraints on contract, such as that against usury. At the time of West Coast Hotel, whose outcome hinged on an unexpected shift in the habits of Associate Justice Roberts, the dissenting Justice Sutherland was critical of the prospect that the interpretation of the Constitution reflected in the decision had been colored by contemporary events—ostensibly, the pressures placed upon workers by the circumstances of the ongoing Great Depression. Time has evidently judged this criticism to have been incorrect, since, while Lochner influenced a ruling whose imprint still remains, individual freedom of contract is not exempt from reasonable laws to protect worker health and safety.    

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