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In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
the even perfect numbers 2 n − 1 (2 n − 1) formed by the product of a Mersenne prime 2 n − 1 with half the nearest power of two, and; the products 2 n − 1 (2 n + 1) of a Fermat prime 2 n + 1 with half the nearest power of two. (sequence A068195 in the OEIS).
Weakly prime numbers. Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number. 294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139 ( OEIS : A050249 )
The number of distinct prime factors of a pronic number is the sum of the number of distinct prime factors of n and n + 1. If 25 is appended to the decimal representation of any pronic number, the result is a square number, the square of a number ending on 5; for example, 625 = 25 2 and 1225 = 35 2. This is so because
Controls and taxes. Federal tax policy was highly contentious during the war, with President Franklin D. Roosevelt opposing a conservative coalition in Congress. However, both sides agreed on the need for high taxes (along with heavy borrowing) to pay for the war: top marginal tax rates ranged from 81% to 94% for the duration of the war, and the income level subject to the highest rate was ...
In 1990, that rate was set at 3%, but in 2010, the General Assembly voted for a temporary increase in the rate to 5%; the new rate went into effect on January 1, 2011; the personal income rate partially sunset on January 1, 2015, to 3.75%, while the corporate income tax fell to 5.25%.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. [1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a ...
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