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A bijection with the sums to n is to replace 1 with 0 and 2 with 11. The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2F n. For example, out of the 16 binary strings of length 4, there are 2F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110. There is ...
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 ...
Free-piston engine used as a gas generator to drive a turbine. A free-piston engine is a linear, 'crankless' internal combustion engine, in which the piston motion is not controlled by a crankshaft but determined by the interaction of forces from the combustion chamber gases, a rebound device (e.g., a piston in a closed cylinder) and a load device (e.g. a gas compressor or a linear alternator).
The index increased 2.6% for the 12 months ending in June, the largest year-over-year gain since March 2023, which could further influence an already cautious Fed to skip July for a rate cut in ...
The 1% Club is an American game show, with its setup identically based on the British game show of the same name.Contestants are given a very short amount time to solve brain teaser questions, with questions getting significantly more difficult as the game continues, as statistically a progressively smaller percentage of people, according to the producers, answered each subsequent question ...
v. t. e. Body mass index ( BMI) is a value derived from the mass ( weight) and height of a person. The BMI is defined as the body mass divided by the square of the body height, and is expressed in units of kg/m 2, resulting from mass in kilograms (kg) and height in metres (m). The BMI may be determined first by measuring its components by means ...
t. e. Charlemagne[ b] ( / ˈʃɑːrləmeɪn, ˌʃɑːrləˈmeɪn / SHAR-lə-mayn, -MAYN; 2 April 748 [ a] – 28 January 814) was King of the Franks from 768, King of the Lombards from 774, and Emperor of what is now known as the Carolingian Empire from 800, holding these titles until his death in 814. He united most of Western and Central ...
30 by 30 (or 30x30) is a worldwide initiative for governments to designate 30% of Earth's land and ocean area as protected areas by 2030. [1] [2] The target was proposed by a 2019 article in Science Advances, "A Global Deal for Nature: Guiding principles, milestones, and targets", highlighting the need for expanded nature conservation efforts to mitigate climate change.
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