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How many indistinguishable candies must be distributed to at least k children?
To distribute candies to at least k children, we need to distribute a minimum of k candies. This ensures that each child receives at least one candy. If the candies are indistinguishable, we can distribute any number of candies equal to or greater than k to ensure that each child receives at least one candy.
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Why is the number of possible outcomes when rolling 2 indistinguishable dice 21?
When rolling 2 indistinguishable dice, the number of possible outcomes is 21 because there are 6 possible outcomes for the first die and 6 possible outcomes for the second die, giving a total of 36 possible combinations. However, since the dice are indistinguishable, we need to divide by 2 to account for the duplicate combinations (e.g. (1,2) and (2,1)). This gives us 36/2 = 18 unique combinations. Additionally, there are 3 combinations where both dice show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6), bringing the total number of possible outcomes to 18 + 3 = 21.
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How many results are there when throwing three indistinguishable dice, where no 5 appears?
When throwing three indistinguishable dice, the total number of outcomes is 216 (6^3). To find the number of outcomes where no 5 appears, we need to subtract the outcomes where at least one 5 appears from the total. There are 125 outcomes where at least one 5 appears (5^3), so the number of outcomes where no 5 appears is 91 (216 - 125).
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Is there an energy drink that is practically indistinguishable in taste from regular Red Bull?
There are several energy drinks on the market that are designed to mimic the taste of Red Bull, such as Monster Energy's "Ultra Red" and Rockstar Energy's "Punched." These drinks often have similar flavor profiles to Red Bull, with a mix of sweetness and tartness. While they may not be identical in taste, they are close enough that some consumers find them practically indistinguishable from regular Red Bull.
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Where has photonics gone?
Photonics has advanced and expanded into various industries and applications, including telecommunications, healthcare, manufacturing, and defense. It has enabled the development of faster and more efficient communication systems, medical imaging technologies, high-precision manufacturing tools, and advanced military equipment. Photonics has also made significant contributions to renewable energy technologies, such as solar cells and LED lighting. Overall, photonics has become an integral part of modern technology and continues to drive innovation in a wide range of fields.
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How advanced is nanotechnology?
Nanotechnology is a rapidly advancing field that involves manipulating materials at the nanoscale, which is on the order of billionths of a meter. It has already led to significant advancements in various industries, including medicine, electronics, and materials science. Researchers are continually developing new techniques and applications for nanotechnology, such as targeted drug delivery, nanoelectronics, and nanomaterials with unique properties. While nanotechnology is still in its early stages, it holds great promise for revolutionizing many aspects of our lives in the future.
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What is NMR spectroscopy?
Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful analytical technique used to study the structure and dynamics of molecules. It provides detailed information about the chemical environment, connectivity, and conformation of atoms within a molecule. By measuring the interactions of atomic nuclei with a magnetic field, NMR spectroscopy can elucidate the molecular structure of organic compounds, proteins, and other biomolecules. This technique is widely used in chemistry, biochemistry, and structural biology for research and drug discovery purposes.
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How is spectroscopy applied?
Spectroscopy is applied in various fields such as chemistry, physics, astronomy, and environmental science. In chemistry, it is used to identify and analyze the chemical composition of substances. In physics, it is used to study the interaction of electromagnetic radiation with matter. In astronomy, it is used to determine the composition, temperature, and motion of celestial objects. In environmental science, it is used to monitor air and water quality by analyzing the presence of pollutants. Overall, spectroscopy is a versatile tool for analyzing the properties of different materials and substances.
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