Q 1143: Fill & Download for Free

EDIT: A smarter way to answer this question is: Howard Ludwig's answer to Is the number 192021222324…201420152016 divisible by 2016?My answerI believe not, because[math]\displaystyle \mod(19\color{red}{20}21…2014\color{red}{2015}2016 \, , \, 2016) = 720[/math]Procedure:[math]\displaystyle \begin{align} \mod(N \, , \, 2016) &= \mod(19\color{red}{20}21…2014\color{red}{2015}2016 \, , \, 2016) \\&= \mod( \left(K\times 10^{3 \times 900} + L\right)\times 10^{4 \times 1017} + M \, , \, 2016) \end{align}[/math]in which:[math]\displaystyle K \equiv 19\color{red}{20}21…97\color{red}{98}99 = \sum_{k=19}^{99} k\times 100^{99-k}[/math][math]\displaystyle L \equiv 100\color{red}{101}102…997\color{red}{998}999= \sum_{k=100}^{999} k\times 1000^{999-k}[/math][math]\displaystyle M \equiv 1000\color{red}{1001}…2014\color{red}{2015}2016= \sum_{k=1000}^{2016} k\times 10000^{2016-k}[/math]Now we will use that for positive integers [math]a,b,c[/math] we have that[math]\mod(a \times b, c) = \mod(\mod(a,c) \times \mod(b,c), c)[/math][math]\mod(a + b, c) = \mod(\mod(a,c) + \mod(b,c), c)[/math]For which we calculate[math]K' = \mod(K,2016) = 1197 \rightarrow[/math] Computational Knowledge Engine[math]L' = \mod(L,2016) = [/math][math]1143[/math][math] \rightarrow[/math] Computational Knowledge Engine[math]M' = \mod(M,2016) = 144 \rightarrow[/math] Computational Knowledge Engine[math]p = \mod(10^{3 \times 900},2016) = 64 \rightarrow[/math] Computational Knowledge Engine[math]q[/math][math] = \mod(10^{4 \times 1017},2016) = 64 \rightarrow[/math]Computational Knowledge EngineAnd so:[math]\displaystyle \begin{align} \mod(N,2016) &= \mod( \left(K\times 10^{2 \times 81} + L\right)\times 10^{3 \times 900} + M ,2016) \\ &= \mod\left( \left( K' \times p + L' \right) \times [/math][math]q[/math][math] + M' , 2016\right) \\&= \mod\left( \left(1197 \times 64 + 1143\right)\times 64 + 144 ,2016\right) \\ &= \mod(4976208,2016) \\ &= 720 \end{align}[/math]

Online, I would google “acrylic beads wholesale” or “bulk acrylic beads” then click on the “shopping” link, it’s just under the address bar. Which is what I did to get the link below. Hope this helpsTry this link:https://www.google.com/search?biw=1143&bih=701&tbm=shop&q=acrylic+beads+wholesale&oq=acrylic+beads+wholesale&gs_l=psy-ab.3..0.53925.60339.0.61508.10.10.0.0.0.0.164.1385.0j10.10.0....0...1.1.64.psy-ab..0.10.1383.cbDXpTugIU4My bad, I didn’t notice the word “custom” in your question, I’ll do it again with “custom bulk acrylic beads”. Link below:https://www.google.com/search?biw=1143&bih=701&tbm=shop&q=custom+bulk+acrylic+beads&oq=custom+bulk+acrylic+beads&gs_l=psy-ab.12...596066.635852.0.639594.14.14.0.0.0.0.376.2680.0j9j3j2.14.0....0...1.1.64.psy-ab..0.3.749...0.MQb-9ZrrzSYI don’t think that’s what you wanted, so lets try “acrylic bead manufacturers” link below:acrylic bead manufacturers - Google SearchWent back to the “all” button under the address bar, gets you to the guys that actually make beads. If you want enough beads I’m sure they help you for a price.Jim Y

Thanks for A2A, Sabrina Ali,Hardy Weinberg equation is the mathematical expression used to calculate the genetic variation of the population at equilibrium[1]. For a particular gene, different alleles are present in a population. The different ratio of alleles in the member of the particular population can be considered as the frequency distribution.Let us begin with the simple background about the equation. Suppose a gene for eye color has two alleles. One allele is for blue (b) color of the eye, and the other allele is for brown (B) color of the eye. If the frequency of the blue allele is p and the frequency of the brown color is q, thenp+q = 1.Now, squaring both the side of the equation:(p+q)^2 = 1^2.p^2 + 2pq + q^2 = 1.p^2 and q^2 are probabilities of getting homozygous conditions, and 2pq will be the probability of getting heterozygous conditions.Some more additional information for your fact file:Whenever the distribution is affected then, the change in the ratio can be considered as the change in the population structure.There can be three different types of changes in the population structure:Stabilization: In the absence of any measure change stabilization takes place in which the individual in an optimum condition increases in the number.Directional shift: Any change in the natural condition results in the change in the number of the individual of a particular optimum level condition. With the time, the graph of the population gets shifted according to the changed condition.Disruption: In this condition, the geographic partitioning of the population results in the development of the different type of the population.Image [1]Now answering your question…For the Equilibrium condition, the following necessary condition needs to be implemented [3]:No evolutionNo selectionPopulation is largeNo genetic drift or population migrationNo net mutation“For Hardy-Weinberg equilibrium, the amount of genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors [1][4][5].”If a new race of population enters the geographic area of an existing population, then there is a possibility that new genes are added to the gene pool of that population. The new race may have a different allele (or a variant of that gene) for the existing gene in the population.For example, if the existing population has alleles for only brown and blue eyes and the new race as allele for black eyes. Thus, the allele for the black eyes will be incorporated into the gene pool of that population. Therefore the equilibrium will be changed. Also, the genetic drift facilitates Macroevolution and Microevolution (evolution on a small scale). Microevolution can be defined as a change in the frequency of gene variants, alleles, in a population over generations [3].The alleles and other variants of the genes from the different race will bring variation to the population and thus acts as a disturbing factor to the equilibrium state.Note: This is a hypothetical answer. If the information is inappropriate, please provide corrections and suggestions. For more information on H-W equation please refer the below suggested readings.Reference and Suggested Readings:Hardy-Weinberg equationEdwards, A.W.F., 2008. GH Hardy (1908) and Hardy–Weinberg Equilibrium. Genetics, 179(3), pp.1143-1150.Khan AcademyPearson - The Biology PlaceHartl, D.L., Clark, A.G. and Clark, A.G., 1997. Principles of population genetics (Vol. 116). Sunderland: Sinauer associates.Wigginton, J.E., Cutler, D.J. and Abecasis, G.R., 2005. A note on exact tests of Hardy-Weinberg equilibrium. The American Journal of Human Genetics, 76(5), pp.887-893.SMITH, C.A., 1970. A note on testing the Hardy‐Weinberg Law. Annals of human genetics, 33(4), pp.377-383.Footnotes[1] Image on flickr.com