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Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 . Occasionally, chained notation is used with inequalities in different directions, in which case the meaning is the logical conjunction of the inequalities ...
In graph theory, isoperimetric inequalities are at the heart of the study of expander graphs, which are sparse graphs that have strong connectivity properties. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory , design of robust computer networks , and the theory of ...
Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The bounds these inequalities give on a finite sample are less tight than those the Chebyshev inequality gives for a distribution. To illustrate this let the sample size N = 100 and let k = 3. Chebyshev's inequality states that at most approximately 11.11% of the distribution will lie at least three standard deviations away from the mean.
Here are eight questions to consider before taking out student loans. Should I Pursue Federal or Private Loans? There are two primary sources of student loans: federal and private.
The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution , where it shows for the bottom x % of households, what percentage ( y %) of the total income they have.
Susie Coughlin was concerned when her daughter struggled with reading skills at her public school.. The mom of two was disappointed her district didn't teach phonics as part of its literacy program.
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