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Equal groupings - when we want to find how many objects there are in several equal-sized sets. (e.g., if there are 3 baskets, each with 4 bananas, 4 oranges and 4 apples, respec
Example Show that p ( x ) = 2 x 3 - 5x 2 -10 x + 5 has a root somewhere in the interval [-1,2]. Solution What we're actually asking here is whether or not the function wi
Introduction: "Mathematical literacy is an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and t
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The winning team''s score in 21 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 11.0 points, find the 90% confiden
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Definition 1: Given the function f (x ) then 1. f ( x ) is concave up in an interval I if all tangents to the curve on I are below the graph of f ( x ) . 2. f ( x ) is conca
By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9. Answer: Let make four groups of two numbers from 1 to 8 like
In the introduction of this section we briefly talked how a system of differential equations can occur from a population problem wherein we remain track of the population of both t
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