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The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There
use 3/8 of a thin of paint, what fraction of the paint is left in thin (show work
Volumes of Solids of Revolution / Method of Rings In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of rev
Standard errors of the mean The series of sample means x¯ 1 , x¯ 2 , x¯ 3 ........ is normally distributed or nearly so as according to the central limit theorem. This can be
what is the length of a line segment with endpoints (-3,2) and (7,2)?
Concrete to Abstract : Mathematics, like all human knowledge, grows out of our concrete experiences. Let us take the example of three-dimensional shapes. Think about how you came
Rolle's Theorem Assume f(x) is a function which satisfies all of the following. 1. f(x) is continuous in the closed interval [a,b]. 2. f(x) is differentiable in the ope
Suppose S = {vi} and T = {ti} are "easy" sets of knapsak weight. Also, P and q are primes p > ?Si and q > ?ti. We can combine S and T into a signle set of knapsack weight as follow
What do we understand by "being able to count"? Think about the following situation before you answer. Example 1: Three year-old Mini could recite numbers from I to 20 in the co
In this part we look at another method to obtain the factors of an expression. In the above you have seen that x 2 - 4x + 4 = (x - 2) 2 or (x - 2)(x - 2). If yo
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