71. Tallest Mountain. The tallest mountain in the world, when measured from base to peak, is Mauna Kea (White Mountain) in Hawaii. From its base 19,684 ft below sea level in the Hawaiian Trough, it rises 33,480 ft. What is the elevation of the peak above sea level? 72. Telephone Bills....

U={1,2,5,7,8,9,12, 15}, A={2,7,8}, and B={9,7,12,2} is represented by the Venn diagram to the right. (A Suppose the set A has 4 elements, the set B has 5 elements, and AB has 2 elements. Can we use this information to figure out the number of elements in AUB?

BUC consists of regions II, III, IV, V, VI, and VII in the Venn Diagram. Regions of the Venn Diagram and Set Relations cont"d. Finally, (AUBUC)" corresponds to region VIII. Which regions make up (AC)UB? Suppose we are given that U = {1,2,3,4,5,6,7,8,9,10,11,12} A =...

[a, b], and f (c) > 0 then there exists an open interval I which contains c such that f (x) > 0 for all x I. 40) Problem. Suppose f is a continuous function dened on the interval [a, b] and suppose f (a) < 0 < f (b). Prove that there exists a number c

What value would you expect the Gini Index to have for an economic system in which income is distributed evenly? What about an economic system in which almost all of the income is concentrated in the hands of a few people?

2y)e2x , y(0) = 2 b) Solve (x2 + 1)y = 3xy + x, y(0) = 0. c) The time rate of change of a population P is proportional to the cube root of P. At time t=0, the population is 1000 and the rate of increase is 100 at that time. What is the population at time t=10? Problem 3. a) Let dx = 5x + 2x3 ....

For every real number x, there exists an integer n such that x N. One statement is true. The other is false. Which is which?

(2) Sketch the graphs of these functions: (a) f (x) = 1 x - 1 3 (b) f (x) = x2 + 1 (c) f (x) = cos x + x (3) For each of the following sets and relations determine whether or not an equivalence relation has been defined. Explain why or why not.

(8) Suppose we have an eight-note scale (with first and eighth notes an octave apart) such that the sequence of intervals of adjacent notes contins only the numbers 1 2 and 1. Is it possible that this scale is a non-trivial standard of itself?

Find an example of such a k in each of the sets below and show how every nonzero element arises as a power of k. (a) Z5 (b) Z7 (c) Z11 5. Let f (x) = x2 + x - 2. (a) Find all the roots of f (x) in Z5 . How many are there? (b) Find all the roots of f (x) in Z10 . How many are there?