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Prove the following using the method suggested:
(a) Prove the following either by direct proof or by contraposition:
Let a ∈ Z, if a ≡ 1 (mod 5), then a2 ≡ 1 (mod 5).
(b) Prove the following by contradiction:
Suppose a, b ∈ Z. If 4|(a2 + b2), then a and b are not both odd.
(c) Disprove the following by counter examples:
(d) Prove the following by cases: For all n ∈ Z, n2 + 3n +4 is even.
(e) Prove the following by induction:
12 + 32 + 52 + ........ + (2n-1)2 = n/3 (2n-1) (2n+1)
Find the probability of making a Type II error.
finding the value of x for which the power series converges.for what values of z does the power series1 - 3x 5x22 -
Customers arrive into a queue, where they are served, and then depart. We model the time between two successive arrivals by an exponential distribution with an arrival rate l=9
Find the best investment using the following decision criteria.
using your text and at least one scholarly source prepare a two to three page paper on the following question explain
Graph the linear equation for the indicated values of the independent variable.Show this on a Graph as well as the formula
what is the probability that tourists will see fewer than four lions on the next one day?
use the vertex (55,30) and the additional point (35,20) from the scatter diagram to find the equation of the parabola in standard form implied by the scatter diagram.
Consider two cases: one in which the ball is not completely submerged and the other in which it is.
The length of a rectangle is 6 times the width. If the perimeter is to be at least 98 meters, what are the possible values for the width?
You walk 105 yards due south, then 127 yards due west, and then 40 yards due north. How far are you from your staring point?
Jane works due north of home. Her husband Ben works due east. They leave for work at the same time. By the time Jane is 3 miles from home, the distance between them is on mile more then Ben's distance from home. How far from home is Ben?
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