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1. Before proceeding, review the formal definition of congruence modulo n.
(a) Prove (directly) that if a ≡ b (mod n) and c ≡ d (mod n), then ac ≡ bd (mod n).
(b) Prove that if a ≡ b (mod n), then ak ≡ bk (mod n).
(c) Is 9257 ≡ 657 (mod 43)? Explain.
2. Describe three different algorithms you use in everyday life. Write them as lists of instructions in human-readable form. What changes would need to be made for these instructions to be specific enough for a machine to follow?
A tank is of the shape of an inversed cone as shown in the following figure. It is filled with water of density ρ =1000 kg/m3. Find the work needed to pump the water in the tank to a point 2 meters above the top of the tank
begin with the distribution beta73.a. what postulated proportion would be associated with that distribution?b. using
Find the critical points.
7- Jensen Enterprises paid $1,300 in dividends and $920 in interest this past year. Common stock increased by $1,200 and retained earnings decreased by $310. What is the net income for the year?
If you have temperature and pressure, can you fully define the state of system, if you are in the superheated region?
The angle of elevation of a balloon from an observer A is 30 degrees and from observer B, 45 degrees. If the distance between A and B is 800 + 800√3 meters, how high is the balloon?
When 300 junior college students were surveyed, 145 said they have a passport. construct a 95% confidence interval for the proportion of junior college students that have a passport.
Sampling distribution of sample mean- key informaiton. What is the probability that the sample mean will be between 28 and 46?
there are many ways to go about solving math problems. for this assignment you will be required to do some work that
24. An old urn is discovered that looks like a cylinder except that the side is wavy. The urn is 6 inches high. Scientists want to estimate the volume of the urn so they measure its circumference at intervals of 2 inches, and produce the follow..
A club has 28 members, and 6 members must be selected to make a committee. Of the 28 members, 15 are men and the rest are women. How many ways can the 6 member committee can be selected if there are to be 4 men and 2 women on the committee?
1. Use Gaussian elimination to determine if each of the following linear systems is consistent. Then use Gauss-Jordan elimination to solve the consistent linear systems. Use Notion 1.4.9 to denote the elementary row operations that you used for ea..
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