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Question: The relation of "congruence modulo n" is the relation ≡ defined by x ≡ y mod n if and only if x mod n = y mod n.
(a) Show that congruence modulo n is an equivalence relation by showing that it defines a partition of the integers into equivalence classes.
(b) Show that congruence modulo n is an equivalence relation by showing that it is reflexive, symmetric, and transitive.
(c) Express the Chinese Remainder theorem in the notation of congruence modulo n.
Prove the following by contradiction and induction
Does the following graph have an Euler circuit, an Euler path, both, or neither? Give reasons for your decision.
A sample size of 150 is to be used to test the hypotheses H0: µ = 8.3 vs. Ha: µ ≠ 8.3 where µ is the true average weight of a newborn American baby. Determine the appropriate rejection region with a significance level of alpha = 0.05.
Jam buys 12 pens for $10.Each pen costs the same amount of money. Write a proportion to find the number of pens Jan can buy for $15.Then solve your proportion for the number of pens.
A, B started business with 50000,60000, C joined later after x months invested 70000 and B withdraws before x months to end of the year. Then what is the ratio of their profit?
enguun earns 17 per hour tutoring student-athletes at brooklyn university. if enguun tutored for 12 hours this month
The following selections were taken from the letters-to-the-editor section of a newspaper. Each can be interpreted as expressing one or more arguments. Begin by identifying the conclusion of each.
Express the volume of the box as a polynomial in the variable x
A merchant has coffee worth $20 a pound that she wishes to mix with 50 pounds of coffee worth $80 a pound to get a mixture that can be sold for $30 a pound. How many pounds of the $20 coffee should be used.
What would be the value of expressing something like the national debt in scientific notation? What information would be lost in such a usage? Is that important? Explain why or why not.
The square of the largest of three positive consecutive integers is 320 less than the sum of the squares of the two smaller integers. Find the three integers.
Find the shortest path a traveling salesperson can take to visit each of the capitals of the 50 states in the United States, traveling by air between cities.
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