How many Gaussian integers have norm 3² . 52. 72 . 294? Try to count them without doing a lot of calculations.

Q: Find the value of n(An B) if n(A)= 6, n(B)= 9, and n(A U B)= 11. n(An B) =(Type a whole number.)

A:

Q: What does Chebyshev’s theorem with k=12 tells us about the number of heads that we may get in 900…

A: Given K=12

Q: Theorem 8.10 (Intermediate Value Theorem). Let ƒ : Rstd map. If a, b e R and r is a point of R such…

A:

Q: Let B(x) `x is not beautiful", V(x): `x is not a village in Lebanon.", and domain of x be dll…

A:

Q: Every Hausdorff space is hereditarily Hausdorff.

A: We have to prove that every Hausdorff space is hereditarily Hausdorff. Consider a Hausdorff…

Q: Theorem 2.1 For every graph G, o (G) ≤ x (G). Proof It suffices to assume that G is a nontrivial…

A: Theorem:(Statement) For every graph G, Proof: Let  us consider two  cases.Case1: G is a  trivial…

Q: Theorem 5.9. Let X be a 2nd countable space. Then X is separable.

A: we have to show that , x be a 2nd countable space then x is separable

Q: сотраct

A:

Q: 3.59 What Proportion of College Students Change Their Major? Exercise 2.16 introduces a survey of…

A: b) It is given that, a survey on 5204 college students is done.

Q: Theorem 6.20 (Heine-Borel Theorem). Let A be a subset of R" with the standard topol- ogy. Then A is…

A: Given :- Let A be a subset of ℝn with the standard topology. To Proof :- A is compact if and only if…

Q: Q: True or false  and explain why  please help with this proof

A:

Q: In this magic square, which uses all the integers from 7 to 15, each of the rows, columns and the wo…

A:

Q: All change 1. Follow the steps to verify the identity. cos e tan e = sin Express the tangent…

A: Given that the identity cosxtanx=sinx. Follow the given steps to verify the identity.

Q: Dx (3,437) - kbraur X IS Week #7- Mathemat X 3Take Test: Week #7: 9 X D(122) Jerry Breaks Up x…

A:

Q: Find the orders of all the elements of Ag.

A: Since A8 consists of only even permutations and so it has maximum order of any element of A8 can be…

Q: A particle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of…

A:

Q: 8. Suppose a, b, c e Z. If a² + b² = c², then a or b is even. 9. Suppose a, b E R. If a is rational…

A:

Q: Theorem 9.19. A function f from a metric space (X, dx) to a metric space (Y, dy) is continuous at…

A: Definition: Let f(x) be a function from X to Y, where X and Y are topological space. Let c∈X. f(x)…

Q: Which among the following statements is (are) true? O There is a finite set with exactly 90 subsets…

A: In general, if you have n elements in your set, then there are exactly 2n subsets and         (2n −…

Q: Prove the following statements. These exercises are cumulative, covering all techniques addressed in…

A: Note: since you posted multiple questions. As per our guidelines we can solve only one problem at a…

Q: Theorem 4.23. Let A be a closed subset of a normal space X. Then A is normal when given the relative…

A:

Q: Which among the following statements is a proposition? O Ignore bad people. O If all of us are human…

A: Solution: Definition: A sentence is a proposition if it is either true or false but not both.

Q: 2.30 Compute the last two digits of 345. Please include steps

A: Given : 345 To Find : last two digit

Q: What is the smallest integer n for which 25n>512?

A: The provided expression is as follow:

Q: Exercise 4.6. (1) Consider R² with the standard topology. Let p ER² be a point not in a closed set…

A: part(a) Let A be a closed set in ℝ2. Let a point p∉A⇒p∈Ac As, we know A is a closed set thus Ac is…

Q: Theorem 6.14. For any a < b in R, the subspace [a, b] is compact.

A: The objective is to prove that any a≤b in ℝ the subspace a,b is compact. Let's prove the theorem by…

Q: (8.9x10-17) + (1-599×10*15) =

A:

Q: 3. Determine all the units of Z40 and of Z11.

A:

Q: Every regular space is hereditarily regular.

A: We have to prove that every regular space is hereditarily regular. Consider a regular topological…

Q: Theorem 9.13. Let (X, d) and (Y,e) be metric spaces. Then X × Y is a metric space.

A:

Q: ad owns a company. However, his business is not going well. He projects that his continuous income…

A: Your given answer is approximately correct but You did mistake in round off to 2 decimal places

Q: Find the order of 4 modulo 49.

A: We have to find the order of 4 in the group of multiplication modulo 49. The order of 4 is the…

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

A:

Q: (9.35 × 10°) (7.47 × 10°) = 6.80 × 10 3.89 x 10-4 – 7.47 × 105 9.35 x 10°) (7.35 × 10° 2.42 х 10

A: Explanation and solution is given below....

Q: Use (9.11) and (9.12) to simplify (ABTC)T, (С-1мс) -1, (АН) -"(АНА-1)"(НА-1) -1.

A: For (ABTC)T by using (9.11) we get (ABTC)T = CT(BT)TAT As (BT)T = B Hence (ABTC)T = CTBAT

Q: Theorem 6.17. Every compact subset C of R contains a maximum in the set C, i.e., there is an m E C…

A: To prove that, every compact subset C of ℝ contains a maximum in the set C, that is, there is an m∈C…

Q: 5. Choose the best answer. Sammi plans on selling Christmas tree ornaments. She figured a profit of…

A:

Q: 6.26. Let n > 2. Show that every element of S, can be written as a product of cranspositions of the…

A: Let n≥2. Show that every element of Sn can be written as the product oftransposition of the form 1,i…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.