7) Note that -2 is a square modulo 11. Indeed, 82 +2 = 6.11. Use this information, and the method of descent to construct a solution of r2+2y? %3D 11.

Q: Since b =2i ̂-j ̂-3k ̂ and c =i ̂-5j ̂+k ̂, what is the result of ( b . c )?

A:

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 4. 8.

A: The given question is solved below.

Q: 7. Solve the following IBVP: Uu = 4uzz, 0 0, u(0, t) = 27, u(27, t) = 0, t20, u(x, 0) = x - 27,…

A:

Q: Solve for n if nP, = 6nP,, where P means permutation.

A: Formula of permutation: Prn=n!n-r! We are given that P5n=6×P3n So, using the formula:…

Q: For which integers c, 0<c < 30, does the congruence 12x == c (mod 30) have solutions? When there are…

A: Given congruence is 12x≡c(mod 30). We know that ax ≡b(mod m) have solutions when gcd(a,m) divides b.…

Q: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: 15 Apply Garass elimination methad to solve the Sy stem, 2X+y+22=3, 3x -Y+ 4Z=7 4X +3y +6 2- S

A:

Q: Use Naïve Gauss elimination to solve 20 x, +15x, +10 x, = 45 — 3х, — 2.249 х, + 7x, %3D 1.751 5x, +…

A: The given system is…

Q: 2. Compute the value of | V25–x² dr

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Q: ). Hence, solve for the system below 7x + 3y = 10 (mod 16) 2x + 5y = 9 (mod 16)

A:

Q: The order of the element 16+ in Z24/ is None of the choices 1 4 8.

A: The order of an element a in a group Gis the number of elements in the cyclic subgroup of G.  Also…

Q: Solve the following IBVP: 0 0, u(x,0) = 2 – 2x2, u(x,0) = 0, 0 0, %3D %3!

A:

Q: A survey of farmers showed that of the farmers, 126 grew only wheat, 111 grew only corn, 93 grew…

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Q: Find all the non-congruent solutions to  4x ≡ 6(mod 21)  express solutions using the stand…

A: Introduction: A linear congruence is generalized as ax≡bmod n. The greatest common divisor of a and…

Q: Solve the following system of equations using Cramer’s rule [5] { −3? + 2? − 6? = 6 5? + 7? − 5? = 6…

A:

Q: Given the system of congruencies: x=1 mod 3, x=2 mod 5, x=3 mod 7. Then the solution is ______

A: We will use here chinese remainder theorem. Chinese remainder theorem. Let n1,n2,n3,. . . nr be…

Q: Suppose that m, n are two integers such that m 2n2 = 1. Does it follow that m and n are relatively…

A: Given that m, n are two integers such that m3-2n2=1. To show m, n are relatively primes we have to…

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 1. 4 2) 8)

A:

Q: If mZNSM = 71°, then what is mZLSP? L. R 1 K 3 2 M

A:

Q: s) Express the infinite contimod fraction [2, 1,5 quadratic irrational- as a ity.

A: We need to express the infinite continued fraction 2, 1, 5¯ as a quadratic irrationality. The…

Q: Suppose that m, n are two integers such that m3 – 2n2 = 1. Does it follow that m and n are…

A:

Q: 7. Solve the following IBVP: Ut=4uzzy 0 0, u, (0, t) = u(2π, t) = 0, t≥ 0, u(x,0)=0, 0≤x≤ 2π, u₁(x,…

A: Given:  utt=4uxx, 0&lt;x&lt;2π, t&gt;0,ux0,t=ux2π,t=0, t≥0,ux,0=0,…

Q: , find P and diagonal D so that A= PDP-1

A:

Q: in= aRo can direetly /KT. by gomma fometion, We write Jo a Kox2 &KT 2

A: If you have any doubts in the solution please ask me  in comments i will reply you as soon as…

Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

Q: 15. Find the general solution of dr bcosedr + rsinode

A: General solution of differential equation

Q: By using the Chinese remainder theorem, solve the following system of congruences x ≡ 4 (mod 11)…

A:

Q: of the apples is equal to 3 of the oranges. If there are 12 mor 5 In a fruit stall, - - annles than…

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Q: Show how to adapt the proof that v3 is irrational (from the video) to prove that v15 is irrational.…

A: 3 is irrigational number: Let 3 is rational number then 3=pq,where p, q are both integers and q≠0…

Q: 9. One-tailed alternatives are phrased in terms of: 00)2 2.0 n zlaarioqy C. # or = A. # B. D. < or…

A: According to one tailed test it is a test in which the critical area of the given distribution is…

Q: 3. Solve the systam using either sab stitetion of ellmattion

A: We solve the given system of equations buy using the substitution method.  Step1 : From the second…

Q: how many integer solutions are there to the equation  X + y + z = 10 for which  a. x,y and z + 10…

A: The positive integers are all the numbers that are greater than 0. The negative integers are the…

Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: or what values of k, x=4 will be a solution for 3x²+4x = k mod31?

A:

Q: Obtain the values of In(/3 – i).

A:

Q: - Opiniones O YouTube Family Vlo. P Create Own Puzzles. Open with Gc 5. Compute (*² – 2) 4

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Q: 19, Obtain the eight incongruent solutions of the linear congruence 3x + 4y = 5 (moi 84 ELEMENTARY…

A: To obtain the eight incongruent solutions of the linear congruence.

Q: Show that if A is singular and Ax = b, b = 0, has one solution, then it has infinitely many.

A: Given: A is singular and Ax = b, b = 0

Q: Show that, by det by b2 92 •92 =TT (ai-bi) br b2 b3 an

A: We have to show that det111⋯1b1a1a1⋯a1b1b2a2a2⋮⋮⋮⋮b1b2b3⋯an=∏i=1nai−bi Let us consider the matrix…

Q: 9. If VW = 9x - 11 and SU = 16x – 12, find WT.

A: Given VW = 9x - 11 , SU = 16x -12 , WT = ? STUV is a rectangle , W is the midpoint of diagnols SU =…

Q: The least positive solution modulo 330 for the system x = 2(mod 5) x = 5(mod 6) x = 3(mod 11) is x =…

A:

Q: Suppose that m,n are two integers such that m3−2n2=1. Does it follow that m and n are relatively…

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Q: How do I use the Chinese Remainder Thm. to solve this system of congruences?? x ≡ 2 (mod 3) x ≡ 6…

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Q: B. Solve the system of congruence's x = 5 (mod 2), x= 7 (mod 5), x= 3 (mod 7)

A:

Q: The number of mutually incongruent solution(s) of 307x = 83 (mod 360)

A: BY THE DEFINITION OF Modulus congruence Modulus congruence means that both numbers, 16 and 21 for…

Q: Find the solution to 2x = 7(mod 17) that is positive and less than 17.

A: We find solution of given congruence relation

Q: Solve the system of congruence x ≡ 3 (mod 6) and x ≡ 4 (mod 7) using the method of back…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.