Question 2. Suppose that r + y3 and x, y, z are positive integers. Show that one of the three must be a multiple of 7.

Q: QUESTION 4 The set of critical numbers of fox) = **-1. are OA 0, OB. (-3,3) OC 13,3} D. {0,1}

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Q: 1 If A= find AB. 0 -1

A: Given,          A=100-1   and   B=055110001177

Q: Problem 2. Find all triples of integers (x, y, z) that satisfy r² + 2y? = z2.

A: (x,y,z)=(k|b2−2a2|,k(2ab),k(b2+2a2)),a,b,k∈Z+

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: QUESTION 9 If A=0 and B=1 then A NOR B is

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Q: Question 5 then For all non-negative ny, n2, k, kz E Z. if n, > nz and k > kz

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Q: verify the given equation. 16.∞∑n=0an(x−1)n+1=∞∑n=1an−1(x−1)n

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Q: Problem 5. Using the definitions for O and N, prove formally that a) n³+15n+2 is O(nª) b) 2n³ +25n…

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Q: Question 2 Show that P.() = %3D 2n+1 IM:

A: To Show : Show that ∑n = 0∞12n+1Pn12 = 13

Q: EX.2.48: Nine people are going on a skiing trip in 3 cars that hold 2, 4, and 5 passengers,…

A: Total People = 9 Cars can hold 2, 4 and 5 passengers respectively Possibility of sharing the cars…

Q: QUESTION 9 In a group of 55 students, 35 students are taking MAT1320 and 42 students are taking…

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Q: Suppose that P(Xi = 1) =pi = 1-P(Xi = 0), i=1,2 If p1>=p2 , show that X1 >= X2.

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Q: QUESTION 7 If A=0 and B=1 then A NOR B is

A: NOR gate give positive output only when both input are negative.

Q: Show that: In(-1+/3i) = In2 + 2 ( n + Ti, where n = 0, ±1, ±2, ±3.... 3

A: Show that    ln-1+3i=ln 2+2n+13πi.

Q: So æ[a + In(1/x)]³dx a= 7.5

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Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: How many integer solutions are there to the equation x1+x2+x3+ x4 25 subject to x; > i? Let y. X,-\,…

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Q: Suppose an = 4an – 1 + 6an – 2 a4 = 96, a5 = 430, and a6 = 2276. Find а1, а2, and аҙ. аз. a1 Preview…

A: Here, recurrence formula is, an=4an-1+6an-2-2an-3

Q: QUESTION 1 Ifliafix) -3 and Linf) - F5) -5 -5 -4, then f5): x-5 O annar be denermined. O equals 3 O…

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Q: Problem 19.1. Prove that 2019 can not be represented as a sum of three fourth powers o integers…

A: Take the fourth power of integers from 1 to 7 and obtain that 74 is greater than 2019. Therefore, to…

Q: 1 -dr. a In r| Find 3.

A: Let's find.

Q: QUESTION 3 Determine anand pn form=45and6 and fillout the table below 2 Alach le rome My Comptar

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Q: (9) Let X b(n,- and E(3x) = E(3-5x) find n.

A: It is an important part of statistics . It is widely used .

Q: Question 37 Evaluate: fo So So (r + y + z) dzdydz O 1/4 O 1/12 O 1/8 O 1/24

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: Question #18 Consider the expression shown in the box. 3(x + y) + 4z -3w -(x + y) Which…

A: Given, The expression   3x+y +4z -3w -x+y  We have to find the equivalent expression of the above…

Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

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Q: If x e R and 0 < x < 4, then 4. ac(4-ac) 2 1.

A: 12. Given that x∈ℝ and 0&lt;x&lt;4. We have to prove that 4x4-x≥1. That is, we have to prove that…

Q: If the sun of the number last from 1 to n is equal to n(n+1)/2 what is the sum of the integers from…

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Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: Question 3 A is between Y and Z and YA = 12x, AZ= 42, and YZ = 78. Find YA. YA =

A: GivenYA=12xAZ=42YZ=78

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: 3. Let A, BE M2(Z3) be given by [1 2] B 0 2 A = 1 Find AB, BA, and A? (recall that A2 = AA).

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Q: Question 6 For x > 0, ev3 In(x) = xV3 O True O False

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Q: Question 4 Let P = 2ax + 5ay - 3az, Q = 3ax - 4ay, and R = ax + ay + az. For what values of k is…

A: We are asked to find the value of k

Q: 3 If A = 1] show that A² - 5A + 7I = 0. %3D %3D -1 2

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Q: Let Г3 -5 -1 A 2 3 3 2 В -3 -3 If possible, compute the following. If an answer does not exist,…

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Q: Which of the following sequeces in GP will have common ratio 3, where n is an Integer? a) gn = 2n2…

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Q: Question 11 of 20 There are 17 players on a Calvinball team At the start of the game, the 13 players…

A: There are 17 players on a Calvinaball team. At the start of the game, the 13 players on the field…

Q: Case 8. Suppose the positive integers q is even and the positive integers p,r, s are odd. In this…

A: The mentioned steps are explained here.

Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: Question 5. Show that () +2 +3 3 = n2"-1 +n Hint: you can use property 4 and 5 in the lecture.

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Q: Question 8 22x+ 3 K M 222° Question 9

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Q: + .... Ex. 5. Prove that P,(-) = P,(-}) P,(4) + P,(-1)P2m -1 () + -. Pa(-)P.().

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Q: If ale the oots of (x-a)*+ Cy-a)3+(2-a)3= in 3D0 find

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Q: 2. If Az? i| Find A 2. a A-l = I

A: Given: A=21-11 To find: A-1 Formula: If A=abcd, then A=ad-bc Formula: A=abcd, then A-1=d-b-ca.

Q: Case 1. Suppose the positive integers p,r,s are even and the positive integer q is odd. In this case…

A: Given: The Difference equation…

Q: Show ther' 3 2

A: