4. Let, a1 = 3, a2 = 4 and for n ≥ 3, an = 2an-1 + an-2 + n2 , express an in terms of n.

Q: 22. Hr. u 2 200 versus Hr: u < 200, a = 0.05,x= 198, s = 5, n= 25 1) (z= -2.00, p-value = 0.0228) 2)…

A: As per our guidelines, we are allowed to answer first question only. Thanks   22) Here we have been…

Q: 37.) Show all step to evaluate: SN NS /3-y² /3-y² dzdxdy

A: We have to find the value

Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

A:

Q: In 26-36, write a proof. 3 12 1. a Ex. 26 Ex. 27 26. Given: mz1 + mz2% 180°, mz3 + m2 180°. Prove:…

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Q: Suppose two members of the group of twelve insist on working as a pair---any team must contain…

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Q: Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same as

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Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

A:

Q: Consider the following IVP: у зу -10у - 1, уo) --1, у(0) - 2 Find the general solution. A 13 St re…

A:

Q: For this problem, assume the box contains 6 red balls, 7 blue balls, and 5 white balls, and that we…

A: Given that  box contains 6 red balls, 7 blue balls, and 5 white balls. Total number of balls is…

Q: Show that for all n, m∈Z if n+m is even, then either n and m are both even or n and m are both odd.

A: Use the results of addition of integers.

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

Q: Prove that in Q(/-5) we have (3,1+ 2v-5)(3, 1 – 2-5) = (3).

A: To show the equality, first we take an element of the product and show that it is in (3) and then we…

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

A:

Q: in in Signed-Rank Test a two-sided alternative, we may reject H0 in favor of H1 if either w+ or w-,…

A: Signed rank test for  two tailedHo:M≠Mowe reject Ho, if W+≤Wα and W-≤Wα

Q: 2. Count the number of rearrangements of the word TASTE in which no letter appears in any of its…

A:

Q: Let {Xi} be i.i.d.∼ Exp(θ) and ai > 0. Denote by Z = min{a1X1, . . . , anXn}. Suppose that sum 1/ai…

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Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: to: explicitly state the te- Σ2/ n=1

A:

Q: =3. Let a = [2₁1,-1], 5o = [4₁-5, 3] and C-[-1,-2,5]. compute ax (b + c). Show full steps.

A: We have to solve given Questions.

Q: (c) Show that a permutation o E S, commutes with r if and only if the permu- tation f(o) commutes…

A:

Q: For n>2, let an=5n/n2-2 determine for which n, |an|< 1

A: For n&gt;2, let an=5n/n2-2 determine for which n, |an|&lt; 1

Q: P-value = 0.072, a = 0.05 O reject Ho O do not reject Ho P-value = 0.005, a = 0.001 O reject Ho O do…

A: We need to determine the decision based on the given p-values and significance level.

Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

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: 3. Show that if A-1 exists, then eAT dr = A-1(eAt – I) = (eAt – I)A-1.

A:

Q: Now, from the relations in (6) we get Wn = µ+ kn (Wn-1 + Wn-2) and zn = € + Vn (žn-1 + Zn-2). (9)…

A:

Q: S Sech (ax-

A: Evaluating the integral of hyperbolic function using substitution.

Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

A: Seriese expansion

Q: Compute [rN (1- ) ]- d. K

A:

Q: 4. Demonstrate that Re(iz) = -Im(z);

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Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

A:

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

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Q: 3. Suppose (a,n) is Cauchy and that for all m, k 2 100, Jam - as 0. Does it follow that the…

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Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

A:

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: Suppose that X, Y ⊆ U. If n(X) = 24, n(Y ) = 18, and n(X ∩ Y ) = 14, what is n(X Compliment ∪ Y ) if…

A:

Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

A:

Q: Let, a1 = 1, az = 2, b1 = 0, b2 = 1, for n 2 3, 2ап-1 + bn-1 for n 22 b, = bn–1+ an-1 an express an…

A:

Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: 3. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1+ an-2 + n² + 1, express a, in terms of n. %3D

A: Recurrence relation - it  is an equation that denotes  the nth term of a sequence as a function of…

Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

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Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: 8 Show that 1+2++ In S 1|+ |r2|++|rn| for any numbers r1, 22, ....

A: To show,    x1+x2+.....+xn≤x1+x2+.....xn   for any numbers  x1, x2,....., xn . Which is generalized…

Q: 3. Suppose at a small college, 30% of the students are freshmen, and 60% of the students live on…

A: Given, The probability that the students are freshmen is pf=0.30 The probability that the students…

Q: Therefore we obtain that U1 +h +P U2 12 0, U1 > 0. 1- p 12 U2 Thus, we get that -h = 0, U2 – 12 =…

A:

Q: Given that Z - N(O, 1) use tables to evaluate correct to three decimal places then P(1.24 < Z <…

A: Required probability is P(1.24&lt;Z&lt;2.36)

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

Q: The Domain of f (z) is [3, 00) and range of f(z) is [2, 3], then Select one: O a. domain of f(x) is…

A: Suppose we have a function f(x) whose inverse is f-1(x). Then the domain of the inverse function…

Q: 8. Following the idea of Exercise 6 and referring to Exercise 7, express the positive gcd of 49,349…

A: