1. Which is equivalent to 8+7 +2 2十1 O (e+1)(z-7) #十2 e+1 +2

Q: In(z,) – In(-V3 – 1) = -In(2) – 1

A: given the argument ∅ of the complex number -3-i as -5π6.and also the modulus of a complex number say…

Q: 2. 3. NOR A NAND A OR A AND A NOT A NOT A NOT B NOT B NOR A NOT C NOT C MAND B NAND A

A: Theory: OR gate: A OR B ⇒ A+B AND gate A AND B ⇒A.B NOT gate NOT A ⇒A' NOR gate: A NOR B ⇒ (A+B)'…

Q: 6. (a) UL0,i +1] = (b) N[0, i+1]= ieN ieN

A: .

Q: 5- Determine whether each of the following is singular or nonsingular: [4 1 -21 [3 2 41 il - A =5 1…

A:

Q: n If E (ak + bk) 2n and n+1 k=1 E(ak – br) +, then ak = n n+2 k=1 k=1 3 2 5 2 O None 2

A:

Q: 4. Conclude that n2 n=1 ||

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Q: 4. If 2 3 -1 1 A %3D 1 Then det(A) -34 -26 34 26 O 5 3

A:

Q: Evaluate O O O O K|4 2 6 wo|= • S² +2²+1 dt. - 3

A: Here is the solution:

Q: 15. If an+2 = 3an+1 - 2an and ao = 3, a1 = 4, then an = O 3(2") - 3" + 1 O 5(2") - 2(3") O 7(2") -…

A: See the attachment

Q: 14. Given this diagram: 12 10 11 (a) What definition allows you to conclude that 410 is…

A: Given:

Q: Disprove by Contradiction If a,b,c ∈ ℕ, then at least one of a-b, a+c and b-c is even.

A:

Q: أ- اوجد الحل الامثل باستخدام طريقة The Assignment Jlac l aaj * Model 1 3 4 5 7 4 2 10 8 11 10 3 6.…

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Q: 10. Given: MN || PO, MP || NO Prove: MP = ON Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 7.…

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Q: 5. (1). Prove by contraposition: m, n E Z, if m + n is odd, then m² + n² is odd."

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Q: 2.6.49 9- Use - o or 0o where appropriate = JO au pue ane uouny upeo pug (B)-20) (X u O) JAIR-10)

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Q: 7. I) Find, if possible, AB ond BA A= 3212/ 2.

A:

Q: 5- Determine whether each of the following is singular or nonsingular: [4 1 -21 i- A=1 7 15 8 [3 2…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: In a prefabricated building factory, 1000 molds, 400 of which are made of wood, found that 10% of…

A: GivenThe total number of molds =1000The molds made up of wood =400 The percentage of molds which are…

Q: 5- Determine whether each of the following is singular or nonsingular: [4 1 -21 i- A=1 7 l5 8 [3 2…

A:

Q: 4. х%3D 26 5. х%3 18 PHILI

A: Let X be the random variable from normal distribution with mean (μ) = 17, standard deviation (σ) = 4…

Q: Is 12n + 18 equivalent to (2n + 6) (n + 3) ? True O False

A: Answer: True.

Q: Converges or diverges

A:

Q: 5. Which of the following is equivalent to (v2/2 – iv2/2) ? O -2 O 1 O -1/2 O -1 O 2 O 1/2

A: We have to find the equivalent of given complex number.

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: 21. Compute A100, and A-1, where A 5 0 0 -3 -2 0 -305

A: given matrix A=50-30-20-305 compute A100 and A-1

Q: If X ~N (6.7,25), then 1) u = ; 2) o² = ; o = 3) P(8<X<14) = .

A: Reviewing information, Given, X~N(6.7 , 25)

Q: (-1)" In(nº) Σ 20. 4n n=2

A:

Q: 12 + 22,., +n? =n(n+ 1)(2n + 1), Vn eN

A: We will prove this as following.

Q: 5- Determine whether each of the following is singular or nonsingular: [4 1 -21 i- A=1 7 3 [5 8 [3 2…

A:

Q: 3 Let A = 4 1 Write 5A. Is det 5A = 5 det A?

A:

Q: What is the coefficient of x' in (3-x)10 O a. -C(10,3)* 33 O b. C(10,3)* 33 O . P(10,7)* -33 O d.…

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Q: 5 3 compute 2A Given A -1 -1

A: The matrix is given by A = 53-1-1 To evaluate : The value of 2A

Q: 4. Given that ! n+1 0.47199 determine the value of " +1

A: Here we have to find the given value.

Q: 45, n-1 on? 12 1 2, ns 1, Al 7(n 11, what is the

A: This is a problem of inhomogeneous recurrence relation and counting.

Q: -In 4 et dt Ve2t +9

A: Solution - We are given let y, y = ∫0ln4ete2t + 9dt…

Q: 423. et dt 1- e2t

A: Since, we have to evaluate the integral given below:-I=∫ex(1-e2t)dt -(i)

Q: 2. (a) Evaluate e²-dr, where a > 0.

A: Let, I=∫0∞e-x2-a2x2dxI=∫0∞e-x2e-a2x2dx Let F(x,a)=e-x2-a2x2DaF=-2ax2e-x2-a2x2DxF=-2x+2a2x3e-x2-a2x2

Q: Ice O 3.19 O 13.9 O 12.6 O 16.1 O none of the above (ezt - e-²t)² dt

A: Given that a integration and we solve this integration by using general formula of integration. Here…

Q: 3 13 4)2 =V81, state true or false. 4 Compare the following with , or = %3D 25 Answer: m/2

A: Given:  (1) 13 - (√4)2 = √81 (2)  √(5/2) ?  3/2

Q: Evaluate: [x(1-2²) da ¾ O ³(1-x²) + C 3 0-² (1-x²) O 3 + C O 2/(1-x²) + C 3 O ㅇ글 (1-22) : + C (1-x²)…

A: Here we have to find the integral.

Q: 口 4. Evaluate the expression 2(5 -(Gm)) – 7 where m = 4. %3D -1 O -5 O1 O -3

A: Given:-the expression 25-12m-7To find: evaluate the expression when m=4

Q: Is 2 (n² + 6n + 9) equivalent to (2n + 6)(n + 3)? O True False

A: (1) Function ht=15+60t-16t2 Given that value t=10…

Q: 14. If an+1 = 2a, + 2 and ao = 2, then an O 2n + 1 O 2n + n + 1 2n+2 - 2 O 3(2") - 1

A: a0 = 2 an+1 = 2an +2 We need to find an. The solution is given below.

Q: Which of the following is equivalent to 10 5 3(x–2) .? 3(x+1) 10(z+1) + 3(z–2)(z+1) 5(z–2)…

A: Given:   To determine: The equivalent expression from the given choices.

Q: Assume there are 3500 undergraduate students studying at AUA, 1800 students have taken Business Math…

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

Q: 35. A'U (Bn C") and (A'U B) n C'

A: In this question we have to prove equality using venn diagram.

Q: If m 3 = 2x°, then what is m 5? 1. 7. 8. O 90° O 180° - 2x° O x° O 90° - 2x°

A:

Q: 4, Suppose P(A) 2 0.8 and P(B) > 0.5. Prove P(AN B) > 0.3. Hint: You may use P(AUB)< 1.

A:

Q: a) How has he arrived at this conclusion? b) What assumption is he making? c) Do you agree with his…

A: Given, P( Harvard accepted)=0.053 P(Dartmouth accepted)=0.1 P(Penn accepted)= 0.099 P(atleast one…