A) Find P(B) B) Find P(B|H) C) Are A and H independent? Explain.

Q: The Direct Method of Formal proof 5. S→ P P→ (W VJ) SA¬W :. J

A: To find- The Direct Method of Formal Proof S→PP→W ∨ JS∧¬W∴J     Rules of Inference Used-…

Q: Find z given that P(.24 <Z <z) = .12

A:

Q: Given two points (x1, y1) and ( x2 ,y2 ), Derive the linear interpolation formula in terms of these…

A: Let y=fx be  a function which takes the value x1, y1, x2, y2 So, there are two pairs of values of x…

Q: O How does one fin d the domain of the q40tient of two furctiong t

A: In order to find domain for the quotient of 2 functions  make sure that the denominator will not…

Q: 7. Apply Lagrange interpolation formula to find k, given that P2(3) = 35 2 5 f (x) 2 k 275

A:

Q: Find P(A), given that P(A) 0.493.

A: Given,      P A=0.493

Q: B. Prove that (P – R) × (P + R) = 2(P × R) %3D

A: Properties of cross product of vector:

Q: loes it follow that P(3) = 0 as well? Why

A: We have to explain the given condition

Q: Find the exact values of x and r. (X, r) 12, 30V3 x ) ) 3D 30° 12

A: From the given figure, it is observed that the opposite side is 12, adjacent side is x and the…

Q: Determine whether (p→q)→(q→r) is equivalent to q→r. Justifyyour claim.

A: we have to check whether  (p→q)→(q→r) is equivalent to q→r

Q: Find all values of x so that u · u = 50, where

A: Given u·u=x34.

Q: To show that ANMQ = AQPN by SAS, what must be the value or x? N P 51° 5х- 1 Зх + 5 51° X = M Q

A: We have  to find x

Q: Q3- Find the numerical value of xdz, ifc = c, + C2 + C3.defined in the given figure. (2,2) C2 (1,1)…

A: Integrate in parametric form.

Q: In Exercises 3 and 4, find the values of x and y. 3. AXYZ = ARST

A: Given,            △XYZ≅△RST            XZ≅YZ            RT≅ST

Q: Find the value of t so that t 4 -4| 2 3 3=4 4 5 0

A:

Q: a) In the figure, are AB, CD, and EF C A- B concurrent? b) Are CD, EF, and GH E concurrent? F D G

A: Concurrent lines: Three and more than three lines are called concurrent if the intersection point of…

Q: B. by using Rules of Replacement 1. [p V (~ p ^q)] → (p A q) 2. {~ (pvq) v [(~ p^ q) v ~q]} +→ ~…

A:

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

A:

Q: What value of x would prove that p || q? A (5x+14) 19x-28) C

A: we have to find the value of X from the given figure

Q: 8 {4} {{ {}₁ s² + a² s² +6² (1)

A: Given: L-1as2+a2·ss2+b2............(1)12∫sin2t+3u+sin7u-2tdu............(2) We have to find the…

Q: What additional information would be needed in order to prove A CAT = A DOG by Side-Side-Side (SSS)?…

A: Given that △CAT≅△DOG by side-side-side(SSS) write down the additional information to be needed to…

Q: Show that ¬∀x∈A ¬P(x) is equivalent to ∃x∈A P(x)

A:

Q: The Direct Method of Formal proof 5. S → P P→ (W V J) SA¬W

A: To prove:            S→PP→W ∨ JS∧¬W∴ J

Q: r* – 2 Show, using the definition, that is O(z²). z +1

A: Here, To satisfy the definition of O(x2), we need to find an appropriate choice of c and k.Let’s…

Q: Find the degree of Q(V2, V5) over Q.

A:

Q: 4. proj, u 5. u x v

A: This question is related to vectors.

Q: that P = X 12 B. 3. 1, 2.

A: The plane figure bounded by the union of three lines, which join three non-collinear points, is…

Q: Q7. V(x, y) = x³ + y³ and x = 2t +r,y = 2t – r , what av? is ? ar

A:

Q: Find the converse of q p.

A: q⇒p means "if q, then p"The converse of it will be " if p, then q"which has been symbollically…

Q: Q8 Let P(A) = 0.9 and P(B) = 0.8. Show that P(A n B) 2 0.7.

A:

Q: E K 7 21

A: Please see the explanation below

Q: What does Q represent?

A:

Q: Assume that P (A n B) = 0.25, P (B) = 0.65, and P ( A 0.15. Find P (A).

A:

Q: 3. Show that a2 + b2 + c2 > ab + bc + ca and using this result show that (a) (a + b + c)2 > 3(ab +…

A:

Q: P[N;(1) = k/{N¡(1) + N2(t) = n}] = nC p q"-k, where and q = P = 21 + 12 21 + 12

A:

Q: B. Prove that (P- R) × (P + R) = 2(p × R)

A: We have to show that the given expression.  For this we will use the results of cross product

Q: In the previous exercise, let G = G-{a,c,e,f} Gq = G[{a,8,e}] Draw G,U Ga. %3D

A:

Q: Given that Q11 = 50, Q12 = 45, Q21 = 60, and Q22 = 90, calculate the value of P using bilinear…

A: There are several ways to calculate the value of P. An easy way to calculate the value of P would be…

Q: j) Is there a number n with the prop- erty that f(n) +2=5?

A: Given: There are 10 peoples in a line. Let A=1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and f be a function that…

Q: (d) Verify that for v= (a, b) E R², P[v]s' = [v]s and Q[v]s = [v]s•.

A: d) First find the matrix P that is the change of basis from S to S'. 1,3=31,2-12,31,4=51,2-22,3…

Q: Show that p v ((-p ^ q) → q) = T

A:

Q: Determine whether i is an element of Q (V2+ i).

A:

Q: (a) What is the support of Y? (b) Find P(Y = 2).

A:

Q: Use resolution to show ∀x∀y[p(x,y) → ¬p(y,x)] models ∀x¬p(x,x)

A: Please look into the next step for detailed answer

Q: Use the theorems and given information to show that r | 8. %23 1 2 3 4 87 6/5

A:

Q: (a) What is the behavior of V(r) as r→0? As r-0, V(r)→ O What is the behavior of V(r) as r→0? As…

A: Given that, the function is Vr=1r6-Ar3. Find the behavior of Vr as r→0 as follows, Apply the left…

Q: Use the P-value Decision Rule to either reject or do not reject H, when: p = 0.4958 0.10 a = A)…

A: The p-value of the hypothesis test is, 0.4958. The level of significance is, α=0.10

Q: Q3/ The value of k such that P2 (1) = 2.8, 2 4 of 1 2 Is

A: Lagrange interpolating polynomial for n=2 is:…