Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

Q: Let f : R R:f(x) = 10x + 7. Find the function g : R→R such that gof = fog = IR. %3D %3D

A: Given f: R -> R  such that f(x) = 10x + 7 and  g : R -> R such that g o f = f o g = IR

Q: Let E and F are mutually exclusive and Pr(E) = 0.2 and Pr(F) = 0.6. Find Pr(E ∪ F).

A: Given :

Q: 18. Determine whether each of these functions is a bijec- tion from R to R. a) f(x) = -3x + 4 b)…

A: As per guidelines, we will solve first three subparts of the question. a) Given function is fx=-3x+4…

Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

A:

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

A:

Q: Use the change of variables X1 X2 X3 X4 = = G(r, 01, 02, 03): = to compute the content of the 4-ball…

A:

Q: pYq (pA-q) V (-p ^ q) Show that each of the following holds. a. p ≤ p = 0 b. pvp = I

A: Let's prove each of these statements: (a):  To show p⊽p≡0: We'll first express p⊽p using the…

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

A:

Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: 4. Let A and B be sets and let T C B. Also let f : A → B. (a) Use a diagram to show that f(f-'(T)) C…

A: According to the given information,

Q: Let f e E(0, ox) and let a be a positive real number. Define the function fa as follows Sal) = {";…

A: Properties of Laplace transformation

Q: vx(A x s) = (B · v) A - (a.o)o +a (v-t) – 3 (v. A) %3D

A:

Q: Find a ≤ b such that

A: ∫abx2-9dxApply the Sum Rule:…

Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when…

A:

Q: Which of the following is the parent function for a) f(x) = x b) flx) = x c) fx) = Ix| d) flx) = Vx

A: Given function is y=23x2. We have to find the parent function of y=23x2. The parent function is…

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Q: A third student keeps buying chocolate bars until he finds 5 prize vouchers. Let W be the numbers of…

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: Show that the set of functions 1,cosx,sinx,cos2x,sin2x,…,cosmx,sinmx,… is orthogonal on the interval…

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Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…

A: y=(5x+4)3

Q: If Sc F · dr = Sc(x + 4y?) dæ + (x²y) dy, what is F?

A: Given ∫F→dr→=∫x+4y2dx+x2ydy

Q: Determine U(Z[x]).

A:

Q: Prove that bx q = b. ((Vt) - Vt), where q = V x t

A: We have to prove b→×q→=b→·∇t→Tr-∇t→ for q→=∇×t→ b→×q→=b→×∇×t→          =b→×∑i^∂∂ti×t→…

Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

A:

Q: Show that if f (x) = anxn + an−1xn−1 +⋯+ a1x + a0, where a0, a1,…, an−1, and an are real numbers and…

A: We are given that f (x) = anxn + an−1xn−1 +⋯+ a1x + a0, where a0, a1,…, an−1, and an are real…

Q: u = [2, 6, –5] and v= [-3,–1,6] %3D A · A + (A + ng-) · (A x n)

A:

Q: 6. Prove that |xy| = |x|ly| for all real numbers x, y.

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Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

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Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

A:

Q: b) Find 4°f(x) if f(x) = (3x+1)(3x+4)(3x+7) ... (3x + 19) %3D

A: We will answer the first question only as we don't answer multiple question at a time. Please…

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Q: Let y = 7 and U-span(u), with u = x1 = x2 = -21 TT -4. Write y=x1 + x2, where x1 in U and x2 in U+.…

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Q: (a) Let x1,.., Xn+2 € R". Show that there must exist some sets A and B such tha i. ANB=Ø, ii. AUB=…

A: Let x1,x2,....,xn+1∈ℝn We take n=5. then x1,x2,x3,x4,x5,x6,x7∈ℝn There exists two sets A and B,…