Suppose for this problem that Pr[E]=2/3 and Pr[F]=2/3. Just as in the book, Pr[(E∪F)′]=0. (1) What is Pr[E|F]? (2) What is Pr[F|E]?

Q: The law of cosines. Prove this generalization of Pythagoras' theorem (see Figure 2.7): || X - Y||² =…

A: As per Bartleby answering guidelines when multiple questions are posted in single picture then the…

Q: Find F(s). F(s)

A: We use the table of Laplace transform to answer the given question.

Q: 2. Consider the functions g, h: R → R defined by g(x) = x² and h(x) = x³ + 1. A. Evaluate f(g(x) ·…

A: g(x)=x2h(x)=x3+1∫xndx=xn+1n+1+c

Q: determine L−1[F].

A:

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: Set f(x) = In(9x - 8). Question 1 For k > 1, f (k) (1) =

A:

Q: Find f"(3) if A) = (x- 3) (x² - 2). x): %3D a) -1 O b) 25 O d) -25

A:

Q: I only need answers to questions (b) (f) (g)

A: (b)   The test statistic is 22.99 and it is calculated below:   From the given information, the…

Q: Which of these functions are even ? A = f(t)= ₤²+2t B- m(t) = +4 +2 C- n(t)= tcos(t) - Sen² (+) P-…

A: Option (B)Explanation:A function f(x) is defined as an even function if f(-x) = f(x) Here out of all…

Q: (c) Will it always be true that W C X f(W) S (X)?

A:

Q: . Let f(x) = ka. Determine the constant a so that f(-1) = 10 and f(2) = 5 19 4

A: Given query is to find the constants of the function.

Q: Determine L−1[F(s)]for the given F. Q) F(s)=s+4/s2+6s+13

A: Consider the given function: Here the objective is to find the Inverse Laplace Transformation of…

Q: Find f(t). e s2 + 1

A:

Q: determine L−1[F].

A: Given Data The function is F(s)=4/(s+2)3.   The general inverse transform rule is,

Q: determine L−1[F].

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.