Let xer" and ge I show that =yex is an imer product.

Q: Find the domain of * y = V2x +12 ?

A:

Q: and

A: We will find the value of x.

Q: a (1, 0, 1), b = (2, 1, −1) and c = (1, -1, 4). Calculate |ax (b+c)].

A:

Q: Express in terms of i. 1. V - 100

A:

Q: Define nullspace.

A: We have to define, what is null space.

Q: Verify the following identities. Be sure to show all steps in a clear and neat sequence. 1. sin x +…

A:

Q: If (2x, 3) = (2, 3y). What is the value of x and y? *

A:

Q: Let a = (-4, 5, -2) and 6=(-1,0, 4). Find à x b.

A:

Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

A:

Q: Ifnd the alevieting () = 8VX

A:

Q: find all real such that 12x-11>x

A: The inequality can be calculated using absolute values. The absolute value function takes a positive…

Q: 5V2 + 6/64

A: We need to find the solution of 525+6645

Q: Could you please expand on how you found the linear combinations?

A:

Q: What is x?

A:

Q: Find a and b such that 2 1 = a -4 + b -4

A:

Q: The height of 10 plants is measured in inches and found to be 12,6,15,3,12,621,15,18 and 12. Verify…

A: We know that, Mean, X bar = (summation Xi)/m Here n= 10 X bar = (12+6+15+3+12+6+21+15+18+12)/10 = 12

Q: If A=(7,8) and B=(2,4,6) find A x B

A: Explanation of the answer is as follows

Q: where is the res

A: We can find rest parts .

Q: Show that the sum of a positive number and its reciprocal is at least 2.

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Q: Compute/x²dx 2. using trog

A:

Q: ! = [2, 2, 4, 2, 2] =

A: Just notice the method of writing denominators carefully.

Q: a = [, = ; ine 4 Find A· B 1. 3 B

A:

Q: 4. Show that it has a real value!

A:

Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: Show that 0. x+1

A:

Q: 2. Factor x from ax + bx

A: We have to factor x from ax+bx.

Q: 20/√3

A: Given : 20/√3              Because √3 = 1.73205.....              We taka approximate value of √3 =…

Q: Where did the C come from

A: Here the C stands for “combinations”. In general, if we want to choose r objects from a total of n…

Q: of 2X+ス× 3.

A:

Q: If a variable, lets say a, is >0, does that mean a goes to infinity?

A: No, this does not imply that a variable, like a, goes to infinity only because it is bigger than 0.

Q: Exc. Eind. Lim (x-1) y3

A: Solution:

Q: Secza (3tan 2a - 4seczx blx

A: Given : ∫sec(2x)(3tan(2x)−4sec(2x))dx

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.