4 The equation of the line CD passing through the origin is y = 3x. Write down the equa- %3D tion of this line when it is (a) translated up by 4 units to give line PQ (b) translated down by 3 units to give line 1 RS. (c) draw the three lines on the same axes. 5 Determine the equation of a line that cuts the y-axis at -3 that is parallel to the line

Q: Find dy 2 2.

A: From the given problem:   x2y2=x2+y2   As we know that the Power law:   dxndx=nxn-1   Now…

Q: 21 2. 6.

A:

Q: 75 - 3.5y - 4y = 4y + 6

A:

Q: -5 dx Evaluate 2x 10 A B c) 1 (D) 2

A: formula:

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A:

Q: -7 5 1 9 0 -2 -1 2 -1 4

A:

Q: 48y3 - 27y

A:

Q: 1.25a +3> 0.5a-6 and 2.5a 129-1.5a

A:

Q: 60 27 2. + $6

A:

Q: 2.3 Q13

A: The objective of this question is to use the Squeeze Theorem to show that the limit as x approaches…

Q: +2 1/2 215

A:

Q: 5/14+1/6

A: 514+16=15+742

Q: 1 S- V9 81z2

A:

Q: 22n+1 3n+1 2.

A:

Q: 9 – 4x > –3

A: The given inequality is 9-4x>-3

Q: 3 dx 9

A: The given integral is: I=∫x3x2-9dx

Q: 1 7. 27 2.

A:

Q: Let Mbe as in Equation (3.14) and let X = [1, 0, ½]¹. Show that the entries of Y=MX sum to 1.

A:

Q: 0 1 2 4 0 2 4 0 0 3 9 12

A:

Q: 1-0 1-V

A: The given function for integration is,

Q: Simplify. (3 + 2x)(3-2x) 0 9+ 4x 09-4x² O 3-4x O9-4x

A:

Q: 6 2/5 ÷ 4

A: Given query is to solve the expression.

Q: Add. 4 4a + 3

A: Here given

Q: -11/6+3/4

A:

Q: 2. 9=x-2y 3x + 5 = 2y

A: The given equations are system of linear equations in variables x and y. We solve these by…

Q: 4/10 divided 1/2

A: Answer

Q: Find x 14 Q x n

A:

Q: 1.2x – 3.6 + .3x = 2.4

A:

Q: 36 70

A:

Q: -5/9 + 1/2

A: The given expression is

Q: -3 -2 -1 1 2 0000000 3.

A:

Q: /2 2. 1/2

A: (a12+b12)(2a12-3b12)=2a12a12+2a12b12-3a12b12-3b12b12=2a+2a12b12-3a12b12-3b=2a-a12b12-3b

Q: 2/5 +7/12

A: Please see the answer below.

Q: 12 2х A = 2x

A: (6(a):- Given matrix Q is                              6(b) Singular Matrix:- A matrix is called…

Q: Simplify. -4x + 4x | -2x 是A 3. -4x +4x 2. 3 2. X -2x

A:

Q: 3 3/4 + 2 7/28

A:

Q: find 4 j! j30

A: Simply expand the summation and add all values after calculation.

Q: y - Sy = 0

A: The given differential equation is: y''-5y=0

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.