##### How do you calculate the probability of compound events?

How do you calculate the probability of compound events?

##### Find and Simplify where ................................

Find f(a+h) - f(a) / h where f(x) = 6x - 9

##### What is the number of group homomorphisms from z12 to z13?

What is the number of group homomorphisms from z12 to z13?

##### What is the vertex of y = 2x² + 6 x + 4 ?

What is the vertex of

y=2x²+6x+4  ? Give details explaination

##### concave function

What x values is the function concave down if  f(x)=15x⅔+5x ?

##### Number Theory

Given integers a, b, c,

g.c.d.(a, b, c) = 1 if and only if g.c.d.(a, b) = 1 and g.c.d.(a, c) = 1

##### syllw subgroup

The number of involutions in G is |G|/4, and every right coset of a Sylow 2-subgroup S of G not contained in NG(S) contains exactly one involution.

##### Integer property ( Real Analysis)

An integer n is called even if n = 2m for some integer m, and odd if n + 1 is even. Prove the following statements:

(a) An integer cannot be both even and odd.

(b) Every integer is either even or odd.

(c) The sum or product of even integers is an even integer. What can you say about the sum or product of odd integers?

##### Density property of Real number

If x and y are arbitrary real numbers such that x < y, prove that there exists at least one rational number r satisfying x < r < y, and hence infinitely many.

##### Differential equation

Solve the differential equation with details explaination :

x²y" + 6xy' - 24y=x^9

##### Kernal ( Homomorphisms)

Prove that φ : Z ⊕ Z → Z by φ(a, b) = a − b is a homomorphism. Determine the kernel.

##### Homomorphisms

How many (group) homomorphisms are there from Z20 onto (surjective to) Z8. How many are there to Z8?

##### Gaussian Elimination Solve using Gaussian elimination with partial pivoting and 4 digit arithematic

##### Maclaurin Series

Find the Maclaurin Series of the following functions:

(a) f(x)= Ln(3+x)

(b) f(x)= cos(3x)

(c) f(x) = x^(2)(e^(-x))