Mersenne Primes

Determine whether m_13 = 2^13 - 1 = 8191 and m_23 = 2^23 -1 = 8388607 are prime.

Statistics

A random sample of 51 observations was selected from a normally distributed population. The sample mean was 88.6, and the sample variance was 38.2. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method. ...continues

Systems of Equations

Solve the following systems of equations. Procedure should be in matrix form: x1 + x2 = 1 -x1 + x2 + x3 = -1 -1x2 + x3 = 3

Matrix Form of a System of Equations

Determine the solutions of the system of equations whose matrix row is equivalent to 1011 0131 0000 Give three examples of the solutions. Verify that the solutions satisfy the original system of equations.

Inverse Functions and Compositions of Functions

Consider the following function f: R-->Rdefined by f(x)=x^3+1 see attached

Group Theory Proofs

a) Let H be a subgroup of some group G. Prove that if g1H and g2H are not disjoint, the they must be equal. b) Prove that g1H = g2H if and only if g1^-1g2 is an element of H. Thanks

Coefficient problem.

Please show me how to find the coefficient of x^11 in (1-x)^n * (1+x^2)^2m . Thank you.

Initial value problem using the Laplace transform.

Can someone please show me how to solve the following initial-value problem using the Laplace transform. y' + y = 8e^(3t) , y(0) = 2

Discrete Math Multiple Choice

Please help with the following questions. Only answers are needed for clarification.

Descrete Math multiple choice

Note: Please see attachment for full details. 3. A grammar that has no restrictions on production is called a: A) phrase-structure grammar. B) context-sensitive grammar. C) context-free grammar. D) regular grammar. 5. A Karnaugh map for 6 variables will have __________ squares. A) 16 B) 32 C) 64 D) ...continues