mod

Prove that: if bd= bc (mod p) where p is a prime (and p does not divide b) , then d= c (mod p)

Independent and Dependent Variables

In a typical algebraic expression, there are two variables: an independent variable and a dependent variable. The independent variable is the number or the value that can change. The dependent variable's value depends on the value of the independent variable. For example, in the following formula, X=Y*5 Y is the independent ...continues

Divide, Complete the Square, Quadratic Formula

1.) Divide: 5x^2y^5z67+8xyz/2x^3yz^2 2.) Solve by completing the square: x^2 +12x = 3 3.) Solve using the quadratic formula: 3t^2 - 9t = 4 4.) Solve by the factoring method: 21p^2 - 36p = 9

Determine whether the given mapping is an isomorphism between the given binary structures. If not, explain why and given a counter-example.

Determine whether the mapping phi: Z -> Z which is defined by phi(n) = n + 1 is an isomorphism from the binary structure (Z, +) to the binary structure (Z, +). If not, explain why and give a counter-example.

Determine whether the following binary operation give a group structure on the given set. If not, give all reasons they fail and supply counter-examples. a*b = ab in Q.

Modern Algebra Group theory Determine whether the following binary operation give ...continues

Modern Algebra

For any x ... the following equalities hold... Prove either a or b. State any properties used in your proof. Please see attached for full question.

Modern Algebra

Consider the set R=... a) Construct addition and multiplication tables for R, using the operations in... Please see attached for full question.

Probability; Interest Rate; Bacteria Multiplication

PLEASE SHOW ALL WORK FOR COMPLETE UNDERSTANDING! 1) A bacteria culture starts with 7 batceria which multiply simultaneously every three house. If the first generation is born fromt he initial group at 12 midnight a. How many bacteria will be in the culture at midnight the next night? b. Also what time will there be 224 ...continues

Arithmetic Sequence

I am trying to determine and prove the general law for the following sequence: I would like to express it in notation. 1+2=3 4+5+6=7+8 9+10+11+12=13+14+15 16+17+18+19+20=21+22+23+24

finding an odd ball out of a lot of 12 balls

You have 12 balls out of which one is odd ie lighter or heavier than others. You cant identify the odd ball just by looking at it.So how you would find out the ball , using the weighing scale and maximum weighings allowed are three only ?