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
Division, Complete the Square, Factoring and 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 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.
Modern Algebra Group theory Determine whether the following binary operation give ...continues
For any x,y E R (i.e. Ring R) the following equalities hold. a) 0.x=0 b) a(-b)=(-a)b=-(ab) Prove either a or b. State any properties used in your proof. Please see attached for full question.
Set Operations : Commutativity, Unity, Zero Divisors and Multiplicative Inverses
Consider the set R={0,2,4,6,8} C Z10. a) Construct addition and multiplication tables for R, using the operations in Z10. b) Is R a commutative ring? Does it have unity and, if so, which element is unity? c) Does R have zero divisors? d) Which elements of R have multiplicative inverses? Please see the attached fi ...continues
Probability; Interest Rate; Bacteria Multiplication
PLEASE SHOW ALL WORK FOR COMPLETE UNDERSTANDING! 1) A bacteria culture starts with 7 bacteria 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
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
Logic : Finding a lighter or heavier ball out of 12 balls, with only three weighings allowed
You have 12 balls out of which one is odd ie lighter or heavier than others. You can't 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?
Congruences : Binomial Formula and Common Factors
Is 5^((10^5)^(10^5)^(10^5)) congruent to 1(mod 11)? I know this answer is yes but do not know how to prove this. Please see the attached file for the fully formatted problems.
