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Which of the following demonstrates the associative property of addition

Solve for a in the following equation using the quadratic formula:    

Expand through multiplication: (4-x)(x+6)

Solve the equation for t by factoring: 

Madison knows that YGX is a solution with 20% active ingredient for dosages, if the total volume of the standard dose of YGX is 120 ml (cc’s) then:   a) How many ml of active ingredients are in a standard dose of YGX? b) How many standard doses can be made from 375ml of pure (100%) active ingredient? c) The last person working accidentally made 3L of 35% active ingredient solution, how much water does Madison need to add to make it 20% active ingredient?

Make true: 15 ? 7

Graph the linear equation,

Consider a preference relation on bundles of two goods (x,y) defined as follows: (x,y) is at least as good as (x’,y’) whenever the following is true: either x>x’, or x=x’ and y≥y’-1. Is it transitive?

Consider a preference relation on a finite set X={x1,x2,…,xn}. Suppose that it is complete and transitive. Then, the following function represents it: U(xi)= 3log|{j=1,…,n: xi at least as good as xj}|-2020, where |.| represents the cardinality of a set.

A marketing firm is interested in learning about millennials’ preferences on learning experiences. In order to do this, they survey students at a university. They ask them six questions as follows. They consider the following leaning experiences: a traditional class, a flipped course (half of the content is delivered online), and an online class. For each pair of these alternatives, say a and b, they ask the students “is a at least as good as b.” In order to make this operational, they provide the students with a picture in which the three alternatives are depicted as circles with their description next to it. The students are asked to draw arrows between the alternatives whenever the answer to a question is affirmative. That is, if a student finds alternative a is at least as good as alternative b, the student is asked to draw an arrow from the circle with label a to the circle with label b. (No question is a at least as good as a was asked; assume that the answer to each of these trivial questions is affirmative.) Suppose that a student’s answer has no arrows.