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Question: 1. Let ∼ be an equivalence relation on a set S. Using the definition of equivalence class, prove that [a]=[b] if and only if a ∼ b.
2. You hang a 3×3×3 cube of pressed birdseed outside your window in order to attract avian wildlife. A grackle comes every day and eats a 1 × 1 × 1 cubelet of birdseed. You wonder can it eat the entire cube of birdseed by always eating a cubelet adjacent to the cubelet it ate the previous day?
Compare parallelograms,rectangles, rhombi, squares, and trapezoids as they relate to sides, side length, angles, diagonals, and created triangles.
Find the maximum margin separating hyperplane by solving the dual lagrangian constrained optimization problem. What is the value of the margin?
Use Exercise I to construct an algorithm for determining whether a directed graph contains a circuit.
SALES GROWTH Moderne Furniture Company had sales of $1,500,000 during its first year of operation. If the sales increased by $160,000/year thereafter.
a city park is shaped like a right triangle with length of one leg twice the length of the other leg. The area is 2500 m2. What are the lengths of the legs?
A national caterer determined that 37% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. If sample proportio..
Aproximately what percentage of household incomes in this state is betwee $27,000 to $63,000/year? Show all work as to how this is obtaines.
Determine the number of three digits which can be formed from digits 1,2,3,4,5, and 6 if no repetitions are not allowed and if repetitions are allowed.
The equation C=mx+b can be used to model the monthly cost, C, of a cell phone plan where b is the flat monthly cost, m represents the cost in dollars per minute and x is the number of minutes used in the month.
Explain the concept of "rational subgroups". Why is it imperative that this concept is carried out in practice?
In a 1993 study, researchers took a sample of people who claimed to have had an intense experience with an unidentified flying object (UFO) and a sample of people who did not claim to have had such an experience. They then compared the two groups ..
What is the probability that each result has four heads in each flip - How many positive integers not exceeding 8154 are divisible by neither 9 nor 12?
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