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a. Express the prime number 31 as the difference of two squares?
b. Express the prime number 53 as the difference of two squares?
Calculate the value of the appropriate test statistic
For the matrix A given below, find a permutation matrix P such that Post multiplication of A by P interchanges the fourth and the first columns of A.
Theorem: Every sequence of real numbers contains either an increasing subsequence or a decreasing subsequence, and possibly both.
The half-life of cesium-137 is 30 years. Suppose we have a 170 mg sample.
Define a pushdown automaton. Explain how pushdown automata are used to recognize sets. Which sets are recognized by pushdown automata? Provide an outline of a proof justifying your answer.
Melissa of Melissa's Landscaping Service mows many of the lawns in her neighborhood for $100 per lawn, per month.
Eva created a coffee blend for her restaurant by mixing Kenya and French Roast coffee beans. The Kenya beans cost $15 per pound and the French Roast costs $8 per pound. She bought a total of 10 pounds of coffee for a total of $97.50.
An agent lives for two periods and has an endowment of one unit of a homogeneous consumption good in the first period, and ? units in the second period.
Write differential equations for the following scenarios: The rate of infection is constant. The rate of infection is increasing at a rate that is proportional to the number of infected people.
Quadratic equations may be solved by graphing, using quadratic formula,completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Explain why?
What is the probability that the next ramdomly chosen score is less than 84? B) What score is the lowest score you can have and still
Let α be an irrational number with continued fraction expansion [α0, α1, ...]. Show that the continued fraction expansion of -α is
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