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Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically.
1) (x1,y1)R(x2,y2) if and only if x1 = x2
2) (x1,y1)R(x2,y2) if and only if x1 + y1 = x2+y2
3) (x1,y1)R(x2,y2) if and only ifx1^2 + y1^2 = x2^2 + y2^2
Simon does not complete his homework, Both Simon and Hannah complete their homework
Let R be the region bounded by the curves f(x) = ln(x+3) +2 and g(x) = x^2 - 8x + 18. Using the washer method, find the volume of the shape which is formed if R is rotated around the x- axis.
A package contains 9 candy canes, 6 of which are cracked. If 2 are selected, find the probability of getting no cracked candy canes.
What is the mathematical model for the total profit earned by producing and selling x units ? What is the optimal solution for this production model?
If the minute hand and the hour hand on the clock both start at 12:00 when will the two hands first coincide? How many times will they coincide in 12 hours?
The Probability of a Random Number. A number n is chosen at random from the set {1, 2, ..., 20}. We are interested in k, the integer power of 2 which exactly divides n. Recall that we say that 2k exactly divides n if 2^k|n but 2^(k+1) |/ n. We wri..
Important information about Probability and Statisics. Find the probability that a randomly selected adult has an IQ between 90 and 110
Write the complex number in rectangular form. 7(cos120degrees + i sin120degrees) =
Describe a real world situation that could be modeled by a function that is increasing, then constant, then decreasing. What would be the difficulties associated with modeling this situation?
Find the natural domain of the given functions.
Different ways to schedule appearances of 4 performers. There are 4 performers who will present their comedy this weekend at a comedy club
Detailed Explanation to Probability Distribution, A small bag of Skittles candies has the following assortment
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