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1. Let f (x) = 3x + 1 and g(x) = -x2 - x. Is it true that f (g(x)) = g(f (x)) for any x ∈ (-∞, ∞)? If not, is there any particular real value of x, which satis?es the above equation?
2. For the following demand and supply functions of a product, state the economically sensible values of price and quantity for which each of them are de?ned. Draw the market diagram for this product with price shown on the vertical axis.
What are the equilibrium price and quantity? Carefully explain why the price you obtained is the equilibrium price.
r qS = -5 + 3p,
qD = 20 - 2p.
During the year they made only a nominal amount of disbursements of the type that qualify as itemized deductions. What is their standard deduction on a 2011 joint return?
Compute the total present value of a series of 5 future payments of $20,000 each which are to be received 12, 14, 16, 18, and 20 years from now when interest is compounded continuously at rate 10% per year.
you have been hire to design a rose garden for a client. the client wants the roses to surround a rectangular
A 380 in. piece of wire is divided into two pieces and each piece is bent into a square. How should this be done in order to minimize the sum of the areas of the two squares?
An overnight delivery service accepts packages of up to 165 inches in length and girth combined. (Girth is the distance around the package.) A package has a fixed girth of 53 inches. Determine (in terms of an inequality) those lengths for which a ..
At every subsequent stage, a ball is randomly selected from the urn whose color is the same as that of the ball previously selected and is then returned to that urn. In the long run, what proportion of the selected balls are red? What proportion a..
trees occur in various venues in computer science decision trees in algorithms search trees and so on. in linguistics
Why do we use pseudorandom numbers in simulation? How do pseudorandom numbers affect the accuracy of a simulation?
The minute hand on a watch is 9 mm long and the hour hand is 5 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)
Find the probability that B beats A, that is, that the number that appears on die B is greater than the number on die A.
using the formula NI = [ U * ( P - VCu )] - FC , in which order must you complete the calculation? Why does the order of operations matter?
Dividing a complex number with another number.
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