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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.
find the midpoint of the midsegment of a trapezoid with vertices o(0,0),A(4p,4q),B(4r,4q)and C(4s,0)
find the following probabilities for the stand normal random variable fora. pzgt1.23b. pzlt-1.27c. p0.31lez2.68d.
A speedboat could travel at 3 times the speed of the current. Thus, it could travel 525 miles downriver in 1 hour more than it took to travel 200 miles upriver. What was the speed of the boat in still water?
find the probability that the airline will have a seat for each person who has reserved one and who shows up
Determine the correlation coefficient, rounded to two decimal places, between percentage of people in a country who are literate and the percentage who are undernourished.
The average molecular velocity v (m/s) of a gas in a certain container is given by the formula below, where T is the temperature in kelvins. The temperature is related to the pressure (in atmospheres) by T = 400P. Find the indicated derivative. v=..
q in a group of 97 students the number taking english is twice the number of those taking math. 53 students are taking
Two planes left an airport at noon. one flew east at a certain speed and the other flew west at twice the speed. The planes were 2700 mi. apart in 3 hours. how fast was each plane flying?
Explain how the formula for standardizing z-scores forces a given normal distribution to have a mean of 0 and a standard deviation of 1.
Find the regression coefficients.
Given S is a subset of R. Suppose S' (set of all accumulation points in S) = emptyset. Prove S is countable.
A hat contains n coins, f of which are fair and b of which are biased to land on heads with a probability of 2/3. A coin is drawn from the hat and tossed twice.
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