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The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 392 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Kellam Images prints snack food bags on long rolls of plastic film. The plant operates 250 days a year. The daily production rate is 6000 bags, and the daily demand is 3500 bags. The cost to set up the design for printing is $300. The holding cost..
A 12-centimeter rod is held between a flashlight and a wall as shown. Find the length of the shadow on the wall if the rod is 45 cm from the wall and 15 cm from the light.
A spring with a 2 kg mass attached to it has spring constant 8 N/m and no damping. There is an external force given by F(t) = 24 sin 2t N, where t is time. The mass is initially stretched 2 m beyond the equilibrium position and released with an in..
You drop a coin down a wishing well of unknown depth h and hear a splash 4 seconds later. You know that the distance the coin covers t seconds after being dropped is 1/2 gt2, where g = 9.8 m/s2 is the acceleration due to gravity, and that the spee..
If 9 less than the product of a number and -4 is greater than 7, which of the following could be that number?
Evaluate the tangent line approximation of the two values and compare with the true value - what about the graph cases
Find the hypothesis
Out of 32 students in a finite math class, 20 are male, 20 are business majors, 22 are first-year students, 13 are male business students, 16 are male first-year students, 14 are first-year students who are business majors, and 10 are male first-y..
Mathematicians say that division by zero is forbidden. The expression 5/0, for example, is undefined. "Undefined" in this sense means "unable to be determined". Why is this?
If A and U are two subsets of a normed vector space, and U is open, show that A+U is open. Here A+U={a+u | a belongs to A and u belongs to U}.
A merchant has coffee with $20 a pound that she wishes to mix with 70 pounds of coffee $90 a pound to get a mixture that is worth $30 a pound. How many pounds (lb) of the $20 coffee should be used?
Retailers will buy 45 cordless phones from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 35 phones at $30 each and 49 at $38 each. Assuming the supply and demand functions are linear, find the ma..
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