For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.

p= - 0.3x + 5.9 and p = 0.15x + 0.05
equilibrium quantity __________ units
equilibrium price $ __________


13,000:2

Mathematics

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For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists.

A. Absolute maximum: f(7) = 4; Absolute minimum: f(0) = 2 B. Absolute maximum: f(3) = 6; Absolute minimum: f(0) = 2 C. Absolute maximum: f(3) = 6; Absolute minimum: none D. Absolute maximum: f(3) = 6; Absolute minimum: f(5) = 1

Mathematics

Give a verbal representation for the given function. f(x) =  + 19 . Let y = f(x).

A. To obtain y: Multiply x by 3, then add 19 to the result. B. To obtain y: Add 19 to x, then divide the result by 3. C. To obtain y: Multiply x by 19, then divide the result by 3. D. To obtain y: Divide x by 3, then add 19 to the result.

Mathematics

Verify the identity.  = cot 

What will be an ideal response?

Mathematics

Find the volume of the solid. Use 3.14 for ?. Round to the nearest hundredth, if necessary.

A. 414.48 cm3 B. 2486.88 cm3 C. 828.96 cm3 D. 4973.76 cm3

Mathematics