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question:Which of the following factors does NOT influence the equilibrium price of a product in a free market? a) Supply b) Demand c) Government intervention d) Production costs

answer:c) Government intervention Explanation: In a free market, the equilibrium price is determined by the forces of supply and demand. Government intervention, such as price controls or subsidies, can distort the market and prevent the equilibrium price from being reached. Supply, demand, and production costs all influence the equilibrium price by affecting the supply and demand curves.

question:Sort {frac{3}{2}, 3, -3 sqrt{5}} from smallest to largest.

answer:First, we can convert the fraction frac{3}{2} to a decimal: frac{3}{2} = 1.5. Next, we can compare the three numbers: -3 sqrt{5} approx -6.71 1.5 3 Therefore, the numbers in order from smallest to largest are: -3 sqrt{5}, frac{3}{2}, 3 The answer is {-3 sqrt{5}, frac{3}{2}, 3}

question:In a chemical plant, the cost associated with effluent treatment is classified as which of the following? Options: A) Fixed cost B) Overhead cost C) Utilities cost D) Capital cost

answer:The correct classification for effluent treatment cost in a chemical plant is C) Utilities cost.

question:Rewrite the given equation 2x^2 + 5x - 5y^2 - 7y + 7 = 0 in standard form and classify the conic, then provide relevant properties such as the center, foci, eccentricity, and asymptotes.

answer:The given equation can be rewritten and classified as follows: Classification: Hyperbola Standard Form: 2 left(x+frac{5}{4}right)^2 - 5 left(y+frac{7}{10}right)^2 = -frac{253}{40} This equation represents a hyperbola with the following properties: - Center: left(-frac{5}{4}, -frac{7}{10}right) - Foci: left( begin{array}{cc} -frac{5}{4} & frac{1}{20} left(-14-sqrt{1771}right) -frac{5}{4} & frac{1}{20} left(sqrt{1771}-14right) end{array} right) - Eccentricity: sqrt{frac{7}{2}} - Asymptotes: y = frac{1}{20} left(-14 - 5sqrt{10}right) - sqrt{frac{2}{5}}x y = sqrt{frac{2}{5}}x + frac{1}{20} left(5sqrt{10} - 14right) The hyperbola opens horizontally, with its center, foci, eccentricity, and asymptotes as stated above.