Correct Answer: D

Rationale: The correct answer is D: 4.412 10^3. To simplify the expression, rewrite 4.71 10^3 as 47.1 10^2. Subtract the values in front of 10^2: 47.1 - 2.98 = 44.12. Rewriting this gives 44.12 10^2 = 4.412 10^3. Choice A is incorrect as it does not account for the correct subtraction result. Choice B is incorrect as it does not correctly simplify the expression. Choice C is incorrect as it provides an incorrect power of 10 in the simplified expression.

Correct Answer: C

Rationale: To find the number of hosts in the restaurant, first, express the ratio algebraically as 9x + 2x + 1x = 36, where x represents the common factor. Combine like terms to get 12x = 36. Solve for x by dividing both sides by 12 to get x = 3. To find the number of hosts, multiply the coefficient of hosts (2) by x, which equals 6. Therefore, there are 6 hosts at the restaurant. Choice A, 3, is incorrect as it represents the number of servers. Choices B and D are incorrect as they do not correspond to the number of hosts based on the given ratio.

Correct Answer: D

Rationale: To simplify the expression, first multiply 6.4 by 2.8 to get 17.92. Then, divide the result by 0.4 to find the final answer. Therefore, (6.4)(2.8) · 0.4 equals 44.8. Choices A, B, and C are incorrect because they do not represent the correct result of the given expression.

Correct Answer: B

Rationale: Using PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction): (3/2)(8/3) · (5/4) = (24/6) · (5/4) = (4/1) · (5/4). To divide fractions, the second fraction is flipped and then multiplied by the first fraction, resulting in (4/1)(4/5) = (16/5), which simplifies to 3(1/5) or 2.

Correct Answer: B

Rationale: The cost of gas per mile, c, is calculated by dividing the price of gas, represented by p, by the car's average mileage, represented by m. Therefore, the correct equation is c = p/m. Choice A (dp/m) incorrectly multiplies the price of gas and distance, while choice C (mp/d) incorrectly multiplies the average mileage and price of gas. Choice D (m/p) incorrectly divides the average mileage by the price of gas, which does not represent the cost of gas per mile.