Add and simplify: 4â…” + 6½ =

Correct Answer: C

Rationale: To add 4â…” and 6½, we first need to convert the fractions to have the same denominator. Converting 4â…” to 6ths gives us 8/6, and 6½ to 6ths gives us 7/2. Adding them together gives 15/2, which simplifies to 7½ or 9â…™. Therefore, the correct answer is 9â…™. Choices A, B, and D are incorrect as they do not represent the correct sum of the fractions after conversion and simplification.

Correct Answer: C

Rationale: To divide mixed numbers, we first convert them to improper fractions. Converting 4â…› to an improper fraction gives us 33/8, and converting 1½ gives us 3/2. Dividing 33/8 by 3/2, we multiply the first fraction by the reciprocal of the second. This gives us (33/8) / (3/2) = (33/8) * (2/3) = 66/24 = 11/4, which simplifies to 2¾. Therefore, the correct answer is 2¾. Choices A, B, and D are incorrect as they do not represent the correct result of dividing 4â…› by 1½.

Correct Answer: C

Rationale: To add 4â…” and 6½, we first need to convert the fractions to have the same denominator. Converting 4â…” to 6ths gives us 8/6, and 6½ to 6ths gives us 7/2. Adding them together gives 15/2, which simplifies to 7½ or 9â…™. Therefore, the correct answer is 9â…™. Choices A, B, and D are incorrect as they do not represent the correct sum of the fractions after conversion and simplification.

Correct Answer: C

Rationale: Since the scale of the plan is 1:40, this means that 1 inch on the plan represents 40 inches in reality. Therefore, the actual length of the living room can be calculated as 5 inches on the plan multiplied by the scale factor of 40, which equals 200 inches. Converting 200 inches to feet gives us 15 feet as the actual length of the built living room. Choice A (45 feet) is incorrect because it miscalculates the conversion from inches to feet. Choice B (25 feet) is incorrect as it does not consider the scale factor provided. Choice D (12 feet) is incorrect as it does not apply the correct scale factor to convert the plan's measurements to reality.

Correct Answer: D

Rationale: To find the result of multiplying 6 by 55, you perform the operation 6 55, which equals 330. To express this product in decimal form, you place the decimal point one place from the right, resulting in 3.3. Therefore, the correct answer is D (3.3). Choices A, B, and C are incorrect as they do not represent the correct decimal equivalent of the multiplication of 6 and 55.

Correct Answer: B

Rationale: Geoff paid a total of 5 paperbacks x $0.35/paperback + 3 hardcover books x $50/hardcover book = $1.75 + $150 = $8.75. Since he gave the clerk a $10 bill, he received $10 - $8.75 = $1.25 change. However, since the options are in increments of $0.25, the closest amount is $0.75, so Geoff received $0.75 change. Option A is incorrect because it's not the closest amount to the actual change. Option C is incorrect as it represents the total change Geoff received, not the closest increment. Option D is incorrect as it overestimates the change Geoff received.

Correct Answer: A

Rationale: The Roman numeric system does not use place value as the Arabic, Decimal, and Binary systems do. In the Roman numeral system, the value of each symbol is independent of its position, unlike in the other systems where the position of a digit affects its value. This unique characteristic of Roman numerals distinguishes them from place-value systems like Arabic, Decimal, and Binary. Therefore, the correct answer is Roman (Choice A). Choices B, C, and D (Arabic, Decimal, and Binary) all utilize place value, where the position of a digit within a number determines its value, unlike Roman numerals.

Correct Answer: C

Rationale: Given that a gross is equal to 12 dozen, 15 gross of eggs would be equal to 15 * 12 = 180 dozen eggs. Since the eggs are packaged in one dozen egg containers, Lanyard Farms would need 180 containers for a week's worth of eggs. Choice A (15) is incorrect as it represents the number of gross, not containers. Choice B (150) is incorrect as it miscalculates the total number of containers needed. Choice D (2,160) is incorrect as it overestimates the number of containers required.

Correct Answer: B

Rationale: To find the final concentration, first, calculate the total volume of the solution (2 ml + 8 ml = 10 ml). Then, determine the concentration by dividing the volume of the concentrated medication by the total volume and multiplying by 100%: (2 ml / 10 ml) * 100% = 20%. Therefore, the correct answer is B. Choice A (16.67%) is incorrect as it does not represent the correct calculation. Choices C (25%) and D (50%) are both incorrect as they do not reflect the accurate concentration resulting from the dilution process.