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A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cups of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
- A. 2 2/5 cups
- B. 7 1/5 cups
- C. 6 cups
- D. 3 8/15 cups
Correct Answer: B
Rationale: To determine the amount of milk needed for the bigger batch, we first establish the ratio of flour to milk, which is 1/3 : 1 1/5. Converting 1 1/5 to an improper fraction gives us 6/5. Therefore, the ratio becomes 1:6/5 = 1:1.2. If the chef uses 2 cups of flour, the calculation would be 2 x 1.2 = 2.4 cups of milk needed. This is equivalent to 2 2/5 cups. Hence, the correct answer is 7 1/5 cups.
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Simplify the expression: [2(3 + 5 - 3)] / (12 + 2). What is the result of this expression?
- A. 12
- B. 1
- C. 8
- D. 2.57
Correct Answer: D
Rationale: To simplify the given expression [2(3 + 5 - 3)] / (12 + 2), follow the order of operations (PEMDAS/BODMAS). First, calculate the operations within the parentheses: 3 + 5 - 3 = 5. Substitute the result back into the expression to get [2(5)] / (12 + 2). Next, calculate within the brackets: 2(5) = 10. Now, the expression becomes 10 / 14. Simplifying further, 10 / 14 = 5 / 7 = 0.7142 (rounded to two decimal places). Therefore, the result of the expression is approximately 0.71, which corresponds to choice D.
A circle has an area of 49Ï€ square inches. What is the circumference of the circle in terms of pi?
- A. 7Ï€ inches
- B. 28Ï€ inches
- C. 14Ï€ inches
- D. 3.5Ï€ inches
Correct Answer: C
Rationale: To find the circumference of a circle with an area of 49π square inches, you first need to find the radius using the area formula A = πr^2. Given the area is 49π, then 49π = πr^2, which simplifies to r^2 = 49, resulting in r = 7. The circumference formula is C = 2πr. Substituting r = 7 gives C = 2π(7) = 14π. Therefore, the correct circumference of the circle in terms of pi is 14π inches.
A person weighed 180 lb. Three months later, they weighed 160 lb. What is the percentage of weight the person lost over 3 months? (Round to the nearest percent.)
- A. 13%
- B. 20%
- C. 10%
- D. 5%
Correct Answer: B
Rationale: To calculate the percentage of weight lost, subtract the final weight from the initial weight, divide by the initial weight, and multiply by 100. In this case: (180 - 160) / 180 * 100 = 20%, which rounds to the nearest percent as 20%. Therefore, the person lost 20% of their initial weight over the three months. This calculation represents the relative decrease in weight from the initial weight to the final weight, indicating that the person lost 20% of their initial weight during the three-month period.
A circle has an area of 49π square inches. What is the circumference of the circle in terms of π?
- A. 7Ï€ in
- B. 14Ï€ in
- C. 28Ï€ in
- D. 3.5Ï€ in
Correct Answer: B
Rationale: To find the circumference of a circle in terms of π, we first determine the radius using the formula for the area of a circle, A = πr^2. Given that the area is 49π square inches, we have 49π = πr^2, which simplifies to r = 7. The circumference of a circle is calculated using the formula C = 2πr. Substituting r = 7, we get C = 2π(7) = 14π. Therefore, the circumference of the circle is 14π inches.
What is the area of the largest circle that can fit entirely inside a rectangle measuring 8 centimeters by 10 centimeters?
- A. 18Ï€ cm^2
- B. 16Ï€ cm^2
- C. 8Ï€ cm^2
- D. 10Ï€ cm^2
Correct Answer: B
Rationale: To find the largest circle that fits inside the given rectangle, the circle's diameter should match the shorter side of the rectangle, which is 8 cm. The radius of the circle is half the diameter, making it 4 cm. The area of a circle is determined using the formula A = πr^2, where r is the radius. Substituting r = 4 cm, we get A = π*(4)^2 = 16π cm^2. Therefore, the correct answer is 16π cm^2, as this is the maximum area circle that can fit entirely inside the given rectangle.