An irrigation pivot makes a circle with a radius of about 400 meters. Which of the following values is closest to the area, in square meters, of the circle?
- A. 1300
- B. 2500
- C. 160000
- D. 502700
- E. 1579100
Correct Answer & Rationale
Correct Answer: D
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. With a radius of 400 meters, the area calculates to approximately \( A = \pi \times (400)^2 \approx 502700 \) square meters, making option D the closest value. Option A (1300) is far too low, indicating a misunderstanding of the formula. Option B (2500) is also significantly underestimated for such a large radius. Option C (160000) is closer but still incorrect, as it neglects the multiplication by \( \pi \). Option E (1579100) overestimates the area, suggesting a miscalculation of the radius or the area formula.
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. With a radius of 400 meters, the area calculates to approximately \( A = \pi \times (400)^2 \approx 502700 \) square meters, making option D the closest value. Option A (1300) is far too low, indicating a misunderstanding of the formula. Option B (2500) is also significantly underestimated for such a large radius. Option C (160000) is closer but still incorrect, as it neglects the multiplication by \( \pi \). Option E (1579100) overestimates the area, suggesting a miscalculation of the radius or the area formula.
Other Related Questions
Mallory loaded 200 digital pictures into a digital picture frame. 78 are pictures of family members, 26 are pictures of pets, the rest are pictures of friends. The frame displays one picture every 10 seconds. Which value is closest to the probability that the next picture the frame displays will be a picture of a friend?
- A. 0.33
- B. 0.43
- C. 0.48
- D. 0.52
- E. 0.96
Correct Answer & Rationale
Correct Answer: C
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
One online movie-streaming service costs $8 per month and charges $1.50 per movie. A second service costs $2 per month and charges $2 per movie. For what number of movies per month is the monthly cost of both services the same?
- A. 3
- B. 6
- C. 5
- D. 12
- E. 20
Correct Answer & Rationale
Correct Answer: D
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
The expression 6a + 4c represents the total price, in dollars, of admission to an air show for a adults and c children. On Saturday, 380 adults and 120 children paid admission to the air show. What was the total price of admission for those people?
- A. 524
- B. 2240
- C. 2760
- D. 5000
- E. 12000
Correct Answer & Rationale
Correct Answer: C
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
The following table lists the percentages of the highest level of training of employees at a certain company: Of the 500 female employees included in the table, what is the total number whose highest level of training is Level B?
- A. 100
- B. 150
- C. 200
- D. 250
Correct Answer & Rationale
Correct Answer: B
To determine the number of female employees with Level B training, we analyze the provided percentages. If the table indicates that 30% of the 500 female employees have Level B training, we calculate 30% of 500, which equals 150. Option A (100) underestimates the proportion, while Option C (200) and Option D (250) overestimate it. Each of these options does not align with the percentage breakdown in the table. Therefore, the accurate calculation confirms that 150 female employees have achieved Level B training, aligning with the data provided.
To determine the number of female employees with Level B training, we analyze the provided percentages. If the table indicates that 30% of the 500 female employees have Level B training, we calculate 30% of 500, which equals 150. Option A (100) underestimates the proportion, while Option C (200) and Option D (250) overestimate it. Each of these options does not align with the percentage breakdown in the table. Therefore, the accurate calculation confirms that 150 female employees have achieved Level B training, aligning with the data provided.