| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To find the data rate for the motion-video, we need to calculate the total bits per second transmitted. First, we calculate the number of bits per pixel. Since the video is in RGB format, it has 3 color channels (Red, Green, Blue). If we assume 8 bits per channel, then each pixel is represented by 24 bits. Next, we calculate the number of pixels per frame. The video resolution is 352 x 288 pixels. So, the number of bits per frame is: \[ \text{Bits per frame} = \text{Pixels per frame} \times \text{Bits per pixel} = 352 \times 288 \times 24 \] \[ = 24,576,768 \, \text{bits/frame} \] Since the video plays at 30 frames per second, the data rate is: \[ \text{Data rate} = \text{Bits per frame} \times \text{Frames per second} \] \[ = 24,576,768 \, \text{bits/frame} \times 30 \, \text{frames/s} \] \[ = 737,303,040 \, \text{bits/s} \] To convert bits per second to megabits per second (Mbits/s), we divide by 1,000,000. \[ \text{Data rate} = \frac{737,303,040 \, \text{bits/s}}{1,000,000} \] \[ = 737.30304 \, \text{Mbits/s} \] Rounded to 3 significant figures: \[ \boxed{737 \, \text{Mbits/s}} \] |
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| deepseekr1 | To calculate the data rate for the motion-video: 1. **Pixels per frame**: \(352 \, \text{pixels} \times 288 \, \text{pixels} = 101,\!376 \, \text{pixels/frame}\) 2. **Bits per pixel (RGB)**: \(3 \, \text{channels} \times 8 \, \text{bits/channel} = 24 \, \text{bits/pixel}\) 3. **Bits per frame**: \(101,\!376 \, \text{pixels/frame} \times 24 \, \text{bits/pixel} = 2,\!433,\!024 \, \text{bits/frame}\) 4. **Frames per second**: \(30 \, \text{frames/second}\) 5. **Data rate (bits/second)**: \(2,\!433,\!024 \, \text{bits/frame} \times 30 \, \text{frames/second} = 72,\!990,\!720 \, \text{bits/second}\) 6. **Convert to megabits/second**: \(\frac{72,\!990,\!720 \, \text{bits/second}}{1,\!000,\!000} = 72.99072 \, \text{Mbits/s}\) **Rounded to 3 significant figures**: \(73.0 \, \text{Mbits/s}\) \(\boxed{73.0}\) |
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| gpto1 | To find the data rate for the given motion-video, we'll follow these steps: **1. Calculate the number of pixels per frame:** The video frame size is \( 352 \times 288 \) pixels. \[ \text{Number of pixels per frame} = 352 \times 288 = 101,376 \text{ pixels} \] **2. Determine the number of bits per pixel:** In RGB digitization, each color component (Red, Green, Blue) is typically represented by 8 bits, so each pixel requires: \[ \text{Bits per pixel} = 8 \text{ bits (Red)} + 8 \text{ bits (Green)} + 8 \text{ bits (Blue)} = 24 \text{ bits} \] **3. Calculate the number of bits per frame:** \[ \text{Bits per frame} = \text{Number of pixels per frame} \times \text{Bits per pixel} = 101,376 \times 24 = 2,433,024 \text{ bits} \] **4. Calculate the data rate in bits per second:** The frame rate is 30 frames per second. \[ \text{Data rate (bits/s)} = \text{Bits per frame} \times \text{Frames per second} = 2,433,024 \times 30 = 72,990,720 \text{ bits/s} \] **5. Convert the data rate to megabits per second:** \[ \text{Data rate (Mbits/s)} = \frac{\text{Data rate (bits/s)}}{1,000,000} = \frac{72,990,720}{1,000,000} = 72.99072 \text{ Mbits/s} \] **6. Round the result to 3 significant figures:** Since the fourth significant digit is 9 (which is greater than 5), we round up the third significant digit. \[ \text{Data rate} = 73.0 \text{ Mbits/s (to 3 significant figures)} \] **Answer: 73.0 Mbits/s** |
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| GPT-4o | To determine the data rate for the given motion-video, we need to calculate the amount of data generated per second and express it in megabits per second (Mbits/s). Let's break down the problem step-by-step: 1. **Video Specifications:** - Resolution: \(352 \times 288\) pixels - Color format: RGB (3 bytes per pixel, since RGB uses 1 byte for each of the Red, Green, and Blue channels) - Frame rate: 30 frames per second 2. **Calculate the data per frame:** Each frame is composed of \(352 \times 288\) pixels. - Number of pixels per frame = \(352 \times 288\) - Each pixel requires 3 bytes (RGB). So, the data per frame is: \[ \text{Data per frame} = 352 \times 288 \times 3 \text{ bytes} \] \[ \text{Data per frame} = 304,128 \times 3 \text{ bytes} \] \[ \text{Data per frame} = 912,384 \text{ bytes} \] 3. **Convert bytes to bits:** Since 1 byte = 8 bits, \[ \text{Data per frame in bits} = 912,384 \times 8 \text{ bits} \] \[ \text{Data per frame in bits} = 7,299,072 \text{ bits} \] 4. **Calculate the data rate per second:** The video is 30 frames per second. \[ \text{Data rate} = 7,299,072 \text{ bits/frame} \times 30 \text{ frames/second} \] \[ \text{Data rate} = 218,972,160 \text{ bits/second} \] 5. **Convert bits per second to megabits per second:** Since 1 Mbit = \(10^6\) bits, \[ \text{Data rate in Mbits/second} = \frac{218,972,160 \text{ bits/second}}{10^6} \] \[ \text{Data rate in Mbits/second} = 218.972 \text{ Mbits/second} \] 6. **Round to three significant figures:** \[ \text{Data rate in Mbits/second} \approx 219 \text{ Mbits/second} \] Therefore, the data rate for this motion-video is approximately **219 Mbits/s** (rounded to three significant figures). |
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| llama3.1-70B-Instruct | To find the data rate for the motion-video, we need to calculate the total number of bits required to represent each frame of the video and then multiply it by the frame rate. First, let's calculate the total number of pixels in each frame: 352 pixels/frame × 288 pixels/frame = 101,376 pixels/frame Since each pixel is represented by 3 bytes (RGB), the total number of bytes per frame is: 101,376 pixels/frame × 3 bytes/pixel = 304,128 bytes/frame Now, let's convert the number of bytes to bits: 304,128 bytes/frame × 8 bits/byte = 2,433,024 bits/frame The video is played at 30 frames per second, so the total number of bits per second is: 2,433,024 bits/frame × 30 frames/second = 72,990,720 bits/second To convert this to megabits per second (Mbits/s), we divide by 1,000,000: 72,990,720 bits/second ÷ 1,000,000 = 72.99 Mbits/s Rounded to three significant figures, the data rate for the motion-video is: 73.0 Mbits/s |
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| llama3.1-405B-Instruct | To find the data rate for the motion-video, we need to calculate the total number of bits required to represent the video sequence per second. First, let's calculate the total number of pixels in one frame: 352 pixels/row x 288 rows/frame = 101,376 pixels/frame Since the video is in RGB format, each pixel is represented by 3 bytes (24 bits). Therefore, the total number of bits required to represent one frame is: 101,376 pixels/frame x 24 bits/pixel = 2,433,024 bits/frame Since the video is at 30 frames per second, the total number of bits required to represent the video sequence per second is: 2,433,024 bits/frame x 30 frames/second = 73,000,720 bits/second To convert this to megabits per second (Mbits/s), we divide by 1,000,000 (since there are 1,000,000 bits in 1 megabit): 73,000,720 bits/second ÷ 1,000,000 = 73.0 Mbits/s Therefore, the data rate for this motion-video is approximately 73.0 Mbits/s. |
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| DeepSeek-Coder-V2 | To find the data rate for the given motion-video in Mbits/s, we need to follow these steps: 1. **Determine the size of a single frame in bits:** - The video has a resolution of 352 x 288 pixels. - Each pixel is represented in RGB format, which means each pixel has 3 color channels (Red, Green, Blue), and each channel is typically 8 bits (1 byte). - Therefore, the size of one pixel in bits is 3 channels * 8 bits/channel = 24 bits. - The total number of pixels in one frame is 352 * 288. - The size of one frame in bits is (352 * 288) pixels * 24 bits/pixel. 2. **Calculate the size of one frame in bits:** \[ \text{Size of one frame} = 352 \times 288 \times 24 \text{ bits} \] \[ \text{Size of one frame} = 352 \times 288 \times 24 = 2433024 \text{ bits} \] 3. **Determine the number of frames per second:** - The video is recorded at 30 frames per second. 4. **Calculate the data rate in bits per second:** \[ \text{Data rate} = \text{Size of one frame} \times \text{Frames per second} \] \[ \text{Data rate} = 2433024 \text{ bits} \times 30 \text{ frames/second} \] \[ \text{Data rate} = 72990720 \text{ bits/second} \] 5. **Convert the data rate to Mbits/s:** - 1 Mbit = 1,000,000 bits. \[ \text{Data rate in Mbits/s} = \frac{72990720 \text{ bits/second}}{1,000,000 \text{ bits/Mbit}} \] \[ \text{Data rate in Mbits/s} = 72.99072 \text{ Mbits/s} \] 6. **Round to 3 significant figures:** \[ \text{Data rate in Mbits/s} \approx 73.0 \text{ Mbits/s} \] Therefore, the data rate for this motion-video is: \[ \boxed{73.0} \] |
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| Qwen2-72B-Instruct | To find the data rate for the motion-video, we need to calculate the total bits per second transmitted. First, we calculate the number of bits per pixel. Since the video is in RGB format, it has 3 color channels (Red, Green, Blue). If we assume 8 bits per channel, then each pixel is represented by 24 bits. Next, we calculate the number of pixels per frame. The video resolution is 352 x 288 pixels. So, the number of bits per frame is: \[ \text{Bits per frame} = \text{Pixels per frame} \times \text{Bits per pixel} = 352 \times 288 \times 24 \] \[ = 24,576,768 \, \text{bits/frame} \] Since the video plays at 30 frames per second, the data rate is: \[ \text{Data rate} = \text{Bits per frame} \times \text{Frames per second} \] \[ = 24,576,768 \, \text{bits/frame} \times 30 \, \text{frames/s} \] \[ = 737,303,040 \, \text{bits/s} \] To convert bits per second to megabits per second (Mbits/s), we divide by 1,000,000. \[ \text{Data rate} = \frac{737,303,040 \, \text{bits/s}}{1,000,000} \] \[ = 737.30304 \, \text{Mbits/s} \] Rounded to 3 significant figures: \[ \boxed{737 \, \text{Mbits/s}} \] |
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| baichuan4 | To calculate the data rate for the motion-video, we need to determine the amount of data in one frame and then multiply it by the number of frames per second. First, let's calculate the data in one frame: Each pixel has three bytes (one for each RGB component), so the total data in one frame is: 352 pixels (width) * 288 pixels (height) * 3 bytes/pixel = 305,280 bytes/frame Now, let's convert this to bits: 305,280 bytes/frame * 8 bits/byte = 2,442,240 bits/frame Next, we need to determine the data rate by multiplying the data in one frame by the number of frames per second: 2,442,240 bits/frame * 30 frames/second = 73,267,200 bits/second Finally, let's convert this to Mbits/s: 73,267,200 bits/second / 1,000,000 = 73.267 Mbits/s So, the data rate for this motion-video is 73.267 Mbits/s (rounded to three significant figures). |
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| doubao | Each frame has 352 x 288 pixels. Each pixel has 3 bytes (RGB). So each frame has 352 x 288 x 3 bytes. There are 30 frames per second. So the data per second is 352 x 288 x 3 x 30 bytes. To convert to bits, multiply by 8. So it becomes 352 x 288 x 3 x 30 x 8 bits. To convert to Mbits, divide by 1024 x 1024. Data rate = (352 x 288 x 3 x 30 x 8) / (1024 x 1024) ≈ 25.3 Mbits/s. |
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| minimax | To calculate the data rate for the motion-video, we need to determine the amount of data that is generated per second and then convert it to megabits per second (Mbits/s). First, let's calculate the number of pixels per frame: 352 pixels (width) * 288 pixels (height) = 101,376 pixels per frame Each pixel is represented by 3 bytes (one byte for each color channel: Red, Green, and Blue): 101,376 pixels/frame * 3 bytes/pixel = 304,128 bytes/frame Now, convert bytes to bits (since there are 8 bits in a byte): 304,128 bytes/frame * 8 bits/byte = 2,433,024 bits/frame Next, calculate the number of bits per second: 2,433,024 bits/frame * 30 frames/second = 72,990,720 bits/second Finally, convert bits per second to megabits per second: 72,990,720 bits/second / (10^6 bits/Mbit) = 72.990720 Mbits/s Rounding to three significant figures, the data rate for the motion-video is: 73.0 Mbits/s |
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| kimi | To calculate the data rate for the motion-video, we need to determine the amount of data transferred per second. Here's how we can do it: 1. **Determine the number of pixels per frame:** \(352 \text{ pixels (width)} \times 288 \text{ pixels (height)} = 101,376 \text{ pixels}\) 2. **Determine the number of bytes per pixel:** Since the video is in RGB format, each pixel has 3 color channels (Red, Green, Blue). Each color channel is typically represented by 8 bits (1 byte). \(1 \text{ pixel} = 3 \text{ bytes}\) 3. **Calculate the total number of bytes per frame:** \(101,376 \text{ pixels} \times 3 \text{ bytes/pixel} = 304,128 \text{ bytes}\) 4. **Calculate the total number of bytes per second (data rate in bytes/s):** The video has 30 frames per second. \(304,128 \text{ bytes/frame} \times 30 \text{ frames/s} = 9,123,840 \text{ bytes/s}\) 5. **Convert bytes per second to megabits per second (Mbits/s):** There are 8 bits in a byte and 1,000,000 bytes in a megabyte. \(9,123,840 \text{ bytes/s} \times \frac{8 \text{ bits}}{1 \text{ byte}} \div \frac{1,000,000 \text{ bytes}}{1 \text{ Mbyte}} = 72.99 \text{ Mbits/s}\) 6. **Round to three significant figures:** \(72.99 \text{ Mbits/s} \approx 73.0 \text{ Mbits/s}\) So, the data rate for the motion-video is approximately \(\boxed{73.0}\) Mbits/s. |
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| wenxinyiyan | To find the data rate for the motion-video, we need to calculate the total amount of data transmitted per second. Let's break down the problem into steps: 1. **Determine the number of pixels per frame**: - The video format is 352x288 pixels, so there are 352 * 288 = 101,376 pixels per frame. 2. **Calculate the number of bits per pixel**: - Since the video is RGB digitized, each pixel requires 24 bits (8 bits for red, 8 bits for green, and 8 bits for blue). 3. **Calculate the total number of bits per frame**: - Total bits per frame = number of pixels per frame * bits per pixel - Total bits per frame = 101,376 * 24 = 2,433,024 bits 4. **Determine the data rate**: - The video is at 30 frames per second. - Data rate (bits/s) = total bits per frame * frames per second - Data rate (bits/s) = 2,433,024 * 30 = 72,990,720 bits/s 5. **Convert the data rate to Mbits/s**: - 1 Mbit = 1,000,000 bits - Data rate (Mbits/s) = 72,990,720 / 1,000,000 ≈ 72.991 Mbits/s Rounding to 3 significant figures, the data rate is approximately 73.0 Mbits/s. |
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| zhipu | To find the data rate for the given motion-video, we need to calculate the total amount of data transmitted per second. Here's a step-by-step breakdown of the calculation: 1. **Determine the size of one frame:** - The resolution of each frame is 352 x 288 pixels. - Each pixel is represented by RGB digitization, which means 3 bytes per pixel (1 byte for Red, 1 byte for Green, and 1 byte for Blue). So, the size of one frame in bytes is: \[ \text{Frame size} = 352 \times 288 \times 3 \text{ bytes} \] 2. **Calculate the total data for one second:** - The video runs at 30 frames per second. So, the total data per second in bytes is: \[ \text{Data per second} = 352 \times 288 \times 3 \times 30 \text{ bytes} \] 3. **Convert the data rate to bits per second:** - Since 1 byte = 8 bits, we need to multiply the byte count by 8 to get the bit count. So, the data rate in bits per second is: \[ \text{Data rate (bps)} = 352 \times 288 \times 3 \times 30 \times 8 \text{ bits} \] 4. **Convert the data rate to Megabits per second (Mbits/s):** - Since 1 Megabit = \(10^6\) bits, we divide the bit count by \(10^6\). So, the data rate in Mbits/s is: \[ \text{Data rate (Mbits/s)} = \frac{352 \times 288 \times 3 \times 30 \times 8}{10^6} \] Now, let's plug in the numbers and calculate: \[ \text{Data rate (Mbits/s)} = \frac{352 \times 288 \times 3 \times 30 \times 8}{10^6} \] \[ = \frac{352 \times 288 \times 900 \times 8}{10^6} \] \[ = \frac{8294400 \times 8}{10^6} \] \[ = \frac{66355200}{10^6} \] \[ = 66.3552 \text{ Mbits/s} \] Rounded to three significant figures, the data rate is: \[ \boxed{66.4 \text{ Mbits/s}} \] So, the data rate for the motion-video is 66.4 Mbits/s. |
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| gpto1 | To find the data rate for the given motion-video, we'll follow these steps: **1. Calculate the number of pixels per frame:** The video frame size is \( 352 \times 288 \) pixels. \[ \text{Number of pixels per frame} = 352 \times 288 = 101,376 \text{ pixels} \] **2. Determine the number of bits per pixel:** In RGB digitization, each color component (Red, Green, Blue) is typically represented by 8 bits, so each pixel requires: \[ \text{Bits per pixel} = 8 \text{ bits (Red)} + 8 \text{ bits (Green)} + 8 \text{ bits (Blue)} = 24 \text{ bits} \] **3. Calculate the number of bits per frame:** \[ \text{Bits per frame} = \text{Number of pixels per frame} \times \text{Bits per pixel} = 101,376 \times 24 = 2,433,024 \text{ bits} \] **4. Calculate the data rate in bits per second:** The frame rate is 30 frames per second. \[ \text{Data rate (bits/s)} = \text{Bits per frame} \times \text{Frames per second} = 2,433,024 \times 30 = 72,990,720 \text{ bits/s} \] **5. Convert the data rate to megabits per second:** \[ \text{Data rate (Mbits/s)} = \frac{\text{Data rate (bits/s)}}{1,000,000} = \frac{72,990,720}{1,000,000} = 72.99072 \text{ Mbits/s} \] **6. Round the result to 3 significant figures:** Since the fourth significant digit is 9 (which is greater than 5), we round up the third significant digit. \[ \text{Data rate} = 73.0 \text{ Mbits/s (to 3 significant figures)} \] **Answer: 73.0 Mbits/s** |
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| deepseekv3 | server error: Error code: 400 - {'error': {'code': 'RequestTimeOut', 'param': None, 'message': 'Request timed out, please try again later.', 'type': 'RequestTimeOut'}, 'id': 'chatcmpl-bc83dbae-f897-94b3-98bb-a95af15c9f52', 'request_id': 'bc83dbae-f897-94b3-98bb-a95af15c9f52'} | 69.6 |