This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Let's test each description against the actual relationship between the number of black dots (n) and grey dots (G). From the previous problem, we established that the correct relationship is G = 4n + 4. 2.11.1 The number of black dots → × 4 → + 2 → the number of grey dots This description translates to the formula G = 4n + 2. Step 1: Test for n=1 (1 black dot). According to the description: G = 4(1) + 2 = 4 + 2 = 6. From the pattern, for n=1, the number of grey dots is 8. Since 6 ≠ 8, the description is incorrect for n=1. Step 2: Test for n=2 (2 black dots). According to the description: G = 4(2) + 2 = 8 + 2 = 10. From the pattern, for n=2, the number of grey dots is 12. Since 10 ≠ 12, the description is incorrect for n=2. Conclusion: This description is Incorrect. 2.11.2 To calculate the number of grey dots you multiply the number of black dots by 2 and add 1 and multiply the answer by 2. This description translates to the formula G = (2n + 1) × 2. Simplifying this formula: G = 4n + 2. Step 1: Test for n=1 (1 black dot). According to the description: G = (2(1) + 1) × 2 = (2 + 1) × 2 = 3 × 2 = 6. From the pattern, for n=1, the number of grey dots is 8. Since 6 ≠ 8, the description is incorrect for n=1. Step 2: Test for n=2 (2 black dots). According to the description: G = (2(2) + 1) × 2 = (4 + 1) × 2 = 5 × 2 = 10. From the pattern, for n=2, the number of grey dots is 12. Since 10 ≠ 12, the description is incorrect for n=2. Conclusion: This description is Incorrect. 2.11.3 The number of grey dots = 2 x the number of black dots + 4. This description translates to the formula G = 2n + 4. Step 1: Test for n=1 (1 black dot). According to the description: G = 2(1) + 4 = 2 + 4 = 6. From the pattern, for n=1, the number of grey dots is 8. Since 6 ≠ 8, the description is incorrect for n=1. Step 2: Test for n=2 (2 black dots). According to the description: G = 2(2) + 4 = 4 + 4 = 8. From the pattern, for n=2, the number of grey dots is 12. Since 8 ≠ 12, the description is incorrect for n=2. Conclusion: This description is Incorrect. It appears none of the provided descriptions correctly describe the relationship. The correct relationship is G = 4n + 4. What's next?