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
Let's knock this out. First, let's complete the table based on the robot's rule. The robot shows inputs 5, 6, 7 and outputs 20, 24, 28. The rule is to multiply the input by 4 (5 × 4 = 20, 6 × 4 = 24, 7 × 4 = 28). Robot Table Completion: | Input | Output | | :---: | :----: | | 5 | 20 | | 6 | 24 | | 7 | 28 | | 8 | 32 | | 9 | 36 | | 10 | 40 | Now, let's complete and label the flow diagrams. a) Input numbers: 2, 4, 6, 8, 10 Rule: × 5 Step 1: Apply the rule to each input. 2 × 5 = 10 4 × 5 = 20 6 × 5 = 30 8 × 5 = 40 10 × 5 = 50 The completed diagram is: |c| Input \\ 2 \\ 4 \\ 6 \\ 8 \\ 10 \\ × 5 |c| Output \\ 10 \\ 20 \\ 30 \\ 40 \\ 50 \\ b) Input numbers: 1, 3, 5, 7, 9 Rule: × 4 Step 1: Apply the rule to each input. 1 × 4 = 4 3 × 4 = 12 5 × 4 = 20 7 × 4 = 28 9 × 4 = 36 The completed diagram is: |c| Input \\ 1 \\ 3 \\ 5 \\ 7 \\ 9 \\ × 4 |c| Output \\ 4 \\ 12 \\ 20 \\ 28 \\ 36 \\ c) Input numbers: 2, 4, 6, 8, 10 Rule: × 9 Step 1: Apply the rule to each input. 2 × 9 = 18 4 × 9 = 36 6 × 9 = 54 8 × 9 = 72 10 × 9 = 90 The completed diagram is: |c| Input \\ 2 \\ 4 \\ 6 \\ 8 \\ 10 \\ × 9 |c| Output \\ 18 \\ 36 \\ 54 \\ 72 \\ 90 \\ d) Input numbers: 2, 4, 6, 8, 10 Rule: × 2 + 5 Step 1: Apply the rule to each input. (2 × 2) + 5 = 4 + 5 = 9 (4 × 2) + 5 = 8 + 5 = 13 (6 × 2) + 5 = 12 + 5 = 17 (8 × 2) + 5 = 16 + 5 = 21 (10 × 2) + 5 = 20 + 5 = 25 The completed diagram is: |c| Input \\ 2 \\ 4 \\ 6 \\ 8 \\ 10 \\ × 2 + 5 |c| Output \\ 9 \\ 13 \\ 17 \\ 21 \\ 25 \\ e) Input numbers: 1, 3, 5, 7, 9 Rule: × 5 + 2 Step 1: Apply the rule to each input. (1 × 5) + 2 = 5 + 2 = 7 (3 × 5) + 2 = 15 + 2 = 17 (5 × 5) + 2 = 25 + 2 = 27 (7 × 5) + 2 = 35 + 2 = 37 (9 × 5) + 2 = 45 + 2 = 47 The completed diagram is: |c| Input \\ 1 \\ 3 \\ 5 \\ 7 \\ 9 \\ × 5 + 2 |c| Output \\ 7 \\ 17 \\ 27 \\ 37 \\ 47 \\ f) Input numbers: 1, 2, 4. Missing inputs for outputs 18 and 30. Rule: × 2 × 3 (which simplifies to × 6) Step 1: Apply the rule to the given inputs. 1 × 6 = 6 2 × 6 = 12 4 × 6 = 24 Step 2: Find the missing inputs for the given outputs. For output 18: Input × 6 = 18 Input = (18)/(6) = 3 For output 30: Input × 6 = 30 Input = (30)/(6) = 5 The completed diagram is: |c| Input \\ 1 \\ 2 \\ 3 \\ 4 \\ 5 \\ × 2 × 3 |c| Output \\ 6 \\ 12 \\ 18 \\ 24 \\ 30 \\ What's next?