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Complete the table and flow diagrams for the robot. The rule is 'x 4'. Inputs are 5, 6, 7, 8, 9, 10. For the flow diagrams, rules are 'x 5', 'x 4', 'x 9' with inputs 2, 4, 6, 8, 10; 1, 3, 5, 7, 9; and

Mathematics

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Answers

6 parts
a

10, 20, 30, 40, 50\text{10, 20, 30, 40, 50}

b

4, 12, 20, 28, 36\text{4, 12, 20, 28, 36}

c

18, 36, 54, 72, 90\text{18, 36, 54, 72, 90}

d

9, 13, 17, 21, 25\text{9, 13, 17, 21, 25}

e

7, 17, 27, 37, 47\text{7, 17, 27, 37, 47}

f

1, 2, 3, 4, 5\text{1, 2, 3, 4, 5}

6, 12, 18, 24, 30\text{6, 12, 18, 24, 30}

Step-by-step solution

7 steps

Here are the completed tables and flow diagrams.

Complete the table for the robot:

Step 1: Determine the rule from the given input and output pairs.
For input 5, output is 20. 20÷5=420 \div 5 = 4.
For input 6, output is 24. 24÷6=424 \div 6 = 4.
For input 7, output is 28. 28÷7=428 \div 7 = 4.
The rule is "x 4".

Step 2: Apply the rule to the remaining input numbers to find the outputs.
For input 8: 8×4=328 \times 4 = 32
For input 9: 9×4=369 \times 4 = 36
For input 10: 10×4=4010 \times 4 = 40

The completed table is:

InputOutput
520
624
728
832
936
1040

1. Complete and label the flow diagrams.

Part a· 1 step

Rule: x 5

Input numbers: 2, 4, 6, 8, 10

  1. Apply the rule to each input.

    2×5=102 \times 5 = 10
    4×5=204 \times 5 = 20
    6×5=306 \times 5 = 30
    8×5=408 \times 5 = 40
    10×5=5010 \times 5 = 50
    The output numbers are 10, 20, 30, 40, 50\boxed{\text{10, 20, 30, 40, 50}}

Part b

4, 12, 20, 28, 36\text{4, 12, 20, 28, 36}

Rule: x 4

Input numbers: 1, 3, 5, 7, 9

  1. Apply the rule to each input.

    1×4=41 \times 4 = 4
    3×4=123 \times 4 = 12
    5×4=205 \times 4 = 20
    7×4=287 \times 4 = 28
    9×4=369 \times 4 = 36
    The output numbers are 4, 12, 20, 28, 36\boxed{\text{4, 12, 20, 28, 36}}

Part c

18, 36, 54, 72, 90\text{18, 36, 54, 72, 90}

Rule: x 9

Input numbers: 2, 4, 6, 8, 10

  1. Apply the rule to each input.

    2×9=182 \times 9 = 18
    4×9=364 \times 9 = 36
    6×9=546 \times 9 = 54
    8×9=728 \times 9 = 72
    10×9=9010 \times 9 = 90
    The output numbers are 18, 36, 54, 72, 90\boxed{\text{18, 36, 54, 72, 90}}

Part d

9, 13, 17, 21, 25\text{9, 13, 17, 21, 25}

Rule: x 2 + 5

Input numbers: 2, 4, 6, 8, 10

  1. Apply the rule to each input.

    2×2+5=4+5=92 \times 2 + 5 = 4 + 5 = 9
    4×2+5=8+5=134 \times 2 + 5 = 8 + 5 = 13
    6×2+5=12+5=176 \times 2 + 5 = 12 + 5 = 17
    8×2+5=16+5=218 \times 2 + 5 = 16 + 5 = 21
    10×2+5=20+5=2510 \times 2 + 5 = 20 + 5 = 25
    The output numbers are 9, 13, 17, 21, 25\boxed{\text{9, 13, 17, 21, 25}}

Part e

7, 17, 27, 37, 47\text{7, 17, 27, 37, 47}

Rule: x 5 + 2

Input numbers: 1, 3, 5, 7, 9

  1. Apply the rule to each input.

    1×5+2=5+2=71 \times 5 + 2 = 5 + 2 = 7
    3×5+2=15+2=173 \times 5 + 2 = 15 + 2 = 17
    5×5+2=25+2=275 \times 5 + 2 = 25 + 2 = 27
    7×5+2=35+2=377 \times 5 + 2 = 35 + 2 = 37
    9×5+2=45+2=479 \times 5 + 2 = 45 + 2 = 47
    The output numbers are 7, 17, 27, 37, 47\boxed{\text{7, 17, 27, 37, 47}}

Part f

1, 2, 3, 4, 5\text{1, 2, 3, 4, 5}

Rule: x 2 x 3 (which simplifies to x 6)

Input numbers: 1, 2, 4 (and two blanks)
Output numbers: 18, 30 (and three blanks)

  1. Calculate outputs for the given inputs.

    For input 1: 1×6=61 \times 6 = 6
    For input 2: 2×6=122 \times 6 = 12
    For input 4: 4×6=244 \times 6 = 24

  2. Calculate inputs for the given outputs by reversing the rule (divide by 6).

    For output 18: 18÷6=318 \div 6 = 3
    For output 30: 30÷6=530 \div 6 = 5

    The completed flow diagram has:
    Input numbers: 1, 2, 3, 4, 5\boxed{\text{1, 2, 3, 4, 5}}
    Output numbers: 6, 12, 18, 24, 30\boxed{\text{6, 12, 18, 24, 30}}

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