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A robot shows inputs 5, 6, 7 and outputs 20, 24, 28. Complete the table and flow diagrams for inputs 8, 9, 10. Use the rules x 5 and x 4.

Mathematics

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Step-by-step solution

7 steps

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=205 \times 4 = 20, 6×4=246 \times 4 = 24, 7×4=287 \times 4 = 28).

Robot Table Completion:

InputOutput
520
624
728
832
936
1040

Now, let's complete and label the flow diagrams.

Part a· 1 step

Input numbers: 2, 4, 6, 8, 10
Rule: ×5\times 5

  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 completed diagram is:

    Input246810→×5Output1020304050\begin{array}{|c|} \hline \textbf{Input} \\ \hline 2 \\ 4 \\ 6 \\ 8 \\ 10 \\ \hline \end{array} \xrightarrow{\quad \times 5 \quad} \begin{array}{|c|} \hline \textbf{Output} \\ \hline \boxed{10} \\ \boxed{20} \\ \boxed{30} \\ \boxed{40} \\ \boxed{50} \\ \hline \end{array}

Part b· 1 step

Input numbers: 1, 3, 5, 7, 9
Rule: ×4\times 4

  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 completed diagram is:

    Input13579→×4Output412202836\begin{array}{|c|} \hline \textbf{Input} \\ \hline 1 \\ 3 \\ 5 \\ 7 \\ 9 \\ \hline \end{array} \xrightarrow{\quad \times 4 \quad} \begin{array}{|c|} \hline \textbf{Output} \\ \hline \boxed{4} \\ \boxed{12} \\ \boxed{20} \\ \boxed{28} \\ \boxed{36} \\ \hline \end{array}

Part c· 1 step

Input numbers: 2, 4, 6, 8, 10
Rule: ×9\times 9

  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 completed diagram is:

    Input246810→×9Output1836547290\begin{array}{|c|} \hline \textbf{Input} \\ \hline 2 \\ 4 \\ 6 \\ 8 \\ 10 \\ \hline \end{array} \xrightarrow{\quad \times 9 \quad} \begin{array}{|c|} \hline \textbf{Output} \\ \hline \boxed{18} \\ \boxed{36} \\ \boxed{54} \\ \boxed{72} \\ \boxed{90} \\ \hline \end{array}

Part d· 1 step

Input numbers: 2, 4, 6, 8, 10
Rule: ×2+5\times 2 + 5

  1. Apply the rule to each input.

    (2×2)+5=4+5=9(2 \times 2) + 5 = 4 + 5 = 9 (4×2)+5=8+5=13(4 \times 2) + 5 = 8 + 5 = 13 (6×2)+5=12+5=17(6 \times 2) + 5 = 12 + 5 = 17 (8×2)+5=16+5=21(8 \times 2) + 5 = 16 + 5 = 21 (10×2)+5=20+5=25(10 \times 2) + 5 = 20 + 5 = 25

    The completed diagram is:

    Input246810→×2+5Output913172125\begin{array}{|c|} \hline \textbf{Input} \\ \hline 2 \\ 4 \\ 6 \\ 8 \\ 10 \\ \hline \end{array} \xrightarrow{\quad \times 2 + 5 \quad} \begin{array}{|c|} \hline \textbf{Output} \\ \hline \boxed{9} \\ \boxed{13} \\ \boxed{17} \\ \boxed{21} \\ \boxed{25} \\ \hline \end{array}

Part e· 1 step

Input numbers: 1, 3, 5, 7, 9
Rule: ×5+2\times 5 + 2

  1. Apply the rule to each input.

    (1×5)+2=5+2=7(1 \times 5) + 2 = 5 + 2 = 7 (3×5)+2=15+2=17(3 \times 5) + 2 = 15 + 2 = 17 (5×5)+2=25+2=27(5 \times 5) + 2 = 25 + 2 = 27 (7×5)+2=35+2=37(7 \times 5) + 2 = 35 + 2 = 37 (9×5)+2=45+2=47(9 \times 5) + 2 = 45 + 2 = 47

    The completed diagram is:

    Input13579→×5+2Output717273747\begin{array}{|c|} \hline \textbf{Input} \\ \hline 1 \\ 3 \\ 5 \\ 7 \\ 9 \\ \hline \end{array} \xrightarrow{\quad \times 5 + 2 \quad} \begin{array}{|c|} \hline \textbf{Output} \\ \hline \boxed{7} \\ \boxed{17} \\ \boxed{27} \\ \boxed{37} \\ \boxed{47} \\ \hline \end{array}

Part f· 2 steps

Input numbers: 1, 2, 4. Missing inputs for outputs 18 and 30.
Rule: ×2×3\times 2 \times 3 (which simplifies to ×6\times 6)

  1. Apply the rule to the given inputs.

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

  2. Find the missing inputs for the given outputs.

    For output 18:

    Input×6=18\text{Input} \times 6 = 18 Input=186=3\text{Input} = \frac{18}{6} = 3

    For output 30:

    Input×6=30\text{Input} \times 6 = 30 Input=306=5\text{Input} = \frac{30}{6} = 5

    The completed diagram is:

    Input12345→×2×3Output612182430\begin{array}{|c|} \hline \textbf{Input} \\ \hline 1 \\ 2 \\ \boxed{3} \\ 4 \\ \boxed{5} \\ \hline \end{array} \xrightarrow{\quad \times 2 \times 3 \quad} \begin{array}{|c|} \hline \textbf{Output} \\ \hline \boxed{6} \\ \boxed{12} \\ 18 \\ \boxed{24} \\ 30 \\ \hline \end{array}
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