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Solve the following arithmetic problems and sequence patterns.

Mathematics

ScanSolve AI Answer

Step-by-step solution

16 steps

1.1.1

  1. Perform the operation inside the parentheses.

    (8+19)−54÷2=27−54÷2(8+19) - 54 \div 2 = 27 - 54 \div 2
  2. Perform the division.

    27−2727 - 27
  3. Perform the subtraction.

    00

    The answer is 0\boxed{0}.

    1.1.2

  4. Perform the multiplication.

    12×500−(−250)=250−(−250)\frac{1}{2} \times 500 - (-250) = 250 - (-250)
  5. Subtracting a negative number is equivalent to adding the positive number.

    250+250250 + 250
  6. Perform the addition.

    500500

    The answer is 500\boxed{500}.

    1.1.3

  7. Calculate the division to get the decimal.

    150÷450=150450=13≈0.3333...150 \div 450 = \frac{150}{450} = \frac{1}{3} \approx 0.3333...
  8. Convert the decimal to a percentage by multiplying by 100.

    0.3333...×100%≈33.33%0.3333... \times 100\% \approx 33.33\%

    The answer is approximately 0.33 and 33.33%\boxed{0.33 \text{ and } 33.33\%}.

    1.2
    To arrange the numbers 0;−32;6;200; -32; 6; 20 in descending order, we list them from largest to smallest.
    The order is 20;6;0;−32\boxed{20; 6; 0; -32}.

    1.3.1

  9. Identify the pattern.

    The sequence is 9;18;36;...9; 18; 36; .... Each term is multiplied by 2 to get the next term (9×2=189 \times 2 = 18, 18×2=3618 \times 2 = 36).

  10. Apply the pattern to find the next two numbers.

    The next number is 36×2=7236 \times 2 = 72.
    The number after that is 72×2=14472 \times 2 = 144.
    The missing numbers are 72;144\boxed{72; 144}.

    1.3.2

  11. Identify the pattern.

    The sequence is 27;9;3;...27; 9; 3; .... Each term is divided by 3 to get the next term (27÷3=927 \div 3 = 9, 9÷3=39 \div 3 = 3).

  12. Apply the pattern to find the next two numbers.

    The next number is 3÷3=13 \div 3 = 1.
    The number after that is 1÷3=131 \div 3 = \frac{1}{3}.
    The missing numbers are 1;13\boxed{1; \frac{1}{3}}.

    1.3.3

  13. Check for constant difference.

    9−27=−189 - 27 = -18
    3−9=−63 - 9 = -6
    The difference is not constant.

  14. Check for constant ratio.

    927=13\frac{9}{27} = \frac{1}{3}
    39=13\frac{3}{9} = \frac{1}{3}
    The ratio is constant.
    The pattern in 1.3.2 is an example of a constant ratio. This is because each term is obtained by multiplying the previous term by a constant factor of 13\frac{1}{3} (or dividing by 3).

    1.4

  15. Recall the conversion factor between kilometers and meters.

    1 km=1000 m1 \text{ km} = 1000 \text{ m}

  16. Multiply the given value in kilometers by the conversion factor.

    3.86 km×1000mkm=3860 m3.86 \text{ km} \times 1000 \frac{\text{m}}{\text{km}} = 3860 \text{ m}

    The answer is 3860 m\boxed{3860 \text{ m}}.

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