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1 Evaluate without using a calculator: 4x(5-20) 3.1.1 5x(-3+7) + 20 ÷ (-4) 3.1.2 V25 - V8 + V125 3.1.3 3.1.4 16,014 + 2,45 - 0,4 (round your answer correct to 2 decimal places) 3.2 3.3 3,45 x 2,7 3.4 1,450 ÷ 5

Mathematics

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Here are the solutions to your math problems:

3.1.1

  1. Evaluate the expression inside the parentheses.

    4×(5−20)=4×(−15)4 \times (5 - 20) = 4 \times (-15)
  2. Perform the multiplication.

    4×(−15)=−604 \times (-15) = -60

    The final answer is −60\boxed{-60}.

    3.1.2

  3. Evaluate the expression inside the parentheses.

    5×(−3+7)+20÷(−4)=5×(4)+20÷(−4)5 \times (-3 + 7) + 20 \div (-4) = 5 \times (4) + 20 \div (-4)
  4. Perform the multiplication and division.

    5×4=205 \times 4 = 20 20÷(−4)=−520 \div (-4) = -5
  5. Perform the addition.

    20+(−5)=1520 + (-5) = 15

    The final answer is 15\boxed{15}.

    3.1.3

  6. Calculate each root.

    25=5\sqrt{25} = 5 83=2\sqrt[3]{8} = 2 1253=5\sqrt[3]{125} = 5
  7. Substitute the values back into the expression and perform the operations.

    5−2+5=3+5=85 - 2 + 5 = 3 + 5 = 8

    The final answer is 8\boxed{8}.

    3.1.4

  8. Find the cube root of the numerator and the denominator.

    −383=−3383\sqrt[3]{-\frac{3}{8}} = \frac{\sqrt[3]{-3}}{\sqrt[3]{8}}

    Since −33\sqrt[3]{-3} is not a rational number, and the problem asks to evaluate, it implies a simplification if possible. However, the expression is −383\sqrt[3]{-\frac{3}{8}}.
    We can write −383=−1×383=−13×383=−1×3383\sqrt[3]{-\frac{3}{8}} = \sqrt[3]{-1 \times \frac{3}{8}} = \sqrt[3]{-1} \times \sqrt[3]{\frac{3}{8}} = -1 \times \frac{\sqrt[3]{3}}{\sqrt[3]{8}}

    =−1×332=−332= -1 \times \frac{\sqrt[3]{3}}{2} = -\frac{\sqrt[3]{3}}{2}

    The final answer is −332\boxed{-\frac{\sqrt[3]{3}}{2}}.

    3.2

  9. Perform the addition and subtraction from left to right.

    16.014+2.45−0.4=18.464−0.4=18.06416.014 + 2.45 - 0.4 = 18.464 - 0.4 = 18.064
  10. Round the answer to 2 decimal places.

    The third decimal place is 4, which is less than 5, so we round down.

    18.064≈18.0618.064 \approx 18.06

    The final answer is 18.06\boxed{18.06}.

    3.3

  11. Perform the multiplication.

    3.45×2.73.45 \times 2.7

    Multiply 345×27345 \times 27:
    345×7=2415345 \times 7 = 2415
    345×20=6900345 \times 20 = 6900
    2415+6900=93152415 + 6900 = 9315
    Since there are a total of 2+1=32+1=3 decimal places in 3.45 and 2.7, place the decimal point 3 places from the right in the product.

    3.45×2.7=9.3153.45 \times 2.7 = 9.315

    The final answer is 9.315\boxed{9.315}.

    3.4

  12. Perform the division.

    1450÷51450 \div 5 1450÷5=2901450 \div 5 = 290

    The final answer is 290\boxed{290}.

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