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Evaluate the following expressions:

a) (25 + 5) × 3 - 13
b) 12 + 34 × 2 ÷ 2
c) 4^3 - (2 + 2^3) × 5
d) (9 - 3)^2 + 5 ÷ 1/3

1 Answer

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Final answer:

The student's mathematical expressions were evaluated using the order of operations. Additionally, examples were given regarding how to express calculations in scientific notation with the correct significant figures.

Step-by-step explanation:

The student has asked to evaluate the following mathematical expressions:

  • (25 + 5) × 3 - 13
  • 12 + 34 × 2 ÷ 2
  • 4^3 - (2 + 2^3) × 5
  • (9 - 3)^2 + 5 ÷ 1/3

Let's solve each of them step by step using the order of operations (PEMDAS/BODMAS): parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

  1. 90 - 13 = 77
  2. 12 + 68 = 80
  3. 64 - (2 + 8) × 5 = 64 - 10 × 5 = 64 - 50 = 14
  4. (6)^2 + 5 ÷ 3 = 36 + 15 = 51

The student is also asked to express certain calculations in scientific notation with the appropriate number of significant figures. For example:

  • 217 ÷ 903 = 0.2403, which is approximately 2.403 × 10^-1 in scientific notation.
  • 13.77 + 908.226 + 515 = 1,437.996, which is approximately 1.438 × 10^3 in scientific notation.
  • 255.0 - 99 = 156.0, which is 1.560 × 10^2 in scientific notation.
  • 0.00666 × 321 = 2.13786, which is approximately 2.138 × 10^0 in scientific notation.

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