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to which subsets of the real numbers does each number belong?

A. 9 squared
B. 3/10
C. -0.45
D. 12 squared

5 answers

To determine the subsets of the real numbers to which each number belongs, let's evaluate each option and their properties.

A. 9 squared:

  • Calculation: \( 9^2 = 81 \)
  • 81 is a positive integer, so it belongs to the following subsets:
    • Natural numbers (\(\mathbb{N}\))
    • Whole numbers (\(\mathbb{W}\))
    • Integers (\(\mathbb{Z}\))
    • Rational numbers (\(\mathbb{Q}\))
    • Real numbers (\(\mathbb{R}\))

B. 3/10:

  • This is a fraction which is a positive rational number.
  • It belongs to the following subsets:
    • Rational numbers (\(\mathbb{Q}\))
    • Real numbers (\(\mathbb{R}\))

C. -0.45:

  • This is a negative decimal number.
  • It belongs to the following subsets:
    • Rational numbers (\(\mathbb{Q}\)) (since it can be expressed as \(-\frac{45}{100}\))
    • Real numbers (\(\mathbb{R}\))
  • Note: It does not belong to natural numbers, whole numbers, or integers.

D. 12 squared:

  • Calculation: \( 12^2 = 144 \)
  • 144 is a positive integer, so it belongs to the following subsets:
    • Natural numbers (\(\mathbb{N}\))
    • Whole numbers (\(\mathbb{W}\))
    • Integers (\(\mathbb{Z}\))
    • Rational numbers (\(\mathbb{Q}\))
    • Real numbers (\(\mathbb{R}\))

Summary of Subset Membership:

  • A. \( 81 \): \(\mathbb{N}, \mathbb{W}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}\)
  • B. \( \frac{3}{10} \): \(\mathbb{Q}, \mathbb{R}\)
  • C. \( -0.45 \): \(\mathbb{Q}, \mathbb{R}\)
  • D. \( 144 \): \(\mathbb{N}, \mathbb{W}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}\)
so whats the answer?

Here are the subsets of the real numbers to which each number belongs:

A. 9 squared (81):

  • Natural numbers (\(\mathbb{N}\))
  • Whole numbers (\(\mathbb{W}\))
  • Integers (\(\mathbb{Z}\))
  • Rational numbers (\(\mathbb{Q}\))
  • Real numbers (\(\mathbb{R}\))

B. 3/10:

  • Rational numbers (\(\mathbb{Q}\))
  • Real numbers (\(\mathbb{R}\))

C. -0.45:

  • Rational numbers (\(\mathbb{Q}\))
  • Real numbers (\(\mathbb{R}\))

D. 12 squared (144):

  • Natural numbers (\(\mathbb{N}\))
  • Whole numbers (\(\mathbb{W}\))
  • Integers (\(\mathbb{Z}\))
  • Rational numbers (\(\mathbb{Q}\))
  • Real numbers (\(\mathbb{R}\))

Summary Answer:

  • A. 81: \(\mathbb{N}, \mathbb{W}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}\)
  • B. \(\frac{3}{10}\): \(\mathbb{Q}, \mathbb{R}\)
  • C. -0.45: \(\mathbb{Q}, \mathbb{R}\)
  • D. 144: \(\mathbb{N}, \mathbb{W}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}\)
is it a b c or d

I apologize for any confusion in my previous response. Here's the breakdown of each item by its numeric value and relevant subsets:

  1. A. \( 9^2 = 81 \)

    • Belongs to: Natural numbers (\(\mathbb{N}\)), Whole numbers (\(\mathbb{W}\)), Integers (\(\mathbb{Z}\)), Rational numbers (\(\mathbb{Q}\)), Real numbers (\(\mathbb{R}\))

  2. B. \( \frac{3}{10} \)

    • Belongs to: Rational numbers (\(\mathbb{Q}\)), Real numbers (\(\mathbb{R}\))

  3. C. \( -0.45 \)

    • Belongs to: Rational numbers (\(\mathbb{Q}\)), Real numbers (\(\mathbb{R}\))

  4. D. \( 12^2 = 144 \)

    • Belongs to: Natural numbers (\(\mathbb{N}\)), Whole numbers (\(\mathbb{W}\)), Integers (\(\mathbb{Z}\)), Rational numbers (\(\mathbb{Q}\)), Real numbers (\(\mathbb{R}\))

If you are asking for a classification based on being a rational or real number or similar, then:

  • A and D are both natural (and thus whole, integer, rational, real) numbers.
  • B and C are rational numbers but not natural or whole numbers.

If your question is which numbers belong to each specific category (e.g., rational, real), please clarify, and I can provide a definitive answer (like "A, B, C, or D" based on specific criteria). If you're looking for just a singular response or choice, please specify the criteria you're using!