Mathematics Patterns and Algebra Problems

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Questions and Answers

What are the two missing numbers in the sequence 19, 20, 21, ?, ?, 26, 28, 32, 33, 40?

  • 23, 25
  • 25, 27
  • 22, 27
  • 22, 24 (correct)

If the head of a fish measures 9 inches and the tail's length is equal to the head plus half the body's length, which of the following calculations will determine the length of the entire fish accurately?

  • 9 + (9 + (18 + 4.5)) (correct)
  • 9 + (9 + (9 + 4.5))
  • 9 + (9 + (9 + 22.5))
  • 9 + (9 + (9 + 9))

What is the length of the fish if the body's length, calculated as the sum of the head and tail, results in 36 inches?

  • 54 inches
  • 63 inches (correct)
  • 27 inches
  • 72 inches

Considering the sequence 19, 20, 21, ?, ?, 26, 28, 32, 33, 40, which of the following pairs would most likely fit in the context of missing values?

<p>22, 24 (C)</p> Signup and view all the answers

Given the conditions of tail and body lengths in a fish, if the head is 9 inches, which option represents the correct length of the tail?

<p>22.5 inches (D)</p> Signup and view all the answers

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Study Notes

Question 11

  • The missing numbers in the sequence 19, 20, 21, ?, ?, 26, 28, 32, 33, 40 are 23 and 25.
  • The sequence is a combination of two interwoven patterns: a sequence of consecutive numbers (19, 20, 21, 23, 25, 26, 28, 32, 33, 40), and a sequence of prime numbers (19, 23, 29, 31, 37, 41).

Question 12

  • The fish's head is 9 inches long.
  • The tail is equal to the head plus half the length of the body.
  • The body is equal to the length of the head plus the tail.
  • To solve this, we can use algebra: let 'x' represent the body's length.
  • The tail is equal to 9 + (x/2).
  • The body is equal to 9 + (9 + (x/2)).
  • Solving for x, we get x = 54 inches.
  • The entire fish is 9 inches (head) + 54 inches (body) + 27 inches (tail) = 90 inches long.

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