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Evan and Peter have a radio show which consist of two segments They need four less than 11 songs in the first segment and the second segment they need five less than three times the number of songs in the first segment write an expression for the total number of songs They need for their show A (11 - 4)+ 3 * 11 - 4 - 5 B (11-4) + 3 * (11 - 4)-5 C (11 - 4) + 3 - 4 * 11 - 5 D (11 - 4) + 3 - 5 * (11 - 4)

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First, let's determine how to express the number of songs for both segments based on the information provided.

  1. First Segment: They need four less than 11 songs. This can be expressed as: \[ 11 - 4 = 7 \text{ songs} \]

  2. Second Segment: They need five less than three times the number of songs in the first segment. Since the first segment has 7 songs, this can be calculated as: \[ 3 \times 7 - 5 = 21 - 5 = 16 \text{ songs} \]

Now, we can combine the two segments to find the total number of songs: \[ \text{Total} = \text{First Segment} + \text{Second Segment} = 7 + 16 = 23 \text{ songs} \]

Now, let’s analyze the provided options to find which expression represents this calculation:

  • A: \( (11 - 4) + 3 \times 11 - 4 - 5 \)
  • B: \( (11 - 4) + 3 \times (11 - 4) - 5 \)
  • C: \( (11 - 4) + 3 - 4 \times 11 - 5 \)
  • D: \( (11 - 4) + 3 - 5 \times (11 - 4) \)

The expression from Option B matches our workings:

  • The first segment is represented as \( (11 - 4) \) which equals 7.
  • The second segment is represented as \( 3 \times (11 - 4) - 5 \) which corresponds to \( 3 \times 7 - 5 = 21 - 5 = 16 \).

So, the total number of songs is: \[ (11 - 4) + 3 \times (11 - 4) - 5 \]

Thus, the correct answer is: B: \( (11 - 4) + 3 \times (11 - 4) - 5 \).