The graph shows the number of productions of operas composed by each of 7 composers that a certain opera company...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

Puccini, with 15 productions, has exactly \(50\%\) more productions than Donizetti, who has 10; this is the only composer pair in the dataset with this precise '\(50\%\) more' relationship. The number of productions for other composers ranges from 5 to 14. The data covers a 40-year history from a single opera company and allows analysis of production frequency and proportional relationships.

Step-by-Step Solution

Question 1: Identify the Composer With 50% More Productions

Complete Statement:

In the last 40 years, the opera company presented exactly \(50\%\) more productions of operas composed by [BLANK 1] than by [BLANK 2].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: exactly 50% more
  • Meaning: The number of productions for one composer is \(1.5\) times the number for another composer.
  • Relation to Chart: We need to look at the chart for pairs where one count is exactly \(1.5\) times another.
  • Important Implications: Not all pairs fit this ratio exactly; the question requires a precise numerical match.
• Statement Breakdown 2:
  • Key Phrase: opera company presented ... productions of operas composed by
  • Meaning: Look for the total number of productions for each composer as shown in the chart.
  • Relation to Chart: Chart bars give the number of productions per composer.
  • Important Implications: We directly compare the bar heights/numbers for specific composers.
• What is needed: Which composer from the first list has \(50\%\) more productions than a composer from the second list.

Solution:

• Condensed Solution Implementation:
  Examine the first list for any composer whose production number is \(1.5\) times that of a composer in the second list.
• Necessary Data points:
  Donizetti: 10, Puccini: 15, plus numbers for all other options.
  • Calculations Estimations:
    Puccini: 15, Donizetti: 10. \(10 \times 1.5 = 15\). All other pairs do not match the \(1.5x\) relation exactly.
  • Comparison to Answer Choices:
    From the first dropdown (Donizetti, Mozart, Puccini, Verdi), only Puccini has exactly \(50\%\) more productions than Donizetti from the second list.

FINAL ANSWER Blank 1: Puccini

Question 2: Identify the Composer With Fewer Productions

Complete Statement:

In the last 40 years, the opera company presented exactly \(50\%\) more productions of operas composed by Puccini than by [BLANK 2].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: Puccini
  • Meaning: The count of productions by Puccini is 15 (from the chart).
  • Relation to Chart: Pinpoints Puccini's bar (value: 15).
• Statement Breakdown 2:
  • Key Phrase: than by [BLANK 2]
  • Meaning: We are comparing Puccini's number to another composer from the list.
  • Relation to Chart: Consider which composer's count fits the \(50\%\) less relationship with Puccini's 15.
• What is needed: Which composer from the second list has exactly 10 productions (since 15 divided by \(1.5\) equals 10).

Solution:

• Condensed Solution Implementation:
  Check each composer in the second choice list for 10 productions.
• Necessary Data points:
  Britten: 7, Donizetti: 10, Menotti: 5, Rossini: 9.
  • Calculations Estimations:
    \(15 \div 1.5 = 10\). Only Donizetti matches.
  • Comparison to Answer Choices:
    Among Britten, Donizetti, Menotti, and Rossini, only Donizetti has exactly 10 productions.

FINAL ANSWER Blank 2: Donizetti

Summary

By examining the production counts for each composer, we determined Puccini (15 productions) is exactly \(50\%\) more than Donizetti (10 productions), and this is the only matching pair in the lists.

Question Independence Analysis

The blanks are dependent; knowing one answer immediately determines the other due to the unique numerical relationship.