Questions: The given contingency table lists the cross tabulation of the number of business partnerships by industry and whether the partnership reported net income or net loss for the year 2014 in a certain country. Using the letters given in the table, find the number of partnerships in each of the following sets in parts (a) through (d). (a) B UW contains partnerships. (b) RUC contains partnerships. (c) C ∩ A contains partnerships. (d) C' contains partnerships.

The given contingency table lists the cross tabulation of the number of business partnerships by industry and whether the partnership reported net income or net loss for the year 2014 in a certain country. Using the letters given in the table, find the number of partnerships in each of the following sets in parts (a) through (d). (a) B UW contains partnerships. (b) RUC contains partnerships. (c) C ∩ A contains partnerships. (d) C' contains partnerships.
Transcript text: The given contingency table lists the cross tabulation of the number of business partnerships by industry and whether the partnership reported net income or net loss for the year 2014 in a certain country. Using the letters given in the table, find the number of partnerships in each of the following sets in parts (a) through (d). (a) B UW contains $\square$ partnerships. (b) RUC contains $\square$ partnerships. (c) C $\cap A$ contains $\square$ partnerships. (d) $\mathrm{C}^{\prime}$ contains $\square$ partnerships.
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Solution

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Solution Steps

To solve the given problem, we need to interpret the contingency table and calculate the number of partnerships for each specified set. Let's proceed step by step.

Step 1: Understand the Contingency Table

The contingency table provides a cross-tabulation of partnerships by industry and their financial outcome (net income or net loss). The letters in the table represent the number of partnerships in each category.

Step 2: Calculate the Number of Partnerships for Each Set
(a) Calculate B UW
  • B UW: This set represents the number of partnerships in industry B that reported a net income (U) or a net loss (W).
  • To find this, sum the partnerships in industry B for both net income and net loss.
(b) Calculate RUC
  • RUC: This set represents the number of partnerships in industry R that reported a net income (U) and are also in category C.
  • To find this, identify the partnerships in industry R that are both in category C and reported a net income.
(c) Calculate C ∩ A
  • C ∩ A: This set represents the number of partnerships that are in both category C and industry A.
  • To find this, identify the partnerships that are in category C and also belong to industry A.

Final Answer

  • (a) B UW contains \(\boxed{\text{number of partnerships}}\).
  • (b) RUC contains \(\boxed{\text{number of partnerships}}\).
  • (c) C ∩ A contains \(\boxed{\text{number of partnerships}}\).

Note: The actual numbers for each set would be determined by the specific values in the contingency table, which are represented by letters in the problem statement.

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