Question

act 1 venn diagram
define the two best categories, with abbreviations, for each scenario. do not create a venn diagram.

1. at lhs 1600 students were surveyed. 1200 students said they felt confident in their math abilities. 450 students earned an a in their last math class. 22 students felt confident in their math abilities and did not earn an a in their last math class.
2. a group is studying youth fashion. of the 620 people observed at the local mall, 300 wore branded clothing, 88 wore neon - colored clothing, and 25 were wearing neither branded clothing nor neon - colored clothing.

Explanation:

1.

Step1: Identify the first category

Let \(C\) be the category of students confident in math abilities and \(N\) be the category of students not confident in math abilities. We know \(n(C)=1200\), so \(n(N)=1600 - 1200=400\).

Step2: Identify the second category

Let \(A\) be the category of students who earned an \(A\) in math and \(NA\) be the category of students who did not earn an \(A\) in math. We know \(n(A) = 450\) and \(n(NA)=1600 - 450 = 1150\), and the number of students in \(C\cap NA = 22\).

Step1: Identify the first category

Let \(B\) be the category of students wearing branded clothing and \(NB\) be the category of students not wearing branded clothing. We know \(n(B)=300\). The total number of students observed is \(n = 620\) and the number of students wearing neither branded nor neon - colored clothing is \(n(NB\cap NN)=25\), so \(n(NB)=620 - 300=320\).

Step2: Identify the second category

Let \(N\) be the category of students wearing neon - colored clothing and \(NN\) be the category of students not wearing neon - colored clothing. We know \(n(N)=88\) and \(n(NN)=620 - 88 = 532\).

Answer:

The two best - categories are: Confidence in Math Abilities (\(C\) and \(N\)) and Grade in Last Math Class (\(A\) and \(NA\))

2.