Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Problem Summary for Educational Purposes

**Context:**
The provided table and accompanying information summarize the distribution of eighth-grade students at Keisel Middle School based on their handedness (left-handed or right-handed) and gender.

**Table Data:**

| Gender | Left-handed | Right-handed |
|--------|-------------|--------------|
| Female | -           | -            |
| Male   | -           | -            |
| **Total** | **18**        | **122**         |

**Problem Details:**

1. **Given Information:**
   - There are 5 times as many right-handed female students as there are left-handed female students.
   - There are 9 times as many right-handed male students as there are left-handed male students.
   - The total number of left-handed students is 18.
   - The total number of right-handed students is 122.

2. **Objective:**
   Determine which given probability is closest to the probability that a randomly selected right-handed student is female.

3. **Assumptions:**
   - None of the eighth-grade students are both right-handed and left-handed.

**Options for Probability Calculation:**

A) 0.410  
B) 0.357  
C) 0.333  
D) 0.250

### Explanation of Probabilities:

To solve for the probability, we can follow these steps:

1. **Let F_l represent left-handed females, M_l represent left-handed males, F_r represent right-handed females, and M_r represent right-handed males.**

2. **Initial Information Setup:**
   - F_l + M_l = 18 (total left-handed students)
   - F_r + M_r = 122 (total right-handed students)
   
3. **Using Ratios:**
   - F_r = 5 * F_l (since right-handed females are 5 times the number of left-handed females)
   - M_r = 9 * M_l (since right-handed males are 9 times the number of left-handed males)
   
4. **Total Students:**
   - Total left-handed students: F_l + M_l = 18
   - Total right-handed students: (5 * F_l) + (9 * M_l) = 122

5. **Probability Calculation:**
   - First solve the equations to find the actual numbers of left-handed and right-handed students for each gender.
   - Then calculate the
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Transcribed Image Text:### Problem Summary for Educational Purposes **Context:** The provided table and accompanying information summarize the distribution of eighth-grade students at Keisel Middle School based on their handedness (left-handed or right-handed) and gender. **Table Data:** | Gender | Left-handed | Right-handed | |--------|-------------|--------------| | Female | - | - | | Male | - | - | | **Total** | **18** | **122** | **Problem Details:** 1. **Given Information:** - There are 5 times as many right-handed female students as there are left-handed female students. - There are 9 times as many right-handed male students as there are left-handed male students. - The total number of left-handed students is 18. - The total number of right-handed students is 122. 2. **Objective:** Determine which given probability is closest to the probability that a randomly selected right-handed student is female. 3. **Assumptions:** - None of the eighth-grade students are both right-handed and left-handed. **Options for Probability Calculation:** A) 0.410 B) 0.357 C) 0.333 D) 0.250 ### Explanation of Probabilities: To solve for the probability, we can follow these steps: 1. **Let F_l represent left-handed females, M_l represent left-handed males, F_r represent right-handed females, and M_r represent right-handed males.** 2. **Initial Information Setup:** - F_l + M_l = 18 (total left-handed students) - F_r + M_r = 122 (total right-handed students) 3. **Using Ratios:** - F_r = 5 * F_l (since right-handed females are 5 times the number of left-handed females) - M_r = 9 * M_l (since right-handed males are 9 times the number of left-handed males) 4. **Total Students:** - Total left-handed students: F_l + M_l = 18 - Total right-handed students: (5 * F_l) + (9 * M_l) = 122 5. **Probability Calculation:** - First solve the equations to find the actual numbers of left-handed and right-handed students for each gender. - Then calculate the
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