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a. In a class of 465 students, \(54 \%\) of the students were right-handed. How many right-handed students are there? b. A pharmaceutical company recently hired 182 pharmacy graduates and 94 of them are male. What percentage of these graduates are female? c. A publishing house comprises \(56 \%\) male editors, or 280 male editors. What is the total number of editors at the firm?

Short Answer

Expert verified
The results are a) Approximately 251 right-handed students b) Approximately \(48.35\%\) are female graduates c) There are 500 total editors .

Step by step solution

01

Calculating the number of right-handed students

The number of right-handed students can be found by calculating \(54\%\) of the total students. So, right-handed students = \(54\%\) of 465 = \(\frac{54}{100} * 465 = 251.1\). However, number of students can't be in fractions so, we will consider 251 as the closest integer.
02

Calculating the percentage of female graduates

First, calculate the number of female graduates. It's the total number of graduates minus the number of male graduates i.e., 182 - 94 = 88. The percentage of female graduates = \(\frac{88}{182} * 100 = 48.35\%.\)
03

Calculating the total number of editors

If \(56\%\) of the editors are males and the number of male editors is 280, the total number of editors = \(\frac{280}{56} * 100 = 500\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Right-Handed Students Calculation
In order to determine the number of right-handed students in a class of 465, we need to calculate what 54% of 465 is. Understanding percentages is key here, as they are a way to express a number as a fraction of 100.
To find 54% of 465, you multiply 465 by 0.54. Mathematically, this process is represented by the equation: \[ \frac{54}{100} \times 465 = 251.1 \] Since you cannot have a fraction of a student, we round 251.1 down to 251 to arrive at the nearest whole number.
This calculation demonstrates the concept of applying percentages to real-world scenarios, such as measuring how many students belong to a particular group based on their handedness.
Female Graduates Percentage
When calculating the percentage of female graduates in a group, it's essential first to find out how many individuals belong to the subgroup you are focused on. In this problem, we start with the total number of graduates, subtract the male graduates, and are left with the female graduates.
Given:
  • Total graduates = 182
  • Male graduates = 94
We find the number of female graduates by subtracting the number of male graduates from the total: \[ 182 - 94 = 88 \]
Next, to find the percentage of female graduates, divide the number of female graduates by the total number of graduates, and then multiply by 100 to convert it into a percentage:\[ \frac{88}{182} \times 100 = 48.35\% \]
This calculation highlights the importance of knowing how to express part of a group as a percentage of the whole, a valuable skill both academically and professionally.
Total Number of Editors
To calculate the total number of editors in a publishing house given the percentage and count of male editors, we need to reverse-engineer the problem. Start by understanding that if 56% of the editors are male, and the number of male editors is given, you can find the total by dividing the number of male editors by the percentage they represent.
In this scenario:
  • Percentage of editors who are male = 56%
  • Number of male editors = 280
To find the total number of editors, use the following equation: \[ \frac{280}{56} \times 100 = 500 \]
By performing this calculation, you get the total number of editors. This type of problem teaches you to navigate percentage-based questions, especially when you need to derive the total quantity from a specific part, which is a frequent requirement in data analysis and interpretation.

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