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Chapter 5: Problem 136

At a workshop on enhancing creativity, \(\frac{1}{4}\) of the participants are musicians, \(\frac{2}{5}\) are artists, \(\frac{1}{10}\) are actors, and the remaining participants are writers. What fraction of the people attending the workshop are writers?

Short Answer

Expert verified
The fraction of people attending the workshop who are writers is 0

Step by step solution

01

Add the fractions of musicians, artists, and actors

We first add the fractions that represent musicians (\(\frac{1}{4}\)), artists (\(\frac{2}{5}\)) and actors (\(\frac{1}{10}\)): \(\frac{1}{4} + \frac{2}{5} + \frac{1}{10} = \frac{10}{20} + \frac{8}{20} + \frac{2}{20} = \frac{20}{20}\)
02

Calculate the fraction of writers

The fraction of writers is calculated by subtracting the total fraction of musicians, artists, and actors from 1. Since all fractions should add up to 1, this will give us the fraction of writers: \(1 - \frac{20}{20} = \frac{0}{20}\)
03

Simplify the fraction

The fraction \(\frac{0}{20}\) simplifies to 0. This means that the fraction of writers is 0.

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Most popular questions from this chapter

You will develop geometric sequences that model the population growth for California and Texas, the two most populated U.S. states. The table shows the population of California for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 33.87 & 34.21 & 34.55 & 34.90 & 35.25 & 35.60 \\ \hline \end{array} $$ $$ \begin{array}{|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 36.00 & 36.36 & 36.72 & 37.09 & 37.25 \\ \hline \end{array} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that California has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling California's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project California's population, in millions, for the year 2020 . Round to two decimal places.

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