Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter5: Linear Inequalities
Section5.1: Solving Inequalities By Addition And Subtraction
Problem 57PFA
Related questions
Question
![---
### Determining the Number of Possible 4-Digit Phone Extensions for a Company
A company wants to have 4-digit phone extensions with the first digit not being zero.
---
**Question:**
How many different phone extensions are possible?
---
**Solution:**
To determine the number of different possible phone extensions, consider the following constraints:
1. The phone extension is 4 digits long.
2. The first digit cannot be zero.
**Calculation Strategy:**
1. **First digit options:**
- Can be any digit from 1 to 9. (9 possible options)
2. **Second, third, and fourth digit options:**
- Can be any digit from 0 to 9. (10 possible options each)
The total number of different phone extensions can be calculated by multiplying the number of options for each digit:
\[ 9 \times 10 \times 10 \times 10 \]
**Result:**
The number of different 4-digit phone extensions the company can have is:
\[ 9 \times 10^3 = 9 \times 1000 = 9000 \]
Therefore, the company can have **9,000 different phone extensions**.
---
This calculation ensures that the first digit is never zero, meeting the company's constraint for their phone extension system.
### Visualization:
To visualize the options, consider a representation where each position in the 4-digit extension is defined:
- **First digit:** 9 options (1-9)
- **Second, third, and fourth digits:** 10 options each (0-9)
\[
\text{First digit (9 options)} \quad \text{Second digit (10 options)} \quad \text{Third digit (10 options)} \quad \text{Fourth digit (10 options)}
\]
This effectively creates \( 9 \times 10 \times 10 \times 10 = 9,000 \) unique 4-digit extensions.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6c3136-3b78-4c3b-95a7-be26ea6fb45d%2F22c03617-c9cc-474b-9f69-64687bc41fdd%2F5phadii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Determining the Number of Possible 4-Digit Phone Extensions for a Company
A company wants to have 4-digit phone extensions with the first digit not being zero.
---
**Question:**
How many different phone extensions are possible?
---
**Solution:**
To determine the number of different possible phone extensions, consider the following constraints:
1. The phone extension is 4 digits long.
2. The first digit cannot be zero.
**Calculation Strategy:**
1. **First digit options:**
- Can be any digit from 1 to 9. (9 possible options)
2. **Second, third, and fourth digit options:**
- Can be any digit from 0 to 9. (10 possible options each)
The total number of different phone extensions can be calculated by multiplying the number of options for each digit:
\[ 9 \times 10 \times 10 \times 10 \]
**Result:**
The number of different 4-digit phone extensions the company can have is:
\[ 9 \times 10^3 = 9 \times 1000 = 9000 \]
Therefore, the company can have **9,000 different phone extensions**.
---
This calculation ensures that the first digit is never zero, meeting the company's constraint for their phone extension system.
### Visualization:
To visualize the options, consider a representation where each position in the 4-digit extension is defined:
- **First digit:** 9 options (1-9)
- **Second, third, and fourth digits:** 10 options each (0-9)
\[
\text{First digit (9 options)} \quad \text{Second digit (10 options)} \quad \text{Third digit (10 options)} \quad \text{Fourth digit (10 options)}
\]
This effectively creates \( 9 \times 10 \times 10 \times 10 = 9,000 \) unique 4-digit extensions.
---
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