Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine which piecewise function correctly represents the charges based on Tracy's cell phone plan, we need to carefully analyze each option given the details provided:
1. Understand the plan:
- Tracy pays a flat rate of \[tex]$29 for the first 250 minutes. - For any additional minutes beyond 250, Tracy is charged \$[/tex]0.35 per minute.
2. Analyze each option:
Option A:
[tex]\[ f(x) = \begin{cases} 29, & x > 250 \\ 29 + 0.35x, & x \leq 250 \end{cases} \][/tex]
- For [tex]\(x > 250\)[/tex], it states the charge remains \[tex]$29, which is incorrect because there should be an additional charge for the extra minutes. - For \(x \leq 250\), it states the charge is \(29 + 0.35x\), which means it incorrectly adds \$[/tex]0.35 per minute for all minutes, even the first 250, which are free.
Option B:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
- For [tex]\(x \leq 250\)[/tex], it correctly states the charge is a flat \[tex]$29. - For \(x > 250\), it correctly computes the charge as the flat \$[/tex]29 plus \[tex]$0.35 for each additional minute over 250. Option C: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$35 per minute for all minutes, which doesn't make sense according to the plan. Option D: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$29 plus \$[/tex]35 per minute for all minutes, which is an erroneous interpretation of the plan.
After evaluating each option:
- Option A is incorrect because it miscalculates the charges for both [tex]\(x \leq 250\)[/tex] and [tex]\(x > 250\)[/tex].
- Option C is incorrect because it applies an erroneous \[tex]$35 charge for all minutes when \(x > 250\). - Option D is incorrect because it adds an excessive \$[/tex]35 per minute charge on top of the flat \$29.
The correct representation is found in Option B, which accurately models the charges:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
Thus, Option B is the correct piecewise function representing Tracy's cell phone plan charges.
1. Understand the plan:
- Tracy pays a flat rate of \[tex]$29 for the first 250 minutes. - For any additional minutes beyond 250, Tracy is charged \$[/tex]0.35 per minute.
2. Analyze each option:
Option A:
[tex]\[ f(x) = \begin{cases} 29, & x > 250 \\ 29 + 0.35x, & x \leq 250 \end{cases} \][/tex]
- For [tex]\(x > 250\)[/tex], it states the charge remains \[tex]$29, which is incorrect because there should be an additional charge for the extra minutes. - For \(x \leq 250\), it states the charge is \(29 + 0.35x\), which means it incorrectly adds \$[/tex]0.35 per minute for all minutes, even the first 250, which are free.
Option B:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
- For [tex]\(x \leq 250\)[/tex], it correctly states the charge is a flat \[tex]$29. - For \(x > 250\), it correctly computes the charge as the flat \$[/tex]29 plus \[tex]$0.35 for each additional minute over 250. Option C: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$35 per minute for all minutes, which doesn't make sense according to the plan. Option D: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$29 plus \$[/tex]35 per minute for all minutes, which is an erroneous interpretation of the plan.
After evaluating each option:
- Option A is incorrect because it miscalculates the charges for both [tex]\(x \leq 250\)[/tex] and [tex]\(x > 250\)[/tex].
- Option C is incorrect because it applies an erroneous \[tex]$35 charge for all minutes when \(x > 250\). - Option D is incorrect because it adds an excessive \$[/tex]35 per minute charge on top of the flat \$29.
The correct representation is found in Option B, which accurately models the charges:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
Thus, Option B is the correct piecewise function representing Tracy's cell phone plan charges.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
