Answered

Join IDNLearn.com and start getting the answers you've been searching for. Our platform is designed to provide accurate and comprehensive answers to any questions you may have.

Select ALL the correct answers.

Martha works at a small jewelry store. She designs 2 rings in the first hour. Every additional hour, she designs 3 new rings.

Select all the functions that can be used to find the number of rings, [tex]$r(n)$[/tex], she designs in [tex]$n$[/tex] hours.

A. [tex]r(1)=3 ; r(n)=r(n-1)+2[/tex], for [tex]n \geq 2[/tex]
B. [tex]r(1)=2 ; r(n)=r(n-1)+3[/tex], for [tex]n \geq 2[/tex]
C. [tex]r(n)=3n-1[/tex]
D. [tex]r(n)=3n+2[/tex]
E. [tex]r(n)=2n+3[/tex]
F. [tex]r(1)=3 ; r(n)=r(n-1)-1[/tex], for [tex]n \geq 2[/tex]

Sagot :

GinnyAnsweridn
Let's analyze each function based on the information given.

Martha designs 2 rings in the first hour and every additional hour she designs 3 more rings. We need to find which functions correctly describe the number of rings, [tex]\( r(n) \)[/tex], she designs in [tex]\( n \)[/tex] hours.

### 1. [tex]\( r(1)=3 ; r(n)=r(n-1)+2 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( r(1) = 3 \)[/tex] [This does not match the given initial condition [tex]\( r(1)=2 \)[/tex]]
- Therefore, this function does not satisfy the criteria.

### 2. [tex]\( r(1)=2 ; r(n)=r(n-1)+3 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( r(1) = 2 \)[/tex] [matches initial condition]
- For [tex]\( n = 2 \)[/tex]: [tex]\( r(2) = r(1) + 3 = 2 + 3 = 5 \)[/tex]
- For [tex]\( n = 3 \)[/tex]: [tex]\( r(3) = r(2) + 3 = 5 + 3 = 8 \)[/tex]
- This function correctly describes the number of rings designed each hour after the first.

### 3. [tex]\( r(n)=3n-1 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( r(1) = 3(1) - 1 = 2 \)[/tex] [matches initial condition]
- For [tex]\( n = 2 \)[/tex]: [tex]\( r(2) = 3(2) - 1 = 5 \)[/tex]
- For [tex]\( n = 3 \)[/tex]: [tex]\( r(3) = 3(3) - 1 = 8 \)[/tex]
- This function also correctly describes the number of rings designed over time.

### 4. [tex]\( r(n)=3n+2 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( r(1) = 3(1) + 2 = 5 \)[/tex] [does not match initial condition]
- This function does not satisfy the criteria.

### 5. [tex]\( r(n)=2n+3 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( r(1) = 2(1) + 3 = 5 \)[/tex] [does not match initial condition]
- This function does not satisfy the criteria.

### 6. [tex]\( r(1)=3 ; r(n)=r(n-1)-1 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( r(1) = 3 \)[/tex] [does not match initial condition]
- This function does not satisfy the criteria.

### Conclusion
Based on the above analysis, the functions that correctly determine the number of rings Martha designs are:

[tex]\[ r(1)=2 ; r(n)=r(n-1)+3, \text{ for } n \geq 2 \][/tex]
[tex]\[ r(n)=3n-1 \][/tex]

These functions accurately represent the situation and are consistent with the information given. Therefore, the correct answer is:

[tex]\[ [2] \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.