3. The amount of money ($125 per day) paid to substitutes at LHS depends on how many teachers are out; however it is not a direct relationship. Since teachers don't teach every block, we can hire slightly fewer substitutes than there are teachers absent. Here are the functions that are used to find the number of substitutes needed and the cost of substitutes per day. f(x) = 0.8x + 2 and g(x) = 125x %3D If 20 teachers are absent one day, find out how much money LHS pays to substitutes. Show your work. a. b. What order did you evaluate the functions and why did you do it that way?
3. The amount of money ($125 per day) paid to substitutes at LHS depends on how many teachers are out; however it is not a direct relationship. Since teachers don't teach every block, we can hire slightly fewer substitutes than there are teachers absent. Here are the functions that are used to find the number of substitutes needed and the cost of substitutes per day. f(x) = 0.8x + 2 and g(x) = 125x %3D If 20 teachers are absent one day, find out how much money LHS pays to substitutes. Show your work. a. b. What order did you evaluate the functions and why did you do it that way?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Educational Context: Understanding Substitute Costs at LHS**
**Problem 3:**
The amount of money ($125 per day) paid to substitutes at LHS depends on how many teachers are out; however, it is not a direct relationship. Since teachers don’t teach every block, we can hire slightly fewer substitutes than there are teachers absent. Here are the functions used to find the number of substitutes needed and the cost of substitutes per day:
\[ f(x) = 0.8x + 2 \]
\[ g(x) = 125x \]
**a.** If 20 teachers are absent one day, find out how much money LHS pays to substitutes. Show your work.
**b.** What order did you evaluate the functions and why did you do it that way?
**c.** What domain for the composition makes sense for this context?
**d.** If \( h(x) - f(x) = x^3 - 6x + 12 \), find \( h(x) \). Show work that leads to your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4117cac-23e7-449a-b251-99443c1e90ff%2F0c2bfc4e-24c5-451a-9229-d6847b52d1eb%2Fpn0qqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Context: Understanding Substitute Costs at LHS**
**Problem 3:**
The amount of money ($125 per day) paid to substitutes at LHS depends on how many teachers are out; however, it is not a direct relationship. Since teachers don’t teach every block, we can hire slightly fewer substitutes than there are teachers absent. Here are the functions used to find the number of substitutes needed and the cost of substitutes per day:
\[ f(x) = 0.8x + 2 \]
\[ g(x) = 125x \]
**a.** If 20 teachers are absent one day, find out how much money LHS pays to substitutes. Show your work.
**b.** What order did you evaluate the functions and why did you do it that way?
**c.** What domain for the composition makes sense for this context?
**d.** If \( h(x) - f(x) = x^3 - 6x + 12 \), find \( h(x) \). Show work that leads to your answer.
Expert Solution
Step 1
a)
Number of substitutes
= 20*0.8 + 2
= 18
Hence,
Money paid by LHS for substitutes
= 125 * 18
= $ 2350
Step by step
Solved in 3 steps
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