Answer :
Sure! Let's break down each part of the problem step-by-step:
1. Interpreting the statement [tex]\(C(S(3)) = 11\)[/tex]:
- This notation involves two functions, [tex]\(S(t)\)[/tex] and [tex]\(C(s)\)[/tex].
- [tex]\(S(t)\)[/tex] represents the number of shoppers in the mall after [tex]\(t\)[/tex] hours from opening.
- [tex]\(C(s)\)[/tex] represents the number of store clerks needed for [tex]\(s\)[/tex] shoppers.
- The statement [tex]\(C(S(3)) = 11\)[/tex] means that 3 hours after the mall opens, the amount of shoppers is such that 11 store clerks are needed to attend to them.
2. Writing an expression using a composition of functions for oven temperature adjustments:
- You need to convert a given temperature in degrees Celsius (°C) to degrees Fahrenheit (°F), and then adjust it because your oven runs hot.
- The formula to convert Celsius to Fahrenheit is: [tex]\(F = \frac{9}{5}C + 32\)[/tex].
- Since your oven runs 15°F hotter than set, you need the actual setting to be 15°F lower.
- Therefore, for a recipe that calls for [tex]\(t\)[/tex]°C, the conversion to Fahrenheit is:
[tex]\[
F(t) = \frac{9}{5}t + 32
\][/tex]
- Adjust for the oven running hot by subtracting 15°F:
[tex]\[
\text{Adjusted Fahrenheit} = F(t) - 15 = \left(\frac{9}{5}t + 32\right) - 15
\][/tex]
By following these steps, you can interpret the statement and calculate the adjusted oven temperature using the given conversion formula and correction for your oven running hot.
1. Interpreting the statement [tex]\(C(S(3)) = 11\)[/tex]:
- This notation involves two functions, [tex]\(S(t)\)[/tex] and [tex]\(C(s)\)[/tex].
- [tex]\(S(t)\)[/tex] represents the number of shoppers in the mall after [tex]\(t\)[/tex] hours from opening.
- [tex]\(C(s)\)[/tex] represents the number of store clerks needed for [tex]\(s\)[/tex] shoppers.
- The statement [tex]\(C(S(3)) = 11\)[/tex] means that 3 hours after the mall opens, the amount of shoppers is such that 11 store clerks are needed to attend to them.
2. Writing an expression using a composition of functions for oven temperature adjustments:
- You need to convert a given temperature in degrees Celsius (°C) to degrees Fahrenheit (°F), and then adjust it because your oven runs hot.
- The formula to convert Celsius to Fahrenheit is: [tex]\(F = \frac{9}{5}C + 32\)[/tex].
- Since your oven runs 15°F hotter than set, you need the actual setting to be 15°F lower.
- Therefore, for a recipe that calls for [tex]\(t\)[/tex]°C, the conversion to Fahrenheit is:
[tex]\[
F(t) = \frac{9}{5}t + 32
\][/tex]
- Adjust for the oven running hot by subtracting 15°F:
[tex]\[
\text{Adjusted Fahrenheit} = F(t) - 15 = \left(\frac{9}{5}t + 32\right) - 15
\][/tex]
By following these steps, you can interpret the statement and calculate the adjusted oven temperature using the given conversion formula and correction for your oven running hot.
