To solve the given problems, let's break down each part and find the answers step-by-step.
### Part (a)
We need to determine how much lower the temperature in Montreal was compared to Miami at 6 a.m.
1. Temperature in Montreal at 6 a.m.: [tex]\(-23^\circ F\)[/tex]
2. Temperature in Miami at 6 a.m.: [tex]\(79^\circ F\)[/tex]
To find how much lower Montreal's temperature was compared to Miami's temperature, we calculate the difference between Miami's temperature and Montreal's temperature.
[tex]\[
\text{Difference} = 79^\circ F - (-23^\circ F)
\][/tex]
Subtracting a negative number is the same as adding the absolute value of that number:
[tex]\[
\text{Difference} = 79^\circ F + 23^\circ F = 102^\circ F
\][/tex]
So, the temperature in Montreal was [tex]\(102^\circ F\)[/tex] lower than in Miami.
### Part (b)
We need to find the temperature in Milwaukee at noon, knowing that the temperature at 6 a.m. had risen by [tex]\(20^\circ F\)[/tex] by noon.
1. Temperature in Milwaukee at 6 a.m.: [tex]\(-15^\circ F\)[/tex]
2. Temperature rise: [tex]\(20^\circ F\)[/tex]
To find the temperature at noon, we add this rise to the 6 a.m. temperature:
[tex]\[
\text{Temperature at noon} = -15^\circ F + 20^\circ F = 5^\circ F
\][/tex]
Thus, the temperature in Milwaukee at noon was [tex]\(5^\circ F\)[/tex].
### Summary of Answers
(a) The temperature in Montreal was [tex]\(102^\circ F\)[/tex] lower than in Miami.
(b) The temperature in Milwaukee at noon was [tex]\(5^\circ F\)[/tex].
