The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.
Time of Day
10 AM
12 Noon
2 PM
4 PM
6 PM
8 PM
10 PM
Temperature ((Degrees Fahrenheit))
30
35
36
36
34
30
28

Over which period(s) of time is the average rate of change zero? What, if anything, can you conclude about the actual temperature fluctuation within this period?
a.
The average rate of change of temperature is 0 from 2 PM to 4 PM; Nothing can be concluded about the actual temperature fluctuation.
b.
The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.
c.
The average rate of change of temperature is 0 from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.
d.
The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; The conclusion that can be drawn is that the temperature will not change for that time period.

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Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24