THE FUNCTION IS CONTINUOUS - True
The table indicates that for every hour indicated, there is a corresponding amount of juice (cups) provided. The graph would represent a linear progression between the hours of 4 and 8 without any discontinuities.
TIME IS THE DEPENDENT VARIABLE - False
Time acts as the independent variable since it remains unaffected by any other factors. Conversely, the number of cups is contingent upon the hours, categorizing it as a dependent variable.
THE SCENARIO IS CHARACTERIZED BY
A LINEAR FUNCTION AS THE RATE OF CHANGE IS CONSTANT - True
The rate of change is a steady 53 cups per hour, indicating a linear function.
AS TIME INCREASES, THERE ARE FEWER CUPS OF JUICE POURED EACH HOUR - False
Since the rate of change is positive, the cups poured each hour will actually increase.
FOR EACH EXTRA HOUR, 53 CUPS OF JUICE ARE POURED - True
The hourly difference in cups poured is consistently 53.
Answer: D) randomized comparative design
Step-by-step explanation:
A randomized comparative design involves comparing two or more treatments and is characterized by an experiment intended to highlight differences between two groups or populations subjected to distinct conditions or treatments. In the scenario described, pre-existing data was juxtaposed with information collected after the alcohol dangers course.
Response:
, indicating the amount of earnings per working hours, designated as x
Detailed Explanation:
We have two distinct functions to analyze:
This function delineates the earnings based on units of x
Then the second function is
which illustrates the quantity of gallons of ice cream produced by Barrett each hour, with x representing the hours worked.
Our aim is to determine the composite function
resulting from substituting the output of 
as input for 
. Within this framework, the function signifies the amount of money accrued per number of working hours, x.
By substituting g(x) into the x variable of f(x), we obtain:
