Answer:
Attached is the histogram illustrating the marathon runners’ times.
Step-by-step explanation:
The provided data is as follows;
2.21
2.25
2.76
3.1
3.3
3.5
3.6
3.77
3.8
4.23
4.25
4.25
4.6
4.9
From this data, we can determine;
The count of runners finishing between 0 and 1 hour = 0
The count of runners finishing between 1 and 2 hours = 0
The count of runners finishing between 2 and 3 hours = 3
The count of runners finishing between 3 and 4 hours = 6
The count of runners finishing between 4 and 5 hours = 5
Based on these frequencies across the various time ranges, the histogram for the provided data has been constructed and is attached.
V = x³ - 6x²y + 12xy² - 8y³
V = (x - 2y)³
= (x - 2y)(x - 2y)(x - 2y) ( start by expanding the first pair of factors )
= (x² - 4xy + 4y²)(x - 2y) ( multiply the terms from the first group with those in the second )
= x³ - 4x²y + 4xy² - 2x²y + 8xy² - 8y³ ( combine similar terms )
= x³ - 6x²y + 12xy² - 8y³
Answer:
To summarize the answer:
Step-by-step explanation:
Given:
Here is the graph associated with this question:
The second function, denoted as 
, does not qualify as a function.
Keep in mind that the g(x) function is the inversion of the f(x) function. Recognizing this pattern indicates a reflection on the Y-axis.
Reflection on the axes:
In the x-axis:
Enhance the function by -1 to illustrate an exponential curve around the x-axis.
In the y-axis:
Decrease the input of the function by -1 to depict the exponential function around the y-axis.
