What is a reasonable distance between two cities?
1 answer:
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Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: 
Rate of change of
:
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of:
The average rate of change of the function over the interval [0,2] is 1.5
Rate of change of
:
Here the end points are (0,0) and (2,2)
The average rate of change of the function over the interval [0,2] is 1
Rate of change of
:
Here the end points are (0,-1) and (2,0)
The average rate of change of the function over the interval [0,2] is 0.5
Rate of change of
:
Here the end points are (0,0.5) and (2,2.5)
The average rate of change of the function over the interval [0,2] is 1
We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>
Rate of change of
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of
The average rate of change of the function
Rate of change of
Here the end points are (0,0) and (2,2)
The average rate of change of the function
Rate of change of
Here the end points are (0,-1) and (2,0)
The average rate of change of the function
Rate of change of
Here the end points are (0,0.5) and (2,2.5)
The average rate of change of the function
We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>
Answer:
the standard deviation increases
Step-by-step explanation:
Let x₁ , x₂, . . . , x₂₃ be the actual data observed by the student
The sample means = x₁ + x₂ + . . . , x₂₃ / 23
= 2.3hr
⇒
let x₁ , x₂, . . . , x₂₃ arranged in ascending order
Then x₂₃ was 10 and has been changed to 14
i.e x₂₃ increase to 4
Sample mean
therefore, the new sample mean is 2.47
2) For the old data set
the median is values
when we use the new data set only x₂₃ is changed to 14
i.e the rest all observation remain unchanged
Hence, sample median = remain unchange
sample median = 2.5hrs
The Standard deviation of old data set is calculated
The new sample standard sample deviation is calculated as
Now, when we compare (1) and (2) the square distance between each observation xi and old mean is less than the squared distance between each observation xi and the new mean.
Since,
(xi - 2.3)² ∑ (xi - 2.47)²
Therefore , the standard deviation increases