John is standing on a set of bleachers and throws a baseball into the air. the baseball lands on the field. the height of the ba
ll, in meters, is modeled by the function shown in the graph. what's the average rate of change of the height of the ball from the point when John throws it to its maximum height? 
1 answer:
Answer:
2 m/s
Step-by-step explanation:
Given the graph of the baseball thrown into air.
John throws the baseball into the air from a given height and then the baseball reaches a maximum height and then comes back to ground.
The height of the baseball (in metres) is modeled by the function graph with respect to time.
To find:
The average rate of change of height of the ball from the point the ball is thrown to the maximum height.
Solution:
Here, the average rate of change can be found by dividing the distance between the two points with the change in time.
The starting time is 0 seconds.
The starting height is 3 metres.
The ending time is 2 seconds i.e. at which the ball reaches the maximum height.
The height is 7 metres.
Therefore, the average rate of change is:
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Answer:
a) The sample mean is of 49 and the sample standard deviation is of 11.7.
b) The range of the true mean at 90% confidence level is of 9.62 hours.
c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Step-by-step explanation:
Question a:
Sample mean:
Sample standard deviation:
The sample mean is of 49 and the sample standard deviation is of 11.7.
b)Determine the range of the true mean at 90% confidence level.
We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0.150
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample. So
The range of the true mean at 90% confidence level is of 9.62 hours.
(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.
This is the confidence interval, so:
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.
The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.
The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.