Answer:
Last option: It is not a function because there are two different y-values for a single x-value.
Step-by-step explanation:
It is necessary to remember that, by definition, a relation is a function if each input value (x-value) has one and only one output value (x-value) .
In this case, the following points:
You can observe that the input value 4 (
) has two ouput values. These are:
Therefore, since there are two different y-values for a single x-value, you can conclude that the given graph is not a function.
Answer:
first one
Step-by-step explanation:
Answer:
Step-by-step explanation:
Confidence interval is written in the form, sample mean ± margin of error
The sample mean is an estimator for the population mean. The confidence level is used to express how confident we are that the population mean is within the calculated confidence interval. The lower limit of the given confidence interval is 2.619 hours/day while the upper limit of the confidence interval is 3.401 hours/day
Therefore, the INVALID interpretations of the 95% confidence interval are
A. About 95% of all Cal Poly students spend between 2.619 and 3.401 hours/day watching TV.
B. There is a 95% chance that, on average, Cal Poly students spend between 2.619 and 3.401 hours/day watching TV.
D. In the long run, 95% of the sample means will be between 2.619 and 3.401 hours.
E. None of the above.
Answer:
dy/dx = -1/√(1 - x²)
For 0 < y < π
Step-by-step explanation:
Given the function cos y = x
-siny dy = dx
-siny dy/dx = 1
dy/dx = -1/siny (equation 1)
But cos²y + sin²y = 1
=> sin²y = 1 - cos²y
=> siny = √(1 - cos²y) (equation 2)
Again, we know that
cosy = x
=> cos²y = x² (equation 3)
Using (equation 3) in (equation 2), we have
siny = √(1 - x²) (equation 4)
Finally, using (equation 4) in (equation 1), we have
dy/dx = -1/√(1 - x²)
The largest interval is when
√(1 - x²) = 0
=> 1 - x² = 0
=> x² = 1
=> x = ±1
So, the interval is
-1 < x < 1
arccos(1) < y < arxcos(-1)
= 0 < y < π
