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2 answers:
Note:
The area of a circle with radius r is πr².
An entire circle has a central angle of 360°.
For the sector with radius = (3+4) = 7cm and a central angle of 120°, the area is
For the sector with radius = 3 cm and a central angle of 120°. the area is
The area of the shaded sector (see the figure) is
Answer:
The area of a circle with radius r is πr².
An entire circle has a central angle of 360°.
For the sector with radius = (3+4) = 7cm and a central angle of 120°, the area is
For the sector with radius = 3 cm and a central angle of 120°. the area is
The area of the shaded sector (see the figure) is
Answer:
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Answer:
Step-by-step explanation:
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less than 10 minutes, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.