Answer:
x = 9.8
Step-by-step explanation:
(please refer to attached)
after labeling the picture with all the known information, we can see that
OF = OR = Radius of the circle -----(eq 1)
Consider triangle OFP, by Pythagorean theorem,
OF² = PF²+OP²
r² = 11.5² + 11²
r² = 253.25 -----(eq 2)
Consider triangle ORQ, by Pythagorean theorem,
OR² = RQ²+OQ²
r² = 12.5² + x²
r² = 156.25 + x² ----(eq 3)
equating (eq 2) and (eq 3)
253.25 = 156.25 + x²
x² = 253.25 - 156.25
x² = 97
x = √97
x = 9.8 (nearest tenth)
Answer:
(a) and (e)
Step-by-step explanation:
Given
Required
Select the true statements
First, is a statement about the area.
The area is calculated as:
So, we have:
(a) is true
Next, is a statement about the circumference.
This is calculated as:
So, we have:
(e) is true
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,and we have enough evidence to conclude that the true mean is significantly lower thn 4.8 at 10% of signficance.
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 thetrue mean is below the specifications, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 and we know the population deviation so 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 one sided 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,and we have enough evidence to conclude that the true mean is significantly lower thn 4.8 at 10% of signficance.