Circle P is shown. Tangents R S and T S intersect at point S outside of the circle to form angle x. The first arc formed is arc
2 answers:
Answer:
The true statement is " The difference of z and y must be 2x " ⇒ 3rd
Step-by-step explanation:
If two tangents to a circle intersected outside it, then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs.
∵ P is a circle
∵ RS and TS are to tangents to circle P
∵ The tangents RS and TS intersected at point S outside the circle
∵ They formed angle x between them
∴ x = (m major arc RT - m minor arc RT)
∵ The first arc formed is arc y
∴ The minor arc RT is y
∵ The second arc formed is arc z
∴ The major arc RT is z
∴ x = (z - y)
- Multiply both sides by 2
∴ 2 x = z - y
∴ The difference of z and y must be 2 x
The true statement is " The difference of z and y must be 2x "
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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 fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t 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 true mean is different from 5, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but 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 two 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 fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance