7 |r/5|=7 solve the equation
2 answers:
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The arc length can be found using the formula, ∅ × r, which is: (5π)/3.
<h3>What is the Arc Length?</h3>Arc length = ∅ × r, where ∅ is the central angle in radians, and r is the radius of the circle.
Given the following:
- ∅ = 60° = 60° × π/180 (in radians)
- r = 5 cm
Length of the arc = 60° × π/180 × 5 = (60 × π × 5)/180
Length of the arc = (300π)/180 = (5π)/3
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Answer:
Step-by-step explanation:
The summary of the given statistics data include:
sample size n = 400
sample mean = 6.86
standard deviation = 4.37
Level of significance ∝ = 0.01
Population Mean = 6.00
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
To start with the hypothesis;
The null and the alternative hypothesis can be computed as :
The test statistics for this two tailed test can be computed as:
z = 3.936
degree of freedom = n - 1
degree of freedom = 400 - 1
degree of freedom = 399
At the level of significance ∝ = 0.01
P -value = 2 × (z < 3.936) since it is a two tailed test
P -value = 2 × ( 1 - P(z ≤ 3.936)
P -value = 2 × ( 1 -0.9999)
P -value = 2 × ( 0.0001)
P -value = 0.0002
Since the P-value is less than level of significance , we reject at level of significance 0.01
Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 5.00 km.