ADC is a straight line.
1 answer:
Applying the triangle sum theorem, the size of ∠BDC = 95°.
<h3>What is the Triangle Sum Theorem?</h3>All three interior angles of any triangle have a sum that equals 180 degrees, based on the triangle sum theorem.
The diagram attached below shows the following:
- m∠BAD = 55°
- m∠BCD = 25°
- m∠ABD = 2x°
- m∠CBD = 3x°
Thus:
55 + 2x + 3x + 25 = 180 (triangle sum theorem).
- Add like terms
80 + 5x = 180
5x = 180 - 80
5x = 100
x = 20
Therefore,
m∠BDC = 180 - (3x + 25) (triangle sum theorem)
- Plug in the value of x
m∠BDC = 180 - (3(20) + 25)
m∠BDC = 95°
Therefore, applying the triangle sum theorem, the size of ∠BDC = 95°.
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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.