In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8. To prove that △DFE ~ △GFH by the SSS similarity theorem using the informat
ion provided in the diagram, it would be enough additional information to know that
A) HF is 2 units and GH is 3 units.
B) HF is 3 units and GH is 2 units.
C) HF is 4 units and GH is 2 units.
D) HF is 3 units and GH is 4 units.
A) HF is 2 units and GH is 3 units.
B) HF is 3 units and GH is 2 units.
C) HF is 4 units and GH is 2 units.
D) HF is 3 units and GH is 4 units.
2 answers:
Answer: C) HF measures 4 units and GH is 2 units.
Step-by-step explanation:
The SSS similarity theorem asserts that triangles are similar if the lengths of their corresponding sides are in proportion.
For triangles ΔDFE and ΔGFH:
DG equals 15, GF is 5, EH equals 12, and DE is 8.
To demonstrate the similarity of ΔDFE and ΔGFH according to the SSS similarity theorem, we require:
Thus, to confirm that △DFE is similar to △GFH utilizing the SSS similarity theorem and the data from the diagram, it is essential to establish that HF measures 4 units and GH measures 2 units.
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Answer:
(B) 0.2843
Step-by-step explanation:
Let d represent the difference in proportions between Country X and Country Y for adults who first married from ages 18 to 32.
The hypotheses can be stated as
: d=0.15
: d<0.15
The test statistic can be computed with the formula
where
- p1 corresponds to the sample proportion from Country X (0.36)
- p2 corresponds to the sample proportion from Country Y (0.26)
- p indicates the pooled proportion of p1 and p2 (
)
- n1 is the sample size from Country X (60)
- n2 is the sample size from Country Y (50)
Thus, is approximately 0.5646
The p-value for this test statistic is approximately 0.2843
The p-value indicates the likelihood that the difference in proportions between a random sample of 60 adults from Country X and a sample of 50 adults from Country Y who were first married at ages 18 to 32 is at least 0.15.
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Please refer to the attachment.
