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 is 4 units and GH is 2 units.
Step-by-step explanation:
The SSS similarity theorem says that if the side-lengths of the corresponding sides of two triangles are proportional then the triangles are similar.
In ΔDFE and ΔGFH ,
DG = 15, GF = 5, EH = 12, and DE = 8.
To prove ΔDFE and ΔGFH are similar by using SSS similarity theorem we need :-
Hence, To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that HF is 4 units and GH is 2 units.
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Answer:
a. 68% of the workers will earn between $47300 and $69700.
b. 2.5% of workers will earn above $89000
c. Approximately 0
Step-by-step explanation:
The standard normal distribution curve in the attached graph is used to solve this question.
a. The value $47300 is a standard deviation below the mean i.e. 58500-11200=47300. While $69700 is a standard deviation above the mean. I.e. 58500+12000=69700.
Between the first deviation below and above the mean, you have 34%+34%=68% of the salary earners within this range. So we have 68%of staffs earning within this range
b. The second standard deviation above the mean is $80900. i.e. 58500+11200+11200=$80900
We have 50%+13.5%+2.5%= 97.5% earning below $80900. Therefore, 100-97.5= 2.5% of the workers earn above this amount.
c. From the Standard Deviation Rule, the probability is only about (1 -0 .997) / 2 = 0.0015 that a normal value would be more than 3 standard deviations away from its mean in one direction or the other. The probability is only 0.0002 that a normal variable would be more than 3.5 standard deviations above its mean. Any more standard deviations than that, and we generally say the probability is approximately zero.
