Help with this two column proof
1 answer:
We're given LM = NO which will be used in substitution later.
By the segment addition postulate, we can write
LN = LM+MN
which basically says "glue LM and MN together to get LN". All three segments fall on the same line.
Now substitute or replace LM with NO. This works because LM = NO is given
So we go from this
LN = LM+MN
to this
LN = NO+MN
Rearrange terms to go from
LN = NO+MN
to
LN = MN+NO
The formal property used is the "Commutative Property of Addition"
Now notice on the right hand side we can combine MN and NO to get MO. Again this is using the segment addition postulate.
So the last step is going from
LN = MN+NO
to
LN = MO
Have a look at the attached image to see how to format this proof into a two-column proof.
By the segment addition postulate, we can write
LN = LM+MN
which basically says "glue LM and MN together to get LN". All three segments fall on the same line.
Now substitute or replace LM with NO. This works because LM = NO is given
So we go from this
LN = LM+MN
to this
LN = NO+MN
Rearrange terms to go from
LN = NO+MN
to
LN = MN+NO
The formal property used is the "Commutative Property of Addition"
Now notice on the right hand side we can combine MN and NO to get MO. Again this is using the segment addition postulate.
So the last step is going from
LN = MN+NO
to
LN = MO
Have a look at the attached image to see how to format this proof into a two-column proof.
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Answer:
The answer is D. 0.75
Step-by-step explanation:
Let call R the event that a person is rascal, RC a person is not rascal, TH a person use top hat and NTH a person don’t use top hat.
From the information on the question we have 4 options with their respective probability:
1. A person could be rascal and use top Hat: this probability is calculate as the multiplication of the probability of be a rascal (0.5) and use a top hat (0.9), then:
P(R y TH)=0.5*0.9=0.45
2. A person could be rascal and don’t use top Hat: this probability is calculate as the multiplication of the probability of be a rascal (0.5) and not use a top hat (0.9), then:
P(R y NTH)=0.5*0.1=0.05
3. A person could be not rascal and use top Hat: this probability is calculate as the multiplication of the probability of not be a rascal (0.5) and use a top hat (0.3), then:
P(RC y TH)=0.5*0.3=0.15
4. A person could be not rascal and not use top Hat: this probability is calculate as the multiplication of the probability of not be a rascal (0.5) and not use a top hat (0.7), then:
P(RC y NTH)=0.5*0.7=0.35
Then the probability that a person is a rascal given that he is wearing a top hat could be written and calculate as:
For calculate P(TH) we need to sum all the option in which TH is involve so:
P(TH) = P(R y TH)+ P(RC y TH)
P(TH)=0.45+0.15=0.6
Replacing values on the first equation we get:
So, the probability that a person is a rascal given that he is wearing a top hat is 0.75