What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If e
ither is false, give a counterexample.
If two lines are parallel, they do not intersect.
Select one:
a. If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
b. If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
c. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
d. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
If two lines are parallel, they do not intersect.
Select one:
a. If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
b. If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
c. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
d. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
2 answers:
Answer: A
Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:
Conditional: If someone like ice cream, they have brown hair
Converse: If someone has brown hair, they like ice cream
The converse of our given conditional would be:
If two lines do not intersect, they are parallel
This eliminates Option D
Next, the converse is false.
Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they <em>could</em> be either parallel or skew.
This eliminates Option C and B, leaving us with Option A
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Answer:
μ=23.710740....
σ=3.592592....
Step-by-step explanation:
At first, we are told that it´s a normal distribution and the following:
P(x≤15.34)=0.1
P(x≤16.31)=0.2
We start looking for those values (0.1 and 0.2) and the probabilities that gives us those values in a normal standard distribution. There´s some tools that´ll help us out but i´ll be using a chart with the values of some probabilities in a normal standard distribution (That it´s attached).
The probability of P(z≤ a.b) where "a" is the whole part of a number and "b" the decimal part is in the coordinates (a,b). For example for our problem:
P(z≤-2.33)=0.099≈0.1
P(z≤-2.06)=0.197≈0.2
To find a probability of a normal (not standard) distribution we use a method called Normalize that proceeds:
P(x≤a)=P( (x-μ)/σ ≤ (a-μ)/σ )
Where μ is the Mean of the data and σ is the Standard deviation. P( (x-μ)/σ ≤ (a-μ)/σ ) is now part of a normal standard distribution and we are able to look for it in the chart.
We will use it to find the Mean and the STD for our distribution.
P(x≤15.34)=P(z≤-2.33)≈0.1
P(x≤16.31)=P(z≤-2.06)≈0.2
so we have the equations:
(15.34 - μ)/σ= -2.33 and (16.31 - μ)/σ= -2.06
And we solve them for μ and σ:
(15.34 - μ)/-2.33= σ and (16.31 - μ)/-2.06= σ
(15.34 - μ)/-2.33 = (16.31 - μ)/-2.06
2.06*(15.34 - μ) = 2.33(16.31 - μ)
2.33μ - 2.06μ = 2.33(16.31) - 2.06(15.34)
μ= 6.4019 / 0.27
μ= 23.710740...
With this value we find σ in one equation:
(15.34 - (23.710740...)/σ = -2.33
(15.34 - (23.710740...)/-2.33 = σ
σ=3.592592...
We finally have our answers:
μ=23.710740....
σ=3.592592....
