Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.
1 answer:
Answer:
The answer in the attached figures
Step-by-step explanation:
we know that
When two lines are crossed by another line, the angles in matching corners are called <u>Corresponding Angles</u>. If the lines are parallel then the corresponding angles are congruent
see the attached figure N 1
When two lines are crossed by another line, the pair of angles on the inner side of each of those two lines but on opposite sides of the transversal, are called <u>Alternate Interior Angles</u>. If the lines are parallel then the alternate interior angles are congruent.
see the attached figure N 2
<u>Vertical Angles</u> are the angles opposite each other when two lines cross
see the attached figure N 3
When two lines are crossed by another line, the pair of angles on the outer side of each of those two lines but on opposite sides of the transversal, are called <u>Alternate Exterior Angles</u>. If the lines are parallel then the alternate exterior angles are congruent.
see the attached figure N 4
When two lines are crossed by another line, the pairs of angles on one side of the transversal but inside the two lines are called <u>Consecutive Interior Angles.</u> If the lines are parallel then the consecutive interior angles are supplementary.
see the attached figure N 5
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Its 3/7
Answer:
a) P(Y > 76) = 0.0122
b) i) P(both of them will be more than 76 inches tall) = 0.00015
ii) P(Y > 76) = 0.0007
Step-by-step explanation:
Given - The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.
To find - (a) If a man is chosen at random from the population, find
the probability that he will be more than 76 inches tall.
(b) If two men are chosen at random from the population, find
the probability that
(i) both of them will be more than 76 inches tall;
(ii) their mean height will be more than 76 inches.
Proof -
a)
P(Y > 76) = P(Y - mean > 76 - mean)
= P( ) >
)
= P(Z > )
= P(Z > )
= P(Z > 2.25)
= 1 - P(Z ≤ 2.25)
= 0.0122
⇒P(Y > 76) = 0.0122
b)
(i)
P(both of them will be more than 76 inches tall) = (0.0122)²
= 0.00015
⇒P(both of them will be more than 76 inches tall) = 0.00015
(ii)
Given that,
Mean = 69.7,
= 1.979899,
Now,
P(Y > 76) = P(Y - mean > 76 - mean)
= P( )) >
)
= P(Z > )
= P(Z > ))
= P(Z > 3.182)
= 1 - P(Z ≤ 3.182)
= 0.0007
⇒P(Y > 76) = 0.0007