How would you draw a counterexample to this?
1 answer:
Melanie said:
Every angle bisector in a triangle bisects the opposite side perpendicularly.
A 'counterexample' would show an angle bisector in a triangle that DOESN'T
bisect the opposite side perpendicularly.
See my attached drawing of a counterexample.
Both of the triangles that Melanie examined have equal sides on both sides
of the angle bisector. That's the only way that the angle bisector can bisect
the opposite side perpendicularly. Melanie didn't examine enough different
triangles.
Every angle bisector in a triangle bisects the opposite side perpendicularly.
A 'counterexample' would show an angle bisector in a triangle that DOESN'T
bisect the opposite side perpendicularly.
See my attached drawing of a counterexample.
Both of the triangles that Melanie examined have equal sides on both sides
of the angle bisector. That's the only way that the angle bisector can bisect
the opposite side perpendicularly. Melanie didn't examine enough different
triangles.
You might be interested in
Answer:
(a) 0.5899
(b) 0.9166
Step-by-step explanation:
Let X be the random variable that represents the height of a woman. Then, X is normally distributed with
= 62.5 in
= 2.2 in
the normal probability density function is given by
, then
(a) = 0.5899
(in the R statistical programming language) pnorm(63, mean = 62.5, sd = 2.2)
(b) We are seeking where n = 37.
is normally distributed with mean 62.5 in and standard deviation
. So, the probability density function is given by
, and
= 0.9166
(in the R statistical programming language) pnorm(63, mean = 62.5, sd = 2.2/sqrt(37))
You can use a table from a book to find the probabilities or a programming language like the R statistical programming language.