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1. D: The overlap of the two sets represents the intersection, which is the set of elements common to both sets <em>M</em> and <em>C</em>. In this case, it's the set {4, 5, 6}.
2. D: <em>P</em> is the set of the first 100 multiples of 8 (8*1 = 8, 8*2 = 16, and so on)
3. C: <em>n</em>(<em>A</em>) represents the number of elements in the set <em>A</em>. When
that means the sets <em>A</em> and <em>B</em> are disjoint, represented by the two circles with no overlap.
4. E:
is the set of elements belonging to either set <em>A</em> or <em>B</em>. The three elements of <em>A</em> are all in <em>B</em>, so <em>A</em> is a subset of <em>B</em>. This means
.
Because <em>A</em> is a subset of <em>B</em>, we have .
is the complement of
, which refers to the set of elements *not* belong to
. These are all the numbers in <em>U</em> that are not in this union, which would be
.
Because we know , we have
.
The complete question in the attached figure
we know that
<span>An<span> exterior angle</span></span><span> is one that has its vertex at an outer point of the circumference.
</span><span>The measure of the external angle is the semi-difference of the arcs that it covers.
in this problem the external angle is </span>∡(9x-5)°
and
the semi-difference of the arcs that it covers is (1/2)*(158°-64°)=47°
then
(9x-5)=47-------> 9x=47+5----------> 9x=52--------> x=5.78°
the answer is
x=5.78°
we know that
<span>An<span> exterior angle</span></span><span> is one that has its vertex at an outer point of the circumference.
</span><span>The measure of the external angle is the semi-difference of the arcs that it covers.
in this problem the external angle is </span>∡(9x-5)°
and
the semi-difference of the arcs that it covers is (1/2)*(158°-64°)=47°
then
(9x-5)=47-------> 9x=47+5----------> 9x=52--------> x=5.78°
the answer is
x=5.78°