Equilateral triangle PBJ is inscribed in a circle as shown. determine the measure of arc PB
2 answers:
Answer:
The measure of arc PB is 120°
Step-by-step explanation:
Given: A equilateral triangle PBJ is inscribed in a circle with centre O as shown in attachment.
PBJ is an equilateral triangle. Equilateral triangle has equal angles and sides.
Measure of each angle equilateral triangle is 60°
Hence, ∠BJP=60°
∠BOP and ∠BJP lie on same arc of circle but ∠BJP make at circumference of circle and ∠BOP make at centre of circle.
∠BOP=2∠BJP (Because the angle which is subtended by an arc at the centre of a circle is double the size of the angle subtended at any point on the circumference)
Thus, ∠BOP=2 x 60 = 120°
Hence, The measure of arc PB is 120°
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Answer:
Thus, the expected value of points for Derek and Mia are and
respectively.
Step-by-step explanation:
Number of green marbles = 2 and Number of Yellow marbles = 1
Then, total number of marbles = 2+1 = 3
A person selects two marbles one after another after replacing them.
So, the probabilities of selecting different combinations of colors are,
Now, we have that,
If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.
If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.
<h3>Also, the expected value of a random variable X isThen, the expected value of points for Derek is,
And the expected value of points for Mia is,
.
Thus, the expected value of points for Derek and Mia are and
respectively.
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