Peter is planning on spendind 2/3 as many hours watching television this week as he did last week. Is Peter going to spend more
2 answers:
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The probability that he would have done at least this well if he had no ESP is 0.99979
<h3>What is the probability of determining that he would have done well with no ESP?</h3>To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
There are = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
Learn more about probability here:
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There are several ways to find the angle at A.
One is to realize the bisector of angle A will make a right angle with BC, creating two congruent triangles with short leg 2 and hypotenuse 7. Then the sine of the half-angle at A will be 2/7, so
A = 2*arcsin(2/7)
A ≈ 2*16.6015° = 33.203°
The measure of the angle at A to the nearest degree is
33°
_____
Another way to find the angle is to use the Law of Cosines. After solving for the angle (A) in terms of sides a, b, c, you find
A = arccos((b²+c²-a²)/(2bc)) = arccos(7²+7²-4²)/(2*7*7))
A = arccos(82/98) ≈ 33°
And you can always use a triangle solver application.
One is to realize the bisector of angle A will make a right angle with BC, creating two congruent triangles with short leg 2 and hypotenuse 7. Then the sine of the half-angle at A will be 2/7, so
A = 2*arcsin(2/7)
A ≈ 2*16.6015° = 33.203°
The measure of the angle at A to the nearest degree is
33°
_____
Another way to find the angle is to use the Law of Cosines. After solving for the angle (A) in terms of sides a, b, c, you find
A = arccos((b²+c²-a²)/(2bc)) = arccos(7²+7²-4²)/(2*7*7))
A = arccos(82/98) ≈ 33°
And you can always use a triangle solver application.