What are two angles within 0°-360° that has a cosine of negative root three over 2? Show work please
1 answer:
Answer:
150° and 210°
Step-by-step explanation:
1) according to the condition the required cosine is <0, it means the required angles are in the II-d and III-d quaters (see the attached picture no. 1);
2) it is known, that arccos(√3/2)=30°- the angle is between 0° and 90°, - but the requred angles are between 90° and 270° (see the picture no. 2), then
3) (angle)₁=180°-arccos(√3/2) and (angle)₂=180°+arccos(√3/2), then finally
(angle)₁=180°-30°=150°; (angle)₂=180°+30°=210°.
PS. note, the suggested way is not the only one.
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Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) =
=
=
= <u>0.63</u>