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OLga [1]
3 years ago
11

At a large university, the probability that a student takes calculus and is on the dean's list is 0.042. the probability that th

e student is on the deans list is 0.21. Find the probability that the student is taking calculus, given that he or she is on the deans list.
Mathematics
1 answer:
cestrela7 [59]3 years ago
4 0
As this is probability, we can use the next formulas and tell how is this going to be:
P(A) = student on the dean's list 
<span>P(B) = student taking calculus </span>
<span>P(A n B) = 0.042 </span>
<span>P(A) = 0.21 </span>
<span>So, P(B) = 0.042/0.21 </span>
<span>= 0.2
So the probability here is of 0.2</span>
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Each table in a banquet room seats 8 people. The room can seat no more than 360 people. Write and solve an inequality to represe
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If q is directly proportional to p and q = 28 when p = 4 (Express q in teams of p.)
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Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

  • \cos{\theta} = \pm \frac{2\sqrt{2}}{3}
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<h3>What is the trigonometric identity using in this problem?</h3>

The identity that relates the sine squared and the cosine squared of the angle, as follows:

\sin^{2}{\theta} + \cos^{2}{\theta} = 1

In this problem, we have that the sine is given by:

\sin{\theta} = \frac{1}{3}

Hence, applying the identity, the cosine is given as follows:

\cos^2{\theta} = 1 - \sin^2{\theta}

\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2

\cos^2{\theta} = 1 - \frac{1}{9}

\cos^2{\theta} = \frac{8}{9}

\cos{\theta} = \pm \sqrt{\frac{8}{9}}

\cos{\theta} = \pm \frac{2\sqrt{2}}{3}

The tangent is given by the sine divided by the cosine, hence:

\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}

\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}

\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}

\tan{\theta} = \pm \frac{\sqrt{2}}{4}

More can be learned about trigonometric identities at brainly.com/question/24496175

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