40. In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of the women received an A in
1 answer:
Answer:
a) 56.67% probability that the student is a woman
b) 16.67% probability that the student received an A
c) 63.33% probability that the student is a woman or received an A.
d) 83.33% probability that the student did not receive an A.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We have that:
30 students
13 men
17 women
2 men that got an A and 11 men that did not get an A.
3 women that got an A and 14 women that did not get an A.
a. Find the probability that the student is a woman.
30 students, of which 17 are women.
56.67% probability that the student is a woman
b. Find the probability that the student received an A.
30 students, of which 5 received an A
16.67% probability that the student received an A
c. Find the probability that the student is a woman or received an A.
30 students, of which 17 are women and 2 are men who received an A. So
63.33% probability that the student is a woman or received an A.
d. Find the probability that the student did not receive an A.
30 students, of which 25 did not receive an A.
83.33% probability that the student did not receive an A.
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Answer:
c
Step-by-step explanation:
Here's how this works:
Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:
In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:
Put everything over the common denominator now:
Since , we will make that substitution:
We could separate that fraction into 2:
×
and
Therefore, the simplification is
sec(x)csc(x)
Answer:
To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.
Begin with the right hand side:
R.H.S = cot θ =
L.H.S = sin θ cos θ
so, sin θ cos θ ≠
So, the equation is not a trigonometric identity.
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<u>Anther solution:</u>
To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.
Assume θ with a value and substitute with it.
Let θ = 45°
So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2
R.H.S = cot θ = cot 45 = 1
So, L.H.S ≠ R.H.S
So, sin θ cos θ = cot θ is not a trigonometric identity.