In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. what is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course? a. 0.45 b. 0.32 c. 0.20 d. 0.13 e. 0.05

The required probability is 0.13

Step-by-step explanation:

Consider the provided information.

It is give that 17% of the student are enrolled in a psychology course.

Let P(A) is the student enrolled in psychology course.

Thus. P(A)=17%=0.17

28 % are enrolled in a foreign language course.

Let P(B) represents the student enrolled in foreign language course.

Thus. P(B)=28%=0.28

32 % are enrolled in either a psychology course or a foreign language course or both.

That means P(A∪B) = 32% = 0.32

We need to find the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course.

That means we need to find P(A∩B).

P(A∪B) = P(A)+P(B)-P(A∩B)

0.32 = 0.17 + 0.28 - P(A∩B)

0.32 = 0.45 - P(A∩B)

P(A∩B) = 0.13

The required probability is 0.13

The required probability will be D. 0.13

Based on the information given,

Since we are told that 32% of the students are enrolled in either a psychology course or a foreign language course or both. This will be P(A∪B) = 32% = 0.32

Then, we need to find P(A∩B) and.this goes thus:

P(A∪B) = P(A)+P(B)-P(A∩B)

0.32 = 0.17 + 0.28 - P(A∩B)

Therefore, 0.32 = 0.45 - P(A∩B)

P(A∩B) = 0.45 - 0.32 = 0.13

Therefore, the required probability is 0.13

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answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.