Among 18 students in a room, 7 study mathematics, 10 study science, and 10 study computer programming. Also, 3 study mathematics and science, 4 study mathematics and computer programming, and 5 study science and computer programming. We know that 1 student studies all three subjects. How many of these students study none of the three subjects?

3 students study none of the three subjects

Step-by-step explanation:

The Venn diagram representing the situation is shown in the attached photo.

M represents the sub set of mathematics students.

S represents the sub set of science students.

CP represents the sub set of computer programming students.

From the diagram,

The number of students studying mathematics and science only is

3 - 1 = 2

The number of students studying mathematics and computer programming only is

4 - 1 = 3

The number of students studying science and computer programming only is

5 - 1 = 4

The number of students studying mathematics only is

7 - (2 + 1 + 3) = 1

The number of students studying mathematics only is

10 - (2 + 1 + 4) = 3

The number of students studying computer programming only is

10 - (3 + 1 + 4) = 2

Let x represent the number of students that study none of the three subjects. Since the total number of students is 18, it means that

2 + 3 + 4 + 1 + 3 + 2 + x = 18

15 + x = 18

x = 18 - 15 = 3

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

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.