Out of a group of 63 students, 22 study Biology, 26 study Chemistry and 25 study Physics. 18 study both Physics and Chemistry, four study both Biology and Chemistry
and 3 study both Physics and Biology. One student studies all three subjects. How
many students study Biology only?

14 students

Step-by-step explanation:

Data: Out of a group of 63 students,

22 study Biology, 26 Study Chemistry, and 25 study Physics

8 study both Physics and Chemistry, 4 study both Biology and Chemistry,  3 study both Physics and Biology, and 1 student studies all three subjects.

Number of people who only take Biology=x

Step one, Add up all of the people who take Biology with another subject

4+3+1=8

Reason, Since we want to find the number of people who only take biology, we have to find the number of people who take Biology with another subject so we can seperate them later in the problem.

Step two, Subtract the number of people who take Biology with another course with the number of people who take Biology as a whole

22-8=14

Reason: Since we know how many people take biology with another course, we can subtract that from the people who take Biology in general to get the number of people who only take Biology.

That's how we get to our answer of 14 students

I hope this helps!

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.

it would open into a square depending on the type of envelope i’m not sure about the second part