A basketball team has three pure centers, four pure forwards, four pure guards and one swing- man who can play either guard or forward. A "pure" position player can play only the designated position. If the coach must start a lineup with one center, two forwards and two guards, how many possible lineups can the coach choose?

We conclude that he coach can choose  252  lineups.

Step-by-step explanation:

We have three pure centers, four pure forwards, four pure guards and one swing- man who can play either guard or forward.

First case: swing- man play guard.

So now we count the number of combinations: to select from 3 centers 1 center, from 4 forwards to choose 2, and from 4 from the guards to choose 1.

Second  case: swing- man play forward.

So now we count the number of combinations: to select from 3 centers 1 center, from 4 forwards to choose 1, and from 4 from the guards to choose 2.

Third case: swing- man not play.

So now we count the number of combinations: to select from 3 centers 1 center, from 4 forwards to choose 2, and from 4 from the guards to choose 2.

Now, we get 72+72+108=252.

We conclude that he coach can choose  252  lineups.

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.

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.