University x needs to send a delegation of athletes to represent the university at a soccer tournament. assume that the soccer roster has n athletes. (a) if the soccer sund expected is of size k, how many different ways can the squad be made up of? (b) in addition, if the soccer squad must also have a captain (selected from the k athletes), how many different "captained" squads are there? note here that selecting the same set of players but assigning a different captain counts as different "captained" squads. (e) if every member of the delegation is to be assigned a jersey numbers range from 1 to k), how many different ways are there of sending a "jerseyed" squad?
(d) the squash team has all its players injured and the coach decides to pick her squad from the soccer roster assume that there are no conflicts among the squash and soccer schedules to any player is free to get selected for both squads (if deemed worthy). the constraint for the squash squad is that there must be at least one player on the squad (and at moet n). again, this squad should have a captain (picked from amongst the squad). use the following 2 equivalent ways to construct the squad and count the number of squash squads possible for each way: • pick a squad of sizer and then select a captain from this lot. any valid squad of size r looks like this. since the size of the squad can range from 1 ton, count the total number of valid squads that may be formed this way. note that any squad picked must have a captain. so, first pick a captain from the roster of size n. how to set up the rest of the squad? well, for every other member (non-captain) of the router, either decide to have them on the squad or not. give an expression that counts the number of squads that can be formed by this process. use the answers from the above two questions to give an identity involving binomial coefficients.

entering that problem on the tube might get you an answer

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.

i think it would be c

mark brainliest if im right

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.