Randall, kira and sean have 100 baseball cards altogether. randall has twice as many as kira and 10 more than sean. how many baseball cards does each person have?

Kira has 22 cards, Randall has 44 cards, and Sean has 34 cards

Solution:

Given that, Randall, Kira and Sean have 100 baseball cards altogether.

Randall has twice as many as Kira and 10 more than Sean.  

We have to find how many baseball cards does each person have?

Now, let the number of cards with Kira be "n", then number of cards with Randall will be "2n"

As Randall has "2n" cards, Sean will have 2n – 10

Now, total cards = 100  

Randall cards + Kira cards + Sean cards = 100  

2n + n + 2n – 10 = 100  

5n = 100 + 10  

5n = 110  

n = 22

So, kira has 22 cards, then, randall will have 2(22) = 44 cards and cards with sean = 44 – 10 = 34 cards.

Hence, kira has 22 cards, randall has 44 cards, and sean has 34 cards.

-6 is the correct option from the above given options

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.