Alice has 40 red beads and 88 green beads to make necklaces. each necklace will have red and green beads. each necklace will have the same number of red beads. each necklace will have the same number of green beads. she will use all the beads. what is the greatest number of necklaces alice can make?

As per the given statement: Alice has 40 red beads and 88 green beads to make necklaces.

Also, each necklace will have the same number of red beads and each necklace will have the same number of green beads.

Greatest Common factor(GCF) states that the greatest factor that divides the two numbers.

Using GCF,  to find the greatest number of necklace Alice can make.

GCF of 40 and 88 :

Factor of 40 are;  1, 2, 4, 8, 10, 20, 40

Factor of 88 are; 1, 2, 4, 8, 11, 88

Common factors of 40 and 88 are: 1, 2 , 4, 8

Greatest common factor of 40 and 88 is 8.

therefore, the greatest number of necklaces Alice can make is 8

45

step-by-step explanation:

30+15

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.