A box contains 2 plain pencils and 2 pens. A second box contains 3 color pencils and 5 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second hoy are selected?

50% pen first box and 62.5% crayon from second box

Step-by-step explanation:

The first box contains 4 items, 2 of each. This means there are pens. This gives you a chance of picking out a pen. This can be written as 50%.

The second box contains 8 items, 3 color pencils and 5 crayons. This means of the contents are crayons, meaning you have a or 62.5% chance of picking a crayon.

*For working out the percentages, you should convert the fraction to a decimal and then multiply that by 100.

**This content involves fractions, decimals and percentages, as well as basic probability, which you may want to revise. I'm always happy to help!

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.