A company has two types of machine that run 24 hours a day, 7 days a week. Type A machine breaks down on average 10 breakdowns per day. This is equivalent to saying the mean wait time per breakdown is days per breakdown. For type B machine, the mean wait time between breakdowns is 0.7 days per breakdown.

For each type of machine, assume breakdowns occur as a time homogeneous Poisson process, so that for each type of machine the waiting time for a breakdown has exponential distribution, but with differing parameters depending on whether the machine is type A or type B.

Suppose 25% of the machines at this company are type A.

You observe a machine but cannot tell what type it is. But you do observe that within the next 5 hours it does not break down. What is the posterior probability this is a type A machine? Answer as a decimal accurate to 4 decimal places.

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.

step-by-step explanation:

well if you round, things become much more simple. round 5.95 to 6, 4.25 to 4, and 1.05 to 1. now, add 6+4+1 and that would equal 11. so the items together would equal to about $11.

$119.20

step-by-step explanation:

$372.50 - 60% off is $149. $149-20% off is $119.20

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1