The probability that a pharmaceutical firm will successfully develop a new drug that will return $750 million dollars is 0.14. Of the research is unsuccessful, the company incurs a cost of $100 million dollars. What is the expected return in the long run for continually trying to develop new drugs?

The expected return in the long run for continually trying to develop new drugs is $19 million dollars.

Step-by-step explanation:

We have these following probabilities for the pharmaceutical firm:

A 14% probability that the research to develop a new drug is successful, earning $750 million dollars.

An 86% probability that the research to develop a new drug is unsucessful, losing $100 million dollars.

What is the expected return in the long run for continually trying to develop new drugs?

14% probability of earning $750 million, 86% probability of losing $100 million. So

The expected return in the long run for continually trying to develop new drugs is $19 million dollars.

your answer would be 12

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.