Can someone help me with this question? The one-year survival rate for pancreatic cancer is 20%. Of 12 people diagnosed with pancreatic cancer at one hospital, 6 survived one year. What is the probability of that happening.

The required probability is 0.0155.

Step-by-step explanation:

We are given that the one-year survival rate for pancreatic cancer is 20%.

Of 12 people diagnosed with pancreatic cancer at one hospital, 6 survived one year.

The above situation can be represented through binomial distribution;

where, n = number of trials (samples) taken = 12 people

            r = number of success = 6 survived

            p = probability of success which in our question is probability of

                  one-year survival rate for pancreatic cancer, i.e; p = 20%

Let X = Number of people survived one year

So, X ~ Binom(n = 12 , p = 0.20)

Now, the probability that 6 survived one year is given by = P(X = 6)

              P(X = 6)  =  

                             =  

                             =  0.0155

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.

the correct option is b

step-by-step explanation: