Researchers are interested in whether wearing seat belts protects against fatal injury in automobile accidents. They compiled the following data from all people involved in automobile accidents in the state of Florida: Fatal

Not Fatal

No Seat Belt

1,581

161,227

Seat Belt

588

412,368

Using these data, calculate

a. The simple probability that a seat belt is not worn.

b. The simple probability that a fatal injury occurs.

c. The probability that both a fatal injury occurs and a seat belt is not worn

P(Fatal injury ∩ No Seat Belt)

d. The probability of a fatal injury or that the seat belt was not worn or both.

P(Fatal injury U No Seat Belt)

e. The conditional probability that a fatal injury occurs given that a seat belt was not worn.

f. Is the event of having a fatal injury independent of not wearing a seat belt?

(show your work).

My answer so far but im completly stuck on f:

Fatal Not Fatal Total
No Seat Belt 1,581 161,227 162,808
Seat Belt 588 412,368 412,956
Total 2,169 573,595 575,764
a. 162808/575764= 0.282769
b. 2169/575764= 0.003767
c. 1581/162808= 0.009711
d. (2169+162808-1581)/575764= 0.28379
e. (0.003767*.009711)/0.009711= 0.003767
f.

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:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32

4+3x hope you like mark as brainliest✔

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