Chemicals in butter-flavoring: Workers in a microwave popcorn production plant in Missouri breathe chemicals that are part of the butter-flavoring. Are these workers at greater risk of developing lung problems? To investigate this question, 135 workers at the plant receive a survey, and 117 respond.

Researchers want to compare workers in the popcorn production area with workers who have jobs in other parts of the plant. People in these other jobs are not directly exposed to the butter flavorings. Of the 97 workers in the production area, 30 reported experiences of “shortness of breath.” Of the 20 workers in other jobs, only 1 reported “shortness of breath.”

What can we conclude from this study?

The study was found that 1/3 of 97 were short of breath and 1 of 20 were reported to have shortness of breath else where.

The conclusions would be environmental factors such as production environment, alongside exposure preventives would need to be considered for new report. The other workers cannot be used as part of contrast due to the sample data being under 30 for other workers.  Sample data can only be used if it is over 30 for such comparison (contrast) tests.

Step-by-step explanation:

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 terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: