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Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper c
ar loader is set to put 84 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 84 tons and standard deviation σ = 0.7 ton. (a) What is the probability that one car chosen at random will have less than 83.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 29 cars chosen at random will have a mean load weight x of less than 83.5 tons of coal? (Round your answer to four decimal places.)
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The volume of the sphere in the given image, to the nearest tenth, is: 2,143.6 cm³.
<h3>How to calculate the Volume of a Sphere?</h3>A sphere is a solid shape that is round. The volume of a sphere is the amount of space it contains, which is calculated by the formula expressed as:
Volume = 4/3 × π × r³, where r is the radius of the sphere.
The parameter of the sphere is given below:
Radius of the sphere (r) = 8 cm.
π = 3.14
Substitute r = 8 into 4/3 × π × r³ to find the volume of the sphere
Volume of the sphere = 4/3 × π × r³ = 4/3 × 3.14 × 8³
Volume of the sphere = 4/3 × 3.14 × 512
Volume of the sphere = (4 × 3.14 × 512)/3
Volume of the sphere = (6,430.72)/3
Volume of the sphere = 2,143.6 cm³
In summary, the volume of the sphere in the given image, to the nearest tenth, is: 2,143.6 cm³.
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