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Answer:
The rotation of the rectangle, of area 12 squared units, about y-axis produces a cylinder, with a volume of 48 cubic units.
Step-by-step explanation:
Rotation about x-axis or y-axis at an angle requires some general rules. When a 2D figure is rotated about a line a 3d figure would be produced. This can be done through a process called solid of revolution.
From the question, connecting the given coordinates produces a rectangle with a length of 4 units and width 3units.
Area of the rectangle = Length × width
= 4 × 3
= 12 square units
The required rule for rotation of a figure about y-axis is: (x, y) → (-y, x).
If the given rectangle is rotated about y-axis, a cylinder would be formed.
The volume of the cylinder = V = h
where: r = 4 units and h = 3 units.
V = ×
× 3
= 48 cubic units
Therefore, the rotation of the rectangle of area 12 squared units produces a cylinder with volume of 48 cubic units.
Answer:
As a rule of thumb, it is usual to define discrete data in 5 to 10 groups or bins. When graphed, the height of each group or bin defines the frequency for the group or bin.
Explanation:
When discrete data is graphed into a histogram, it defines a frequency distribution. Because information becomes lost when too many groups or bins are used, it is customary to use 5 to 10 bins.
Example:
Consider the following random data which has a sample size of 16.
x = [1, 3, 6, 2, 9, 8, 4, 5, 10, 3, 5, 4, 3, 5, 7, 5]
When fewer groups or bins are used to construct the histogram, the centralized nature of the distribution is easy to discern.
As the number of bins increases, the distribution becomes more difficult to define.
As a rule of thumb, it is usual to define discrete data in 5 to 10 groups or bins. When graphed, the height of each group or bin defines the frequency for the group or bin.
Explanation:
When discrete data is graphed into a histogram, it defines a frequency distribution. Because information becomes lost when too many groups or bins are used, it is customary to use 5 to 10 bins.
Example:
Consider the following random data which has a sample size of 16.
x = [1, 3, 6, 2, 9, 8, 4, 5, 10, 3, 5, 4, 3, 5, 7, 5]
When fewer groups or bins are used to construct the histogram, the centralized nature of the distribution is easy to discern.
As the number of bins increases, the distribution becomes more difficult to define.