Can somebody help me answer this please
1 answer:
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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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Answer:
The 90% confidence interval using Student's t-distribution is (9.22, 11.61).
Step-by-step explanation:
Since we know the sample is not big enough to use a z-distribution, we use student's t-distribution instead.
The formula to calculate the confidence interval is given by:
Where:
is the sample's mean,
is t-score with n-1 degrees of freedom,
is the standard error,
is the sample's size.
This part of the equation is called margin of error:
We know that:
degrees of freedom
Replacing in the formula with the corresponding values we obtain the confidence interval: