Which expression represents the volume, in cubic units, of the shaded region of the composite figure? (14)(10)(8) – π(2.52)(8) (
14)(10)(8) + π(2.52)(8) (10)(8)(14) – π(2.52)(8) (10)(8)(14) + π(2.52)(8)
2 answers:
Answer:
<u>(0.5)(14)(10)(8) – π(2.5²)(8)</u>
Step-by-step explanation:
The rest of the question is the attached figure.
The volume of the shaded region = volume of the prism - volume of the cylinder
The volume of the prism = The area of triangle * height
= 0.5 * 10 * 14 * 8
The volume of the cylinder = The area of the circle * height
= π r² h
= π (5/2)² * 8 = π * 2.5² * 8
<u>So, The volume of the shaded region = (0.5)(14)(10)(8) – π(2.5²)(8)</u>
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Answer:
If the weight is higher than 5.8886 gr would be considered significantly high
If the weight is lower than 5.6121 gr would be considered significantly low
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where and
And the best way to solve this problem is using the normal standard distribution and the z score given by:
For the case when z =-2 we can do this:
And if we solve for X we got:
And for the other case when Z=2 we have:
And if we solve for X we got:
If the weight is higher than 5.8886 gr would be considered significantly high
If the weight is lower than 5.6121 gr would be considered significantly low