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tangare [24]
3 years ago
5

A right rectangular prism has a square base with side lengths of 5 inches and a height of 9 inches. What is the volume of the ri

ght rectangular prism?
A.
90 cubic inches
B.
225 cubic inches
C.
19 cubic inches
D.
45 cubic inches
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
4 0

Answer:

  B.  225 cubic inches

Step-by-step explanation:

The volume is the product of the base area and the height:

  V = Bh

The area of the square base is the product of the side lengths:

  B = (5 in)^2 = 25 in^2

For a height of 9 in, the volume is ...

  V = (25 in^2)(9 in) = 225 in^3

The volume of the right rectangular prism is 225 cubic inches.

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Of the cars sold during the month of July, 89 had air conditioning, 99 had an automatic transmission, and 74 had power steering.
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Answer:

There are a total of 23 cars with air conditioning and automatic transmission but not power steering

Step-by-step explanation:

Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.

Remember that for 2 sets E and F, we have that

|E \cup F| = |E| + |F| - |E \cap F|

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|E| = |E ∩F| + |E∩F^c|

We now alredy the following:

|A| = 89

|B| = 99

|C| = 74

|A \cap B \cap C| = 5

|(A \cup B \cup C)^c| = 24

|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).

|B \ (AUC)| = 65

|C \ (AUB)| = 26

|B \cap C| = 11

We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things

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99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|

Therefore, |B∩C^c| = 99-11 = 88

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