One way of proving that two REs are equivalent is to construct their minimized DFAs and then compare them. If they differ only by state names, then the REs are equivalent. Use this technique to check the following pairs of REs and state whether or not they are equivalent. (a) (0 | 1)* and (0* | 10*)* (b) (ba) (a*b* | a*) and (ba)*ba (b*|)

Question

A rectangular pyramid has a height of 5 units and a volume of 60 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

a) A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

b) A rectangular prism in which BA = 12 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

c) A rectangular prism in which BA = 36 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.

d) A rectangular prism in which BA = 12 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.

a) A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

Step-by-step explanation:

The formula for the volume of a Rectangular Pyramid = 1/3 × Base Area × Height

In the question,

Base Area = ?

Height = 5 units

Volume = 60 units³

So,

60= 1/3 × BA × 5

Cross Multiply

180 = 5BA

BA = 180/5

BA = 36 units²

Also, the Volume of a Rectangular Prism =

Base Area × Height

From the above question

Base Area = 36 units²

Height = 5 units

Volume of the Rectangular prism = 36 units² × 5 units

= 180 units³

Therefore , the statement that explains whether Shannon is correct is option a,

" A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.