Advanced Placement (AP), 19.08.2020 01:01 jeremiahhart13

Would two bits be enough to assign a unique binary number to each vowel in the English language?

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Answer from: emmaraeschool

No. Two bits are not enough to assign a unique binary number to each vowel in the English language.

Explanation:

The vowel in the English language is made up of 5 lowercase letters (a, e, i, o, u) and their corresponding 5 uppercase letters (A, E, I, O, U). All together, there are 10 unique vowel letters.

The number, x, of unique characters that can be stored by n bits is given by:

x = 2ⁿ

So if we have 2 bits, it implies that, the number of different characters that can be stored is:

2² = 4

Therefore, with 2 bits, there are 4 unique characters that can be stored.

But then, we need to store a total of 10 characters representing the English Language vowels. Therefore, two bits will not be enough to assign a unique binary number to each vowel.

It can also be seen this way

For two bits, we have the following possibilities:

Now, let's assume we have assigned the vowels as follows:

00 = a

01 = e

10 = i

11 = o

Then, only four of the vowel letters can be assigned a unique binary number.

Therefore, two bits are not enough to assign a unique binary number to each vowel of the English language.

We need at least 4 bits which will yield 2⁴ = 16 different combinations. And from that, we are able to assign each vowel a unique binary number like so:

Used

0000 = a

0001 = e

0010 = i

0011 = o

0100 = u

0101 = A

0110 = E

0111 = I

1000 = 0

1001 = U

Remaining:

1010

1011

1100

1101

1110

1111

10 out of 16 different combinations of binary numbers have been used by the 10 vowel characters. We will be left with 6 binary numbers. Better being surplus than being deficit.

Answer from: Quest

renewable resources- resources that can be replenished (such as trees)

nonrenewable resources- resources that are gone once they are used (such as fossil fuels)

producer-person who makes goods or provides services

consumer- person whose wants are satisfied by using goods and services

allocate- distribute

choice- option

(hope this ! )

Answer from: Quest

See diagram.we use washers to get the area and we will be integrating with respect to xouter radius is the distance between y = e^x and y = -1 $r_{\text{out} } = e^x ) = e^x + 1$ inner radius of washer is the distance between y = 1 and y = -1 $r_{\text{in} } = 1 - (-1) = 2$ the area of one cross-section of a washer is $\begin{aligned} a(x) & = \pi(r_{\text{out} } )^2 - \pi(r_{\text{in} } )^2 \\ & = \pi(e^x + 1 )^2 - \pi(2)^2 \\ & = \pi \big[(e^x + 1 )^2 - 4 \big] \end{aligned}$ solid lies between x = 0 and x = 2. the volume is $\begin{aligned} v & = \int_0^2 a(x) dx \\ & = \int_0^2 \pi \big[(e^x + 1 )^2 - 4 \big] dx \end{aligned}$ if you need this expanded, then $\begin{aligned} v & = \int_0^2 \pi \left(e^{2x} + 2e^x + 1 - 4 \right) dx \\ & = \int_0^2 \pi \left(e^{2x} + 2e^x -3 \right) dx \end{aligned}$ the question doesn't say to evaluate, so we're done.

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