Help me plz i need help

Using the bijection rule to count binary strings with even parity.

AleksandrR [38]

Answer:

Lets denote c the concatenation of strings. For a binary string <em>a</em> in B9, we define the element f(a) in E10 this way:

f(a) = a c {1} if a has an odd number of 1's
f(a) = a c {0} if a has an even number of 1's

Step-by-step explanation:

To show that the function f defined above is a bijective function, we need to prove that f is well defined, injective and surjective.

f is well defined:

To see this, we need to show that f sends elements fromo b9 to elements of E10. first note that f(a) has 1 more binary integer than a, thus, it has 10. if a has an even number of 1's, then f(a) also has an even number because a 0 was added. On the other hand, if a has an odd number of 1's, then f(a) has one more 1, as a consecuence it will have an even number of 1's. This shows that, independently of the case, f(a) is an element of E10. Thus, f is well defined.

f is injective (or one on one):

If a and b are 2 different binary strings, then f(a) and f(b) will also be different because the first 9 elements of f(a) form a and the first elements of f(b) form b, thus f(a) is different from f(b). This proves that f in injective.

f is surjective:

Let y be an element of E10, Let x be the first 9 elements of y, then f(x) = y:

If x has an even number of 1's, then the last digit of y has to be 0, and f(x) = x c {0} = y
If x has an odd number of 1's, then the last digit of y has to be a 1, otherwise it wont be an element of E10, and f(x) = x c {1} = y

This shows that f is well defined from B9 to E10, injective, and surjective, thus it is a bijection.

3 0

3 years ago

In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation

Aloiza [94]

a) situation you’re familiar with where one quantity changes constantly in relation to another quantity is Velocity = Distance/Time

b) the velocity is in direct proportion to distance and inverse relation to time.

c) The graph shown by velocity- time is a straight line graph.

<h3>what is algebra?</h3>

Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.

There is a equation we are familiar with , the equation of motion

Velocity = Distance/Time

Here, velocity increases or decreases if the distance also increases or decreases. But if time increases velocity decreases.

So, the velocity is in direct proportion to distance and inverse relation to time.

The graph shown by velocity- time is a straight line graph.

Learn more about algebra here:

brainly.com/question/953809

#SPJ1

3 0

1 year ago

A right triangular prism is shown. Find (A) the total surface area and (B) the volume. You must show formulas and your work.

enyata [817]

Hello!

We are going to use the rectangular prism of the image as a guide:

First of all, the AC segment is calculated using the Pythagoras' theorem:

$AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m$

(A) The surface area of a prism is the sum of the surface areas of each face.

For the 2 triangles ABC and DEF

$A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m$

For the ABEF Rectangle

$A=w*l=10,77m*10m=107,7m^{2}$

For the ACDE Rectangle

$A=w*l=10,77m*12,81m=137,96 m^{2}$

For the BCDF Rectangle

$A=w*l=10,77m*8m=86,16 m^{2}$

To finish you need to sum up the areas of each face:

$SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2}$

(B) The volume of a prism is the product of the area of its base and the height of the prism. In this case, the base is a triangle so the formula and the calculations for the volume are as follows

$V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3}$

7 0

3 years ago

Ms. Pierce LOVES Oreo Thins. When she went to Costco, a bulk size box of Oreos had a 47% discount. What a deal! How much was she

asambeis [7]

100%-47%(discount) so she is paying 53% of original price now,

100%. $13.99
53%. $X

X=13.99•53/100
X=741.47/100
X=7.4147
She was charged $7.41

6 0

3 years ago

What are two numbers that multiply to make 12 and add to make 7

mixas84 [53]

3 and 4.

3*4=12

3+4=7

:D

7 0

3 years ago

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