Is this a function?

The number of permutations of the 26 letters of the English alphabet that do not contain any of the strings fish, rat, or bird is 402619359782336797900800000

Let

[tex]\mathcal{E}=\{\text{All lowercase letters of the English Alphabet}\}\\\\B=\overline{\{b,i,r,d\}} \cup \{bird\}\\\\F=\overline{\{f,i,s,h\}} \cup \{fish\}\\\\R=\overline{\{r,a,t\}} \cup \{rat\}\\\\FR=\overline{\{f,i,s,h,r,a,t\}} \cup \{fish,rat\}[/tex]

Then

[tex]Perm(\mathcal{E})=\{\text{All orderings of all the elements of } \mathcal{E}\}\\\\Perm(B)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing bird}\}\\\\Perm(F)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing fish}\}\\\\Perm(R)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing rat}\}\\\\Perm(FR)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing both fish and rat}\}\\[/tex]

Note that since

[tex]F \cap R=\varnothing[/tex], [tex]Perm(F)\cap Perm(R)\ne \varnothing[/tex]

But since

[tex]B \cap R \ne \varnothing[/tex], [tex]Perm(B)\cap Perm(R)= \varnothing[/tex]

and

[tex]B \cap F \ne \varnothing[/tex] , [tex]Perm(B)\cap Perm(F)= \varnothing[/tex]

Since

[tex]|\mathcal{E} |=26 \text{, then, } |Perm(\mathcal{E})|=26! \\\\|B|=26-4+1=23 \text{, then, } |Perm(B)|=23!\\\\|F|=26-4+1=23 \text{, then, } |Perm(F)|=23!\\\\|R|=26-3+1=24 \text{, then, } |Perm(R)|=24!\\\\|FR|=26-7+2=21 \text{, then, } |Perm(FR)|=21!\\[/tex]

where [tex]|Perm(X)|=\text{number of possible permutations of the elements of X taking all at once}[/tex]

and

[tex]|Perm(F) \cup Perm(R)| = |Perm(F)| + |Perm(R)| - |Perm(FR)|\\= 23!+24!- 21! \text{ possibilities}[/tex]

What we are looking for is the number of permutations of the 26 letters of the alphabet that do  not contain the strings fish, rat or bird, or

[tex]|Perm(\mathcal{E})|-|Perm(B)|-|Perm(F)\cup Perm(R)|\\= 26!-23!-(23!+24!- 21!)\\= 402619359782336797900800000 \text{ possibilities}[/tex]

This link contains another solved problem on permutations:

https://brainly.com/question/7951365

Answer:

9.2

Step-by-step explanation:

We can use the Pythagorean Theorem, a^2 + b^2 = c^2 to solve this. Since a and b are the lengths of the two sides and c is the length of the hypotenuse, we modify the original formula to c = [tex]\sqrt{a^{2} +b^{2} }[/tex] to find the length of the diagonal. We would get c = [tex]\sqrt{7^{2} +6^{2} }[/tex] = 9.2.

Answer:

F = 110°

I'm not sure, but since no one answered, here it goes...

Step-by-step explanation:

∵ FD = FE (Given in Diagram)

∴ ΔDFE is isosceles , ∴m∠E = m∠D

1 ) 3x  +  14  =  5x

   14  =  5x  -  3x

   14  =  2x

   14 / 2  =  x

   7  =  x  

m∠E = 3*7 + 14 = 35°

m∠D = 5*7 = 35°

m∠F = 180 - (35+35)

m∠F = 110°

Answer:

Both triangles are congruent.

so 30/36 = 5/6 = 0.83333333333...

35/x  should also be 0.83333333333.. so 35/0.83333333333.. is x

x = 42

C? im pretty sure its c

hope this helps!

C. It is a decimal, it is true of Gemma’s divisor.

The correct answer is: C. It is a decimal.

When Gemma moves the decimal point directly up to the quotient, she is essentially performing long division by powers of 10.

This is because when you divide a number by a power of 10, you are essentially shifting its decimal point to the left by the number of positions determined by the power of 10.

For example, if she is dividing by 100 [tex](10^2)[/tex], she is moving the decimal point two places to the left.

If she is dividing by 1000 [tex](10^3)[/tex], she is moving the decimal point three places to the left, and so on.

Moving the decimal point up to the quotient means that the divisor is a decimal number, and its value determines how many decimal places Gemma needs to move the decimal point in the dividend to get the quotient.

So, the correct answer is C. It is a decimal.

To know more about Whole Numbers refer to the link:

brainly.com/question/11082740

#SPJ3

Answer:

y = c+r-7t

Step-by-step explanation:

7t- y+7t=c+r -7t

y = c+r-7t

Answer:

I think the answer is c

Step-by-step explanation:

please give me brainlist

Answer:

30

Step-by-step explanation:

The answer is said in the question. It said that 30 students of them have a birthday in the summer so it's 30

Answer:

I am pretty sure the correct answer is never true

Step-by-step explanation:

This is because when,

Δ JKL ≅ Δ MNP

Then, ∠J ≅ ∠M

∠K ≅ ∠N

∠L ≅ ∠P

so ∠L ≠ ∠N

i hope this is right haha

if the value of x is 1 then the y value is 6

Answer:

8n+2 first let’s plug in n which is 1

8(1)+2=10

The answer is 10 but Brian said the expression is equal to 83. He is incorrect because 8 times 1 is 8 and then plus 2 is 10.

I hope it helps.

Answer:

5*jjjjjjjjkkkkkkkkkk

Answer:

Divide both sides by -10

-10n+2=40

subtract 2 from both sides so

40-2=38

10n/10= 38/10

3.8 = n

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number is x.

2/3 of a number is 10:

0.15 times of the number is:

Correct choice is d

Answer:

B) 1/4 x 88

Step-by-step explanation:

25%=25/100=1/4

25% of 88, of is basically multiplication

=1/4 x 88

Answer:

D)

Step-by-step explanation:

A is incorrect because:  2(6) -3(-4)<9 which is 24<9 which is not true

B is incorrect because:  2(-1) -3(-9)<9 which is 25<9 which is not true

C is incorrect because: 2(2) -3(-5)<9 which is 19<9 which is not true

D is correct because: 2(-3) -3(-3)<9 which is 3<9 which is true

Answer:

4 b 2 + 2 b

Step-by-step explanation:   hope it helps

Answer:

New eq: 11x + 1. The line will become steeper.

Step-by-step explanation:

Slope is rise over run. In the original equation, y increased 4 times everytime x increased by one. In the new equation, y increased 11 times everytime x increased by one making it steeper.

Answer:

l will print A2 inches cause each side of the scale of the map is 1inch

We want to graph the linear function that models how much Maggie saves, the graph can be seen below.

So we know that maggie starts with $30, and she saves another $30 per week, then after x weeks, the total amount that she has saved is:

S(x) = $30 + $30*x

Now we have the function, to graph it, we just need to get two points of the function and then connect them with a line, to get these points, we just evaluate the function in two different values of x:

S(0) = $30 + $30*0 = $30

S(1) = $30 + $30*1 = $60

So we have the points (0, $30), (1, $60).

Now we just need to graph these points and connect them with a line, the graph can be seen below.

If you want to learn more, you can read:

https://brainly.com/question/20853486

Answer:

(0,30) and (1,70)

Step-by-step explanation:

I took the quiz in USATestprep.

Answer:

1050.67213

Step-by-step explanation:

The following are deductive reasoning for each statement in the algebraic proof given:

1. CD + DE = CE (Segment Addition Postulate)

2. 8 + (3x + 7) = 6x (Substitution)

3. 3x + 15 = 6x (Combining like terms)

4. 15 = 3x (Subtraction Property of Equality)

5. x = 5 (Division Property of Equality)

6. CE = 6(5) (Substitution)

Recall:

Thus, the following are deductive reasoning for each statement in the algebraic proof given:

1. CD + DE = CE (Segment Addition Postulate)

2. 8 + (3x + 7) = 6x (Substitution)

3. 3x + 15 = 6x (Combining like terms)

4. 15 = 3x (Subtraction Property of Equality)

5. x = 5 (Division Property of Equality)

6. CE = 6(5) (Substitution)

Learn more about Segment Addition Postulate on:

https://brainly.com/question/2134445

The number of dollars for one peso is 20 dollars.

Exchange rate is the rate at which one currency is exchanged for another currency.

In order to determine how many pesos can be exchanged for a dollar, the value of pesos would be divided by the amount of dollars exchanged.

Exchange rate = 5000 / 250 = 20 dollars

This means that 1 peso would be exchanged for 20 dollars.

A similar question was answered here: https://brainly.com/question/18236223

Answer:

3a

Step-by-step explanation:

9÷3=3

a³-a²=a¹ or just a

b-b= 0

= 3a

Hope this helped you- have a good day bro cya)

Answer:

Step-by-step explanation:

The equation would be y=12000(2)ˣ.

This equation is of the form y=a*bˣ, where a is the initial population and b is the rate that it increases by.  In this problem, a = 12000 and b=2, since it doubles each time.

brainlest

Answer:

this is so easy and the answer of this all questions is54

H(3) means to replace x in the equation with 3 and then solve:

15(3) - 171

45-171

-126

Answer: -126

Answer:

All percent's can be written as a fraction out of 100.

Step-by-step explanation:

Percent's are usually percent's out of 100, so if you had 63%, it would be 63% out of 100, so your answer is 100