Miko wants to build a toy
box for her sister. It is to be 2 feet high,
and the width is to be 3 feet less than its
length. If it needs to hold a volume of
80 cubic feet, find the length and width
of the box.

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:

1, Stay calm

2, be confident

3, if you know the type of questions they are gonna ask practiece those type of questions

Also good luck

Answer:

22.84

Step-by-step explanation:

Answer:

A Matrix is an array of numbers:

2x3 Matrix

A Matrix

(This one has 2 Rows and 3 Columns)

To multiply a matrix by a single number is easy:

Matrix Multiply Constant

These are the calculations:

2×4=8 2×0=0

2×1=2 2×-9=-18

We call the number ("2" in this case) a scalar, so this is called "scalar multiplication".

Answer:

Raul

Step-by-step explanation:

Since 8 groups of building blocks has a smaller amount than 6 equal groups of building blocks, so Raul has more blocks in each group

Answer:

75.4 to 1 decimal place

If you want an explanation comment on the answer.

Answer:7 to 9? Years

Step-by-step explanation: I’m not sure but if you got a couple trys try to do it.

Answer:

6 years

Step-by-step explanation:

Y = IA (r)^t

600 = 3100 (.75)^t

then just solve for T i recommend using guess and check, but thats me

and youll get 6 years.

4/3=1.3 repeating

1.3repeatingx9= 12/9

Answer:

14

Step-by-step explanation:

First fond 40% of 20

20×40/100 = 8

So now there is a total of 20+8 =28

At the store you spend exactly half

28×50/100 =14

So now you are left with 28-14 =14

She can buy 16 pens and 16 pencils.

Answer: ≈ 26 lb

Step-by-step explanation:

11,800 grams x [tex]\frac{1 kilograms}{1000 grams}[/tex] x [tex]\frac{1 pound}{0.45kilograms}[/tex] ≈ 26 lb

Answer:

Option D: [tex]y= -\frac34x+14[/tex]

Step-by-step explanation:

In order for two lines to be perpendicular, the product of the slopes has to be [tex]-1[/tex]. That allows you to rule out A and C. Let's plug the coordinate of the point in B. If the equality holds, we found or line. Else, it's D.

[tex]11 =-\frac34(4) +8 \rightarrow 11 = -3+8 \rightarrow 11=5[/tex] Which is obviously impossible. Our line has to be D

Answer:

B

Step-by-step explanation:

[tex]4x^{2}-11x-3=0\\4x^{2}-12x+x-3=0\\4x(x-3) + (x-3) = 0\\(4x+1)(x-3)=0[/tex]

B is factorable through this method

Answer:

Angle 2 = 64°

Step-by-step explanation:

Angle 2 = 180°-116° (int angles, 12//34)

=64°

Answer:

1/10 x 30/10=30/100 then simplify =3/10  

Step-by-step explanation:

Hope I helped please mark brainliest!

Answer: D. 1 1/2.

Step-by-step explanation: -3/8÷-1/4                                                                 (-3/8)(-4/1)                                                                                                           -3/8/-4/1                                                                                                             Cancel out the terms of 8 and -4.                                                                       8/4                                                                                                                               (-3)(-1)/2                                                                                                                   3/2                                                                                                                             D. 1 1/2                                                                                                                                                                            

First of all, 4.7 * 2.9 = 13.63, so I think a mistake has occurred there and second, comma does not come here because this is not a big number, it is a small number. If you meant a dot instead. it would placed in the middle AKA 13.63

Would appreciate brainliest <3

Step-by-step explanation:

that means we divide 2/3 by 4.

2/3 / 4 = 2/3 / 4/1 = 2/3 × 1/4 = 2/12 = 1/6

so each quarter of the remaining 2/3 pizza is actually 1/6 of the complete pizza.

Answer:

I believe the correct answer would be A: 3/5 = 60

Step-by-step explanation:

Firstly, the second option is wrong because 0.06 would be 6 hundredths, so that is wrong, the third option would be incorrect because 0.002 would equal 2 thousandths so that is also wrong, and the fourth option would be 25% instead of 75%, so your answer should be A.

Answer:

at an x intercept

Step-by-step explanation:

You need to calculate sin 0 = 0. Which means it's crossing (or at least touching) the x axis.

Answer:

432

24*36

---------- = 432

2

Answer:

13/15

Step-by-step explanation:

I took the quiz and solved it out. I would give further explaination but it is kinda hard to do that in text form. Have a nice day!

The value of the expression if m = 3 is 13/15

Given the expression as shown below:

If the value of m = 3, hence the expression will become;

2/5(3) - 1/3

6/5 - 1/3

Find the LCM

6/5 - 1/3 = 3(6)-5/15\

6/5 - 1/3 = 18-5/15

6/5 - 1/3 = 13/15

Hence the value of the expression if m = 3 is 13/15

Learn more on equations here: https://brainly.com/question/13763238

Answer:

35/72

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

There is no pause and the use of a connection word (and) makes the sentence seem longer. Hope this helps :) brainliest?? <3