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
use the long division method to divide 120÷24
Step-by-step explanation:
120÷24
0 24⟌120
0 24⟌120 0
0 24⟌120 -0 1
00 24⟌120 -0 12
0 24⟌120 -0 12
00 24⟌120 -0 12 - 0 12
00 24⟌120 -0 12 - 0 120
PARALLEL PERPENDICULAR OR NEITHER OR SAME slope
Answer:
21. Same Line
22. Same Line
23. Perpendicular
24. Neither
25. Parallel
26. Neither
27. Neither
28. Neither
29. Perpendicular
30. Perpendicular
31. Neither
32. Perpendicular
33. Parallel
34. Perpendicular
35. Perpendicular (?)
36. Neither
37. Neither
38. Parallel
39. Neither
40. Parallel
How many of the following statements are true?
19)
a
d Any set of ordered pairs is a function.
d The domain of a relation is the set containing the first
member of its ordered pairs.
d The independent variable in a relation is the variable
used for the range.
d A function is a relation in which each domain value is
paired with exactly one range value.
A) 1
B) 2
C) 3
D) 4
Answer:
A) 1
Step-by-step explanation:
yeah-ya,.................. right?
How to do the 9 multiplication trick.
Answer:
0123456789
9876543210
Step-by-step explanation:
09
18
27
36
45
54
63
72
81
90
Answer:
Step-by-step explanation:
for each 9 you add, take away 1 from the first number and add 10, like
81
72
63
52
41
32
23
18
9
A recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quarts of grape juice. How much of each ingredient would you need to make 100 quarts of punch?
Answer:
Step-by-step explanation:
Sparkling grape juice is made with 1.5 quarts sparkling water and 0.75 quarts grape juice. When these two get mixed we get 2.25 quarts sparkling grape juice
So for 2.25 quarts sparkling grape juice we require 1.5 quarts sparkling water
⇒ For 100 quarts sparkling grape juice we require * 100 quarts of sparkling water
⇒ Sparkling water required for 100 quarts of sparking grape juice = 66.67 quarts
expand and simplify 4(x+3)+4(x+5)
How to multiply mixed fractions with same denominators.
Answer:
multiply the numerators; express that product over the product of the denominators
Step-by-step explanation:
Multiplication of fractions is done the same way regardless of whether the denominators are the same or different.
[tex]\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}[/tex]
The numerator of the product is the product of the numerators.
The denominator of the product is the product of the denominators.
Describe if the function is linear, exponential, or neither. Explain how you can tell
A rectangular prism is 7.1 millimeters long and 10 millimeters high. Its volume is 213.0 cubic millimeters . What is the width of the rectangular prism?
Answer:
5 milimeters
Step-by-step explanation:
What is the mean absolute deviation (MAD) of the data set?
2, 6, 8, 12, 12
Enter your answer as a decimal in the box.
Answer:
2+6+8+12+12=40
40 divided by 5=8
6+2+0+4+4=16
16 divided by 5=3.2
MAD=3.2
Step-by-step explanation:
Answer:
3.2
Step-by-step explanation:
I took the test
plss help i'll give 80 points!! no links please
Answer:
domain [-1, ∞)
range [ -3, ∞)
Step-by-step explanation:
Brainliest?
You are solving 5 – 8/3
=y/3
. Which equation will you get if you multiply both sides by 3?
Answer:
y=0.76
Step-by-step explanation:
5-8/3 = 3y
(5-8/3) x 3 = 3y x 3
6.9=9y
9y=6.9
y=6.9/9
y=0.76
-----------------------------------------------------------
Standard form / Slope intercept form
_____________1. 3x -y = 7
_____________2. y = 5x - 2
_____________3. 2x + y = -4
_____________4. y = - ¾ x + 1
_____________5. 4 x - y = -8
_____________6. y= -x + 9
_____________7. 3x + 6y = 12
_____________8.y = ⅔x + 5
-----------------------------------------------------------
Answer:
1.) y=3x-7
2.) 2=5x-y
3.) y=-4-2x
4.) 1=3/4x+y
5.) y=4x+8
6.) 9=3/4x+8
7.) 9=y+x
8.) y=-2/6x+2
9.) 5=-2/3x+y
Step-by-step explanation:
Standard form is Ax=By=C and Slope form is y-mx+b
for all of the equations fiqure out which is standard and which is slope, 3x-y=7 is standard and just switch it to slope ie:
3x-y=7
+7 -7
3x-7=y
then switch around so y is in the front and vice versa, also divde any y or C by negative 1 if the answer is negative or if there is a number in front of it like in 9, and 8
Please help me
Thank you x
Answer:
l think that the answer is 56576
Evaluate the expression below.
5^{0}5
0
The 5-0-5 Agility Test is one of the most commonly recognised agility tests, despite its inability to actually measure agility. Instead, this is a change of direction speed test, which contrary to common belief, may not be capable of distinguishing between dominant and non-dominant leg performances.
Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21? select each correct answer. (−1, −6) (7, 0) (11, 3) (−3, 3).
Answer:
(-1, -6), (7, 0) , and (11, 3)
Step-by-step explanation:
3x - 4y = 21 Solve the equation for y
3x - 21 = 4y
(3x - 21)/4 = y
Now use the ordered pair and find the true ordered pair
(-1, -6) [ (3)(-1) - 21]/ 4 ; (-3 -21)/4 ; (-24)/4 = -6 True
(7, 0) [(3)(7) -21]/4 ; (21 - 21)/4; 0/4 = 0 True
(11, 3) [(3)(11) - 21]/4; (33 - 21)/4; 12/4 = 3 True
(-3 ,3) [(3)(-3) - 21]/4 (-9 -21)/4 ; -30/4 = -7.5 No
Help me with this very confused
Answer:
[tex] \frac{3 - 5x}{2} [/tex]
Step-by-step explanation:
Set g(x)=y
y=-2/5x+3
5y=-2x+3
2x=3-5y
x=3-5y/2
So g^-1(x)=
[tex] \frac{3 - 5x}{2} [/tex]
can anyone help me with this?
Find the missing angle measure.
Answer:
116
Step-by-step explanation:
Given shape has 6 angles and the sum of interior angles for this shape is calculated as following:
180*(6-2) = 720 now to find x we need to find the sum of given angles first:
144 + 163 + 50 + 131 + 126 x = 720
614 + x = 720 subtract 614 from both sides
x = 116
help me please!!!!!!!!!!!
Answer:
I did mostly everything for you bestiieee on the pictureee :3
Step-by-step explanation:
hope this helped :3
:3 byeeeeeeeeeee
If you have one quarter, nine pennies, six dimes, and one nickle, how much money would you have?
Answer:
99 cents
Step-by-step explanation:
one quarter=25 cents
nine pennies= 9 cents
six dimes= 60 cents
one nickle= 5 cents
25+9+60+5=85+14=99
Answer:
99 cents
Step-by-step explanation:
quarter = 25 cents
pennie = 1 cent
dime = 10 cents
nickle = 5 cents
1 quarter = 25 cents
9 pennies = 9 cents
6 dimes = 60 cents
1 nickle = 5 cents
25 + 9 + 60 + 5 = 99 cents
7⋅5+(4^2−2^3)÷4 answers: 49 41 34 9
On evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.
What is Expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. For example -
5x + 7 = 6
7r + π = 4
Given is the following expression -
7.5 + (4² − 2³) ÷ 4
The given expression is -
7.5 + (4² − 2³) ÷ 4
Using the BODMAS rule, we can solve -
7.5 + (16 - 8) ÷ 4
7.5 + 8 ÷ 4
7.5 + 2
9.5
Therefore, on evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.
To solve more questions on evaluating expressions, visit the link below-
https://brainly.com/question/13589173
#SPJ5
How do you do the elimination method on these equations: 3x = y+5 and 2x+y=5
Answer:
[tex](2,1)[/tex]
Step-by-step explanation:
Let's first write down the first in traditional form:
[tex]\left \{3x-y=5} \atop {2x+y=5}} \right.[/tex]
At this point, let's choose the order we want to do it.
Eliminating x: Let's multiply the first by 2, the second by 3, and subtract one from the other. Rest is simple algebra
[tex]2I-3II: 6x-2y -6x-3y = 10-15\\-5y=-5 \rightarrow y=1[/tex]
Eliminating y: Let's simply add the two equations together. Rest is simple algebra
[tex]I+II:3x-y+2x+y = 10\\5x=10 \rightarrow x = 2[/tex]
PLEASE HELP ME OUT!!!
Convert the following
0.005 kg = _____ dag
0.075 m = ______ cm
Answer: 0.5 dag and 7.5 cm
Step-by-step explanation:
1 Decagram (dag) =10^-2 kg
We can change this into a conversion factor by dividing either side into the other. Since we want to change Kg into dag, I'll divide both sides by 10^-2kg:
1 Decagram (dag)/10^-2 kg = 1
Now we can multiply this times 0.005 kg:
(0.005 kg)*(1 Decagram (dag)/10^-2 kg)
this equals 0.5 dag
------------
100 cm = 1 meter
(100 cm/1 meter): Conversion factor
(0.075 m)*((100 cm/1 meter) = 7.5 cm
As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag. First the players must decide who is playing black marbles and who is playing red marbles. Then each player takes a turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting the color before returning it to the bag. The point scheme for the game is detailed in the table below.
Point Values for Marble Game
Black Marble Points
Red Marble Points
Both black: +2 points Both red: +4 points
Different colors: –1 point Different colors: –1 point
Both red: 0 points Both black: 0 points
If Seth is challenged to a game by a classmate, which statement below is correct in all aspects in helping him make the correct choice?
Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
Since E(red) = E(black), it is a fair game, so it doesn’t matter which color Seth chooses.
Both options will lose points because there are two ways to lose points and only one
Answer:
ez
Step-by-step explanation:
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
Since E(red) = E(black), it is a fair game, so it doesn’t matter which color Seth chooses.
Both options will lose points because there are two ways to lose points and only one
A curve has the equation y = x^3 – 3x + 2
Find the coordinates of the two turning points. Please help ❤️
Answer:
PLEASE MARK ME BRAINLIEST!!!
Step-by-step explanation:
moddedcraftxdepic
02/28/2021
Mathematics
High School
answered
Y= x^3 + 8x^2 +5x
work out the coordinates of the two turning points 1
which of the following is not a true dilation?
A. The image and preimage have congruent angles
B. The image and preimage have proportional sides
C. The image and preimage are congruent
D. The image and preimage are similar
Answer:
umm i think it is B.
Step-by-step explanation:
7/12 of £72!!!!
i really need the answer lol
Answer: Its ¨undefined¨ hope this helps !!
Answer: 42
Step-by-step explanation:
1/12 of 72 is 6
6x7 = 42
What is the slope of the line?
Step-by-step explanation:
the slope of the line is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
the trick in such a situation is to find good points on the chart that are crossed by the line. and by "good" I mean points with round integer coordinates.
I see 2 such points :
(-3, 4) and (1, -3)
x changes by +4 (from -3 to 1)
y changes by -7 (from 4 to -3)
the slope is therefore -7/+4 = -7/4
Please translate each algebraic expression to English phrase
1. x - 8
2. 13 + 2y
3. 4 ( x+ 5)
4. 7x
5. m + 6
What is the scale factor from ABC to XYZ?
A 1/5
B 1/6
C 5
D 6
Answer:
Is 6
Step-by-step explanation:
5X6=30
3X6=18
4X6=24