How many permutations of the 26 letters of the English alphabet do not contain any of the strings fish, rat, or bird
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
secure.learningblade.com/MyMissions/Index/18?IsGuide Viewed=False&IsAssigned=Not%20As
Calculating Dose
An 8 year old child is running a temperature of 103 degrees F
and his parent would like to give acetaminophen but doesn't
know how much. He has a bottle of suspension (liquid) at
home and says that the bottle reads "80mg/ half-teaspoonful"
and the child weighs about 25kg. He has an oral syringe that is
marked off at 0.2 milliliter intervals and goes up to 10ml. The
standard dose for acetaminophen elixir is 10mg/kg.
Answer:
5*jjjjjjjjkkkkkkkkkk
Is the relation a function? Explain
Answer:
No, does not pass the vertical line test
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
A function is a relation in which that one x-value (input) is related to exactly one y-value (output). For relations shown on graphs, we can use the vertical line test.
Since the line would intercept at 2 points in the graph at one point, it is not a function.
Hope this helps.
What is the mass of 64 mL of a liquid with a
density of 2.7 g/mL?
Answer:
172.8
Step-by-step explanation:
to get density its mass over volume so if you mutiply volume by density you get the mass
Write the equation of the line in fully simplified slope-intercept form
Answer:
try y = 3x + -6 it might be wrong tho
Step-by-step explanation:
slope intercept form is y = mx + b where m = the slope and b = the y intercept. the y intercept is -6 and the slope is 3/1 or 3 so just plug the numbers in
Select the correct answer.
What is the vertex of the function f(x) = |x + 7| − 3?
Maggie needs $180 to pay for a cheer camp. She has $30 already and saves $30 a week that she earns by helping her neighbors.
Use the Segment tool to plot a graph representing the amount of money Maggie has saved from the time she begins saving until she has saved enough for cheer camp.
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.
Write an equation in vertex form for each graph or given information: 31. Vertex (-5, 12) and through the point (-2, 15)
Answer:
(-3,16)
Step-by-step explanation:
(-5,12)
f (x) = ( (x+5) (x+5) ) + 12
f (x) = x^2 + 10x + 37
(-2,15)
f (x) = ( (x+2) (x+2) ) + 15
f (x) = x^2 + 4x + 19
A fisherman has 420 crabs. He sold one tenth of the crabs for a party. Then he sold two-thirds of the remaining crabs to a restaurant. The fisherman estimates that he has 232 crabs left. How far off is the fisherman's estimate?
Answer:
The answer I'd 28464835383637533
Can someone help me with math pls no links pls I lost a lot of points because someone put a link . THANK YOU
Answer:
15
Explanation:
The common denominator for 2/3 and 3/5
Answer:
The answer is 15.
LCD = 15
Determine whether the statement is always, sometimes, or never true.
If △JKL ≅ △MNP, then m∠L = m∠N.
Complete the explanation of your reasoning.
The statement is always/ sometimes/ never true.
∠L corresponds to ∠P.
By [CPCTC/ Triangle Sum Theorem/ SAS Triangle Congruence Theorem], ∠L ≅∠P.
If ∠P ≅∠N, then ∠L [≅/≇ ] ∠N by [CPCTC/ Triangle Sum Theorem/ SAS Triangle Congruence Theorem], ∠L ≅∠P.
and m∠L [≅/≇ ] m∠N.
Please help this is on HMH I will give Brainliest if it's right! :)
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 (8^2)P = 8^4, what is the value of p?
Answer:
The answer is 2
First, we simplify it to 64^p = 4096.
Then, take the log of both sides:
p = log (4096) / log (64)
p = 2
Please mark brainliest i need 1 more
Step-by-step explanation:
Help me pleasee asap !!
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°
3-14. Do you think that an area model can help rewrite expressions that involve multiplication? The area model below relates the expressions and . With your team, discuss how it can be used to show that these expressions are equivalent. Be prepared to explain your ideas.
Answer:
Step-by-step explanation:
HELPPP.!!!
Answer choices:
−y ≥ x + 4
−3x + 3y ≤ −9
−y ≤ 3x + 4
−3x + 3y ≤ −9
y ≤ −x − 4
−x − y ≤ − 4
y ≤ −x + 4
−4x + 4y ≤ 16
Step-by-step explanation:
the second option.
you see that the steeper line has a slope of -3 (when x increases by 1 grid point, y decreases by 3 grid points, that makes the slope ratio of y/x = -3/1 = -3).
the slope is always the factor of x in an equation of
y = ax + b
the only equation provided in the answer options with slope -3 is
-y <= 3x + 4
because when we transform this into the general firm above, we need to multiply both sides by -1 (which flips the inequality symbol, by the way) :
y >= -3x - 4
there you have it. no other equation here can be transformed into this.
as a control we also look at the second equation :
-3x + 3y <= -9
3y <= 3x - 9
y <= x - 3
this has a slope of 1 (so, x and y both increase by the same amount), and the y-inteecept is -3 (the y value when x = 0). that also fits the graph.
so, it is all correct.
which of these government programs encourage hygiene practices
A. transportation regulations to prevent overcrowding
B. vaccination programs
C. cancer research
D. anti-obesity campaigns
Government programs help to protect citizens from possible hazards
exposure.
The government program that encourage hygiene practices is A.
Transportation regulations to prevent overcrowding.
Reasons:
Hygiene practices which include mainly cleanliness measures, meant to
keep a person healthy as well as to prevent contraction of disease.
Government programs such as stipulating social distancing rules reduces
airborne diseases, and other contagious diseases, and such programs are
useful as part of transport regulations.
Therefore, the government program that encourage hygiene practice
transport regulations to prevent overcrowding.
Learn more here:
https://brainly.com/question/10560365
The settlement at Jamėstowi began in 1607. This was
how many years after Columbus reached the Americas
in 14927
Answer:
15
Step-by-step explanation:
jamestown really began in 1606 in may and columbos reached america in 1497
(3/4(3/5) simplify i need the answer because i dont get it
Answer:
35 is already in the simplest form. It can be written as 0.6 in decimal form (rounded to 6 decimal places).
...
Reduce 3/5 to lowest terms
Find the GCD (or HCF) of numerator and denominator. GCD of 3 and 5 is 1.
3 ÷ 15 ÷ 1.
Reduced fraction: 35. Therefore, 3/5 simplified to lowest terms is 3/
Step-by-step explanation:
If 2/3 of a number is 10, then what is 0.15 times of that number?
a) 225 b) 825 c) 22.5 d) 2.25
step by step explanation needed
Answer:
d) 2.25Step-by-step explanation:
Let the number is x.
2/3 of a number is 10:
2/3x = 10x = 3*10/2 = 150.15 times of the number is:
15*0.15 = 2.25Correct choice is d
At camp, Miriam uses a pottery wheel to make 3 bowls in 2 hours
Duane makes 5 bowls in 3 hours.
a) Who makes bowls faster, Miriam or Duane?
b) How long will it take Miriam to make a set of 12 bowls?
c) How long will it take Duane to make a set of 12 bowls?
Answer:
Hope this helps
Step-by-step explanation:
A: Duane makes bowls faster.
B) 18 hours
C) About 19.92 hours
Suppose y varies jointly as x and z. What is y when x = 2 and z = 3, if y = 20 when x = 4 and z = 3?
Answer:
y = 10
Step-by-step explanation:
Given y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 20 when x = 4 and z = 3 , then
20 = k × 4 × 3 = 12k ( divide both sides by 12 )
[tex]\frac{20}{12}[/tex] = k , that is
k = [tex]\frac{5}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] xz ← equation of variation
When x = 2 and z = 3 , then
y = [tex]\frac{5}{3}[/tex] × 2 × 3 = 5 × 2 = 10
what is the ans
1. Add : 12a²b², -7a²b² , and 9a²b²
2. Subtract : -5y² from y²
need a well explained ans :)
no spams , unwanted ans and plagiarism
kindly stay out if u don't know the ans
1. 12a²b² + -7a²b² + 9a²b²
= 14a²b² (the terms a²b² are like terms so don't look at them, just add 12 + (-7) + 9.
= 14 (ab)² (you can write like this too because both a & b are squared).
2. y² - (-5y²)
= 6y² (subtract -5 from 1, y² is the like term).
Complete the multiplication: AB.
Answer:
Option: B is the correct
Step-by-step explanation:
Step-by-step explanation:
We are given two matrices A and B as follows:
\begin{gathered}A=\left[\begin{array}{ccc}3&0\\2&-1\end{array}\right]\end{gathered}
A=[
3
2
0
−1
]
and
\begin{gathered}B=\left[\begin{array}{ccc}2&8\\0.6&3\end{array}\right]\end{gathered}
B=[
2
0.6
8
3
]
We know that the multiplication of two matrices of the type:
\begin{gathered}A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\end{gathered}
A=[
a
c
b
d
]
and
\begin{gathered}B=\left[\begin{array}{ccc}a'&b'\\c'&d'\end{array}\right]\end{gathered}
B=[
a
′
c
′
b
′
d
′
]
is given by:
\begin{gathered}AB=\left[\begin{array}{ccc}aa'+bc'&ab'+bd'\\ca'+dc'&cb'+dd'\end{array}\right]\end{gathered}
AB=[
aa
′
+bc
′
ca
′
+dc
′
ab
′
+bd
′
cb
′
+dd
′
]
Hence, here we have:
\begin{gathered}AB=\left[\begin{array}{ccc}3\times 2+0\times 0.6&3\times 8+0\times 3\\2\times 2+(-1)\times 0.6&2\times 8+(-1)\times 3\end{array}\right]\end{gathered}
AB=[
3×2+0×0.6
2×2+(−1)×0.6
3×8+0×3
2×8+(−1)×3
]
i.e.
\begin{gathered}AB=\left[\begin{array}{ccc}6+0&24+0\\4-0.6&16-3\end{array}\right]\end{gathered}
AB=[
6+0
4−0.6
24+0
16−3
]
i.e.
\begin{gathered}AB=\left[\begin{array}{ccc}6&24\\3.4&13\end{array}\right]\end{gathered}
AB=[
6
3.4
24
13
]
What is the slope of the given slide?
[tex]\text{Slope,~} \tan \theta =\dfrac{15}{18}=\dfrac 56[/tex]
Find the slope of the line
simplify 12b+4b^2-10b
Answer:
4 b 2 + 2 b
Step-by-step explanation: hope it helps
what times 1 over 7 equals 4? correct answer gets brainliest
Answer:
x = 28
Step-by-step explanation:
1/7(x) = 4
Multiply all sides by 7
x = 4 x 7/1
x = 28/1
x = 28
-Chetan K
Answer:
n = 28
Step-by-step explanation:
Let the unknown be n.
Then the word problem translates into n(1/7) = 4.
Multiplying both sides by 7 yields n = 28
Please help me with this homework
Answer:
wow. at this point just guess
Step-by-step explanation:
Seven more than twice a number is less than negative thirteen. Solve the inequality for the unknown number.
Answer:
x < -10
Step-by-step explanation:
First, let x = unknown number. Then create the algebraic equation to solve for x. The equation would be 2x + 7 < -13, so 2x < -20, thus x < -10.
Answer:
If you wanted the in equality equation then your answer is 2n + 7 < -13
If you want the answer to the inequality then its n < -10
Step-by-step explanation:
2n + 7 < -13
-7 -7
2n < -20
/2 /2
n < -10
y = 6x + 11; x = 14; 2y - 4x = 14
Answer:
95=35
35=95
x=14
y=95
x=14
Step-by-step explanation: