The number of different ways in which the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
Further explanation:
A permutation is an arrangement of objects in their order in which we find number of ways that can occur in a period of time.
If all the letters are different then the number of arrangement can be written as follows:
[tex]\boxed{\begin{aligned}P(n)&=n!\\&=n\cdot (n-1)\cdot (n-2)...2\cdot 1\end{aligned}}[/tex]
The number of different permutation can be calculated as follows:
[tex]\boxed{p(n)=\dfrac{n(n-1)(n-2)...2\cdot 1}{n_{1}!\cdot n_{2}!}}[/tex]
Here, [tex]n_{1}[/tex] and [tex]n_{2}[/tex] are the different kind of object such that [tex]n_{1}+n_{2}+n_{3}+\cdot \cdot+n_{k}=n[/tex].
Given:
The given word is “PERSONNEL”.
Calculation:
Step 1:
First consider that all the letters are different i.e, repetition of letter is allowed.
The given word “PERSONNEL” has [tex]9[/tex] letters.
Therefore, the number of ways for arranging nine letters can be calculated as follows:
[tex]\begin{aligned}P(9)&=9\cdot (9-1)\cdot (9-2)\cdot \cdot 2\cdot 1\\&=9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot3 \cdot 2\cdot 1\\&=362,880\end{aligned}[/tex]
Therefore, the different arrangements of the given word is [tex]362,880[/tex].
Step 2:
Since, the letter N and E is repeated two times in given word “PERSONNEL” then the half of the arrangement is repeated of these two letters.
Use the formula for finding the number of distinguishable permutation. It can be calculated as follows:
[tex]\begin{aligned}\text{Number of permutation}&=\dfrac{362880}{2!\cdot 2!}\\&=\drac{362880}{4}\\&=90,720\end{aligned}[/tex]
The number of different ways that the letter of “PERSONNEL” can be arranged is [tex]90,720[/tex].
Thus, the number of different ways that the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Permutation
Keywords: Permutation, combination, personnel, counting, arrangement, different ways, order, letters, different ways, repetition, arranged objects, distinguishable permutation, counting problem.
The number of different ways to arrange the letters of 'personnel' is calculated using combinatorics and permutation formulas, resulting in 151,200 unique arrangements.
To find the number of different ways to arrange the letters of the word "personnel", we must use the principles of combinatorics and permutations.
The word 'personnel' consists of 9 letters with repetitions: there are three E's, two N's, one P, one S, one O, and one L. To count the number of unique arrangements, we start with the total factorial of all letters, which is 9!, but then we need to account for repeated letters by dividing by the factorials of the frequency of each repeating letter.
This results in the following permutation formula:
N! / (n1!)n2!...nk!
Where N is the total number of letters, and n1, n2, ..., nk are the number of times each unique letter is repeated.
So for 'personnel': 9! / (3!)(2!) = 151,200
There are therefore 151,200 unique ways to arrange the letters in 'personnel'.
Average Monthly Temperature Month Temperature January 45 degrees February 42 degrees March 54 degrees April 62 degrees May 78 degrees June 85 degrees July 92 degrees August 94 degrees September 89 degrees October 78 degrees November 65 degrees December 54 degrees The average monthly temperatures for the city of Mathville are given in the chart above. One year was particularly warm, and the average temperature each month increased by 5°. What did this do to the average yearly temperature? A) The average remained the same. B) The average increased by 5°. C) The average decreased by 5°. D) The average increased by 60°.
Which of the following situations models a geometric sequence? Select all that apply.
Answer:
Options 1, 3, 4.
Step-by-step explanation:
We will check each and every option given here.
1) Amount of cell phone users increases by 33% every year.
Its a geometric sequence because the number of users are increasing exponentially every year.
2) Amount of cakes in bake sale increases by 3 each year the fundraiser is held.
amount of cakes is increasing with a common difference of 3 so it's an arithmetic sequence.
3).Uranium loses half of its weight every 415 years.
Exponential decay in every 415 years. So geometric sequence with a common ratio of 1/2.
4).A family of rabbits doubles in size every 3 months.
Exponential series again so geometric sequence with a common ratio of 2.
5).Car drives at a constant speed of 58 mph.
Its a linear function representing an arithmetic sequence with a common difference of 58 mph.
6). Number of students increases by 122 every year.
An arithmetic sequence with a common difference of 122.
7). Number of pieces of chalk in a class room decreases by 10 throughout the school year.
It's an arithmetic sequence having common difference of 10.
Amount of cell phone users increase by 33% every year. Uranium loses half of its weight every 415 years. A family of rabbits doubles in size every 3 months. Then the correct options are A, C, and D.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r.
Then the sequence would look like
a, ar, ar², ar³,..... (till the terms to which it is defined)
Amount of cell phone users increase by 33% every year.
It's a geometric sequence because the number of users is increasing exponentially every year.
Uranium loses half of its weight every 415 years.
Exponential decay every 415 years. So geometric sequence with a common ratio of 1/2.
A family of rabbits doubles in size every 3 months.
Exponential series again so geometric sequence with a common ratio of 2.
Then the correct options are A, C, and D.
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Please help if you do not know the answer don’t comment in the answer box just for points
The box plots show the distributions of daily temperatures, in °F, for the month of January for two cities.
Which statements are true about the distributions? Check all that apply.
a. Both distributions are symmetric.
b. Both distributions are skewed right.
c. Both distributions are skewed left.
d. The mean and standard deviation would be the best measures to compare the data.
e. The median and IQR would be the best measures to compare the data.
Hey, the answers are
Both distributions are skewed right.
The median and IQR would be the best measures to compare the data.
That is B and E
Find two consecutive integers whose product is 24 more than three times the first integer
Let A = 40. If B is complement of A, and C is a supplmenet of B, what is B+C?
A. 60
B. 150
C. 180
D. 210
NEED HELP ASAP
What are the restrictions of:
(n^2 -6) / (n^2 -2)
5 and 2
+/- SQRT5 and +/- SQRT2
5 and -2
Four bars of soap cost $1.12. What would you pay for 2 dozen bars? (1 dozen=12)
Sandra got a 3/27 balloon mortgage and her initial payments were $945. She decided to refinance her balloon payment with a 30-year mortgage and her new payments were $937. What is the total financed cost she paid for her house?
Sandra got a 3/27 balloon mortgage and her initial payments were $945.
This means Sandra paid $945 per month for 3 years. Total payment made in 3 years = 945*3*12 = $34,020
Later, she decided to refinance her balloon payment with a 30-year mortgage. Her new payments were $937.
Payment made under mortgage = 937 * 30 * 12 = $337,320
The total financed cost she paid for her house = $34020 + $ 337320 = $371340
Hope this helps..!!
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Find the area of the triangle. Round the answer to the nearest tenth.
A.
7.8 square units
B.
8.9 square units
C.
19.3 square units
D.
38.5 square units
Answer:
19.3 square units .
Step-by-step explanation:
∠D=∠F=52°
Opposite sides of equal angles are equal .
So, DE=EF =6.3
Now sum of all angles of triangle is 180°
So, ∠D+∠F+∠E = 180°
52°+52°+∠E =180°
104°+∠E =180°
∠E =180°-104°
∠E =76°
Now to find the length of DF we will use law of cosines
[tex]c^2=a^2+b^2+2(a)(b) Cos E[/tex]
[tex]DF^2=DE^2+EF^2+2(DE)(EF) Cos E[/tex]
[tex]DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^{\circ}[/tex]
[tex]DF^2=79.38+79.38 (0.2419)[/tex]
[tex]DF^2=98.582[/tex]
[tex]DF=\sqrt{98.582}[/tex]
[tex]DF=9.9[/tex]
Now we are supposed to find the area of triangle
To calculate the area of given triangle we will use the heron's formula :
[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
a,b,c are the side lengths of triangle
Now substitute the values :
[tex]s = \frac{6.3+6.3+9.9}{2}[/tex]
[tex]s =11.25[/tex]
[tex]Area = \sqrt{11.25(11.25-6.3)(11.25-6.3)(11.25-9.9)}[/tex]
[tex]Area = 19.2907[/tex]
Hence the area of the triangle is 19.2907 ≈19.3 square units .
The circus is coming to town. Cindy is selling tickets. The first day she sold 8 adult tickets and 5 children tickets for a total of 177.50 in sales. The second day she received $255.00 for 12 adult tickets and 6 children tickets.
m ∠ U = (2x−5)° and m ∠W = (x+38)°What is m ∠W?
Question 1 options:
49°
180°
87°
90°
What is the value of y in the parallelogram below?
Answer:
The answer is the option B
[tex]23\°[/tex]
Step-by-step explanation:
we know that
In a parallelogram consecutive angles are supplementary
so
In this problem
[tex]5y\°+65\°=180\°[/tex]
Solve for y
[tex]5y\°=180\°-65\°[/tex]
[tex]y=115\°/5=23\°[/tex]
Answer:
23
Step-by-step explanation:
just took the test
What is the relation between the graphs of f(x)=x^2 and g(x)=x^2+6?
a.
the graph of g(x) is a translation of the graph of f(x) up 6 units
c.
the graph of g(x) is a translation of the graph of f(x) right 6 units
b.
the graph of g(x) is a translation of the graph of f(x) left 6 units
d.
the graph of g(x) is a translation of the graph of f(x) down 6 units
Answer:
I think it is the first one
Step-by-step explanation:
Please give brainliest
Triangle ABC is similar to triangle FGH. Angle A measures 42 degrees. Angle B measures 19 degrees. Find the measure of angle H.
42
19
119
29
Part 1.] Find the value of x in [tex]4,000( 1.5^{x})=25,000[/tex]. Show your work.
Part 2.] Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation. The grid marks represent one unit, the horizontal red line represents the x-axis, and the vertical red line represents the y-axis. [tex]y= log_{2} x[/tex]
The perimeter of an isosceles triangle is 14 cm. One of its sides is twice longer than another of its sides. Find all sides of the triangle.
Answer:
Step-by-step explanation:
2.8, 5.6, 5.6
(02.01 LC) Solve: negative 1 over 2 x + 3 = −x + 7 (5 points) 1 over 2 8 −8 2
Answer:
2 8 -8 2
Step-by-step explanation:
The correct answer is [tex]-\frac{1}{2}x + 3 = -x + 7$ is $x = 8[/tex].
To solve the equation [tex]-\frac{1}{2}x + 3 = -x + 7[/tex], we can follow these steps:
Step 1: Combine like terms on both sides of the equation.
[tex]-\frac{1}{2}x + 3 = -x + 7[/tex]
[tex]\frac{1}{2}x - 3 = x - 7[/tex]
Step 2: Subtract [tex]x[/tex] from both sides to isolate the terms with [tex]x[/tex].
[tex]\frac{1}{2}x - 3 - x = -7[/tex]
[tex]-\frac{1}{2}x - 3 = -7[/tex]
Step 3: Add 3 to both sides to isolate the term with [tex]x[/tex].
[tex]-\frac{1}{2}x = -4[/tex]
Step 4: Multiply both sides by [tex]-2[/tex] to solve for[tex]x[/tex].
[tex]-2 \left(-\frac{1}{2}x\right) = -2(-4)[/tex]
[tex]x = 8[/tex]
Therefore, the solution to the equation [tex]-\frac{1}{2}x + 3 = -x + 7$ is $x = 8[/tex]
Which graph shows a proportional relationship? help!!
Factor x2 – 3x – 28. Identify the values that should be written to complete the X diagram. On the top: On the bottom: On the sides: Rewrite the expression using the numbers on the sides of the X diagram. Use double grouping to factor the four terms. x2 – 3x – 28 =
-28
-3
-7 and 4
(x-7)(x+4)
Write two operations in order that you would use to solve the equation 3x - 2=7 then solve the equation
f(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4 what isf(x)-g(x)
John bought 6 dumplings for $3.00.
Let x represent the number of dumplings purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
1. J. Cole is a successful Hip-Hop recording artist. He has a record contract that pays him $20,000 a month plus an additional $12 for each album that he sells. Last month he earned $24,800. Write an equation to express the money J. Cole earned last month. Let "x" represent the number of albums.
2. How many albums did J. Cole sell last month?
Which example best represents balanced forces
The forces are equal and opposite, the book remains at rest, representing a state of balanced forces.
Balanced forces occur when the net force acting on an object is zero, meaning that the forces are equal in magnitude and opposite in direction. As a result, the object remains in a state of equilibrium and does not accelerate.
One example that best represents balanced forces is:
A book resting on a table.
When a book is placed on a table, it doesn't move because the force of gravity pulling it down (its weight) is balanced by the normal force exerted by the table, pushing the book upward.
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What is the area of this triangle A=bh2
You are working on a proof. You know that A and B are on the perpendicular bisector of CD. What can you conclude? A) AC = BD B) CB = AD C) AC = AD D) AB = CD
WILL GIVE BRAINLIEST ANSWER!!! PLEASE HELP!!! 12 POINTS!!!!!!!
The formula for the volume, V, of a right rectangular pyramid is one-third its base length, l, times its base width, w, times its height, h. Which of the equations below are equivalent to the formula described?
-----Note: more than one must be used-----
ANSWER OPTIONS:
* l = V over 3hw
* w = V over 3lh
* l = 3V over wh
* h = 3Vl over w
* w = 3V over lh
* h = V over 3lw
Jordan is 4 feet 8 inches tall, her mother is 5 ft 10 inches tall, how much taller is Jordan's mother than Jordan? Give your answer in feet and inches.
Serena paid $194.99 for a game system and then bought two equally-priced games. If she spent a total of $284.97, what is the price, p, of one game? Enter your answer in the box.
Serena bought two equally priced game at a price of $44.99 each and the total money spent in buying all three games is $284.97.
Given information:
The price Serena paid for buying the first game is $194.99
The overall price Serena paid for buying three games is $284.97
Let, the price of one of the two equally priced game is [tex]\bold{P}[/tex]
As, the price of second and third game is equal, we can consider the combined price of second and third game.
Thus , the equation formed according to the information given in the question is:
[tex]\bold{194.99+2P=284.97}[/tex]
Solve, the above equation in order to find the price of one game.
[tex]2P=284.97-194.99\\\2P=89.98}\\{P=44.99}[/tex]
Hence, the price of one game in two equally priced game is $44.99
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Melina has 4 sheets of wacky face sticker individually from the sheet. She then divides them evenly into 3 piles to give to friends. How many stickers are in each pile?
The answer explains how to divide 4 stickers into 3 piles, resulting in 1 sticker each.
To find out how many stickers are in each pile:
Count the total number of stickers = 4 sheets x 1 sticker per sheet = 4 stickers.Divide the total number of stickers evenly into 3 piles: 4 stickers ÷ 3 piles = 1 sticker in each pile.