Given:
The word is "CALCULATOR."
To find:
The number of distinct permutations.
Solution:
In the word "CALCULATOR",
The number of letters = 10
In which, we have 2 C, A, L and 1 U, T, O, R.
We know that,
[tex]^nC_r=\dfrac{n!}{(n-r)!}[/tex]
[tex]^nC_n=\dfrac{n!}{(n-n)!}=n![/tex]
To find the number of distinct permutations of the given word need to divide permutation of all letter by the permutations of repeated letters.
[tex]\text{Total ways}=\dfrac{^{10}C_{10}}{^2C_2\ ^2C_2\ ^2C_2\ ^1C_1\ ^1C_1\ ^1C_1\ ^1C_1}[/tex]
[tex]\text{Total ways}=\dfrac{10!}{2!2!2!1!1!1!1!}[/tex]
[tex]\text{Total ways}=\dfrac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2\times 2\times 2\times 1\times 1\times 1\times 1}[/tex]
[tex]\text{Total ways}=453600[/tex]
Therefore, the number of distinct permutations of the word "CALCULATOR" is 453600.
Number of distinct permutation of the word "CALCULATOR." is 453600
How to solve this problem?
permutations of the word "CALCULATOR"Total number of words in "CALCULATOR" is 10
we find out the words that are repeating
A is repeating twice (2)
C is repeating twice (2)
L is repeating twice (2)
Number of permutations = number of letters !/ repeating letters!
Number of distinct permutation =
[tex]\frac{10!}{2!2!2!} \\\frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot2\cdot2} \\453600[/tex]
Number of distinct permutation of the word "CALCULATOR." is 453600
learn more about the distinct permutations here:
https://brainly.com/question/21767354
in a class full of men and women, 4/7 of the class are women. What is the ratio of men to women in it's smplest form?
Answer:
3/4 is the ratio of men to women in the simplest form.
Find In(-112.7)
a. iπ + 4.7247
b. iπ + 6.7247
c. iπ + 5.7247
d. iπ - 7.7247
Answer:
a
Step-by-step explanation:
edge 2021
Find the height of a triangle whose base is 5 inches and area is 12 square inches.
Answer:
Therefore, Height = 4.8 inches.
Step-by-step explanation:
Given : A triangle whose base is 5 inches and area is 12 square inches.
To find : Find the height of a triangle.
Solution : we have given
Triangle base = 5 inches.
Area = 12 square in.
We need to find height of the triangle.
Area = * base * height .
Plugging the values .
12 = * 5 * height .
On multiplying both sides by 2
24 = 5 * height .
On dividing both sides by 5.
Height = 4.8 inches.
Therefore, Height = 4.8 inches.
need help please thxs
Answer:
C.
Step-by-step explanation:
40*(1/4)^0=40
40*(1/4)^1=10
And so on...
Answer:
Step-by-step explanation:
This is a geometric sequence of the form [tex]F=Ir^t\text{ where I=initial value, r=common ratio, and t=number of terms or time. Notice each term is 1/4 of the preceding term. This is the common ratio. So your equation is }f(x)=40\left(\frac{1}{4}\right)^x[/tex]
\begin{aligned} &-x+4y=-9 \\\\ &y=-2x +6 \end{aligned} −x+4y=−9 y=−2x+6 Is (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis a solution of the system?
Answer:
NO
Step-by-step explanation:
Given the system of equation
-x+4y = -9,... 1
y = -2x+6.... 2
To find the solution to the equation
Substitute equation 2 into 1
-x+4(-2x+6) = -9
-x-8x+24 = -9
-9x= -9-24
-9x = -33
x = 33/9
Find y
y = -2x+6
y = -2(33/9)+6
y = -66/9 + 6
y = -66+54/9
y = -12/9
y = -4/3
Hence (2,3) is not the solution to the system of equation
Solving 1 step math equations:
[tex] - 2.5 + w = 3.7[/tex]
Pls help me lol
A machine stamps 3600 metal parts in 12
minutes. Find the unit rate in parts per minute.
Answer:
300
Step-by-step explanation:
you have to find the matal parts for minute. To do this you can do:
3600/12=300
That's your answer
I need help with this equation.
do u know 64/12 as a mixed number.in its simplest form.
5 1/3 is 64/12 in it's simplest form as a mixed number.
Hope it helps you out! Good luck. :)
Answer:
16/3
That's the answer.
Quadrilateral ABCD is a rectangle. BD = 6x – 14 and AC = 8x - 20.
What is BD?
2
3
4
6
Answer 4
Step-by-step explanation:
Answer:
it is c.4
Step-by-step explanation:
He math team does practice drills that each last hour. In February the team did practice drills for a total of 24 hours. How many practice drills did the math team do in feburary
Answer: 24 drills
Step-by-step explanation:
The math team in question does math drills that last for an hour each time.
In February, a total of 24 hours were used to practice drills.
If the team takes an hour to do one drill, the drills that will be done in 24 hours are:
= Number of hours / Drills per hour
= 24 / 1
= 24 drills
I NEED TO PASS!!
Use the information to answer the following question.
A rectangular garden has a length that is 3 feet longer than its width. Let w represent the width of the garden in feet. The entire garden is surrounded by a 2-foot-wide cement walkway.
What does the algebraic expression (w + 4)(w + 7) represent in this context?
A. the perimeter of the walkway only
B. the area of the garden only
C. the perimeter of the garden only
D. the total area of the garden and walkway
Answer:
D. the total area of the garden and walkwayStep-by-step explanation:
Sides of the rectangular garden:
w and w + 3Add the width of the walkway, 2 feet from both sides, the total of 4 feet:
w + 4 and w + 7The product of the above is the area of the garden and the walkway
Correct option is D
Answer:
D. the total area of the garden and walkway
Step-by-step explanation:
Sides of the rectangular garden:
w and w + 3
Add the width of the walkway, 2 feet from both sides, the total of 4 feet:
w + 4 and w + 7
The product of the above is the area of the garden and the walkway
Correct option is D
Hope this helps!
Write an equation that represents the line.
Answer:
COORDANITE GRID
Step-by-step explanation:
Tell me yes or no and explain why
Answer:
yes because this number is an even
Step-by-step explanation:
Answer: yes
Step-by-step explanation:
Hiiioo please help me
Question: how do you find the sum of the interior angles? (*Hint* it’s a formula!)
Answer:
The sum of all of the interior angles can be found using the formula S = (n - 2)*180.
Mathematics 10 points and brainliest.
Answer:
41
Step-by-step explanation:
8 x 7 - 5 ([tex]3^{2}[/tex] - 6)
= 8 x 7 - 5 ( 9 - 6 )
= 8 x 7 - 5 x 3
= 56 - 15
= 41
Answer:
41
Step-by-step explanation:
Use PEMDAS.
3^2 = 9
9 - 6 = 3
3 × 5 = 15
8 × 7 = 56
56 - 15 = 41
what is the value of c?
Answer:
The value of C is 3
Step-by-step explanation:
all of the angles of a triangle add up to 180°. first you would add 92 and 46 and get 138. You then subtract 180 and 138 and get 42. then you divide 42 by 14 and get 3. then substitute 3 back into the equation and you get 180.
ill mark brainlist plss help
Answer:
The second option
Step-by-step explanation:
You just do 19.50/3 to get 6.50
$6.50 per shirt.
Solution
Since three shirts cost $19.50
1 would be $19.50÷3= 6.50
answer for brainliest
Answer:
i believe JL=12
Step-by-step explanation:
Answer:
JL=12
Done
_________________
Tom made fruit punch for a party. He mixed 2 gallons of orange juice, 4 quarts of pineapple juice, 3 pints of cranberry juice, and 8 cups of apple juice. How many quarts did he make in all?
What is the slope of the line below?
Answer:
3
Step-by-step explanation:
Step-by-step explanation:
❀ [tex] \underline{ \underline{ \text{Given \: points}}} : [/tex]
A ( 3 , 0 ) & B ( -3 , 3 )Let the point A ( 3 , 0 ) be ( x₁ , y₁ ) & B ( -3 , 3 ) be ( x₂ , y₂ ).
❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Slope of the line✄ [tex] \boxed{ \boxed{ \sf{slope = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}}}} [/tex]
~Plug all the known values and then simplify !
⟶ [tex] \tt{ \frac{3 - 0}{ - 3 - 3}} [/tex]
⟶ [tex] \tt{ \frac{3}{ - 6}} [/tex]
⟶ [tex] \tt{ - \frac{1}{2}} [/tex]
[tex] \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \underline{ \underline{ \tt{ - \frac{1}{2}}}}}}}} [/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Solve for n. 4n= 30 please
Billy had 5 gallons of paint. Bob had 4 kilograms of paint. How do you make the paint amount equal?
Answer:
We can make the paint amount equal by making sure the parameters have the same unit
Step-by-step explanation:
Billy had 5 gallons of paint. Bob had 4 kilograms of paint. How do you make the paint amount equal?
To solve the above question, we have the conversion rate:
We can make the paint amount equal by making sure the parameters have the same unit
Hence:
1 gallon (gal) = 3.785411784 kilogram (kg).
Billy had 5 gallons of paint.
1 gallon (gal) = 3.785411784 kilogram (kg).
5 gallons of paint = x
Cross Multiply
x = 5 × 3.785411784 kg
18.92705892 kilograms of paint
Approximately 18.93 Kilograms of paint
Therefore, Billy had 18.93 kg of paint and Bob had 4 kg of paint
hi guy's :) :) :)
solve this
goog luck
[tex]9 + 9 + 9 + 9 + 9 - 9 - 9 - 9 - 9[/tex]
9
hope this helps jdhfhd
Answer:
I got 9
Step-by-step explanation:
Hope this can help with your question!
A restaurant charges a standard price for a plain cheese pizza, plus
an extra charge for each topping. The cost of a pizza can be
determined by the function C(t) = 0.50 + 5, where t is the number of
toppings and C() is the cost of the pizza.
3
If (t) $7.50, how many toppings were ordered
Answer:
5
Step-by-step explanation:
Solve this triangle round to the nearest tenth where necessary
Answer:
J =51
Step-by-step explanation:
Your welcome! Have a great day!
There were some pizzas in the library. 13 pizzas were eaten by zombies. There are now 20 pizzas in the library. Which equation can be used to find p, the number of pizzas that were in the library?
Answer:
p - 13 = 20
Step-by-step explanation:
p - 13 = 20
add 13 on both sides
p = 33
there were 33 pizzas in the library.
Answer:
p=13+20? or addition
Step-by-step explanation:its inverse operation i think that's what its called so use addition
I just need help with these 2 questions !
Answer:
-4/3
9/4
Step-by-step explanation:
hope this helped needed a longer answer lol
rearrange the following linear equation into y=mx+b form and identify the slope and the y intercept 2y=2x+6
Answer:
Step-by-step explanation:
we need the equation to be like y=mx+b so we have to simplify our equation
2y=2x+6
divide everything by 2
so it’s y=x+3 and that’s ur answer
What is the area of "triangle " XYZ to the nearest tenth of a square inch? Use special right triangles to help find the height. Show your work.
Answer:
That is a 30 60 90 triangle.
In such a triangle the "middle" size = short side * sq root (3)
height = 5 * sq root (3) = 8.6602540378
Area = (1/2) * 5 * 8.6602540378
Area = 2.5 * 8.6602540378
Area = 21.6506350946 square centimeters
Step-by-step explanation:
Answer:
A=24√3
Put In Decimal Form:41.5692193817^3
Step-by-step explanation:
4 Inches on short side, this means that the long side is 8 inches because the short side is always 1/2 the length of the long side, The medium side length is 4√3. So you need to take the short side and medium side and multiply them by 1/2, look below for how to do it.
A=1/2(4)(4√3)
2(12√3)
24√3