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
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A large hose can fill 7/8 of a water tank in one hour. A small hose can fill 3/4 of a water tank in one hour. How much more of a water
tank can the large hose fill in one hour than the small hose?
can fill
Answer:
The large hose can fill 1/8 more of the tank in on hour than the small hose
Step-by-step explanation:
To understand this, we need to make 7/8 and 3/4 have the same denominator
3/4 and 6/8 are the same in decimal form (0.75)
So we change 3/4 to 6/8
So now we subtract what the small hose fills per hour from what the large hose fills per hour
7/8 - 6/8 = 1/8
So the large hose fills 1/8 more of the tank per hour than the small hose
Round 1.2 to the nearest whole number.
Answer:
1
Step-by-step explanation:
When rounding to the nearest whole number by looking at the tenth's value. Remember if it is 5 or more you would raise the number while if it is 4 or less you would round down. In your case you would round down.
0.5, 0.6, 0.7, 0.8, 0.9=1 if rounded to nearest whole number.
0.1, 0.2, 0.3, 0.4=0 if rounded to nearest whole number.
Hope this helps!
Please omg I need help ASAP please! (Giving brainliest)
Answer:
Step-by-step explanation:
a 4x/5-3=12
4x/5=15
4x=75
x=75/4
b u could have done times 5 first
4x-3=60
i don’t get these at alllll
Answer:
2
Step-by-step explanation:
Just think of f(2) as x, which is part of an ordered pair. Go to where x=2 on the graph, and search for y.
In this case, f(2)=2 because when x=2, y=2.
GHK is a straight angle.
Find LHK
Answer:
<LHK= 101
Step-by-step explanation:
straight lines are 180 degrees
to find LHK take LHG and subtract it from 180
180-79=101
The diameter is 24 cm. Find the length of arc CD.
Answer:
4pi or 12.56637061
Step-by-step explanation:
Answer: 12.57
Step-by-step explanation:
This is if it asks for the nearest hundredth
What is the area of the parallelogram?
A
square units
Answer:
24 square units
Step-by-step explanation:
I googl.ed it
Answer:
24 sq. units
Step-by-step explanation:
The Intuition for why the area of a parallelogram is A=bh (area = base x height)
The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.
Have a great day!
Gabe drew a scale drawing of his media room using a scale in which 1 inch represents 4 feet. The dimensions of the scale drawing are 4 inches by 6 inches. What is the area of Gabe's actual basement?
24 ft?
80 ft2
384 ft2
168 ft2
HELP ASAP
Answer:
C. 384 ft2
Step-by-step explanation: Hope this helps (:
Which ordered pairs are solutions to the equation 4x+2y=4?
Select the correct answer below:
(2,−6)
(1,5)
(−5,5)
(5,3)
none of the above
Evaluate this expression
mn^2
(btw m=2 and n=3)
Answer:
529
Step-by-step explanation:
f(x)=3x+2 what is the rate of change
Answer:
3
Step-by-step explanation:
What is the c-value for the data point that represents the outlier in the scatter plot?
0 195
0 190
0 170
0 160
At this weekend's football game, 15 out of the first 50 people who enter the field were not wearing hats. If this sample is representative of 250 people attending the game, about how many of them will probably not be wearing hats?
A. 65 people
B. 70 people
C. 75 people
D. 80 people
Answer:
the answer is C. 75 people
Step-by-step explanation:
hope this healped
[tex] \sqrt{49} [/tex]
find the square root
[tex]\sqrt{49} =\sqrt{7^2} =7[/tex]
Hope I helped you!Succes!Answer:
7
Step-by-step explanation:
[tex] \sqrt{49} [/tex]
[tex] \sqrt{ {7}^{2} } [/tex]
[tex](7 \times 7) = 49[/tex]
[tex] = 7[/tex]
Please help .... what is the answer ??
Answer:
The Correct Answer Is C
What is 3/4 - 1/3 in fraction form?
Answer:
5/12
Step-by-step explanation:
The required fraction form of the expression 3 / 4 - 1 / 3 is 5 / 12
The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
What is the fraction?Fraction is defined as the number of compositions that constitute the Whole. Fraction Is represented as x = a / b where a is the numerator and b is the denominator.
Question asked to write the given expression3/4 - 1/3 in fraction form
Let the required fraction be x,
x = 3 / 4 - 1 / 3
x = ( 9 - 4 ) / 15
x = 5 / 12
Thus , The required fraction form of the expression 3 / 4 - 1 / 3 is 5 / 12.
Learn more about fractions here: https://brainly.com/question/10708469
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convert 9 1/9 into a improper fraction
Answer:
82/9
Step-by-step explanation:
The improper fraction is 82/9.
What is improper fraction?An improper fraction is a type of fraction where the numerator is greater than or equal to the denominator. For example, 5/2 and 8/5, are improper fractions. Every fraction has two parts, numerator, and denominator. In mathematics, there are two main types of fractions based on the values of numerator and denominator, and those are proper fractions and improper fractions.
A fraction whose numerator is greater than or larger than the denominator is defined as an improper fraction such as 7/3 and 12/5.
Given fraction:
9 1/9
Now, converting into improper fraction
Numerator = 9 x 9 + 1
=81 + 1
= 82
and, Denominator = 9
So, the improper fraction is 82/9.
Learn more about improper fraction here:
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What is the common ratio of the sequence?
-2, 6, -18, 54,...
-3
-2
3
8
I think the ratio of the series is 3
Answer:
ITS THREEEEEEEEEEEEEEEEEEe
Step-by-step explanation:
Please Help:
Translate the sentence into an inequality.
Two subtracted from y is at most -22.
Answer:
[tex]y-2\geq -22[/tex]
Step-by-step explanation:
In the diagram find the value of x
Answer:
x= 5
Step-by-step explanation:
Graph the inequality.
y > -5x + 2
Answer:
The graph is in the screenshot.
Step-by-step explanation:
Carson's bill for dinner at a restaurant was $48. He left a 15% tip. What was the total cost of his dinner, including tip?
Answer: $55.20
Step-by-step explanation:
If $48 = 100%, 15% + bill cost = 115%
115% = 1.15
Multiply 48 × 1.15 = $55.20
Note- It would mean the world to me if you could mark me as brainliest!
Answer:
$55.20
Step-by-step explanation:
48+%15=55.20 based on how much you're bill os affects how much the tip is worth
The equation f(x)= -(x-4)2+3
need help ASAP!!!
Answer:
b. the graph has a maximum
d. the vertex is (4,3)
What is the solution for t in the equation?
3+ - + = 2
A. t=6
B. t = 30/7
C. t= 7/30
D. t = 2/3
Answer:
A
Step-by-step explanation:
Can you help me and explain how to do it? please
Answer:
125.6cm
Step-by-step explanation:
circumference of a circle is 2pir
pi=3.14
r=d/2=40cm/2=20cm
So, 2pir=2X20cmX3.14=40cmX3.14=31.4cmX4=125.6cm
PLEASE MAAKE THIS THE BRAINLIEST ANSWER
Using only an addition, how do you add eight 8’s and get the number 1000?
Answer:
5000000000000000000000
Step-by-step explanation:
Which expression is a factor of 16x^2-81
I will mark brainliest
A: 8x-9
B: 4x-9
C:8x-81
D: 4x-81
Answer:
b
Step-by-step explanation:
Reasoning: the square root of 16 is 4 and 81 square root is 9
so it is b pls give brainliest! have a good day
Write the slope-intercept form of the equation of the line.
Answer:
Your answer is
equation y=-4x+4
Hope that this is helpful. Tap the crown button, Like & Follow me
please help me with this question!
Answer:
It is perpendicular
Step-by-step explanation:
the admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, $5,050 is collected. If 1,000 adults attended the fair, write and solve a linear equation to find the number of children that attended.
IN STANDARD FORM
Answer:
4x + 1.5y = 5,050 then replace x with 1000 then solve for y. which equals 700
so that day there were 700 children
Step-by-step explanation:
pls mark brainliest