Permutations of the word "Congratulations"

Mathematics

1 answer:

Mice21 [21]3 years ago

5 0

Answer:

There are 15 letters, but if the two A's must always be together, that's the same as if they're just one letter, so our "base count" is 14! ; note that this way of counting means that we also don't need to worry about compensating for "double counting" identical permutations due to transposition of those A's, because we don't "count" both transpositions. However, that counting does "double count" equivalent permutations due to having two O's, two N's, and two T's, so we do need to compensate for that. Therefore the final answer is 14!/(23)=10,897,286,400

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Can you help me with this it’s so confusing plz help me with both is this

mars1129 [50]

Answer:

First picture: -4,913

Second picture: 20.25

Step-by-step explanation:

-17^5/-17^2 = -17^3

-17 × -17 × -17 = -4913

4.5^5/4.5^3 = 4.5^2

4.5 × 4.5 = 20.25

Do you see how I had the same whole number on the top and bottom? (17 was on top and 17 was on bottom)

The exponents were those tiny numbers you saw.

Whenever you are dividing by the same whole number (-17/-17), you can subtract exponents.

When you multiply the same whole number, you can add the exponents.

Hope this helps! Best of luck :)

5 0

3 years ago

X + 3/ 5 = 2 -5 -3 7 13

ahrayia [7]

X 3/5 =2x+15=2x=15-2x=13

answer 13

4 0

3 years ago

Do this for me pls its mdths

Vadim26 [7]

Answer:

A = -1

B = -3

C = -7

Step-by-step explanation:

See attached image.

5 0

2 years ago

The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2

djverab [1.8K]

The correct answer is: [D]: "17" .
______________________________________________________
The radius is: " 17" .
______________________________________________________
Note:
______________________________________________________
The formula/equation for the graph of a circle is:
______________________________________________________
(x − h)² + (y − k)² = r² ;

in which:

" (h, k) " ; are the coordinate of the point of the center of the circle;

"r" is the length of the "radius" ; for which we want to determine;
_______________________________________________________
We are given the following equation of the graph of a particular circle:
_______________________________________________________

→ (x − 4)² + (y + 12)² = 17² ;

which is in the correct form:

→ " (x − h)² + (y − k)² = r² " ;

in which: " h = 4 " ;

" k = -12" ;

"r = 17 " ; which is the "radius" ; which is our answer.

→ { Note that: "k = NEGATIVE 12" } ;

→ Since the equation for this particular circle contains the expression: _________________________________________________________
→ "...(y + k)² ..." ;

[as opposed to the standard form: "...(y − k)² ..." ] ;
_________________________________________________________
→ And since the coordinates of the center of a circle are represented by:
" (h, k) " ;

→ which are: " (4, -12) " ; (for this particular circle) ;
_________________________________________________________
→ And since: " k = -12 " ; (for this particular circle) ;
_________________________________________________________
then:

" [y − k ] ² = [ y − (k) ] ² = " [ y − (-12) ] ² " ;

= " ( y + 12)² " ;

{NOTE: Since: "subtracting a negative" is the same as "adding a positive" ;

→ So; " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
___________________________________________________
Note: The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the: radius, "r" ; is: "17" .
___________________________________________________
→ Since: "r = 17 " ;

→ The radius is: " 17 " ;

which is: Answer choice: [D]: "17" .
___________________________________________________

8 0

3 years ago

Read 2 more answers

What is the inverse of this function? f(x)=-1/2 square root of x+3, x > -3

yuradex [85]

The inverse function of $f(x) = -\frac 12\sqrt{x + 3}$ is $f^{-1}(x) = 4x^2- 3$