Which of the following is a divisor of 12! · 6! + 12! + 6! + 1?

A. 21
B. 77
C. 91
D. 115
E. 143

Hint : Use Wilson's Theorem[tex].[/tex]​

Answers

Answer 1

Answer:

C. 91

Step-by-step explanation:

Rewriting the given as factors:

12! · 6! + 12! + 6! + 1 =12!(6! + 1) + (6! + 1) =(12! + 1)(6! + 1) =((13 - 1)! + 1)((7 - 1)! + 1)

As per Wilson's theorem, if n is prime number, (n - 1)! + 1 is divisible by n

As per above, 13 and 7 are both prime numbers, so the expression is divisible by both 7 and 13:

7*13 = 91

So correct choice is C


Related Questions

Tina is going for a bike ride. When she leaves her house, she starts pedaling and her speed steadily increases. As she approaches the stop sign at the end of her street, she slows down at a steady pace until she comes to a complete stop. After waiting at the stop sign for her turn to go, she starts pedaling again and her speed steadily increases at a slower pace than when she first left her house. She reaches a comfortable speed and rides at this speed until she approaches another stop sign, causing her to steadily slow down until she again comes to a complete stop.

Answers

Answer:

1

Step-by-step explanation:

1212112

Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.
Who is correct and why? Use the drop-down menus to explain your answer.

Answers

Answer:

Yes, hannah is correct.

Yes yo uoui is yo you know what

If a 6-in wide by 12-in long photo is enlarged to 200% of its size, what are the new dimensions?

Answers

Answer:

Step-by-step explanation:

the new dimensions will be 12 in by 24

HW HELP ASAPPP
+10PTS

Answers

Answer:

bruce

y = 1/4 x

Step-by-step explanation:

9 tiles per sq ft for felicia

so 1/9 sq ft per tile

so bruce covers more

1/9 square pile smiiiue keowieiehbe

Simplify.
3y - 4x + 6x - y
The simplified expression is???

Answers

Answer:

2y-4x+6x

=2y+2x

Step-by-step explanation:

Answer:

2x+2y

Step-by-step explanation:

Let's simplify step-by-step.

3y−4x+6x−y

=3y+−4x+6x+−y

Combine Like Terms:

=3y+−4x+6x+−y

=(−4x+6x)+(3y+−y)

=2x+2y

Help me with this!

Select all the relations that represent a function.
(1, 3), (2, 5), (2, 7) (4, 9)
(1, 3), (2, 5), (3, 7) (4, 9)
(1, 3), (1, 5), (1, 7) (4, 9)
(1, 3), (2, 3), (3, 3) (4, 3)
(1, 2), (2, 5), (2, 1) (4, 5)

Answers

Answer:
Relation #2 and #4

2h+y/9h^2-y^2 - 4h^2/3h+y what is the least common denominator in this expression

Answers

Answer: It is 9

Step-by-step explanation:

(4x5)to the power of 2-6+3=​

Answers

Answer:

if i understood right..

Step-by-step explanation:

... 2-6+3= 1

4×5= 20

1×20=20

the answer is 20.

I'm sorry if i understood the wrong thing.

397 i think! hope this is correct!

2. Which equation is true when x=3?
A. 8x = 28
B. X - 19 = 16
C. 28 + x = 25
D. S =1

Answers

the correct answer is c

Answer:c

Step-by-step explanation:

Which equation produces the values in the table?
O y= 4x
O y=4+x
O y=1/4x
Oy=4 - x

Answers

Answer:

Step-by-step explanation: It’s C thank me later

The equation produces the values in the table is y = x/4

What is an equation?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

For example, 2x – 5 = 13.

Given is table (attached) we need to determine an equation that produces the values in the table,

So, seeing the value it is much that the value of x are the 4 times of the values of y,

So, we can write,

4y = x

or, y = x/4

Hence, the equation produces the values in the table is y = x/4

Learn more about equation, click;

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graph each function (equation) by making a table y = |2x| + 1

please help​

Answers

Answer:

the table:

x | y

-2 | 5

-1 | 3

0 |  1

1  | 3

2 | 5

for the graph: go up from the middle point, then right then up by two and repeat on the other side as well, should look something like this

( up one, go left, up 2)  ∨  (up one, go right up two)

                         

How to Rewrite the expression 4(13-10) using distributive property of multiplication over subtraction

Answers

Answer:

52-40

Step-by-step explanation:

distribute 4 to 13 and 10

put the subtraction sign back in

will give brailest Solve the following equation to find the value of r?

r/8.5=16

Answers

Answer:

R=296

Step-by-step explanation:

Multiplication is the opposite of division so you want to multiply both your given numbers.

Hope this helped  

Here is the answer written out. Hopefully this helped

What is the area of this figure?
Enter your answer in the box
Bin
in

Answers

88 in.

Add them together

Find the missing angle.
65°
60°
X=

Answers

Answer:

125

Step-by-step explanation:

sum of 60 and 65 will give you x

Answer:

125

Step-by-step explanation:

65+60=125

Factorise (3m -2n)^2 +5p(3m - 2n)​

Answers

Answer: if you factor it you will get this-->(3m−2n)(3m−2n+5p)

Step-by-step explanation:

help pls ASAP brain list to first and correct​

Answers

Answer:

x = -3/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

2x + 1 = -2

Step 2: Solve for x

Subtract 1 on both sides:                    2x = -3Divide 2 on both sides:                       x = -3/2
answer:

it’s -1.5

explanation:

2x+1=-2
-1 -1
2x = -3
-3/2= -1.5

3 Drag the tiles to the boxes to form correct pairs. Match the expressions with the property used to generate 5y + 2y+ 6+2. Distributive Property 6y - y + 2y + 10 - 4 + 2 5y + 2(y + 3) + 2 combining like terms 5y + 2 + 6 + 2y Commutative Property € cared​

Answers

Answer:

Distributive Property = 5y+2(y+3)+2

combining like terms = 5y+2+6+2y

Commutative Property = 6y-y+2y+10-4+2

Step-by-step explanation:

The correct matching of the properties will be:

Distributive Property = 5y+2(y+3)+2

combining like terms = 5y+2+6+2y

Commutative Property = 6y-y+2y+10-4+2

Original expression: 5y + 2(y + 3) + 2

How to match the value

Apply the distributive property by multiplying 2 to the terms inside the parentheses:

5y + 2y + 6 + 2

Combine like terms:

(5y + 2y) + (6 + 2)

7y + 8

Rearrange the terms using the commutative property:

(7y + 2y) + (6 + 2)

9y + 8 + 8

Simplifying further, we have:

9y + 16

Therefore, the simplified expression is 9y + 16.

Learn more about distributive property

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Gary sold 8 more tickets than Peter. Tracy sold 12 less than Peter. They sold 50
tickets in total. How many tickets did Gary sell?

Answers

Answer:

96 tickets

Step-by-step explanation:

Given the expression 1/4 - 3/5, select the addition problem that is equivalent to it.

Answers

-7/20
The answer and I will explain in the comment

Consider the function given by the graph. What are
these values?
f-2)=
fo) =
f4) =

Answers

The function f(x) for the input values are f(-2) = 2, f(0) = 3 and f(4) = -1

How to evaluate the piecewise function f(x) for the input values

From the question, we have the following parameters that can be used in our computation:

The graph of a function and a set of input values

The input values are given as

–2, 0, and 4

Next, we read the above input values from the graph

Using the above as a guide, we have the following:

f(-2) = 2

f(0) = 3

f(4) = -1

Hence, the values are f(-2) = 2, f(0) = 3 and f(4) = -1

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write the ration in following three ways
12 mangoes to 36 fruits​

Answers

12/36, 12:36, and 1:3 I believe hope this helps

1: The temperature is -2

​∘C

. If the temperature rises by 15

​∘C

, what is the new temperature? (Draw a number line to help)- The temperature is -2 c. If the temperature rises by 15 c, what is the new temperature? Answer {You would do 15c takeaway -2c This would equal to the new temperature as being 13c.}






2: At midnight the temperature is - 6

​∘C

. At midday the temperature is 9

​∘C

. By how much did the temperature rise? (Draw a number line to help)- 15° Celcius {You can add from -6 +1 till you get to 0 then add the rest of the numbers and it will exactly be 15.}






3:Draw a number line to help you with what the final temperature is.

Then write an addition expression that represents the final temperature.

(Hint: Start temp + movement amount = final temperature )


The temperature was and then fell .


__________ + _________ = __________




The temperature was and then rose .


__________ + __________ = __________




The temperature was and then fell .


__________ + __________ = __________



THIS HELP WITH THE LAST QUESTION THIS WILL MEAN ALOT :( FILL IN THE BLANKS!!!

Answers

Answer:

For 1. it's 13 degrees 2. For B it is 15 degrees.

Step-by-step explanation:

thats all i could really answer you should try separating this a little more

Consider a sample with data values of 27, 24, 19, 14, 30, 35, 28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles.

Answers

Answer:

20th percentile = 19

25th percentile = 21.5

65th percentile = 28

75th percentile = 30

Step by Step Explanation:

Computation for the 20th, 25th, 65th, and 75th percentiles

First step is to arrange sample with data values of 27, 24, 19, 14, 30, 35, 28, and 24 in Ascending order

Ascending order of given data

14,19,24,24,27,28,30,35

Now let Compute for the 20th, 25th, 65th, and 75th percentiles

Using this formula

I=P/100*n

Where,

n =8 given data values

Let plug in the formula

1. 20th PERCENTILE

20th PERCENTILE = (20/100) * 8

20th PERCENTILE= 1.6

20th PERCENTILE = 2 (rounded up to the nearest integer)

The 20th percentile is the 2th value in the given date that was arranged in ascending order which is 19

Therefore the 20th percentile is 19.

2. 25th PERCENTILE

25th PERCENTILE = (25/100) * 8

25th PERCENTILE= 2

To get the 25th percentile of 2 we would take the average of 2nd and 3rd value

25th PERCENTILE = (19 + 24)/2

25th PERCENTILE=43/2

25th PERCENTILE= 21.5

Therefore the 25th percentile is 21.5

3. 65th PERCENTILE

65th PERCENTILE = (65/100) * 8

65th PERCENTILE= 5.2

65th PERCENTILE= 6 (rounded up to the nearest integer)

The 65th PERCENTILE is the 6th value which is 28

Therefore 65th percentile is 28

4. 75th PERCENTILE

75th PERCENTILE = (75/100) * 8

75th PERCENTILE = 6

To get the 75th PERCENTILE of 6 we would take the average of 6th and 7th value

75th PERCENTILE = (28+30) / 2

75th PERCENTILE =58/2

75th PERCENTILE = 29

Therefore the 75th percentile is 30

Therefore the 20th, 25th, 65th, and 75th percentiles are:

20th percentile = 19

25th percentile = 21.5

65th percentile = 28

75th percentile = 30

How to explain the question?
[tex]y = 2( { \frac{5}{4} )}^{2} - 5( \frac{5}{4} ) - 3[/tex]

Answers

Answer:

[tex]32[/tex]

[tex]i \: hope \: it \: helps \: mate \\ enjoy \: your \: day \\ \gamma captainpower[/tex]

Need help please!!! it’s important

Answers

Answer:

4/D a reflection fallowed by a rotation.

sorry if I am wrong

RSTUV - EABCD. Find AE.
T
8
C
U
6
4
S
B
D
6
v
4
A
R
m
AE =

Answers

9514 1404 393

Answer:

  AE = 3

Step-by-step explanation:

First of all, we need to find corresponding sides that are defined in both figures. The table below shows the given values.

From the table, we can write the proportion ...

  EA/RS = BC/TU . . . corresponding sides are proportional

  EA/6 = 4/8 . . . . . . . substitute given lengths

  EA = 6(4/8) = 3

The length of AE is 3 units.

Pls help
(Pls just give answers, I’m really tired ok )

Answers

Answer:

See attached

Step-by-step explanation:

The answers are in the picture below

Answer:

1) 11-y= -9

2)41+w= 26

3)r/6= 4

4)18×p= 54

5)v/-4= 13=>v= -54; yes

6)108= -36z=>z= 108/(-36)=>z= -3; yes

7)27=n-16=>n=27+16=>n=43;not a solution

8)84=78+t=>t= 84-78=>t= 6; not a solution

9)a/2=36------------B. What number divided by 2 equals 36?

10)2a=36------------C. 2 times what number equals 36?

11)2+a=36-----------D. 2 plus what number equals 36?

12)a-36=2-----------A. What number minus 36 equals 2?

who want's to do my homework? :D Also this might get deleted cause brainly is out to get me D:
Simplify the following rational expression. Use absolute value symbols when needed.

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1. [tex]\sqrt[3]{\frac{8}{216} }[/tex]

2. [tex]\sqrt[3]{\frac{1}{27} }[/tex]

3. [tex](\frac{1}{27})^{\frac{1}{3} }[/tex]

3. Since [tex](\frac{1}{3}^{3})[/tex] is [tex]\frac{1}{27}[/tex], the answer should be [tex]\frac{1}{3}[/tex].

PLEASE HELP: A rectangular prism has a height of 15 centimeters. The base of the prism has an area of 22 square centimeters.


What is the volume of the prism

Answers

Answer:

330

Step-by-step explanation:

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