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

Which statement about histograms is true?
Data is organized in categories.
Data appears as bars that are all about the same height.
Data is organized in equal intervals.
Data appears as bars that do not touch.

Answers

Answer:

C

Step-by-step explanation:

CCCCCCCCCCCCCCCCCCCCCCCCC

Answer:Data is organized in equal intervals.

Step-by-step explanation:

The choices are =,>,< and greater than or equal to

Answers

Answer:

We conclude that

[tex]4\frac{2}{3}[/tex]    >   [tex]\sqrt{21}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{21}[/tex][tex]4\frac{2}{3}[/tex]

as

[tex]\:\sqrt{21}=4.58[/tex]

and

[tex]4\frac{2}{3}[/tex]

Convert mixed numbers to improper fraction:

[tex]a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]

so

[tex]4\frac{2}{3}=\frac{4\cdot 3+2}{3}=\frac{14}{3}=4.67[/tex]

Thus,

[tex]\:\sqrt{21}=4.58[/tex]

[tex]4\frac{2}{3}=4.67[/tex]

as

4.67      >       4.58

so

[tex]4\frac{2}{3}[/tex]         >        [tex]\sqrt{21}[/tex]

Hence, we conclude that

[tex]4\frac{2}{3}[/tex]    >   [tex]\sqrt{21}[/tex]

helppppp please I'm stuck​

Answers

the correct answer would be 2 because that’s what it leads to. i did it for a few days but i didn’t have any of them to go to the

Answer:

10/5= 2

I hope this helps:

In Progress
What is an equation in slope-intercept form of the line that passes through the points (-2,-2) and (1,7)?
A.
y
C-
B. y = 3.0 +4
=
+
olos
O D. = 3.c – 2

Answers

Answer: y= D.3x-2

Step-by-step explanation:

The answer is “B. y = 3x + 4”

Explanation:

To find the slope of two points, we need to use the formula m=rise/run or m=y2-y1/x2-x1

-2-7 -9
m = ——— = — = 3
-2-1 -3

Now we have to find “b” as in the equation “y=mx+b”

We already have our “m” which is the slope and that is equal to 3

In order to fine “b,” we have to set it up in point slope form which is the formula
“y-y1 = m(x-x1)”

You can choose to set this up with either one of the coordinates given

In this problem, the coordinates given are
(-2, -2) and (1, 7)

I’m going to use the coordinates (1, 7)

y-y1 = m(x-x1)
y-7 = 3(x-1)

The “7” is the y point
The “3” is the slope
The “1” is the x point

Now we simplify the equation:

y-7 = 3(x-1)
y-7 = 3x-3
+7 +7
—————
y = 3x + 4

Hope this helps and makes sense :)

How do you find a unit rate

Answers

Answer:

Divide the numerator and denominator

Step-by-step explanation:

A unit rate is a ratio between two different units with a denominator of 1. To calculate the unit rate, divide the numerator by the denominator. The resulting decimal number is the unit rate. The unit price is a type of ratio where the numerator is the price and the denominator is the quantity of a good or product.

1-27
What is the simplified version of Square root of -27

Answers

Answer:

3√3

Step-by-step explanation:

The discriminant of a quadratic equation is 16. Which number represents the number of real solutions to the equation?

0

3

Answers

Answer:

The

number 2

Step-by-step explanation:

What we need here is just the sign of the discriminant

From the question in this case, the discriminant is positive

Thus, whenever we have a positive discriminant, then the number of real solution is 2 and these two are distinct (different from one another).

I need help pls pls pls

Answers

Answer:

Mantle

Step-by-step explanation:

I think its mantle

Bo, Ryan and Zach walked 1/4 miles from school to Bo’s house. They walked 4/6 miles from Bo's House to the park what is the total distance the boys walk?

Answers

Answer: They walked 11/12 miles

Step-by-step explanation:

1/4 + 4/6

3/12 + 8/12

11/12

If f (x) = 4х + 5, what is the value of f( 2) ? *
8

13

5

3​

Answers

I’m pretty sure the answer is 13

Answer:

The answer is 13

Step-by-step explanation:

First, you replace x with 2. Then you multiply 4 and 2 which you get 8. Lastly, you add 8 and 5 so you get 13.

a forest covers 47,000 acres. a survey finds that 0.2% of the forest is old growth trees. How many acres of old growth are there?

Answers

Answer:

9400

Step-by-step explanation:

I'm not really sure if this is right but I changed 0.2% to 1/5 and 1/5 is 9400. Hope this is right!

If the measure of each base angle of an isosceles triangle is represented by x, then the vertex angles is represented by

Answers

Answer:

vertex angle = 180° - 2x

Step-by-step explanation:

Since, the measure of each base angle of an isosceles triangle is represented by x.

So, by interior angle sum postulate of a triangle, we have:

x + x + vertex angle = 180°

2x + vertex angle = 180°

vertex angle = 180° - 2x

So, the vertex angle is represented by (180° - 2x).

What are the like terms in the expression below?

3x + 8 + 3y + 8x

Answers

Answer:

3x and 8x are like terms.

Step-by-step explanation:

Like terms are the terms that share the same variables. They do not have to share the same coefficients - or, in other words - the numbers in front of the variable do not have to be the same. Only the variable has to match.

So, looking at the expression, the only two terms that have the same variable are 8x and 3x, which both have the variable x. Therefore, 3x and 8x are like terms.

Figure A is a scale image of Figure B. 6 12 Figure A 9 x Figure B What is the value of x?​

Answers

Answer:

18

Step-by-step explanation:

6 is twice less than 12

X=9*2=18

look at Michael expression. Why do you add 6+4 first​

Answers

Answer:

probably cuz its in parentheses but there's no picture

Step-by-step explanation:

if 50% is 10 what is 25%​

Answers

Step-by-step explanation:. The first says “I know that 10 is one-tenth of 100. I will therefore divide 50 by 10. The answer is 5”.

This is fine when the numbers are relatively simple. But suppose the numbers are more complicated.

What is 22% of 46?

Now it’s much less straightforward. You can’t just work out what 22% is, expressed as a fraction, and anyway, it’s not a simple fraction.

Instead, you have to divide 46 into 100 equal parts, and work out what 22 of them would be when added together.

So: 46 ÷ 100 = 0.46 [remember, when you divide by 100, you move the decimal point two places to the left].

0.46 × 22 = 10.12

Answer: 22% of 46 is 10.12.

Hope this helped :)

If your good at math plz help me

Answers

Answer:

If your good at math plz help me

i think this is the answer, hope A(-3)=n-5

Answer for the box:   -5n+2

==================================================

Work Shown:

[tex]a_1 = -3 = \text{ first term}\\\\d = -5 = \text{ common difference}\\\\a_n = a_1 + d(n-1) = \text{ nth term}\\\\a_n = -3 + (-5)(n-1)\\\\a_n = -3 -5n + 5\\\\a_n = -5n + 2\\\\[/tex]

The common difference is due to us adding -5 to each term to get the next one. Example: -3+(-5) = -8, or -8+(-5) = -13.

--------------------

As a way to check if we have the correct nth term formula, plug in values of n to see if we get the correct sequence value

For instance, if n = 1, then

[tex]a_n = -5n+2\\\\a_1 = -5(1)+2\\\\a_1 = -5+2\\\\a_1 = -3\\\\[/tex]

Which matches with the first term given to us.

Or if n = 2, then,

[tex]a_n = -5n+2\\\\a_2 = -5(2)+2\\\\a_2 = -10+2\\\\a_2 = -8\\\\[/tex]

That matches the second term given to us. I'll let you check the others.

find the angle of yzv? ​

Answers

Step-by-step explanation:

12a+24a=180

36a = 180

a =5 °

angle of yzv = 24a = 120°

is 18/20 closed close to 0 1/2 or 1

Answers

Answer:

18/20 is closer to 1

Step-by-step explanation:

Answer:

0 1/2

Step-by-step explanation:

A boat traveled 432 miles downstream and back. The trip downstream took 12 hours. The trip back took 24 hours. What is the speed of the boat in still water? What is the speed of the current?

Answers

speed of the boat in still water would be (432/12=36) 36mph and the speed of the current should be (432/24=18) 18mph

if there are 45 seats in 9 rows how many seats are in 1 row.

Answers

there should be 5 seats

Answer: Their is 5 seats in 1 row.

Step-by-step explanation:    9x5=45 and 45÷9=5

What is the equation in slope-intercept form for graph shown?

Answers

the answer is D. y = -2x + 1

Paula walked on the treadmill for 11 minutes. The machine told her she had a total of 671 strides. What was her rate in strides per minute?

Answers

Answer:

61 strides per minute

Step-by-step explanation:

You just divide 671 by 11

hope this helps:)

Answer:

61

Step-by-step explanation: All you have to do is divide 671 by 11

pls help I need this due today pls ASAP ​

Answers

Answer:

130%

increase

Step-by-step explanation:

the new quantity is 13, the old is 10

divide 13/10

in your calculator this will show 1.3

that means one whole and 30/100ths, or in percents 130%

(to convert decimal to percent just mulitply by 100)

Evaluate 1/3 to the power of 3

Answers

The answer is 0.0369 (4 d.p)
Take 1/3 and convert to a decimal which is 0.333. Then put the decimal to the power of 3. In which you will get 0.0369 if you change to a fraction it will be 369/1000.
Hope it helps.

Image Above.........

Answers

Answer:

4 : 39

5 : 52

6 : 67

7 : 77

Step-by-step explanation:

Can someone please help me do 1-10? I have trouble understanding this so if you can explain the answer that would be amazing!

Thanks!

Answers

by the direction or degree of the angle, that’s how they’re related. pick the ones that are closest in degree or direction. hopefully this helped

please help me with this​

Answers

The answer i presume may perhaps be 12 because 156/12=13

Answer:

13 tables

Step-by-step explanation:

156 ÷ 12 = 13

156 people divided by the number of people each table hold will give u the amount of tables needed

You have 4 keychains on your backpack. How many keychains will you have if you get k more?

Answers

Answer: 4K chains

Step-by-step explanation:

PLEASE HELP
answer please asap​

Answers

Answer:

Step-by-step explanation:

-x+5=9

-x=-9-5

-x=-14

x=14

coefficient of x is -1

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