Let n be an odd integer with exactly 11 positive divisors. Find the number of positive divisors of 8n^3

Answers

Answer 1

Answer: 124

Step-by-step explanation:

As we know, the total number of positive divisors of n is the product of one more than each exponent in the prime factorization of n.

We know this product is equal to 11.

Since 11 is prime, so there can be only one number in this product, so the prime factorization of n must be [tex]$n=p^{10}$[/tex], where p is a prime number.

We take a cube of the prime factorization of n to give us a prime factorization for [tex]n^3[/tex]

[tex]$$n^{3}=\left(p^{10}\right)^{3}=p^{30} .$$[/tex]

We see that [tex]n^{3}\text{ has }$30+1=31$[/tex] positive divisors.

Now, [tex]8n^3=2^3\times p^{30}[/tex]

Totald divisiors = [tex](3+1)(30+1)=4\times31=124[/tex]

Hence, the number of positive divisors of [tex]8n^3=124[/tex]


Related Questions

the ratio of blue to yellow paint when mixed to make green paint is 3:2 what percentage of the green paint is made from yellow paint

Answers

Answer:

40%

Step-by-step explanation:

3 + 2 = 5

Since 2 is the ratio of yellow paint, 2/5 x 100 = 40%

Hope this helped!

Cho ∆ABC;phân giác AD,BE,CF cắt nhau tại I . a, Góc IAC+góc IBC+ góc ICA=? b, Kẻ IH vuông góc với BC . C/m Góc BIH=góc CID

Answers

can you post a pic???

make x the subject of the formula
y=a√x

Answers

Answer:

y=a√x

y/a=a√x/a a will cancel out on the right side of the equation

therefore, √x=y/a

x=√y/x

Round the following values to 2 significant figures 0.0653​

Answers

Answer:

The answer is 0.065

Step-by-step explanation:

0 doesn't count if it's before a start of a number when rounding to a significant figure

6 + {1 + [−(3 + 5) − 8] + 2} + 10 pleasee!!!

Answers

[tex]6 + (1 + ( - (3 + 5) - 8) + 2 \\ 6 + (1 + 2 - 8) + 2 + 10 \\ 6 + ( - 5) + 2 + 10 \\ 6 - 5 + 2 + 10 \\ \\ = 13[/tex]

Final Answer: 13

Step By Step Explanation:

Calculate: Calculate the sumCalculate: Calculate the sum or differenceRemove the parentheses: When there is a + in front of an expression in parentheses, the expression remains the sameCalculate: Calculate the sum or difference

☆彡Hanna

Please help me solve my problem!!!

Answers

Answer:

FH is the smallest angle since it is lesser than all the other ones.

i want 2 equivalent fractions for 25/90 and for 106/300​

Answers

Answer:

25/90 there is 150/270 and 5/18

for 106/300 there is 53/150 and 212/600

Answer:

for 25/90 divide by 5 to get 5/18. For 106/30 divide both by 2 to get 53/150.

Factorise completely the expression below: 6ax+12by-9ay-8bx​

Answers

Answer:

Step-by-step explanation:

6ax +12by -9ay -8bx

=6ax -8bx -9ay +12by

=2x(3a -4b)-3y(3a -4b)

=(2x-3y)(3a-4b)

Figure A is a scale image of Figure B.

What is the value of x?

NO LINK. OR I WILL REPORT YOU.

Answers

Answer:

4.4

Step-by-step explanation:

x / 4 = 11 / 10

x = ( 4 x 11 ) / 10

= 44 / 10

x = 4.4

Answer:

5

Step-by-step explanation:

To measure scale factors, you have to measure how much units apart each triangle is, and apply the same length to x on figure A.

Here is the equation I used:

10-4=6

11-6=5

Both triangles are 6 units in difference.

please help me solve this..​

Answers

Answer:

5

Step-by-step explanation:

Let a = number of pieces of chocolate bought by Amin.

Let b = number of pieces of chocolate bought by Bob.

b = 2a

(a - 3)(b - 3) = 14

ab - 3a - 3b + 9 = 14

a(2a) - 3a - 3(2a) = 5

2a^2 - 3a - 6a = 5

2a^2 - 9a - 5 = 0

(2a + 1)(a - 5) = 0

2a + 1 = 0  or  a - 5 = 0

a = -1/2  or  a = 5

Amin cannot have bought -1/2 pieces of chocolate, so we discard the soluion a = -1/2.

a = 5

Answer: 5

the answer would be 5! i hope this helped you

1 + 4.25n + 3/2p – 3 + (–2p) + 5/4n simplify
A. 5.5n – 1/2p – 2
B. 9.5n + 1.5p – 2
C. 9/4n − 1.5p − 4
D. 3.75n – p + 1

Answers

The answer is B.....

[tex]\longrightarrow{\green{A.\:5.5 \: n - \frac{1}{2} \: p - 2}}[/tex] ✔

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]1 + 4.25 \: n + \frac{3}{2} \: p - 3 + ( - 2 \: p) + \frac{5}{4} \: n [/tex]

Combining like terms, we have

[tex] = 4.25 \: n + \frac{5}{4} \: n + \frac{3}{2} \: p - 2 \: p + 1 - 3 \\ \\= 4.25 \: n + 1.25 \: n + 1.5 \: p - 2 \: p - 2 \\\\ = 5.5 \: n - 0.5 \: p - 2 \\ \\ = 5.5 \: n - \frac{1}{2} \: p - 2[/tex]

[tex]{\huge{\boxed{\sf{\pink{Mystique35}}}}}[/tex]

Calculate the area of a circle with a radius of 16.9 centimeters.
a. about 224.32 cm2
c. about 106.19 cm2
b. about 212.37 cm2
d. about 897.27 cm2

Answers

Answer:

I'd say 897.27cm². That's the vlosest answer that I see.

Find (-3/7) / (-1 1/14).

45/98

2/5

2 1/2

-2/5

Answers

Answer:

option B .   [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

[tex](-\frac{3}{7}) \div (-\frac{15}{14}) = (-\frac{3}{7}) \times (-\frac{14}{15}) = \frac{3 \times 14}{7 \times 15} = \frac{2}{5}[/tex]

Answer:

2/5

Step-by-step explanation:

(-3/7) / (-1 1/14) = 0.4

0.4 = 4/10

simplified = 2/5

I hope this helps uwu.

Given the graph of the line, choose two points and find the slope. Construct the equations for each of the
points you chose in point slope form. Show your work and explain each step.
*The graph is in the picture *
PLEASE HELP I WILL GIVE BRAINLIST

Answers

Step-by-step explanation:

First, given that we must use point slope form, we can define that as

y - y₁ = m (x-x₁), with m being the slope .

To find the slope, we can use the equation

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Two points on the graph are (0, 1) and (1, 3). For these points, when calculating the slope, 0 and 1 represent x₁ and y₁ respectively, while 1 and 3 represent x₂ and y₂ respectively Using this formula, we can plug our points in to get

[tex]\frac{3-1}{1-0} = 2/1 = 2[/tex]

as our slope. Therefore, our equation is

y - y₁ = 2 (x-x₁).

For our first point, (0,1), we can simply plug 0 in for x₁ and 1 in for y₁ to get

y - 1 = 2(x-0) as one equation

Next, for (1,3) we can plug 1 for x₁ and 3 for y₁ to get

y - 3 = 2 (x-1) as our other equation

Solve for x. Assume that lines which appear tangent are tangent. x=

Answers

Answer:

this is a long shot( like rly long) but try either -6 or -3

Step-by-step explanation:

Don't co.e for me if I'm wrong im just a poor girl in year 8

A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is 6 StartRoot 2 EndRoot feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.

Answers

Answer:

a

b

d

e

Step-by-step explanation:

he triangle is isosceles.

The leg-to-hypotenuse ratio is 1:StartRoot 2 EndRoot.

The leg-to-hypotenuse ratio is 1:StartFraction StartRoot 2 EndRoot Over 2 EndRoot. The nonright angles are congruent. The ladder represents the longest length in the triangle.

Answer:

a,b,d,e

Step-by-step explanation:

answer

Math help please thanks

Answers

Answer:

x = 10.5

Step-by-step explanation:

The first thing you have to do is to find out what you multiplied (say) 2 by to get 3.5 and then try it again with another number.

2k = 3.5         Divide by 2

k = 3.5 / 2

k = 1.75

Now try it on another number. What do you multiply 4 by to get 7

4k = 7            Divide by 4

k = 7/4

k = 1.75

So here's what's going on. If you multiply every dimension you are given on the left pentagon (it's not regular) by 1.75, you should get the corresponding number on the right.

To get x you need to multiply 6 by 1.75

x = 6*1.75

x = 10.5

2. Select all the irrational numbers. *
A. 6pi

B. - square root of 49

C. -1.405
_
D. -0.3

E. e

F. square root of 2

Answers

Answer:

F.

Step-by-step explanation:

Find the equation of the parabola that has zeros of x = –2 and x = 3 and a y–intercept of (0,–30).

A)

y = x2 – 5x – 30

B)

y = 5x2+ 5x – 30

C)

y = –5x2 + 5x + 30

D)

y = 5x2 – 5x – 30

Answers

It's the letter B y=-5x2+5x+30.

pa help po............. ............​

Answers

Answer:

ΔABC

∠9 = ∠19 + ∠21

∠7 = ∠20 + ∠21

∠8 = ∠19 + ∠20

ΔXYZ

∠3 = ∠11 + ∠12

∠5 = ∠10 + ∠12

∠4 = ∠10 + ∠11

ΔNOR

∠1 = ∠5 + ∠6

∠2 = ∠ 4 + ∠5

∠3 = ∠4 + ∠6

Step-by-step explanation:

According to the exterior angle theorem, the exterior angle of a triangle is equal in measurement to the sum of the two interior angles of the triangle;

In triangle ΔABC, we have;

∠9 = ∠19 + ∠21

∠7 = ∠20 + ∠21

∠8 = ∠19 + ∠20

In triangle ΔXYZ, we have;

∠3 = ∠11 + ∠12

∠5 = ∠10 + ∠12

∠4 = ∠10 + ∠11

In triangle ΔNOR, we have;

∠1 = ∠5 + ∠6

∠2 = ∠ 4 + ∠5

∠3 = ∠4 + ∠6

Could someone help me with 2, 9, 10, 11, 12 13, and 14?

Answers

Answer:

13.  (1) x + 8x = 32

14.  $337.5

Step-by-step explanation:

14. $270 x 0.25 = 67.5

270 + 67.5 = 337.5

I am sorry. I only got these-

yea 14 is 337.50 that’s all I got tho

Please help…………………………….

Answers

if i'm correct its 7x

Answer:

Domen is [ -2 , infinitely) or can be written as

-2 < x < infinitely in inequality form.

Step-by-step explanation:

if (x+2) is negative than function will be imaginary so to be real function (x+2) should be positive

hence answer is : Domen = -2 < x < infinitely or can be written as [ -2 , infinitely )

Frank has $8000 that he plans to split into two investments. He wrote the following two equations to represent the interests he will earn from each of the two investment options.

Answers

Answer:

I still think you equations are wrong...

4000/4000 not 400/400

Step-by-step explanation:

2000 A+ 6000B=520

4000A+4000B        =480

~~~~~~~~~~~~~~~~~~~~~

2000 A+ 6000B=520

-2000A - 2000B   =-240  

4000B = 280

B=7%

A=5%

Justins rice ball recipe uses 100 grams of rice to make 1 rice ball. Justin has 700 grams of rice. How many rice bals can juctin make with 700 grams of rics?

Answers

Answer:Justin can make 7 rice balls with 700 grams of rice

Step-by-step explanation:

IF 100 grams of rice can make 1 rice ball.

Therefore, 700 grams of rice can make 700grams  x 1 rice ball/ 100 grams

=7 rice balls

Therefore Justin can make 7 rice balls with 700grams of rice

Please answer thanks! Brainliest

Answers

Step-by-step explanation:

The last two answers is correct

Answer:

4

Step-by-step explanation:

The answer to T - H is negative

9. Estimate the solution to the system
of equations by graphing. Write the
solution.
y=4-X
x + 3y = 5
( , )

Answers

5 is the answer
At least I think

if f(x) =4x²+1 and g(x) =x²-5, find (f-g)(x)​

Answers

Answer:

(f-g)(x)=4x^2+1-x^2+5

=3x^2+6

=3(x^2+2)

Can someone help me?It's urgent and thank you!

Answers

Answer:

575.71

Step-by-step explanation:

Year 1: 960 x .88 (100%-12%)=844.80

Year 2: 844.80 x .88 =743.424

Year 3: 743.424x.88=654.21

Year 4: 654.21 x .88=575.71

Molly starts riding her bike to school 20 minutes after her brother Jonas
does. Molly pedals 12 miles per hour, and Jonas pedals 9 miles per hour.
How much time will it take for Molly to catch up to Jonas?

Answers

Answer:

It will take Molly 1 hour to catch up to Jonas.

Step-by-step explanation:

Since Molly starts riding her bike to school 20 minutes after her brother Jonas does, and Molly pedals 12 miles per hour, and Jonas pedals 9 miles per hour, to determine how much time will it take for Molly to catch up to Jonas the following calculation has to be done:

Jonas = 9 miles per 60 minutes = 3 miles per 20 minutes

Molly = 12 miles for 60 minutes

Jonas = 3 miles + 9 = 12

Molly = 12

Therefore, it will take Molly 1 hour to catch up to Jonas.

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system?

Answers

The question is incomplete, the complete question is:

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system?

x + 3y = 42

2x − y = 14

A: Multiply the second equation by -3. The solution is x = 12, y = 9.

B: Multiply the second equation by -2. The solution is x = 12, y = 10.

C: Multiply the second equation by 2. The solution is x = 15, y = 9

D: Multiply the second equation by 3. The solution is x = 12, y = 10

Answer: The correct option is D.

Step-by-step explanation:

The elimination method is a technique wherein we eliminate the coefficient of any one variable.

The given equations are:

x + 3y = 42

2x − y = 14

We multiply the second equation by (3) and the equations formed are:

x + 3y = 42

6x − 3y = 42

The final equation after eliminating the y-term becomes:

7x = 84

x = 12

Putting value of 'x' in any of the original equation, we get:

⇒ 12 + 3y = 42

⇒ 3y = 30

⇒ y = 10

Hence, the correct option is D.

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