how many different perfect cubes are among the positive actors of 2021^2021

Answers

Answer 1

Answer:

hope this helps :D

Step-by-step explanation:

Perfect cube factors:

If a number is a perfect cube, then the power of the prime factors should be divisible by 3.

Example 1:Find the number of factors of293655118 that are perfect cube?

Solution: If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube 4x3x2x3=72

Perfect square and perfect cube

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.

Example 2: How many factors of 293655118 are both perfect square and perfect cube?

Solution: If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are 2x2x1x2=8

Example 3: How many factors of293655118are either perfect squares or perfect cubes but not both?

Solution:

Let A denotes set of numbers, which are perfect squares.

If a number is a perfect square, then the power of the prime factors should be divisible by 2. Hence perfect square factors must have

2(0 or 2 or 4 or 6 or 8)—– 5 factors

3(0 or 2 or 4 or 6)  —– 4 factors

5(0 or 2or 4 )——- 3 factors

11(0 or 2or 4 or6 or 8 )— 5 factors

Hence, the total number of factors which are perfect square i.e. n(A)=5x4x3x5=300

Let B denotes set of numbers, which are perfect cubes

If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube i.e. n(B)=4x3x2x3=72

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are i.e.n(A∩B)=2x2x1x2=8

We are asked to calculate which are either perfect square or perfect cubes i.e.

n(A U B )= n(A) + n(B) – n(A∩B)

=300+72 – 8

=364

Hence required number of factors is 364.


Related Questions

If 20% of a number is 12, then what is 30% of the same number

Answers

Answer:

18

Step-by-step explanation:

0.2x = 12

Same as: 1/5x = 12

Multiply both sides by 5

x = 60

0.3 * 60 = 18

30 POINTS FOR BRAINLIEST ANSWER!!!!!!!​

Answers

I think b not sure it’s the only one that makes sense

Find the missing side of this right
triangle.
12
Х
8
X=
V[?]
Enter the number that belongs in the green box.

Answers

Answer:

The number 80 should go in the green box

Step-by-step explanation:

To solve this equation you will need to use the pythagorean theorem. Which is a^2 + b^2 = c^2. Also you will need to know where the legs and hypotenuse of the triangle are. The hypotenuse is the longest side of the triangle. So that would be the side marked 12. Then the other two sides are legs.

To solve for x you need to input your known numbers into the pythagorean theorem and solve. To know where the numbers go, a and b of the equation are the legs of the triangle and c is the hypotenuse. I solved the equation for you in the photo I inserted.

Hope that helped you!

who is involved in the stimulus check please help me i really need help please

Answers

Answer:

Go on the IRS website and fill out the form.... this is what heard beetween a conversion with my brother and dad

Step-by-step explanation:

depressed ppl say here

Answers

here

hehbsheheuehebdbd

Answer:

lol are you depressed ..........

Write An Equation

Write an equation for a parabola that opens up, is narrower than [tex]y=x^{2}[/tex], and has vertex (2, -5)


Write an equation for a parabola that opens down, is wider than [tex]y=x^{2}[/tex], and has vertex (-4, 3)

Answers

Answer:

1) y = 2(x - 2)² - 5

2) y = -(x + 4)²  / 2 + 3

You want to be able to withdraw $40,000 each year for 15 years. Your account earns 9% interest. How much
do you need in your account at the beginning?

Answers

Answer:

40000×1×9%=3 600 this is for year

Someone needs to hear this. So here it is. God will pull you through. You just need to have faith. You just have to keep going. Do not give up. Things will get better. What is important to you is important to the lord. So pray and He will listen.

Answers

Answer: thank you

Step-by-step explanation:

Answer:

Thanks!

Step-by-step explanation:

Please help!!! Also if you could show work I need it!

Answers

The perimeter is 18+18+20+20=76. 18 square root 2 /2= 12.727. Hypotenuse or triangle is 18 + 12.727+12.727=43.455. 76.18+43.455=119.635. The area is 18x20=360. (12.727x12.727)/2= 161.9765. 161.9765+360= 521.9765.
For the hypotenuse since it is a 45,45,90 triangle the two side lengths are are same so it is x square root 2 divide by 2. Hope that helps!!

Find the value of 24/25 divided by 2/5. Show your reasoning.

Answers

Answer:

12/5 or 2 2/5

Step-by-step explanation:

Multiply by the reciprocal then reduce the numbers with the greatest common factor, leaving 12/25*5 then multiply that and get your answer

can anyone solve these and show work? please help a girl out lol

Answers

17) 45-45-90 triangle so
45 | 45 | 90
n | n | n root 2
15 | x

n=n=x=15 u

y is hypotenuse, since 15 is n, hypotenuse is gonna be n root 2 so 15 root 2



18) 30-60-90 triangle

30 | 60 | 90
n | n root 3 | 2n
x | y | 15

2n=15
n=7.5=x
7.5 root 3=y

Which property is illustrated by each equation?
a. a + (b + c) = (a + b) + C
b. ab
= ba
c. a (b + c) = ab + ac

Answers

Answer:

a. = associative

b. = communitive

c. = distributive

Show work please and thanks

Answers

Answer and working out attached here. Hope it helps :)

In a certain year, there were 300 congressional
seats in a country's congress. The population of
one state was 1,312,127 and its standard quota
was 7.2513. Find the country's population in the
given year.
The country's population was
(Type a whole number.)
people.

Answers

Answer:

There would be 54,307,200 people

Step-by-step explanation:

5) If the property tax on a $100,000 home is $1500, what is the tax on a
$ 120,000 home?

Answers

Answer:

Calculate property taxes based on assessed value and a tax rate. California property tax calculations with annual assessment increases up to 2% ... Tax Rate: The annual tax rate used to compute your property taxes.

Which segment is the MEDIAN of the triangle?

Answers

Answer:

R

Step-by-step explanation:

Question 4 of 25 Use the substitution method to solve the system of equations the correct ordered par x+y=5 y=7​

Answers

Answer:

x = -2

y = 7

Step-by-step explanation:

x+y=5

y=7​

x+y=5

x + 7 = 5

x = -2

x+y=5

-2 + y = 5

y = 7

Which expression is equivalent to ( + )?

Answers

Answer:

No entiendo que es lo que hay qué hacer

Recall that a conflict of interest scenario was presented to a sample of 200 marketing researchers and that 109 of these researchers disapproved of the actions taken. (a) Let p be the proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that a majority (more than 50 percent) of all marketing researchers disapprove of the actions taken.

Answers

Answer: Null hypothesis: [tex]p\leq0.50[/tex]

Alternative hypothesis: [tex]p>0.50[/tex]

Step-by-step explanation:

A null hypothesis is a type of hypothesis that states that there is no difference between a particular parameter of a population whereas an alternative hypothesis states that there is a difference.

Given: p = Proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario.

n= 200

Sample proportion = [tex]\hat{p}=\dfrac{109}{200}=0.545[/tex]

Claim : p>0.50

Null hypothesis: [tex]p\leq0.50[/tex]

Alternative hypothesis: [tex]p>0.50[/tex]

i need help i will crown brainiest

Answers

Answer:25 if your looking for the number of ways to order 5 objects

Step-by-step explanation:

If your looking for the probability of 1 number the ways for it to be arranged l believe It is 5x5 hope this helps

This question: 00:26 Level 4: Multiplying Mixed and Whole Numbers 16.7% Complete Q. One of your clients at Wills, Trusts & Estates Law, PLLC passes away. His estate is worth $72,000. He leaves half to charity, and to each of his four children. How much will each child receive? $ HINT + A Report Content Errors​

Answers

The question is stated in such a garbled, convoluted, ambiguous way that it's hard to go to an answer.

With a few reasonable assumptions, it looks to me like each son gets $9,000.

ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !

Answers

Answer:

[tex] \sqrt{18 } is \: a \: \: answer \: pls \: follow \: me[/tex]

Answer:

Step-by-step explanation:

-3i Square root of 2

help lol sjdnwkfnnsnfnsndnwmdn

Answers

Answer:

m<2 = 40°

Step-by-step explanation:

<1 and <2 area corresponding angles. Corresponding angles are congruent.

m<1 = 40° (given)

Therefore,

m<2 = m<1 = 40°

m<2 = 40°

Write without exponents (y^2)^4

Answers

Answer:

Step-by-step explanation:

Answer: y times y 8 times

Apply Exponent Rule

Simplified Form y^8

To write without exponents is basically just writing out y times itself 8 times.

PLEASE HELP ILL MAKE BRAINLIEST ASAP

The amount of money in a bank account increased by 18.5% over the last year. If the amount of money at the beginning of the year is represented by n, which expression represents the amount of money in the bank account after the increase? Select all that apply.

A
n + 0.185n

B
n + 18.5n

C
1.185n

D
0.185n

E
18.5n

F
19.5n

Answers

Answer:

A

Step-by-step explanation:

please help me fast thanks​

Answers

Answer:

if I am not wrong I think the anwser will be 2.3

Answer:

It's 3

Step-by-step explanation:

7 can't be divided by 3 so you leave it as a fraction

A worm moves forward 3/8 inch every 5 minutes for 1 hour 25 minutes. How far does the worm move in this time? Explain

Answers

Answer:

6 3/8 inches

Step-by-step explanation:

let 'x' = distance in 1 hr, 25 minutes (which is 85 minutes)

(3/8 ÷ 5) = x ÷ 85

cross-multiply:

5x = 255/8

40x = 255

x = 6 3/8

Max used 3 7/8 pounds of yellow potatoes and 2 5/8 pounds of sweet potatoes to make a potato salad. How many more pounds of yellow potatoes than sweet potatoes did Max use?​

Answers

Step-by-step explanation:

[tex]\tt{}3 \frac{7}{8} - 2 \frac{5}{8} [/tex]

[tex]\tt{}(3 -2) + ( \frac{7}{8} - \frac{5}{8} )[/tex]

[tex]\tt{}1 + \frac{1}{4} [/tex]

[tex]\tt{}1 \frac{1}{4} [/tex]

[tex]\tt{} \frac{5}{4} [/tex]

[tex]\tt{}1.25[/tex]

A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink
marbles.
What is P(not yellow)?
A 1/5 B 2/5 C 4/5

Answers

Answer: c 4/5

Step-by-step explanation: out of 5 only four are chosen leaving us with an answer of 4/5 :D hope it helped

(-8, -1); slope = - 3/4
Pleaseee this onee!!​

Answers

Answer:

y = -3/4x - 7

Step-by-step explanation:

Slope intercept:

y - y1 = m(x - x1)

y + 1 = -3/4(x + 8)

y + 1 = -3/4x - 6

y = -3/4x - 7

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