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

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]

(-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

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°

Which expression is equivalent to ( + )?

Answers

Answer:

No entiendo que es lo que hay qué hacer

depressed ppl say here

Answers

here

hehbsheheuehebdbd

Answer:

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

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

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

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 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

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

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.

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

Answers

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

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

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:

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!!

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

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]

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:

Show work please and thanks

Answers

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

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:

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

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:

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!

Which segment is the MEDIAN of the triangle?

Answers

Answer:

R

Step-by-step explanation:

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

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

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

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

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.

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

Other Questions
Which best describes the difference in the way people are created in the Blackfeet and Apache myths Choose the correct preposition.Der Schrank steht(against) die Wand.O anO bergegenO hinter EmuSparrowHow are emus and sparrows alike?A. Both birds build nests in trees.B. Both birds are taller than humans.C. Both birds catch small animals while flying.UD. Both birds have a beak for breaking apart food. I WILL GUVE BRAINLIEST! PLS PLS HELP! ??A stock split: O increases assets and stockholders' equity. O has no effect on total stockholders' equity. decreases assets and increases stockholders' equity. O increases assets and decreases stockho Question 2Any electricity charged object creates an electric field. Walking across carpet in wool socks can create an electric charge. Thisobservation is evidence for which characteristics of electrical forces?They generate electricity by contact.They can be generated by electricity.OOOThey can exert a force across a distance.They are moving due to magnetism. A nurse is creating a plan of care for a child who has sickle cell anemia. Which of the following interventions should the nurse include in the plan?A. discourage a high level of fluid intakeB. apply cold compresses to painful, swollen jointsC. observe for indications of hypokalemiaD. administer meperidine every 4 hours for pain A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket. Use the graph of the function f(x) - (x + 1)2 + 2. Identify the vertex andthe axis of symmetry. Plz HelppA vehicle has a Kinetic Energy of 75000 J and is moving at a velocity of 5 m/s. What is the mass of the vehicle? Please help me, GodBless. Points vectors Apply the Determinant Linear Independence Test to decide whether the [5] 4 0 4 3 2 2 2 V1: 0 3 are linearly independent in R4. a) Evaluate the corresponding determinant. (b) Make your conclusion. The Phillips Company paid total cash dividends of $150,400 on 32,000 outstanding common shares. On the most recent trading day, the common shares sold at $87. What is this company's dividend yield? (NOTE, don't forget ratios from CH 9 are listed out in the instructions part of the exam.) 21.28% 3.60% 5.40% 3.57 pts O 13.18% hi please help me. you can answer it in the comments too ') 1. It is difficult for you to decide what to have when you are in a restaurant? Why? / Why not?2. Do you like to taste new things? Why? / Why not? Una caja A contiene 5 bolas blancas y 4 negras; otra caja B contiene 3 bolas blancas y 5 negras. Se trasladan 3 bolas de la caja A a la B, y se saca una bola de la caja B. Cual es la probabilidad de que esta sea blanca? 27) Read this sentence from lines 60 and 61.Geothermal plants emit 97% less acid rain-causing sulfur compounds than are emitted byfossil fuel plants.In this sentence, emit most clearly means A. permit B. dischargeC. preventD. fulfill ________ allows the readers to learn a lot about the characters, as well as to form an opinion about those characters.DialogueForeshadowingSettingOrganizationExposition Sonic Corporation purchased and installed electronic payment equipment at its drive-in restaurants in San Marcos, TX, at a cost of $27,000. The equipment has an estimated residual value of $1,500. The equipment is expected to process 255.000 payments over its three year useful ite. Per year expected payment transactions are 61,200, year, 140,250, year 2, and 53,550, year 3.Required:Complete a depreciation schedule for each of the alternative methous1. Straight-line.2 Units-of-production3. Double declining balance. The riddle family income is 3400 per month. They spend 1088 per month on housing. Use information to determine the percent of the budget spent on housing hi please help ill give brainliest