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

Find the perimeter of the figure to the nearest hundredth.

Answers

Answer:

perimeter of trapezium =sum of all sides

perimeter of trapezium =10cm+6cm+12cm+8cm

perimeter of trapezium =36cm

perimeter of semicircle =pi×r

perimeter of semicircle =3.14×6cm

perimeter of semicircle =18.84cm

perimeter of the figure =36cm+18.84cm=54.84cm

can someone help me out with these equations?
1. (5+ √3)^2
2. (√6-5√3)^2
3. (6+3√2)^2

Answers

9514 1404 393

Answer:

28 +10√381 -30√254 +36√2

Step-by-step explanation:

It is useful to remember the form for the square of a binomial.

  (a +b)² = a² +2ab +b²

  (a -b)² = a² -2ab +b²

__

1. (5 +√3)² = 5² +2·5·√3 +(√3)² = 25 +10√3 +3

  = 28 +10√3

__

2. (√6 -5√3)² = (√6)² -2·√6·5√3 +(5√3)² = 6 -30√2 +75

  = 81 -30√2

__

3. (6 +3√2)² = 6² +2·6·3√2 +(3√2)² = 36 +36√2 +18

  = 54 +36√2

HELP NEED ANSWER ASAP!

Answers

Answer:

I am pretty sure the anwser is 7

Answer:

The median is 7.

Step-by-step explanation:

The median is 7 because, in a box plot, the line inside of the box is the median. That line is over 7 on the number line.

My sister got stuck on these can you tell me the answers?

Answers

don’t click the link above it’s a scam. also i think you measure the eraser using a ruler and that’s the answer lol

When creating equations for our word problems, we must remember to...

A. write all equations in slope-intercept form.

B. make sure all equations are in the same form.

C. define all variables.

Answers

9514 1404 393

Answer:

  C.  define all variables

Step-by-step explanation:

Equations for word problems will depend on the problem. Not all of the equations will be linear equations. Even if they are, they are not necessarily easily written in any particular form, or easily solved when they are written in that form. The nature of the equations will depend on the problem.

One thing that must be done in any case is define all variables. It is usually a good idea to define the units of the variable(s) as well. Sometimes problems are posed with numbers in incompatible dimensions, or they may ask for an answer in dimensions different from those used in the given information. In order to avoid confusion and to be sure you have the desired answer, you need to make sure the variables and their dimensions are compatible with the solution process.

What's the exact value of tan 15°?
O A) 2 + √3
B) 1
OC2
C) 2 - V3
OD) 1 + v3

Please Help!!!!

Answers

Answer:

C

Step-by-step explanation:

Split

15

into two angles where the values of the six trigonometric functions are known.

The result can be shown in multiple forms.

Exact Form:

2−√3

The exact value of tan 15° is,

⇒ tan 15° =  - (2 - √3)

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

To find the exact value of tan 15°.

Now, We can formulate;

tan 15° = tan (45 - 30)°

          = tan 45° - tan30° / (1 + tan45° tan30°)

          = (1 - √3) / (1 + √3)

          = (1 - √3) (1 - √3) / (1 + √3) (1 - √3)

          = (1 + 3 - 2√3) / (1² - √3²)

          = (4 - 2√3) / (1 - 3)

          = 2 (2 - √3) / - 2

          = - (2 - √3)

Thus, The exact value of tan 15° is,

⇒ tan 15° =  - (2 - √3)

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

pls help i give you brainliest

Answers

kimi no toriko ni natte ti shi mae ba kitto

Obtain the truth value of

(i)
If 5 + 6 = 11, then 11 – 6 = 5.

(ii)
If 5 + 8 = 12, then 12 + 8 = 20.

(iii)
If 6 + 9 = 14, then 14 – 7 = 8

(iv)
If 7 + 8 = 15, then 8 – 7 = 2

Answers

I want to say the answer is (i)

increase 70 in ratio 3:2​

Answers

i believe the answer is 105
The answer is 105 hope this helps

what is the total price including 7% tax of a $14.49 item​

Answers

Answer:

$15.50

Step-by-step explanation:

5th grade math. correct answer will be marked brainliest

Answers

Answer: First 12/8, then 3/2

Step-by-step explanation: 3/2.

If you want the mixed fraction, it would be 1 1/2.

4 times 3 is 12... 12/8

1 whole box (8/8)

So 12/8-8/8=4/8 left

1 whole and 1/2

help me please!! i’m confused!!

Answers

The container will be 270 square centimeters.

The graph of a line has a slope of 2 and passes through the point (–6, –5). What is the equation of the line in point-slope form?
y – 5 = 2(x – 6)
y + 5 = 2(x + 6)
y – 6 = 2(x – 5)
y + 6 = 2(x + 5)

Answers

Answer:

it would be

B. y + 5 = 2(x + 6)

if there is a negative number and you are subtracting it turns positive

Step-by-step explanation:

Select the correct answer from each drop-down menu.

Carla wants to buy a new bike before summer starts in one week. She saves $1 on the first day of the week, $2 on the second day, $4 on the
third day, $8 on the fourth day, and continues this pattern the rest of the week.
If the bike costs $150, Carla will (have or not have)
enough money to buy the bike before the start of summer.
Carla will have ($15, $25 $23,$27,$5,$0)

Answers

Answer:

she will not have enough money

she will have 23 more to save

Step-by-step explanation:

got it right on plato

Answer:

If the bike costs $150, Carla will

not have

enough money to buy the bike before the start of summer.

Carla will have

$23

more to save

.

Step-by-step explanation:

pls answer it i really need the answers : (

Answers

Answer:

Subscribe Single-3 FF on yt

Pls help! This test determines if I take math 1 or 2 for 8th grade!!

Answers

Answer:

My best guess is D she can make 4 dozen cokies

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

it is B because  for number A 1+1 =2 2>1.75.  B= 1.5<175, c= 0.5 <1, d. 2>1.75

9. Complete the following equation using <,>, or =
100% _1
O A. >
O B. <
O C. =

Answers

Answer:

C. =

Step-by-step explanation:

Two ways to think about this problem:

1st way: 100% and 1 are all a whole, therefore, they are equal.

2nd way: 1=1/1. Multiply the denominator and the numerator by 100, 1/1=100/100=100%

f(x) = x - 4 + 1
Describe the transformation

Answers

Answer:

here i gotchu mate:)

Step-by-step explanation:

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Shifted down  

3

units

2. Solve the following problems involving simple interest. Recall
Simple Interest-INT=PV*r*t
An investor decides to offer a business owner a $45,000 loan at simple interest of 3.5%
per year. Find the total amount in dollars, the investor will receive when the loan is
repaid after 7 years.

Answers

Answer:

A = $56025

Step-by-step explanation:

Given that,

An investor decides to offer a business owner a $45,000 loan at simple interest of 3.5%  per year.

Principal, P = 45,000

Rate of interest, R = 3.5%

We need to find the total amount the investor will receive when the loan is  repaid after 7 years.

The formula for the simple is given by :

[tex]I=\dfrac{PRT}{100}\\\\=\dfrac{45000\times 3.5\times 7}{100}\\\\=\$ 11025[/tex]

We know that,

Amount = Principal + simple interest

So,

A = 45,000 + 11025

A = $56025

So, the required amount is equal to $56025.

Find the area of the regular octagon with radius of 14
feet.


Answers

Answer:

uhm- ok ok ok level hard o my gosh

r − 38 = 9
please solve the equation

Answers

Answer:

r = 47

Step-by-step explanation:

r - 38 = 9

r- 38 + 38 = 9 + 38

simplify

r = 47

Answer:

[tex]r=47[/tex]

Step-by-step explanation:

[tex]r-38=9[/tex]

Add 38 to both sides of the equation:

[tex]r-38+38=9+38\\r=47[/tex]

r = 47 is your final answer.

Solve for the area of the smaller
shape.
Round to the nearest TENTH.

Answers

31 I think I don’t really remember cause I’m not working on area anymore

In August an online store sold 213 graphing calculators during their back to school sale. Since then, sales have increased at a rate of 5% each month. Which function can be used to determine the monthly calculator sales sine August?

Answers

Answer:

[tex]y = 213 + 0.05x[/tex]

Step-by-step explanation:

Given

[tex]Initial = 213[/tex]

[tex]Rate = 5\%[/tex]

The equation to o this is:

[tex]y = intial +rate * weeks[/tex]

[tex]y = 213 + 0.05x[/tex]

The formula for finding the area of a square that has a side length, s, is A = s2. If a square has an area of 40 square units,
what is the length of a side?
A. 2./10
B. 10.12
C. 20

Answers

Answer:

2./10

Step-by-step explanation:

It's simply by finding the square root of its area which is √40 giving 6.325 for an answer

If simplified by dividing each side with 3 then the answer would be 2./10

(-10) + 3 = 10 - 3 is true or false??? ​

Answers

(-10) + 3 = -(10 - 3) = -7

10 - 3 = 7

-7 ≠ 7

FALSE

solve the equation. -4/9 f= -3​

Answers

Answer:

27/4

Step-by-step explanation:

Multiply both sides by 9/(-4).

9/−4 * −4/9 f = 9/−4 * −3

f = 27/4

what is the area of the trapozoid?

Answers

Answer:

8units²

Step-by-step explanation:

area of trapezoid=½(a+b)*h

a=2

b=6

h=2

area of trapezoid=½(2+6)*2

area of trapezoid=½(8)*2

area of trapezoid=4*2

=8units²

Using the photo above, describe what type of symmetry it has.

a. if it has reflection symmetry, draw all lines of symmetry.

b. if it has rotational symmetry, what is all the angle of rotational symmetry (the smallest)

c. if has translational symmetry, what is shape is getting repeated​

Answers

B because it’s rotating in a circle

9514 1404 393

Answer:

  b) rotational symmetry: multiples of 120°

Step-by-step explanation:

The figure does not have a line of symmetry, or a point of symmetry. However, rotating it 1/3 turn (120°) will make it look like itself. Hence, it has rotational symmetry of degree 3. A rotation of any multiple of 120° will map the figure to itself.

From a random sample of 16 people in a jail, the number of days remaining in each their sentences was noted. The 16 people have a mean remaining sentence of 645 days with a standard deviation of 31 days. Assume the population of remaining sentences is normally distributed. Construct a 95% confidence interval for the mean remaining sentence of all people in the jail. Round final answer to one decimal place.

Answers

Answer:

The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 16 - 1 = 15

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1315

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1315\frac{31}{\sqrt{16}} = 16.5[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 645 - 16.5 = 628.5 days

The upper end of the interval is the sample mean added to M. So it is 645 + 16.5 = 661.5 days

The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.

What is the value of the expression: x2 + y2 + x - y
when x = -1 and y = 3

Question 1 options:

6


8


12


16

Answers

Answer:    6

Step-by-step explanation:

x^2+y^2+x-y

Put x=-1 and y=1

(-1)^2+(3)^2+(-1)-(3)

1+9-1-3

10-4

6

Other Questions
How does the repetition of the line It is July affect the meaning of the poem?It helps convey the slow and restful nature of the summer.It suggests a feeling of high energy after a period of rest.It acts as a reminder to wake up from the sleepiness that heat can induce.It helps indicate the finite quality of the season as autumn approaches. HELLP ASAP PLEASE!!! PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!! SOCCER PRACTICE BEGAN AT 2:30 P.M 3:30 P.M THROUGH WHAT FRACTION OF A CIRCLE DID THE MINUTE HAND TURN HOW MANY DEGREES DID THE MINUTE HAND TURN I need help on this question and answering it 4) A store donated 4 72 dozen cookies for afundraiser. Another store donated 3 14 dozencookies. How many dozen cookies did theydonate altogether? volcano has both useful and harmful effects give reason Evaluate 3f(2) what is it Quadratic FunctionsDetermine the value of y, if x is 9. y=x^2+8 Write a program that creates a two-dimensional array named height and stores the following data:16 17 1417 18 1715 17 14The program should also print the array.Expected Output[[16, 17, 14], [17, 18, 17], [15, 17, 14]] Read the following passage:Amid the many horrors of the Vietnam War, I found one ofthe worst to be the waiting - those quiet times of inactivitywhen anticipation of the next attack weighed on me like apile of bricks. I might be lying in the mud along a creek bedsomewhere, completely oblivious to the cold, the wetearth, or the smell of gunpowder still fresh in my noshils. Itwas those times of waiting that showed me I had nothingelse in my mindno past, no future, no ideas. Just a rawawareness of the moment.Which sentence best uses figurative language to match the paragraph's tone? A. In the quiet of the jungle, the rippling sounds of the creek carriedme back to happier days on my parents' farm. B. could hear my own pulse drumming in my ears, but my onlythought was to remain still and quiet.C. For years after that, I would remember the terror and suspense ofthose long minutes spent waiting. D. The jungle had reached into my mind, and its thick vines chokedout everything else that had been there. GIVING BRAINLIEST NO LINKSIn the data set shown below, what is the value of the quartiles? {1.3, 1.5, 1.7, 2, 2.5, 2.7, 2.9, 3, 3.1}A.Q1 = 1.6; Q2 = 2.5; Q3 = 2.92B.Q1 = 1.7; Q2 = 2.5; Q3 = 3C.Q1 = 1.7; Q2 = 2.5; Q3 = 2.9D.Q1 = 1.6; Q2 = 2.5; Q3 = 2.95 Before a bill can be voted on by the General Assembly, it must be studied and reviewed by This passage is part of the resolution. falling action. exposition. climax. Please help fast hurryy Whats the answer and work to this? Someone please tell me Which of the following operating systems would allow a user to add functionality and sell or give away their versions? Which is a difference between a mature fern and a heart-shaped plant?A. Heart-shaped plants reproduce sexually, and mature fernplants reproduce asexually.B.The mature fern reproduces sexually, and the heart-shaped plant reproduces asexually. The population of a city decreases by 2.5% per year. If this year's population is 237,000, what will next year's population be, to the nearest individual? if h(x) = 3(x + 6), find h(-1).a.3b.9c.15d.21