If positive integer number n has exactly 8 divisors, what is the least number of divisors can n^2 have?

Answers

Answer 1

Answer:

The simpler case is the number:

n = a^7, where a is prime.

We use this so we avoid having cross numbers by multipliying different prime numbers. because for example lets compare:

2^2 = 4 has 3 divisors, 4, 2 and 1.

(4*4) = 16 has the divisors: 1, 2, 4, 8 and 16. (5 divisors).

Now let's mix primes:

2*3 = 6 has 3 divisors, 3, 2 and 1.

6*6 = 36

(3*2*1)*(3*2*1) = 36

then the divisors are:

3*3, 3*2, 3*1, 2*2, 2*1, 1*1, 3*2*2, ..., etc.

You can clearly see that this has a lot more divisors than the previous case.

Then returning to the answer:

a^7 can be divided by a, a^2, a^3, ..., and by itself, a^7 (and 1, so we have exactly 8 divisors).

Now, we can write:

n^2 = (a^7)^2 = (a^(2*7)) = a^14.

By the same logic that was used above, a^14 has 14 + 1 divisors.

Then the smallest number of divisors possible is 15.


Related Questions

find the x & y intercept for 3x-y=-5?

Answers

Answer:

Turn the answer to

-y = -3x - 5

-3 is the slope, and -5 is the y - intercept. Now graph it and look for the x intercept

Step-by-step explanation:

Calculate each quotient. Write your answers in lowest terms.

Answers

AnswerReanswer into right and left in going to the man

The stem and leaf plot here shows the current sale prices
for 60 houses in Horsham, PA, in thousands of dollars.
Note how the key helps communicate the prices.

Describe the distribution of housing prices.

Answers

Answer:

Symmetric

Step-by-step explanation:

In the stem and leaf plot above which represents the current sale prices of houses in dollars, we can observe the shape of the distribution seem like that of a bell shape. Most of the data values are concentrated towards the center compared to the concentration at both extremes.

This implies that most of the current sales price is centered close to the median price of roughly 49/50 dollars.

Therefore, the distribution of housing price can be described as roughly symmetric.

ASAP PLEASE I NEED HELP explain to me also because i dont understand Thank you!
both questions 7 &8

Answers

Answer:

For 7 I think A- ( I hope its right-) and 8 is D. - . <:)))))

Step-by-step explanation:

Brainliest is given to the right answer.

Roberto has been playing bass 3 times as many years as his brother Felix has.
Write an algebraic expression for the number of years Roberto has been playing bass. Be sure to indicate what the variable in your expression represents.

Answers

Answer:

3f

Step-by-step explanation:

you multiply 3 by f to get the number of years Roberto played bass

Answer:

[tex]R=3(F)[/tex]

Step-by-step explanation:

[tex]R[/tex] = Roberto's years

[tex]F[/tex] = Felix's years

What is the difference between a two step equation and a multi-step equation?

Answers

Answer:

When solving a multi step equation, you use PEMDAS (parentheses, exponents, multiplication, division, add, subtract), and you also use PEMDAS when solving a multi step inequality. However, inequalities are tricky in the fact that if you multiply or divide by a negative number, you must flip the sign. And while normally there are 1 or 2 solutions to a multi step equation, in the form of x= #, you'll have the same thing, but with an inequality sign (or signs).

A two-step equation is an algebraic equation that takes you two steps to solve. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.

hope it helped

X^3= (1/8). Solve for x

Answers

Answer:  x= 21 =0.500

x= 8−2− −12 = 4−1−i 3

​ =−0.2500−0.4330i

x= 8−2+ −12 = 4−1+i 3

​ =−0.2500+0.4330ix= 21 =0.500

Step-by-step explanation:I hope this helped, if not HMU and I will get you a better answer

-Have a great day! :)

can someone help me with this??

Answers

Answer:
Option 4

Explanation:
All the numbers ends with x^2.

There are 6 people at a party. if each person must shake hands with other every other person at the party exactly once how many handshakes will there be

Answers

Answer:

If six people all shake hands with each other, how many hand shakes were made in total?

Publish your book. Become an author in 15 days. Get published.

I assume that no two people shake hands if they've already shaken them earlier, irrespective of who initiated it.

In that case Guest 1 will shake hands with 5 others (Guest 2 to 6)

Guest 2 will shake hands with 4 others (Remember she's already shaken hands with Guest 1).

Guest 3 will shake hands with 3 others (having already shaken hands with Guest 1 and 2)

and so on.....

We end up with 5+4+3+2+1 handshakes or 15 handshakes in all!

Step-by-step explanation:

please mark me as a brainlist...

Answer:

15 handshakes

Step-by-step explanation:

the 1st person shakes hands with 5 people

the 2nd person shakes hands with 4 people

the 3rd person shakes hands with 3 people

the 4th person shakes hands with 2 people

the 5th person shakes hands with 1 person

the 6th person shakes hands with no one

5+4+3+2+1=15

100-4 divided 2x(3+7

Answers

Answer:

Step-by-step explanation:

7+3=10x2=20

100-4= 96

96 divided by 20= 4.8

If triangle HBN ~ triangle LYR, find the values of X. PLEASE HELP

Answers

Answer:

28/21 = 3x - 7/x+11

x = 13

Step-by-step explanation:

The value of x from the given diagram is 13. Option A is correct.

Similarity theorem:

From the given similar triangles;

28/3x-11 = x+11/21

Cross multiply

28(21) = (3x-11)(x+11)

(3x-11)(x+11) = 588

Expand

3x^2 + 33x - 11x - 121 = 588

3x^2+22x- 709 =0

On factorizing, the value of x is 13

Learn more on similar triangles here: https://brainly.com/question/2644832

HELP!!!
The image shown here is a floor-plan of a house.

Make a vertex-edge graph of this floor-plan, where each letter is a vertex and each doorway is an edge.

It is possible to take a tour of the house so that you walk through each doorway only once and finish at your starting point.


True
False

Answers

True! You can start at A and go to B, D, E, F, and then go out the side door of C.

The perimeters of the triangles shown are equal. Find the side lengths of each
triangle
2x+9
2x+8
2x
2x
R
3x+4
2x
PQ =
QR =
AB
BC=
AC = 1
(Type a whole number.)
PR

Answers

Jtzotztkztozitzoyxykzylzotztizittoztizitztizitztozotztoztiztozitztizztizitztizttozoyzoyztto

A toaster is priced at $27.00. The store is have a 1/3 off sale. What is the new price of the toaster?

Answers

Answer:

$18

Step-by-step explanation:

Multiply

27 * 1/3 = 9

Subtract

27 - 9 = 18

Best of Luck!

Thus, a product that normally costs $27 with a 3 percent discount will cost you $26.19, and you saved $0.81.

Identify the constant of
proportionality in the
following tables:
Need help ASAP

Answers

Answer:

Constant of Proportionality = 2

The second one is 2

The third one is 6

And the fourth one is 2.5

Find the slope m of a line parallel to a line with slope -4.​

Answers

Answer:

-4

Step-by-step explanation:

Parallel lines have the same slope so we know that m = -4.

Answer: -4

Step-by-step explanation:

Parallel lines will always have the same lengths. If one side has -4 as a length, the other will also have -4 as it's length.

Hope this helps you!

HELP ILL MARK YOUR brainliest! And give extes points

1. If there are 8 pints in a gallon, what is 56 pints converted to gallons?
a. 14 gallons
b. 7 gallons
c. 3.5 gallons
d. 5 gallons

Answers

Answer:

B

Step-by-step explanation:

Answer:

b 7 gallons

8 pints times 7 gallons is 56 pints

bar graph is also known as​

Answers

Answer:

Step-by-step explanation:

BAR CHART

Hope this helps

plz mark as brainliest!!!!!!!

5-11. A polymer is manufactured in a batch chemical process. Viscosity measurements are normally made on each batch, and long experience with the process has indicated that the variability in the process is fairly stable with 20. Fifteen batch viscosity measurements are given as follows: 724, 718, 776, 760, 745, 759, 795, 756, 742, 740, 761, 749, 739, 747, 742. A process change is made that involves switching the type of catalyst used in the process. Following the process change, eight batch viscosity measurements are taken: 735, 775, 729, 755, 783, 760, 738, 780. Assume that process variability is unaffected by the catalyst change. Find a 90% CI on the difference in mean batch viscosity resulting from the process change. What is the practical meaning of this interval

Answers

Step-by-step explanation:

Confidence interval = 90% = 0.90.

1 - 0.90 = 0.10

Mean of 15 batch:

724+718+776+760+745+759+795+756+742+740+761+749+739+747+742 = 11253/15

= 750.2

Mean of second batch:

735+775+729+755+783+760+738+780

= 6055/8

= 756.875

Sd = 20

Z-alpha/2 = 1.64

= (750.2-756.875)-1.64*√20²/15 + 20²/8

= -21.0348

(750.2-756.875)+1.64*√20²/15 + 20²/8

= 7.68

2. The upper limit of the interval is less than 10 so in conclusion the difference in mean batch viscosity is about 10 or less than 10

Anybody know this helppppp

Answers

Answer:

7.8y - 26.2

Step-by-step explanation:

Answer:

y=-0.15

Step-by-step explanation:

Subtract the 6.4y on the left by the 14.2y, you will get 7.8y. The reason why you subtract instead of add is because you always do the opposite when adding/subtracting from the other side of the equal sign. Next, add the 12.5 to the -13.7 so you get -1.2. The whole equation would be 7.8y=-1.2. Then divide by 7.8 on both sides so that you get y=-0.15. Hope this helps :)

is 4.6 bigger than pi

Answers

Answer:

Yes it is

Step-by-step explanation:

Pi is measured to be around 3.14 and 4.6 is of course bigger than 3.14 so yes it is

answer:

yes

explanation:

pi is 3.14 (and those numbers going on forever) even though pi looks big, the numbers are behind the decimal which is very small.

sorry I'm bad at explaining but I just went over this in class

4 is bigger than 3 so automatically 4.6 is bigger than pi

Wilson paints 40% of a bookcase in 20 minutes. How much more time will it take him to finish his bookcase

Answers

It will take 60 more minutes to complete the entire bookshelf
40%+60%=100% of the bookshelf
20+20+20=60

Nazim is buying rice. The supermarket sells 10 kg of basmati rice for $15.45. Today they have a ‘buy 3, get the 4th free’ offer. The wholesaler also offers 50 kg sacks of rice for $59.00. Based on price, which rice should Nazim buy?

Answers

Answer:

50 kg sacks of rice for $59.00.

Step-by-step explanation:

Lets do the math. First, I want to see how much 50 kg of of the first option costs.

$15.45 is worth 10kg.

$15.45*3=$46.35

Since the fourth on is free, the sum will stay the same.

$46.35+$15.45=$61.80.

50 kg of the first option is worth $61.80.

50 kg of the second option is worth $59.00.

$61.80 > $59.00.

So, the second option is cheaper and the better deal.

Select all of the numbers that Brooke could multiply by 2386 to get a product greater than 2386

Answers

Answer:

Step-by-step explanation:

Any number greater than 1 will give a number greater than 2386

b. Find the rule for this sequence.
_ _ _ 13, 25, 37

Answers

Answer:

You add 12 to the number before to subtract 12 to the number after.

Step-by-step explanation:

13+12=25

37-12=25

Can I have brainliest!

help please asap please​

Answers

Answer:

b

Step-by-step explanation:

Mrs. Ross needs to buy dish soap. There are four differently sized containers. Sort the brands from least to the greatest unit price. Round each unit price to the nearest thousandth.

Answers

Answer: Spotless soap < Bright wash < Lemon bright < lot of suds

Step-by-step explanation:

Given that 8 oz of Lots of suds cost = $0.98

Then unit price of 1 lot of suds = 0.98/8 = $0.1225

Given that 12 oz of Bright wash cost = $1.29

Then unit price of 1 Bright wash = 1.29/12 = $0.1075

Given that 30 oz of Spotless soap cost = $3.14

Then unit price of 1 Spotless soap = 3.14/30 = $0.104666666667

Given that 32 oz of Lemon bright cost = $3.50Then unit price of 1 Lemon bright = 3.50/32 = $0.109375

We also need to round the values to the nearest thousandth means three digits after decimal

Then unit price of 1 lot of suds = $0.123

unit price of 1 Bright wash = $0.108

unit price of 1 Spotless soap = $0.105

unit price of 1 Lemon bright = $0.109

Now we can easily sort them

0.105 < 0.108 < 0.109 < 0.123

respective names in sorted order are:

Spotless soap < Bright wash < Lemon bright < lot of suds

g Programs submitted by programs in a computer science course are examined for syntax errors and logic errors. Suppose 36% of all programs have syntax errors, 47% have logic errors, and 56% have at least one of those two error types. (a) What is the probability a program contains both error types? (b) What is the probability a program contains neither error type? (c) What is the probability a program has logic errors, but not syntax errors? (d) What is the probability a program either has no syntax errors or has no logic errors?

Answers

Answer:

The answer is below

Step-by-step explanation:

Let S denote syntax errors and L denote logic errors.

Given that P(S) = 36% = 0.36, P(L) = 47% = 0.47, P(S ∪ L) = 56% = 0.56

a) The probability a program contains both error types = P(S ∩ L)

The probability that the programs contains only syntax error = P(S ∩ L') = P(S ∪ L)  - P(L) = 56% - 47% = 9%

The probability that the programs contains only logic error = P(S' ∩ L) = P(S ∪ L)  - P(S) = 56% - 36% = 20%

P(S ∩ L) = P(S ∪ L) - [P(S ∩ L') + P(S' ∩ L)] =56% - (9% + 20%) = 56% - 29% = 27%

b) Probability a program contains neither error type= P(S ∪ L)' = 1 - P(S ∪ L) = 1 - 0.56 = 0.44

c)  The probability a program has logic errors, but not syntax errors =   P(S' ∩ L) = P(S ∪ L)  - P(S) = 56% - 36% = 20%

d) The probability a program either has no syntax errors or has no logic errors = P(S ∪ L)' = 1 - P(S ∪ L) = 1 - 0.56 = 0.44

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Programs with syntax errors ; n(S) = 36%

Programs with logic errors; n(L) = 47%

Programs with atleast one of the two errors = 56%

P(S) = 0.36 ; p(L) = 0.47

P(SnL) = x

P(S) only + p(L) only + p(SnL) = 0.56

P(S) only = 0.36 - x

P(L) only = 0.47 - x

P(SnL) = 0.36 - x + 0.47 - x + x = 0.56

0.83 - x = 0.56

x = 0.27

B) probability that program contains neither error :

1 - p(program contains atleast one of the two errors)

1 - 0.56 = 0.44

C) probability of logic error but no syntax error :

P(L) - p(SnL)

= 0.47 - 0.27

= 0.20

Choose the correct answer below.
A. The level of​ significance, ​, is the probability of committing a Type I​ error, rejecting the null hypothesis when it​ is, in​ fact, true.
B. The level of​ significance, ​, is the probability of committing a Type I​ error, rejecting the null hypothesis when it​ is, in​ fact, true.
C. The level of​ significance, ​, is the probability of committing a Type II​ error, not rejecting the null hypothesis when it​ is, in​ fact, false.
D. The level of​ significance, ​, is the probability of committing a Type II​ error, rejecting the null hypothesis when it​ is, in​ fact, true.
E. The level of​ significance, ​, is the probability of committing a Type II​ error, rejecting the null hypothesis when it​ is, in​ fact, true.
F. The level of​ significance, ​, is the probability of committing a Type I​ error, not rejecting the null hypothesis when it​ is, in​ fact, false.

Answers

Answer: The level of​ significance, ​, is the probability of committing a Type I error, rejecting the null hypothesis when it​ is, in​ fact, true.

Step-by-step explanation:

The significance level, which is commonly designated as alpha (α) is defined the probability of rejecting the null hypothesis when it is in fact, true.

To determine statistical significance, a researcher is expected to calculate a p-value. The researcher can reject the null hypothesis if the p -value is less than α as established by the researcher.

What is the solution to this equation? 2x - 5 + 3x = 35 A. x = 6 B. x = 8 C. x = 20 D. x = 15

Answers

Answer:

B. x = 8

Step-by-step explanation:

Other Questions
What is a polar and non-polar molecules? What do plants take into their structures in order to photosynthesize. Name all things they take in. Adam built a rectangular vegetable garden that has a length of 6.6 feet and awith of 3 1 feet. What is the area of his garden? Find the linear function, f(x) , passing through the points: (5,7) and (2,7) .Enter your answer using function notation where did jesus teach?? pls explain Do Some vertebrates' offspring develop inside the mothers body. What is an appropriate way to differentiate alphabet knowledge instruction?-Teachers can make sure to avoid cumulative activities in their lessons.-Teachers can make sure that children are engaged in multiple activities at once.-Teachers can adjust the number of letters introduced at one time.-Teachers can conduct lessons that are above the children's current level so that everyone in the class is challenged. J.S. Hart (Can. J. Zool. (1956) 34, 1, pp. 53-57) described seasonal changes in insulation of the fur of nine species of arctic and North temperate zone mammals. Relative seasonal changes ranged from 12 to 52% of the winter coat insulation value. Absolute changes were greatest in the largest mammals with thickest fur. Indicate if the following statements that are true or false.a. Increasing fur thickness would reduce conduction between the animal and the environment True or Falseb. Animals with thicker fur compared to those with thinner fur have different metabolic rates when measured at the same ambient temperature below the thermal neutral zone (TNZ). True or falsec. Endothermic mammals are most often classified as homeotherms. True or falsed. Fur does not affect the rate of convective and conductive heat loss in the cold. True or falsee. Changes in fur thickness is associated with an expression of a unique phenotype that optimizes fitness for a given environmental temperature. True or false Help ASAP!! Chlorine's 3p sublevel has 5 electrons in it. It needs _____ electron(s) more in the 3p sublevel to make it stable.a). 5b).4c).3d).2e).1 What did Mesopotamian settlers create to protect crops from seasonal droughts? canalsclay pots mud walls reed dams When listening to someone in trouble, you should be They have not done their jobs. change into passive What line of code will import matplotlib in it The general adaptation syndrome response includes __________.A.alarm, resistance, and exhaustionB.instinct, rapid heartbeat, and flightC.depression, shallow breathing, and fightD.none of the above Is a 3.86 weighted gpa good for freshman year of highschool? I am in 4 honors classes, 1 AP, and 2 standard. Keep in mind this is not on the 4.0 scale(unweighted) and is weighted. Residents of South Florida fear which of the following (select all that apply)? PLEASE HELP PLEASE HELP FASTTTTTTT The chemical name for laughing gas is dinitrogen oxide. The two elements found in a sample of this gas are and . Solve, show your work. Solve 5x + 4 = 14x - 14 What is an ecosystem? Why is it important to protect the ecosystem?