One hundred students are assigned lockers 1 through 100. The students assigned to locker 1 opens all 100 lockers. The student assigned to locker 2 closes all lockers that are multiples of 2. The student assigned to locker 3 changes the status of all lockers ( e.g., locker 3 is open gets closed and locker 6 that is closed gets opened) The student assigned to locker 4 changed the status of all lockers whose multiples of 4, and so on for all 100 lockers.

PLEASE HELP ME I HAVEN'T STARTED ITS DUE TMRW

Answers

Answer 1

Answer:

The perfect square lockers are the only ones left open.

Step-by-step explanation:

Here is a legit link to an explanation of this old puzzle problem!

https://36university.com/act-math-locker-problem-solution/

Quoting from that page:

Method 2: Who Touches Which Lockers

Identifying which students touch which lockers is a little less of a brute-force approach and would likely have gotten you to the solution a little more quickly.

Here’s what I mean:

Consider locker #1. The only student who touches locker #1 is student #1. Student 1 opens the locker, and since no one else touches it, it will be left open at the end.

Consider locker #2. Student 1 opens the locker, and student 2 closes it. No one else touches the locker, so it will be closed.

Consider locker #10. Students 1 opens the locker. Student 2 closes it. Students 3 and 4 skip right by it. Student 5 opens it. Students 6, 7, 8, and 9 skip right by it. And student 10 closes it. Locker #10 will be closed.

Mental Milestone 1: After looking at several lockers, you should notice that lockers are only changed by student numbers that are factors of the locker number. In other words, locker 12 is changed by students 1, 2, 3, 4, 6, and 12.

Mental Milestone 2: You should also have noticed that factors always come in pairs. This means that for every student who opens a locker, there is another student who closes it. For locker #12, student 1 opens it, but student 12 closes it later. Student 2 opens it, but student 6 closes it later. Student 3 opens it, but student 4 closes it later.

By this logic, every locker would be closed.

But there are exceptions!

Consider locker #25. Student 1 opens it. Student 5 closes it. Student 25 opens it. The locker will be left open, but why? In this case, the factors do not come in pairs. One and 25 are a pair, but five times five is also 25. Five only counts as one factor. This causes the open-close pattern to be thrown off. Locker #25 is left open.

Mental Milestone 3: When factors don’t come in pairs, the locker will be left open. And factors don’t come in pairs when numbers are multiplied by themselves. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…) are the only numbers whose factors don’t come in pairs because one set of factors, the square root, is multiplied by itself. This means that only perfect square lockers will be left open.

Locker #s 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are left open!


Related Questions

pls help me with this:(((((​

Answers

2: c

Step-by-step explanation:

3: a

by Supplementing each answer Into the equation

Step-by-step explanation:

what don't you understand about this ? did you never solve 2 equations with 2 variables ?

it is really easy. there are 2 main approaches :

1. substitution. you use one of the two equations to express one variable by an expression purely in the other variable. then you use that in the other equation (resulting in one equation with one variable) and solve it. with that result you go back to the other equation and calculate the other variable.

2. equation arithmetic. when the terms of at least one of the variables are similar in both equations, you can multiply (if needed) one or both equations (left and right side !) by a fitting number and then add it subtract one equation from the other, so that you are left with one equation in one variable, which you solve. with that result you go back to any of the original equations and calculate the other variable.

there would be a third option for questions like this :

3. trial and error. simply put the point coordinates as x and y into both equations, and see for what point(s) both remain true.

but in order to show you the methodical approaches, we will use substitution for question 2 and equation arithmetic for question 3.

2)

2x + y = 5

-x + 2y = 5

I use the first equation to transform. and I get

y = 5 - 2x

with that I go into the second equation :

-x + 2(5 - 2x) = 5

-x + 10 - 4x = 5

-5x = -5

x = 1

and with that I get

y = 5 - 2×1 = 5 - 2 = 3

so, C (1, 3) is the right answer.

3)

2x + y = 7

-x + y = 1

let's subtract the second equation from the first :

2x + y = 7

- -x + y = 1

------------------

3x + 0 = 6

3x = 6

x = 2

with that I go into one of the original equations :

-2 + y = 1

y = 3

so, A (2, 3) is the right answer.

kelsey bought a new jackat. the jackat costs $ 150.00 she will pay 7% in sales tax how much money will she pay in sales tax

Answers

Answer:

10.50

Step-by-step explanation:

Answer:

she will pay $10.50 in sales tax and $160.50 in total

Step-by-step explanation:

first, find 7% of 150.

150*.07=10.5

add 10.5 to the total

Can you do it?I can’t understand

Answers

Answer:

489,162

Step-by-step explanation:

Hope it can help you lovelots

What is the equation for this? please help!!

Answers

Answer:

the equation is y=x^2+8

a group can plant 3/4 acres in 1 7/8. What os the unit rate in acres per day? Write your answer in simplest form.

Answers

1 3/5+7 8/9=9 2/5 is the correct answer

h3elpppp pleaseeeehejejrhegss

Answers

Answer:

First is 1, then 2, then 10

Step-by-step explanation:

I think this is right, could be completely wrong but I did blank times 50 equals 50, that is 1. Repeated with all the problems.

if you add 5 to me then divide 7, and add 12 then subtract 7 you get 10 what number am i

Answers

Answer:

hii the answer is 30 :D have a nice day

i dont even think i'm right but ok

didn't you just say you got the number 10? i'm guessing the number is 10

Ellie hikes 1/2 of a mile every 10 minutes. How far does she hike in 1 hour?
Answer choices:
3
5
4
6

Answers

Answer:

3miles

Step-by-step explanation:

10 minutes is 1/6 of an hour, so in 1 hour ellie would hike 1/2*6=3miles

Answer:

Step-by-step explanation:

There are various ways in which we can solve this problem.

If we're told that Ellie can hike 1/2 mile in 10 minutes, then multiplying both sides of "1/2 mile = 10 minutes" by 6 yields 3 miles in 60 minutes.

Alternatively:  "1/2 mile = 10 minutes" becomes "1 mile in 20 minutes" by the same approach.  Then, multiplying both sides by 3 yields "3 miles in 60 minutes," or "3 miles in 1 hour."

Solve:

two fifths plus seven fifteenths equals blank
Question 3 options:

thirteen fifteenths

nine fifteenths

nine twentieths

nine fifths

Answers

Answer:

[tex]\frac{13}{15}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] + [tex]\frac{7}{15}[/tex] = [tex]\frac{2.3}{5.3}[/tex] + [tex]\frac{7}{15}[/tex] = [tex]\frac{6}{15}[/tex] + [tex]\frac{7}{15}[/tex] = [tex]\frac{13}{15}[/tex]

Answer number 11 to see if your smarter than my students

Answers

the awnser 2=2=2=2=22=2=2=2=2=2+0+7867+

What are numbers that add to 50 and subtract to 10

Answers

Answer:

30 plus 20 is 50

30 minus 20 is 10


Find -5(-12) + (-15)
With explanation please i forgot how to do it

Answers

Answer:

45

Step-by-step explanation:

-5(-12)+(-15)

--> Multiply -5 and -12 to get 60

60-15

--> Subtract 15 from 60 to get 45

Hope this helps you!


The steps for deriving the Quadratic Formula are shown. Which is the BEST choice for the missing reason?

A) simplify
B) divide by a
C) complete the square
D) take the square root of both sides

Answers

Answer:

answer choice is B

Step-by-step explanation:

System of equations pls help me

Answers

Answer:

x=6 and y=5

Step-by-step explanation:

We can eliminate the "x" variable by adding the two equations to get 6y=30. This means that y=5.

If we plug y=5 back into one of the original equations:

5x+y=35

5x+5=35

5x=30

x=6

-5x+5y=-5

-5x+5(5)=-5

-5x+25=-5

-5x=-30

x=6

Which confirms that x=6 and y=5 are indeed the correct solutions

Answer:

x=6 ,y=5

Step-by-step explanation:

6y=30,y=5

x=6

Need help with this ASAP I’ll mark brainliest

Answers

Answer:

B' (3, 1 )

Step-by-step explanation:

Given

A (- 1, 3 ) → A' (- 3, 7 )

x- coordinate goes from - 1 → - 3 , that is - 2

y- coordinate goes from 3 → 7 , that is + 4

Translation rule is (x, y ) → (x - 2, y + 4 ) , then

B (5, - 3 ) → B' (5 - 2, - 3 + 4 ) → B' (3, - 1 )

Find the value of x in the equation below. 5.4=2x

Answers

Answer:

x = 2.7

Step-by-step explanation:

5.4 = 2x

2x = 5.4

Divide both sides by 2.

x = 2.7

Answer: x= 2.7

1. Divide 2 on both sides

2. cancel terms who have the same numerator and denominator

Use parallelogram ABCD. What are the values of x and

y?

A

4y-3

B

x=

y =

3x-9

42

D

37

С

Answers

Answer:

the value of x is a number but you can say 1 when you are factorising quadratic expression with the terms

Answer:

x=17

y=10

Step-by-step explanation:

3 2/7 divided by 1 1/4

Answers

Answer:

92/35

Step-by-step explanation:

⇒ 3 2/7 ÷ 1 1/4

⇒ (3*7 + 2) / 7  ÷ (1*4 + 1) / 4

⇒ 23/7  ÷  5/4

⇒ 23 * 4 /  7 * 5

⇒ 92/35

The solution of the expression is 2 22/35.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The expression is,

3 2/7 divided by 1 1/4

Now, Solve the expression as;

3 2/7 ÷ 1 1/4

23/7 ÷ 5/4

23/7 x 4/5

92/35

2 22/35

Hence, The solution of the expression is 2 22/35.

Learn more about the division method visit:

https://brainly.com/question/28783040

#SPJ5

Dija writes 7x 9 = 63 to find the
number of players on 7 baseball teams. Describe what
each of the factors represents in the multiplication equation.

Answers

Answer:

7 represents the number of teams. 9 represents the amount of players on each team. And 63 represents the total number of players.

Step-by-step explanation:

How do the expressions 2q2−3p and 2(p+q)/q compare when p = 8 and q = 4?Drag a symbol into the box to correctly complete the statement.2q2−3p Response area 2(p+q)/q when p = 8 and q = 4.=<>

Answers

Answer:

The answer is ">"

Step-by-step explanation:

I took the quiz epicly

Answer:

>

Step-by-step explanation:

identify the construction that the figure represents

Answers

Answer:

  (b)  congruent segments

Step-by-step explanation:

One copies the length of a segment to make congruent segments. This is done by setting the compass radius to the length of the segment to be copied, then marking the segment length on another line using a given point as a center.

_____

Additional comment

The appearance here is that the segments are not actually congruent, so apparently a mistake has been made in the construction. No angles are shown, and there aren't enough points or arcs shown to support a conclusion that some other construction is being attempted.

Pls answer this and explain!

Answers

Answer:

Well if you add up all 3 angles in a triangle you’d get 180 degrees as the answer.

So we can. Jus substitute.

For number 19 you can do this

57+x+x+87+50=180

Now combine like terms

194+2x=180

Now solve

x=-7

Now we can subsitute that into angle A

57+ (-7) which is 50

Measure of angle A is 50.

For number 19 it’s the same thing.

9x+14+16x-4+80=180

Now combine like terms

25x+90=180

Solve

25x= 90

x= 3.6

Now subsitue for A

3.6*9+4 which is 36.4

A is 36.4

If the area of the trapezoid shown is 200 square feet, what is the height h of the trapezoid?

Answers

Answer:

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]   or  10.42 = h

Step-by-step explanation:

The area of a trapezoid is [tex]A = \frac{1}{2}h(b_{1} + b_{2} )[/tex].

[tex]200 = \frac{1}{2}h(10\sqrt{2} + 14\sqrt{3})[/tex]

[tex]400 = { h(10\sqrt{2} + 14\sqrt{3} )[/tex]             Multiply both sides by 2

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]

 [tex]\frac{400}{38.39} = h[/tex]

10.42 = h  

Please help! :0 :0 PLEASEEEEEE

Answers

Answer:

i would say either F or G

i guess choose F

Answer:

8

Step-by-step explanation:

how to turn 40/3 into mixed fraction please give correct abs for brainliest..

Answers

13 1/3 because 40 divided 3 is 13 ….

x =

12
9
6 2/3
help me out please you guys are awesome ^-^

Answers

the answer is x =  6 2/3

ok done. Thank to me :>

The mass of a tin of paint is 890 grams, correct to the nearest 10 grams. Workout the upper bound of the total mass of 10 tins of paint.

Answers

Answer:

8900

Step-by-step explanation: :þ

Le regioni italiane bagnate dal mare sono un insieme?

Answers

Answer:

non so cosa intendi per intero

Step-by-step explanation:

Può essere più preciso?

Solve the question will mark branliest and with an explantion

Answers

Answer:

The car loses $5,635 every year. Multiply 24,500 by 23% (0.23)

Which number represents a square root of 3 [cos(pi/2) + i sin (pi/2)]?

Answers

Answer:   Choice B

===========================================================

Explanation:

We use De Moivre's Theorem. It says that if you started with

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

then raising both sides to the nth power leads to

[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

The complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

What is a complex number?

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number in the trigonometric form:

Z = √(3[cosπ/2 + i sinπ/2])

It is required to find the square root of the complex number.

To find the square root of the complex number we can use the De Moivre's theorem:

If

Z = r[cosθ + i sinθ]

Zⁿ = rⁿ[cosnθ + i sinnθ]

Using the above theorem:

Z =  √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]

Z =  √3[cosπ/4 + i sinπ/4]

Thus, the complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ5

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