1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
2 years ago
12

Suppose there are 200 lockers and 200 students. Kayla reasons that since there are 10

Mathematics
1 answer:
Rus_ich [418]2 years ago
5 0

Answer:

Kayla's reasoning is not correct.

Step-by-step explanation:

The locker problem is as follows:

Imagine you are at a school that has student lockers. There are 200 lockers, all shut and unlocked, and 200 students. Suppose the first student goes along the row and opens every locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it). The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the 200 students have followed the pattern with the 200 lockers. At the end, which lockers will be open and which will be closed? Why?

Solution:

So from the information we know that the first student goes along the row and opens every locker.

Then the second student shuts every other locker, i.e. locker numbers 2, 4, 6, 8, 10, ..., 196, 198 and 200.

Then the third students changes the state of every third locker, i.e. he/she closes an open locker and opens a closed locker.

So the open lockers are: 1, 5, 6, 12,...

Then the fourth students changes the state of every fourth locker.

So the open lockers are: 1, 4, 5, 6, 8,....

So, on we will observe that the open lockers have a perfect square number such as, 1, 4, 9, 16,....

Consider that the pattern is as follows:

Student 1 opens the locker, Student 2 closes it, Student 3 opens it, person 4 Student and so on.

This is because the square numbers always have an odd number of factors, which leads them to be open at the end.

Take any locker number, 40, for example. Its state (open or closed) is changed for every student whose number in line is a factor of the locker number.

Student      Locker 40 status

     1                    Open

     2                   Close

     4                   Open

     5                   Close

     8                   Open

     10                  Close

    20                  Open

    40                  Close

Like all other lockers numbered with non-square numbers, it ends up closed after all the students have gone through the line because it has an even number of factors.

Consider the locker number 16:

Student      Locker 16 status

     1                    Open

     2                   Close

     4                   Open

     8                   Close

     16                  Open

Thus, we can conclude that all the doors with square numbers on them will remain open because all square numbers have an odd number of factors and the doors with non-square numbers on them will remain close because they have even number of factors.

There will be a total of 14 lockers open.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 and 196

So, if there are 10 lockers open in the first 100 lockers there must be only 4 other lockers opened in the next 100.

You might be interested in
An elementary school is in a growing suburb. The schools principal estimates that the current enrollment of 750 students will in
Murrr4er [49]

Answer:

Step-by-step explanatio2+2 21n:

7 0
3 years ago
Answer question 7, please with steps
vladimir2022 [97]

Answer:

Angles FVE, FVD, and EVD have V as a vertex

Step-by-step explanation:

If V is the vertex of an angle, it's the point of that angle. So, it wants every angle you can make where V is the point of it.

5 0
2 years ago
Read 2 more answers
a container holds 15 pennies 8 nickels and 10 dimes you will randomly select two coins without replacement what is the probabili
AlexFokin [52]
<span>A container holds 15 pennies, 8 nickels, and 10 dimes. 
You will randomly select two coins without replacement. 
-->Fill in the probabilities on a tree diagram.</span>
3 0
3 years ago
One cylinder has a volume that is 8 mc018-1.jpg less than mc018-2.jpg of the volume of a second cylinder. If the first cylinder’
Hatshy [7]
The anwser to it is 57



4 0
3 years ago
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
Kisachek [45]
So, I'm going to break it down to help you understand it a bit more.

If it starts at (0,-2) and crosses through (1,0) that means it moved to the right once and up twice. Which means, that the slope will be 2. If it were one it would be to the right 1 up one, if it were 4 it would be to the right 1 up 4, and finally if it were 1/2 it would be to the right 2 up 1. 

So, your answer is C. or 2. 
7 0
3 years ago
Other questions:
  • Need help with this!!!!!!!!
    8·1 answer
  • Can you help me with question 8?
    12·1 answer
  • How do i evaluate the expression below????<br><br><br><img src="https://tex.z-dn.net/?f=%20%7B4%7D%5E%7B2%7D%20%5Ctimes%20%7B4%7
    12·1 answer
  • If the circle in the diagram revolves about the vertical dashed line, which type of geometrical shape will it generate?
    9·1 answer
  • Law of sines: sin(A)/a=sin(B)/b=sin(C)/c How many distinct
    15·1 answer
  • X 1 2 3 4 5 Y 1 3 5 7 9
    6·1 answer
  • The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systo
    10·1 answer
  • what is the quadratic equation for this graph? will make brainiest if also tell me how to put into vertex from
    9·1 answer
  • PLEASE HELP ASAP 100 POINTSSS!!!!!
    7·1 answer
  • A farm has chickens and cows. All the cows have 4 legs and all the chicken have 2 legs. All together, there are 82 cow and chick
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!