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padilas [110]
2 years ago
13

A The integer with the greatest value is the one that has the greatest absolute value.

Mathematics
1 answer:
pentagon [3]2 years ago
5 0

Answer: B The integer with the greatest value is one that is farthest from zero on the number line.

Step-by-step explanation: hope it correct :D

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Suppose there are 200 lockers and 200 students. Kayla reasons that since there are 10
Rus_ich [418]

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.

5 0
3 years ago
Here is a rectangle ABCD. The length of the rectangle is increased by 10%. The width of the rectangle is increased by 5%. Find t
sladkih [1.3K]

Answer: Width would become 21 and length would become 33. Original perimeter is 100, increased perimeter is 108 which is a 7.69% increase

6 0
2 years ago
Help I forgot how to do this​
lakkis [162]

Answer:

number 5 is 11 and number 6 is 16

Step-by-step explanation:

you substitute a for 4 bc a equals 4 and than finish the equation 4+7=11

6. you substitute b for 2 and c for 8 and multiply which than is 16

4 0
3 years ago
Policeman A and Policeman B hand out 70 speeding tickets in a month.
Inessa05 [86]

Answer:

Policeman A = 56 tickets

Step-by-step explanation:

Policemen A + B = 70

If Policeman B hands out x no of tickets...

Then Policeman A hands out 4x no of tickets

meaning...

x + 4x = 70

5x = 70

x = 70/5

x = 14

Therefore Policeman A hands out..

4x = 4 × 14 = 56 tickets

8 0
3 years ago
How do I do it and show my work along with it?
Rudiy27
Be kind and say please,that is being rude when you don't say it. Well, how much times does 6 go into 34? 5 times right. So then put 30 under the 34. You get 4. So then bring down the 5. How much times does 6 go into 45. 7 right. So then put 42 under 45. You get 3. Now add a decimal point after the 5 and after the 7. Add zero after the 5 . Bring down the zero. How much times does 6 go into 30? 5 times, so you put 30 under 30 and get zero. If you have any more questions,please leave them below in the comments.
8 0
3 years ago
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