Because:

+) Kate is the 18th from the front:

⇒Kate is the 18th child (from the front)

+) John is the 32nd from the back:
​​⇒John is the 8th child (from the front)

⇒There are 9 children between Kate and John

Mai has notebooks is :

     3+4=7 notebooks

James has notebooks is :

      7+4=11 notebooks

           Answer : 11 notebooks

Mai has notebooks is :

     3+4=7 notebooks

James has notebooks is :

      7+4=11 notebooks

           Answer : 11 notebooks

Numbers students femsla are in class is : 

                      60 x 3/5 = 36 (students)

Numbers students male are in class is : 

                      60 - 36 = 24 (students)

                         Answer : 24 students

Numbers sweet is the biggest that he can get from the shop is : 

                                         30 : 3 = 10 (sweet)

                                                 Answer : 10 sweet 

We have : x < -0.8 ⇒ x + 0,8 < 0 ⇒|x + 0.8| = -(x + 0.8)

                 x < -0.8 ⇒ x < 25 ⇒ |x - 25| = 25 - x

Candle A = -(x + 0.8) - (25 - x) + 1.9

                = -x + 0,8 - 25 + x + 1,9

                = -x + x - 0,8 - 25 + 1,9

                = -25,8 + 1,9

            A = -23,8

     A = -x - 0.8 - 25 + x + 1.9

     A = -23.9 

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Put A = 1.2 + 2.3 + 3.4 + ....... + 199.200

 => 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ....... + 199.200.201

=> 3A = 199.200.201

=> A = 199.200.201/3

=> A = 2666600

That worker makes 3 tools out of time is:

                          12 hours - 7 hours 30 minute = 4 hours 30 minute = 4,5 hours

The worker makes 1 product time out is :  

                          4,5 : 3 = 1,5 (hours)

                                 Answer : 1,5 hours

That worker makes 3 tools out of time is:

                          12 hours - 7 hours 30 minute = 4 hours 30 minute = 4,5 hours

The worker makes a product time out is :  

                           4,5 : 3 = 1,5 (hours)

                                 Answer : 1,5 hours

Land : A = 1.3 + 3.5 + 5.7 + ...... + 99.101

=> 4A = 1.3.(5 - 1) + 3.5.(7 - 3) + ...... + 99.101.(103 - 99)

=> 4A = 1.3.5 - 1.3.5 + 3.5.7 - 3.5.7 + ...... + 99.100.101

=> 4A = 99.100.101

=> A = 99.100.101/4

=> A = 249975

From 7m + 5n = 31, we can see that 7m or 5n is even.

- If 7m is even, m is even and prime => m = 2.

=> 5n = 31 - 7 x 2 = 17. n ⋮̸⋮̸ 5, so no numbers sastify the problem.

- If 5n is even, n is even and prime => n = 2.

=> 7m = 31 - 5 x 2 = 21 => m = 3 is a prime number.

The value of: mⁿ + n^m = 32 + 23 = 9 + 8 = 17.

Land A = 1.2 + 2.3 + 3.4 + ....... + 199.200

 => 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ....... + 199.200.201

=> 3A = 199.200.201

=> A = 199.200.201/3

=> A = 2666600

We have : \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.......+\dfrac{1}{99.101}\)

              \(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+.......+\dfrac{2}{99.101}\right)\)

              \(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+......+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

               \(=\dfrac{1}{2}\left(1-\dfrac{1}{101}\right)\)

                \(=\dfrac{1}{2}.\dfrac{100}{101}\)

                \(=\dfrac{50}{101}\)

C = 1² + 2² + 3² + ...... + 100²

    = 1.1 + 2.2 + 3.3 + ...... + 100.100

    = 1.(2 - 1) + 2.(3 - 1) + 3.(4 - 1) + ...... + 100.(101 - 1)

    = 1.2 - 1 + 2.3 - 2 + 3.4 - 3 + ....... + 100.101 - 100

    = (1.2 + 2.3 + 3.4 + ...... + 100.101) - (1 + 2 + 3 + ...... + 100)

    From the calculated results of A and B we should compute

 C = 333300 - 5050

 C = 328250 

B = 1 + 2 + 3 + ...... + 100

B is numbered as:

           100 - 1 + 1 = 100 (số)

Total B is:

           (100 x 101) : 2 = 5050 

We have : A = 1.2 + 2.3 + 3.4 + ...... + 100.101

    =>       3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ....... + 99.100.101 

    =>       3A = 99.100.101

    =>         A = 99.100.101/3

    =>         A = 333300

We have: abcdeg = abc000 + deg
                            = abc. 100000 + deg
                            = abc. 99999 + (abc + deg)
Which  99999 is divisible by 37 so abc. and abc + deg is divisible by 37

Candle 99999 is divisible by 37
So the distribution is divided by 37 (ddcm)