A manufacturer ships its product in boxes of 4 inches if 12 boxes are completely filled the cartoon what is the volume of the cartoon?

Answer:

John's number is 1500

Step-by-step explanation:

* Lets explain how to solve the problem

- Factors of a number are the numbers you multiply to get the number

- Ex: Factors of 12 are 1 × 12 , 2 × 6 , 3 × 4

- The factors of a number smaller than or equal the number

- Multiple of a number is that number multiplied by an integer

- Ex: 2, 4, 6, 8, and 10 are multiples of 2

- The multiples of a number greater than or equal the number

* Lets solve the number

- John is thinking of a number

- He gives the following 3 clues

# The number has 125 as a factor

# The number is a multiple of 30

# The number is between 800 and 2000

∵ 125 is a factor of the number

- Assume that the number is 125 (its factors 1 , 5 , 25 , 125)

∵ The number is a multiple of 30

- Assume the number is 30 (the first multiple of 30)

- To solve the problem lets find the lowest common multiple of 125

  and 30 by using prime numbers only

∵ The prime factors of 125 = 5 × 5 × 5

∵ The prime factors of 30 = 2 × 3 × 5

- L.C.M of the two numbers is the product of their prime factors

 without reputation

∴ L.C.M = 5 × 5 × 5 × 2 × 3 = 750

∵ 750 has 125 as a factor

∵ 750 is a multiple of 30

- But 750 is not between 800 and 2000

∴ Find a multiple of 750 and between 800 and 2000

∵ 2 × 750 = 1500

* lets check the three clues

∵ 1500 has 125 as a factor

∵ 1500 is a multiple of 30

∵ 1500 is between 800 and 2000

∴ John's number is 1500

Answer:

Yes, the ratio of the number of students on the team to the number of students trying out is same for both girls and boys.

               The ratio is: 2:5

Step-by-step explanation:

It is given that:

• Out of 30 girls who tried out for the lacrosse team Euclid middle school 12 were selected.

This means that the ratio of the number of girls on the team to the number of girls trying out is:

   12/30=2/5

• Also, 40 boys Who tried out 16 were selected .

This means that the ratio of the number of boys on the team to the number of boys trying out is:

     16/40=2/5          

Hence, we get that the ratio is same for boys and girls i.e. 2:5

Answer:

Option (b).

Step-by-step explanation:

It is given that Adrian built a structure out of 10 congruent cubes.  

Volume of each cube = 8 cubic centimetres.

We need to find the total volume of the structure.

Total volume = No. of cubes × Volume of each cube

Therefore, the total volume of the structure is 80 cubic centimetres.

Hence, option (b) is correct.