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Nady [450]
3 years ago
15

The number of apples in the box was less than 80. It is possible to divide all the apples evenly among 3, 4, and 5 children. How

many apples were in the box?
Mathematics
1 answer:
ANEK [815]3 years ago
6 0

Answer:

60 apples

Step-by-step explanation:

There are some number of apples in the box which is less than 80.

Now, it is given in the condition that all the apples can be divided evenly among 3, 4, and 5 children.

Therefore, the number of apples is a common multiple of 3, 4, and 5 which is less than 80.

Now, multiples of 3 less than 80 are 78, 75, 72, 69, 66, 63, 60, etc.

And, multiples of 4 less than 80 are 76, 72, 68, 64, 60, 56, etc.

Again, multiples of 5 less than 80 are 75, 70, 65, 60, 55, etc.

Therefore, the common multiple less than 80 is 60.

Hence, there were 60 apples in the box. (Answer)  

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Step-by-step explanation:

<u>Given functions:</u>

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4 years ago
Suppose that you toss a fair six-sided {1,2,3,4,5,6} die and let X represent the outcome obtained. Find the expected volume of a
timofeeve [1]

Answer:

The expected volume of the box is 364 cubic inches.

Step-by-step explanation:

Since the die is fair, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. Let Y represent the volume of the box in cubic inches. For how the box is formed, Y = X²*24. Thus, the value of Y depends directly on the value of X, and we have

  • (When X = 1) Y = 1²*24 = 24, with probability 1/6 (the same than P(X=1)
  • (When X = 2) Y = 2²*24 = 96, with probability 1/6 (the same than P(X=2)
  • (When X = 3) Y = 3²*24 = 216, with probability 1/6 (the same than P(X=3)
  • (When X = 4) Y = 4²*24 = 384, with probability 1/6 (the same than P(X=4)
  • (When X = 5) Y = 5²*24 = 600, with probability 1/6 (the same than P(X=5)
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As a consequence, the expected volume of the box in cubic inches is

E(Y) = 1/6 * 24 + 1/6*96 + 1/6*216+ 1/6*384+ 1/6*600+1/6*864 = 364

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