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lozanna [386]
3 years ago
8

How many liters each of a 25% acid solution and a 50% acid solution must be used to produce 80 liters of a 40% acid solution?

Mathematics
1 answer:
alina1380 [7]3 years ago
4 0

Answer:

  • 32 and 48 liters

Step-by-step explanation:

Let 25% solution is x liters, then 50% solution is (80 - x) liters.

<u>Acid content is going to be same:</u>

  • 0.25x + 0.5(80 - x) = 80*0.4
  • 0.25x - 0.5x + 40 = 32
  • 0.25x = 8
  • x = 8/0.25
  • x = 32 liters

So 32 liters of 25% solution and 80 - 32 = 48 liters of 50% solution

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
sleet_krkn [62]

This question is incomplete, the complete question is;

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.

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Step-by-step explanation:

Given the data in the question;

Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1

this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.

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\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right]

= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]

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= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

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