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Alex73 [517]
3 years ago
7

A chemist mixes an 8% hydrochloric acid solution with a 5% hydrochloric acid solution. How many millilitersof the 5% solution sh

ould the chemist use to make a 750-milliliter solution that is 7% hydrochloric acid?
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0
Let x be volume of 5% acid and y be volume of the 8%


x + y = 750  and 
0.05x + 0.08y = 0.07*750 =  52.5

from first equation y = 750 - x so substituting in the second equation:-

0.05x + 0.08(750 - x) = 52.5
0.05 - 0.08x = 52.5 - 60
-0.03x = -7.5
x =  -7.5 / -0.3 =  250 mls  <------ answer

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The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 a. Is this probability di
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Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

b. Calculate the expected value of x.

c. Calculate the variance of x.

d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x      P(x)         xP(x)           x²            x²P(x)

0    0.25           0               0                0

1     0.20        0.20             1              0.20

2    0.15          0.3               4             0.6

3    0.30         0.9               9             2.7

4    0.10          0.4               16             1.6

   ∑P(x)=1     ∑xP(x)=1.8               ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

\sum P(X)=0.25+0.20+0.15+0.30+0.10

\sum P(X)=1

Yes it is a probability distribution.

b) The expected value of x is defined as

E(x)=\sum xP(x)=1.8

c) The variance of x is defined as

V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86

d) The standard deviation of x is  defined as

\sigma=\sqrt{V}

\sigma=\sqrt{1.86}

\sigma=1.136

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