The concentration of the mixture obtained by mixing two solutions, a and b, is 20%. the concentration of the second mixture obtained by mixing the same two solutions is 14.8%. find the concentration of each of the solutions a and b, if the first mixture is obtained by mixing them in 1: 1 ratio and the second is obtained by mixing them in 3: 7 ratio.

Concentration of solutions A and B are 33% and 7% respectively.

Step-by-step explanation:

Suppose, the concentration of solutions A and B are and respectively.

First mixture

Ratio of solutions A and B is 1 : 1

Lets assume the amount of solution A is and amount of solution B is

Total amount of first mixture and concentration of first mixture is 20%

So, the first equation will be.......

Second mixture

Ratio of solutions A and B is 3 : 7

Lets assume the amount of solution A is and amount of solution B is

Total amount of first mixture and concentration of first mixture is 14.8%

So, the second equation will be.......

From equation (1), we will get :  

Now substituting this into equation (2)......

Plugging this into equation (1), we will get......

So, the concentration of solution A is 0.33 or 33%  and the concentration of solution B is 0.07 or 7%

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

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step-by-step explanation: