The next term in the sequence will be increased by 27.
The difference between 15 and 34 is 19
The difference between 34 and 55 is 21
The difference between 55 and 78 is 23
The difference between 78 and 103 is 25
Following this pattern, the next number will be 130
Answer: choice A. 40 liters
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Explanation:
x = number of liters of the 50% alcohol solution
If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).
So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below
0.50*x + 36 = 0.70*(40+x)
0.50*x + 36 = 0.70*(40)+0.70*(x)
0.50*x + 36 = 28+0.70*x
36 - 28 = 0.70*x - 0.50x
8 = 0.20x
0.20x = 8
x = 8/0.20
x = 40
So that is why the answer is choice A. 40 liters
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant
With our equation, plug in the values:
Next, solve the exponent and multiplications:
Next, solve the subtraction:
Next, factor out i (i = √-1):
Next, solve the square root:
Lastly, divide and <u>your answer is:</u>
