X = amount of 50% solution
y = total amount after mixing
Note that the amount of alcohol in the 20% solution is 80 (0.2) = 16 oz.
We have 2 unknowns, so we need 2 equations:
first, we can write the equation for the total volume:
y = x + 80
next, apply the percentages to get an equation for the amount of alcohol:
0.4 y = 0.5 x + 16
Finally, solve the pair of equations (in this case, by substitution of the 1st into the second:
0.4 (x + 80) = 0.5x + 16
0.4 x + 32 = 0.5X + 16
rearrange and combine like terms:
0.1x = 16
x = 160
from the 1st equation:
y = 160 + 80 = 240
<em>Answer:</em>
<em />
<em>x³ + x² - 6x = 0</em>
<em>x(x² + x - 6) = 0</em>
<em>x(x² + 3x - 2x - 6) = 0</em>
<em>x[x(x + 3) - 2(x + 3)] = 0</em>
<em>x(x - 2)(x + 3) = 0</em>
<em>x₁ = 0</em>
<em>x - 2 = 0 => x₂ = 2</em>
<em>x + 3 = 0 => x₃ = - 3</em>
1. The first 10 multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104, 117, and 130.
2. x - 5
3. x + 80
Answer:
Outliers are often extreme values that are not as representative of the data set as the other points in the cluster. If the outliers are included, a description of the data set might be misrepresented.
Step-by-step explanation:
