x = liters of 20% solution
Mixing the 20% solution with the 60 L of 90% solution gives a new mixture with volume (x + 60) L. Each L of the 20% solution contributes 0.2 L of alcohol and thus a total of 0.2x L of alcohol, while the 60 L of 90% solution contributes 54 L of alcohol.
We want the concentration of the new mixture to be 80%, so we require
Solve for x:
So you will need 30 L of the 20% solution.
Answer:
The value of r is always between
And we have another measure related to the correlation coefficient called the R square and this value measures the % of variance explained between the two variables of interest, and for this case we have:
So then the best conclusion for this case would be:
c. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.
Step-by-step explanation:
For this case we know that the correlation between the height and weight of children aged 6 to 9 is found to be about r = 0.8. And we know that we use the height x of a child to predict the weight y of the child
We need to rememeber that the correlation is a measure of dispersion of the data and is given by this formula:
The value of r is always between
And we have another measure related to the correlation coefficient called the R square and this value measures the % of variance explained between the two variables of interest, and for this case we have:
So then the best conclusion for this case would be:
c. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.