A $13 \mathrm{~kg}$ Sample of a Certain Alloy (Mixture of Metals) Contains

Short Answer

A $13 \mathrm{~kg}$ sample of a certain alloy (mixture of metals) contains $3 \mathrm{~kg}$ of tin and $10 \mathrm{~kg}$ of copper. A chemist decides to study the properties of the alloy as its percentage of tin is varied. Suppose $x$ represents the quantity of tin, in $\mathrm{kg}$ , the chemist adds to the sample. Let $f(x)$ represent the fraction of the mixture's mass composed of tin--that is, the ratio of the tin's mass to the mixture's total mass. A negative value of $x$ represents a quantity of tin removed from the original $13 \mathrm{~kg}$ sample. $f^{-1}(0.4)=$ ------------ kg. Round to 2 decimal places.