A liquid mixture of volume $v$ has two liquids as ingredients with densities $\text{α,β}$. If the density of the mixture is $\sigma$, then calculate the mass of the first liquid in the mixture.

A small solid ball is released from rest while fully submerged in a liquid. Then, its kinetic energy is measured when it has moved $2.0 \mathrm{cm}$ in the liquid. Graph gives the results after many liquids are used, the kinetic energy $K$ is plotted versus the liquid density ${\rho }_{\mathrm{liq}}$ and $K_{\mathrm{s}}=2.4\mathrm{J}$, sets the scale on the vertical axis. What are $\left(a\right)$ the density and $\left(b\right)$ the volume of the ball?

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$