Describe the graphs of the relations y=3 and x=3. Are these relations functions? Explain.

Weights of a certain breed of cat follow a normal distribution with mean 16 kg and variance

$$16 \mathrm { kg } ^ { 2 }$$

. In a sample of 2000 such cats, estimate the number that will have a weight above 13 kg.

Describe how relations and functions are different.

Which of the following statements is true? Justify your choice.

All functions are relations, but not all relations are functions.

All relations are functions, but not all functions are relations.

Find the exact value of each expression. Then evaluate the function on your calculator. Compare the calculator value to your exact value.

$$\tan \left( \frac { \pi } { 4 } + \frac { \pi } { 3 } \right)$$

Identify the rule(s) of algebra illustrated by the statement. $(z − 2) + 0 = z − 2$

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations.

$$\begin{aligned} ( x - 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } & = 4 \\ y & = x - 3 \end{aligned}$$

Compare the meaning of a broken yellow line with the meaning of a broken white line.

Use a graphing utility to create a scatter plot of the data. Decide whether the data could best be modeled by a linear model, an exponential model, or a logarithmic model. (1, 7.5), (1.5, 7.0), (2, 6.8), (4, 5.0), (6, 3.5), (8, 2.0)

Solve each equation. Check your answers. 10(1 – 2y) = -5(2y – 1)

How can ozone be both a pollutant and something beneficial to Earth?

In the thermal processing of semiconductor materials, annealing is accomplished by heating a silicon wafer according to a temperature-time recipe and then maintaining a fixed elevated temperature for a prescribed period of time. For the process tool arrangement, the wafer is in an evacuated chamber whose walls are maintained at $27^{\circ} \mathrm{C}$ and within which heating lamps maintain a radiant flux $q_{s}^{\prime \prime}$ at its upper surface. The wafer is 0.78 mm thick, has a thermal conductivity of $30 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$, and an emissivity that equals its absorptivity to the radiant flux $\left(\varepsilon=\alpha_{l}=0.65\right)$. For $q_{s}^{\prime \prime}=3.0 \times 10^{5} \mathrm{W} / \mathrm{m}^{2}$, the temperature on its lower surface is measured by a radiation thermometer and found to have a value of $T_{w, l}=997^{\circ} \mathrm{C}$. To avoid warping the wafer and inducing slip planes in the crystal structure, the temperature difference across the thickness of the wafer must be less than $2^{\circ} \mathrm{C}$. Is this condition being met?

Explain why a saturated solution containing solid crystals is an example of a dynamic equilibrium.

Find the limit as x approaches c of the average rate of change of each function from c to x. $c=2 ; \quad f(x)=5 x-3$