You are mixing x grams of ingredient A and y grams of ingredient B. Choose the equation or inequality that models the given requirement. There should be at least 3 more grams of ingredient A than ingredient B. (A) $3 x-y \leq 0$, (B) $x-3 y \geq 0$, (C) $x-y \geq 3$, (D) $3 x-y \geq 0$.

$$\begin{array} { c } {\text { calculate } \mu \text { and } \sigma , \text { where } \sigma \text { is the standard deviation} } \\ { \sigma ^ { 2 } = \int _ { - \infty } ^ { \infty } ( x - \mu ) ^ { 2 } p ( x ) d x } \end{array}$$

$$p ( x ) = \frac { 1 } { \pi \sqrt { 1 - x ^ { 2 } } } \quad \text { on } ( - 1,1 )$$

What nominal interest rate per year is equivalent to 11.5% per year, compounded monthly?

Air is expanded in an adiabatic turbine of 90 percent isentropic efficiency from an inlet state of 2800 kPa and $400^{\circ} \mathrm{C}$ to an outlet pressure of 150 kPa. Calculate the outlet temperature of air, the work produced by this turbine, and the entropy generation.

A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)? Explain how you found your answer.

A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to be 5 miles from the Marshall Space Flight Center. What is the angle of depression from the balloon to the airport?

Evaluate the expression when x = 2.

$$6 x + 8$$

Expand each expression. (4+2x)(4-2x)

Sketch the asymptotes and the graph of each equation. $y=\frac{1}{x-3}+4$

You are examining a free-living animal that has a thin, solid body with two surfaces. Into what phylum is this organism classified? Explain.

Reconstruct the table using the two categorical variables "letter listed first (S or Q)" and "ordering of letter chosen (listed first or second).”

What is happening to the U.S. real exchange rate in each of the following situations? Explain. a. The U.S. nominal exchange rate is unchanged, but prices rise faster in the United States than abroad. b. The U.S. nominal exchange rate is unchanged, but prices rise faster abroad than in the United States. c. The U.S. nominal exchange rate declines, and prices are unchanged in the United States and abroad. d. The U.S. nominal exchange rate declines, and prices rise faster abroad than in the United States.

Find the vertices, foci, center (if an ellipse or a hyperbola), and asymptotes (if a hyperbola).

$$16 x ^ { 2 } + 25 y ^ { 2 } - 64 x - 200 y + 64 = 0$$

If $g ( x ) = x ^ { 2 } – 5$ find the value(s) of x so that: a. g(x) = 20 b. g(x) = 6