Find the maximum and minimum values of the objective function f(x, y) and for what values of x and y they occur, subject to the given constraints.

$$\begin{aligned} &f(x, y)=3 x+6 y\\ &y \leq-\frac{1}{2} x+\frac{5}{2}\\ &y \leq 2, y \geq 0\\ &x \leq 3, x \geq 0 \end{aligned}$$

(*) At one time, chemists thought that the for mula of a binary compound was the simplest formula possible. For example, the chemical formula of water was thought to be HO and that of ammonia was thought to be NH. Given that 0.832 grams of oxygen combines with 0.104 grams of hydrogen, calculate the atomic mass of oxygen based upon HO as the for mula for water. Similarly, given that 0.403 grams of nitrogen combines with 0.0864 grams of hydrogen, calculate the atomic mass of nitrogen based upon NH as the formula for ammonia.

Many people believe that an Increase in the price of gasoline will change consumer attitudes and driving behavior. They assume people will drive less often and buy smaller, more efficient cars the price of gasoline increases. However, Imagine that gas prices Increased significantly and people's driving habits and gas consumption levels changed very little. Use this information and your knowledge about elasticity of demand to answer. How might time affect this scenario?

Write two goals that you think would benefit society, and describe an incentive that will accomplish each goal. Goal: ________ Incentive: _________

Describe the distribution and any interesting patterns you notice in the stem-and-leaf plot. Interpret your findings in terms of the number of medals won in the 2016 Summer Olympics.

Horsepower is a unit of power; one horsepower (1 hp) is equivalent to 745 watts. The world record for climbing a 25-feet rope was set by Garvin Smith in Los Angeles in 1947, when he climbed the 25 feet in 4.7 seconds. Assuming that Mr. Smith has a mass of 65 kg, calculate the average power (in both watts and horsepower) that he generated during his climb.

Determine each product. a. $25 \times 0.31$ b. $7.05 \times 3.72$

A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the acceleration of the satellite is equal to $g(R / r)^{2}$, where g is the acceleration of gravity at the surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Knowing that the diameter of the sun is 1.39 Gm and that the acceleration of gravity at its surface is 274 $m/s^2$, determine the radius of the orbit of the indicated planet around the sun assuming that the orbit is circular.

Determine the absolute value of the number. |-4|

A physics student measures the speed of sound in air as $352 \mathrm{m} \cdot \mathrm{s}^{-1}$. A reference source lists the speed as being $344 \mathrm{m} \cdot \mathrm{s}^{-1}$. Calculate the percentage error in the student’s experimental result.

Find the cofactor of each element in the second row of each matrix.

$$\left[\begin{array}{rrr} -2 & 0 & 1 \\ 1 & 2 & 0 \\ 4 & 2 & 1 \end{array}\right]$$

Suppose you have the equation $\frac{1}{2} x=10$. a. Use the Multiplication Property of Equality to write at least 3 equations that have the same solution. b. Use the Division Property of Equality to write at least 3 equations that have the same solution.

Create a description for an algebraic expression and swap descriptions with a classmate.

Find all values of $\theta$ in the interval $0 \leqslant \theta \leqslant 360$ for which (a) $\sin 2 \theta^{\circ}=\cos 36^{\circ}$, (b) $\cos 5 \theta^{\circ}=\sin 70^{\circ}$, (c) $\tan 3 \theta^{\circ}=\tan 60^{\circ}$.