Draw sketches of possible graphs for which the following data hold. Consider only the domain $0 \leqslant x \leqslant 5$, and assume that the graph of $y=f^{\prime \prime}(x)$ is smooth. (a) f(0) = 0, f(2) = 5, f'(2) = 0, f"(2) < 0, f(4) = 3, f'(4) = 0, f"(4) > 0 (b) f(0) = 0, f"(1) < 0, f(2) = 5, f'(2) = 0, f"(3) > 0, f(4) = 7 (c) f(0) = 0, f'(0) = -1, f'(1) = 0, f(3) = 0, f'(3) = 2, f"(3) = 0, f"(4) < 0 (d) f(0) = 1, f'(0) = 1, f''(0) = 1 and f"(x) increases as x increases (e) f(0) = 1, f'(0) = 0, f'(x) < 0 for 0 < x < 5, f(5) = f'(5) = 0 (f) f(0) = 3, f'(0) = -2, f"(x) > 0 for 0 < x < 5, f(5) = f'(5) = 0

The factory will create a lot of noise and fumes. The area is one with a high level of unemployment - people's incomes are below the national average. Before deciding whether or not to grant planning permission the government also considers the external costs and external benefits - that is, the impact on the rest of society other than the business itself.

$$\begin{matrix} \text{External costs} & \text{External benefits}\\ \text{Waste products will cause pollution} & \text{Jobs will be created}\\ \text{Smoke and fumes may damage the health of residents} & \text{Other firms may move into the area to provide services to the chemical firm}\\ \text{Parkland cannot now be used by local residents} & \text{The chemical factory will pay taxes - government might increase spending on social projects e.g. more hospitals}\\ \end{matrix}$$

The government will try to give a value to all of these costs and benefits. This is called cost-benefit analysis. This is not easy to do. For example, what is the cost of losing parkland for children to play on? Estimates are made and then the total costs and benefits of the decision are added up: private costs, added to external costs, give a total social cost, private benefits, added to external benefits, give a total social benefit figure. If the total social benefit is greater than the total social cost, the scheme is likely to be accepted. If, however, the total social cost is greater than the total social benefit, the government will probably refuse permission. Explain why any two stakeholder groups will be worried about the external costs from a new chemical factory.

(*) 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.

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.

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

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.