Anthony measured the dimensions of a rectangular box to be 45 cm by 35 cm by 2 m. Determine the volume of the box in cubic meters.

The sides of a small rectangular box are measured to be $1.80 \pm 0.1 \mathrm{~cm}, 2.05 \pm 0.02 \mathrm{~cm}$, and $3.1 \pm 0.1 \mathrm{~cm}$ long. Calculate its volume and uncertainty in cubic centimeters.

The sides of a small rectangular box are measured to be 1.80 ± 0.1 cm, 2.05 ± 0.02 cm, and 3.1 ± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

Find a value of a so that each objective function has maximum values at the indicated vertex, subject to the following constraints.

$$\begin{aligned} &\begin{array}{l} {x \geq 0} \\ {y \geq 2} \end{array}\\ &x+y \leq 9\\ &-4 x+3 y \leq 6 \end{aligned}$$

$f(x, y)=-4 x+a y,(3,6)$

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.

The average monthly rent for a three bedroom apartment in Denver, Colorado, is $1249. Using an annual inflation rate of 7%, find the average monthly rent in 15 years.

Very loud sounds can damage hearing by injuring the vibration-sensing hair cells on the basilar membrane. Suppose a person has injured hair cells on a segment of the basilar membrane close to the stapes. What type of sound is most likely to have produced this particular pattern of damage? A. Loud music with a mix of different frequencies B. A very loud, high-frequency sound C. A very loud, low-frequency sound

(*) 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?

Overall, 80% of the energy used by the body must be eliminated as excess thermal energy and needs to be dissipated. The mechanisms of elimination are radiation, evaporation of sweat (2 430 kJ/kg), evaporation from the lungs (38 kJ/h), conduction, and convection. A person working out in a gym has a metabolic rate of 2 500 kJ/h. His body temperature is 37$^ { \circ } \mathrm { C }$, and the outside temperature 24$^ { \circ } \mathrm { C }$. Assume the skin has an area of 2.0 m$^2$ and emissivity of 0.97. If he eliminates 0.40 kg of perspiration during that hour, at what rate is thermal energy dissipated by evaporation of sweat?

On a cold winter day the temperature is $2^{\circ} \mathrm{C}$ and the relative humidity is 15%. You inhale air at an average rate of 5500 mL/min and exhale a gas saturated with water at body temperature, roughly $37^{\circ} \mathrm{C}$. If the mass flow rates of the inhaled and exhaled air (excluding water) are the same, the heat capacities $\left(C_{p}\right)$ of the water-free gases are each $1.05 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right)$, and water is ingested into the body as a liquid at $22^{\circ} \mathrm{C}$, at what rate in J/day do you lose energy by breathing? Treat breathing as a continuous process (inhaled air and liquid water enter, exhaled breath exits) and neglect work done by the lungs.

A 68 kg college student's body has a typical density of 1050 $\mathrm{kg} / \mathrm{m}^2$. What is his volume?

Fish can adjust their buoyancy with an organ called the swim bladder. The swim bladder is a flexible gas-filled sac; the fish can increase or decrease the amount of gas in the swim bladder so that it stays neutrally buoyant--neither sinking nor floating. Suppose the fish is neutrally buoyant at some depth and then goes deeper. What needs to happen to the volume of air in the swim bladder? Will the fish need to add or remove gas from the swim bladder to maintain its neutral buoyancy?

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