From The Wall Street Journal (July 23, 1991): "Since peaking in 1976, per capita beef consumption in the United States has fallen by 28.6 percent ... [and] the size of the U.S. cattle herd has shrunk to a 30-year low."

Using firm and industry diagrams, show the short run effect of declining demand for beef. Label the diagram carefully and write out in words all of the changes you can identify.

Write a statement that interprets the P-value and includes a conclusion about linear correlation. Using the data below "Car Weight and Fuel Consumption," the P-value is 0.000.

$$\begin{matrix} \text{Weight (lb)} & \text{2895} & \text{3215} & \text{3465} & \text{4095} & \text{4180} & \text{2740} & \text{3270}\\ \text{Highway (mpg)} & \text{33} & \text{31} & \text{29} & \text{25} & \text{24} & \text{36} & \text{30}\\ \end{matrix}$$

Suppose the percentage of alcohol in the blood t hours after consumption is given by $C(t)=0.12 t e^{-t / 2}.$ a. At what rate is the blood alcohol level changing at time t? b. How much time passes before the blood alcohol level begins to decrease? c. Suppose the legal limit for blood alcohol is 0.04%. How much time must pass before the blood alcohol reaches this level? At what rate is the blood alcohol level decreasing when it reaches the legal limit?

A survey of 7000 California men found little correlation between alcohol consumption and chance of dying during the $5^{1 / 2}$ years of the study. In fact, men who did not drink at all during these years had a slightly higher death rate than did light drinkers. This lack of correlation was somewhat surprising. Explain how common response might account for the higher death rate among men who did not drink at all over a short period.

Isooctane, $\mathrm{C}_8 \mathrm{H}_{18}$, is the component of gasoline from which the term octane rating derives. (a) Write a balanced equation for the combustion of isooctane to yield $\mathrm{CO}_2$ and $\mathrm{H}_2 \mathrm{O}$. (b) Assuming that gasoline is 100 % isooctane and that the density of isooctane is 0.792 g/mL, what mass of $\mathrm{CO}_2$ is produced each year by the annual U.S. gasoline consumption of 4.6 $\times 10^{10}$ L? (c) What is the volume of this $\mathrm{CO}_2$ at STP?

Country food, which includes seals, caribou, whales, ducks, fish, and berries, is a significant component of the diet of the indigenous Inuit people who live in Inuit Nunangat, in what is now known as Canada's far north. A survey of Inuits in Inuit Nunangat reported that 3274 out of 5000 respondents said that at least half of the meat and fish that they eat is country food. ${ }^8$ Find the sample proportion and a $95 \%$ confidence interval for the population proportion of Inuits whose meat and fish consumption consists of at least half country food.

The table shows world average daily oil consumption from 1985 to 2010 measured in thousands of barrels per day.

$$\begin{matrix} \text{Years since 1985} & \text{Thousands of barrels of oil per day}\\ \text{0} & \text{60083}\\ \text{5} & \text{66533}\\ \text{10} & \text{70099}\\ \text{15} & \text{76784}\\ \text{20} & \text{84077}\\ \text{25} & \text{87302}\\ \end{matrix}$$

Compute and interpret the average rate of change from 1990 to 2005. What are the units?

A block of mass $m_{1}=2.00 \mathrm{kg}$ and a block of mass $m_{2}=6.00 \mathrm{kg}$ are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of $\theta=30.0^{\circ}$. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley.

A light rope is attached to a block with mass $4.00 \mathrm{~kg}$ that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $10.0 \mathrm{~N}$. $(a)$ Draw two free-body diagrams, one for the $4.00 \mathrm{~kg}$ block and one for the block with mass $\mathrm{m}$. $(b)$ What is the acceleration of either block? $(c)$ Find the mass $m$ of the hanging block. $(d)$ How does the tension compare to the weight of the hanging block?

Recall Newton's Law of Gravitation, which asserts that the magnitude F of the force of attraction between objects of masses M and $m$ is $F=G M m / r^2$, where $r$ is the distance between them and G is a universal constant. Let an object of mass M be located at the origin, and suppose that a second object of changing mass m (say from fuel consumption) is moving away from the origin so that its position vector is $\mathbf{r}=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}$. Obtain a formula for dF/dt in terms of the time derivatives of m, x,y, and z.

On 21 $3\times 5$ cards, write the integers $-_{10}$ to 10 using one integer per card. Lay the cards on the floor to form a number line. Choose someone from your group to act like the hiker in integer addition and subtraction. Give directions to walk the number line to solve exercises 4 and 11 in Assessment 5-lA. Try other addition and subtraction problems to make sure that the number-line model is understood by everyone in your group and could be used in an elementary classroom.

Table EP-1 shows some possible consumption bundles for a person who consumes MP3s and lattes.

a. Which bundles fall on the lowest indifference curve?

TABLE EP-1

You are trying to decide which of two automobiles to buy. The first is American-made, costs $28,500, and has a rated gasoline mileage of 28 miles/gal. The second car is of European manufacture, costs$35,700, and has a rated mileage of 19 km/L. If the cost of gasoline is $3.25/gal and if the cars actually deliver their rated mileage, estimate how many miles you would have to drive for the lower fuel consumption of the second car to compensate for the higher cost of this car.

Table EP-1 shows some possible consumption bundles for a person who consumes MP3s and lattes.

b. Which bundles fall on the highest indifference curve?

TABLE EP-1