Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces with $F_1=32 \mathrm{~N},\theta_1=30^{\circ}$ from the positive $x$ axis in the first quadrant, $F_2=55 \mathrm{N}$ along the positive $x$ axis and ,$F_3=41 \mathrm{~N}, \theta_3=60^{\circ}$ from the positive $x$ axis in the fourth quadrant. What is the asteroid's acceleration direction relative to the positive direction of the $x$ axis?

For the phrase in the first column, write the letter of the synonymous phrase in the second column.

$$\begin{matrix} \text{attenuated agent } & \text{a. dispute en route}\\ & \text{b. untained paint}\\ & \text{c. short report}\\ & \text{d. inane refrain}\\ & \text{e. delicate delegate}\\ & \text{f. enamored stammering}\\ & \text{g. submissive sister}\\ & \text{h. imbue with the blues}\\ & \text{i. extraneous miscellany}\\ & \text{j. underfeed the steed}\\ \end{matrix}$$

Wrigley Company manufactures chewing gum. Visit its home page at the following address:

www.wrigley.com

From the home page, click on the choices labeled "About Us," then "About Gum,"and then "How Gum Is Made."

c. What do you think are the major types of manufacturing overhead at Wrigley? What activity bases could be used to assign each type of overhead to the processing departments you listed in part $\mathbf{b}$ ?

Sphalerite is a zinc sulfide (ZnS) mineral and an important commercial source of zinc metal. The first step in the processing of the ore consists of heating the sulfide with oxygen to give zinc oxide, $\mathrm{ZnO}$, and sulfur dioxide, $\mathrm{SO}_2$. How many kilograms of oxygen gas combine with $5.00 \times 10^3 \mathrm{~g}$ of zinc sulfide in this reaction? (You must first write the balanced chemical equation.)

Lutetium is a rare-earth element that can be used to speed up the chemical reactions involved in petroleum processing. It has two naturally occurring isotopes.

$$\begin{matrix} \text{Isotope} & \text{Form of Decay} & \text{Percent Abundance}\\ \ {^{175} _{71} Lu} & \text{none} & \text{97,41}\\ \ {^{176} _{71} Lu} & \text{beta} & \text{2,59}\\ \end{matrix}$$

Compare the number of protons and neutrons in each of these isotopes.

Lutetium is a rare-earth element that can be used to speed up the chemical reactions involved in petroleum processing. It has two naturally occurring isotopes.

$$\begin{matrix} \text{Isotope} & \text{Form of Decay} & \text{Percent Abundance}\\ \ {^{175} _{71} Lu} & \text{none} & \text{97,41}\\ \ {^{176} _{71} Lu} & \text{beta} & \text{2,59}\\ \end{matrix}$$

Show the setup and calculate the average atomic mass of lutetium.

True or false: The time needed to gather the goods is about half of all the time it takes to process an order.

Large amounts of depleted uranium $\left({ }^{238} \mathrm{U}\right)$ are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counterweights for aircraft. Suppose you have a 4000-kg block of ${ }^{238} \mathrm{U}$. (a) Find its activity. (b) How many calories per day are generated by the thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.

Ton petit fr$\`{e}$re va faire son premier grand voyage et tu lui dis ce qu'il faut faire avant de partir. Pour chaque description, choisis l'élément qui correspond.

a. un guide

b. un itinéraire

c. des brochures

d. le billet de train

e. un passeport

f. un plan

Tu en as un pour trouver la bonne route.

Large amounts of depleted uranium $(^{238} \mathrm{U})$ are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of $^{238} \mathrm{U}.$ (a) Find its activity. (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.

An important measure of the performance of a locomotive is its "adhesion," which is the locomotive's pulling force as a multiple of its weight. The adhesion of one 4400-horsepower diesel locomotive varies in actual use according to a Normal distribution with mean

$$\mu = 0.37$$

and standard deviation

$$\sigma = 0.04.$$

An adhesion greater than 0.50 for the locomotive will result in a problem because the train will arrive too early at a switch point along the route. On what proportion of days will this happen? Show your method.

Label each of the following examples as a case of time inconsistency, limited processing capacity, status-quo bias, or framing.

a. A person buys a nice bottle of wine for $\$ 50$ and leaves it in the pantry for 20 years. At that point, the wine has aged and the value has appreciated to $\$ 250$. Although he would never be willing to buy a bottle of the same wine for $\$ 250$, the person plans to drink his old bottle rather than sell it.

For the phrase in the first column, write the letter of the synonymous phrase in the second column.

$$\begin{matrix} \text{expostulate on the way} & \text{a. dispute en route}\\ & \text{b. untained paint}\\ & \text{c. short report}\\ & \text{d. inane refrain}\\ & \text{e. delicate delegate}\\ & \text{f. enamored stammering}\\ & \text{g. submissive sister}\\ & \text{h. imbue with the blues}\\ & \text{i. extraneous miscellany}\\ & \text{j. underfeed the steed}\\ \end{matrix}$$

For the phrase in the first column, write the letter of the synonymous phrase in the second column.

$$\begin{matrix} \text{infatuated faltering} & \text{a. dispute en route}\\ & \text{b. untained paint}\\ & \text{c. short report}\\ & \text{d. inane refrain}\\ & \text{e. delicate delegate}\\ & \text{f. enamored stammering}\\ & \text{g. submissive sister}\\ & \text{h. imbue with the blues}\\ & \text{i. extraneous miscellany}\\ & \text{j. underfeed the steed}\\ \end{matrix}$$