In the following sentences, underline the verb in parentheses that agrees with the subject.

Example: These maps, not the globe, ($\underline{contain}$, contains) the needed details.

Some people who look at Argentina on a map (see, sees) a triangular-shaped country.

Underline the gerund phrases in the given sentences. Then, above each gerund phrase, identify its function in the sentence by writing S for subject, PN for predicate nominative, DO for direct object, IO for indirect object, or OP for object of preposition.

My running out of thank-you notes happened at a very bad time.

The maximum shear stress in a solid round bar of diameter, d, due to an applied torque, T, is given by $\tau_{\max }=16 T /\left(\pi d^{\beta}\right)$. A round, cold-drawn 1018 steel rod is subjected to a mean torsional load of $\bar{T}=1.5 \mathrm{kN} \cdot \mathrm{m}$ with a standard deviation of $145 \mathrm{N} \cdot \mathrm{m}$. The rod material has a mean shear yield strength of $\bar{S}_{s y}=312$ MPa with a standard deviation of 23 .5 MPa. Assuming the strength and load have normal distributions, what value of the design factor $\bar{n}_{d}$ corresponds to a reliability of 0 .99 against yielding? Determine the corresponding diameter of the rod.

A rectangular coil of 60 turns, dimensions 0.100 m by 0.200 m, and total resistance $10.0\ \Omega$ rotates with angular speed 30.0 rad/s about the y axis in a region where a 1.00-T magnetic field is directed along the x axis. The time t = 0 is chosen to be at an instant when the plane of the coil is perpendicular to the direction of $\overrightarrow{\mathbf{B}}.$ Calculate (a) the maximum induced emf in the coil, (b) the maximum rate of change of magnetic flux through the coil, (c) the induced emf at t = 0.050 0 s, and (d) the torque exerted by the magnetic field on the coil at the instant when the emf is a maximum.

Find the volume of the given region in space. The region beneath z=4x²+9y² and above the rectangle with vertices (0, 0), (3, 0), (3, 2), (0, 2) in the xy-plane.

Sketch the region in the first quadrant that is bounded by the given curves. Determine the exact area of the region by considering the limit of $S_{n}$ as $n \rightarrow \infty .$ Use the right-hand endpoint of each subinterval. $f(x)=x^{2}+1, y=0, x=0, x=3$

Explain each of the following observations: At room temperature $I_2$ is a solid, $Br_2$ is a liquid, and $Cl_2$ and $F_2$ are both gases.

Reponds aux questions suivantes avec des phrases completes.

C'est combien pour envoyer une lettre a Boise, Idaho?

$\rule{1cm}{1pt}$ $\rule{1cm}{1pt}$ $\rule{1cm}{1pt}$ $\rule{1cm}{1pt}$ $\rule{1cm}{1pt}$

For an arbitrary set $A$, the power set $\mathscr{P}(A)$ as defined earlier by $\mathscr{P}(A)=$ $\{X \mid X \subseteq A\}$, and addition in $\mathscr{P}(A)$ was defined by

$$\begin{aligned} X+Y & =(X \cup Y)-(X \cap Y) \\ & =(X-Y) \cup(Y-X) \end{aligned}$$

a. Prove that $\mathscr{P}(A)$ is a group with respect to this operation of addition.
b. If $A$ has $n$ distinct elements, state the order of $\mathscr{P}(A)$.

$$\begin{array} { l } { \text { Let } R \text { be a commutative ring of prime characteristic } p . \text { Show that } } \\ { \text { the Frobenius map } x \rightarrow x ^ { p } \text { is a ring homomorphism from } R \text { to } R . } \end{array}$$

What are the walls of arteries made from?

Decide whether the following statement is true or false:
Attention-deficit/hyperactivity disorder is a disorder of childhood, but fortunately children outgrow the symptoms with age.

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Find the mass and center of mass of the solid. The portion of the paraboloid $z=x^{2}+y^{2}$ below the plane z=4, $\rho(x, y, z)=2$

A distance of 2 units on a coordinate plane equals an actual distance of 1 mile. Suppose the locations of two lakes on a map are at (26, 15) and (9, 20). Find the actual distance between these lakes to the nearest mile.