Without graphing, decide.

a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?

b. How many solutions does the system have? See the discussed examples.

$$\left\{\begin{array}{l}x+y=4 \\ x+y=3\end{array}\right.$$

To make a golden rectangle, you should a. inscribe a rectangle in a circle. b. draw a rectangle so that the ratio of the long side to the short side is the golden ratio. c. draw a rectangle so that the ratio of the diagonal to the short side is the golden ratio.

How many protons and electrons are there in a neutral atom of element manganese?

The volume V of an elastic container for air—like a tire or a balloon—is related to the temperature T and to the pressure P of the air inside the container. The formula $V = k \cdot \frac { T } { P }$ is one way of expressing that relationship. The number k > 0 is a constant depending on the units of measurement for volume, temperature, and pressure. How will volume of a balloon change if: i. pressure remains constant, but temperature increases? ii. pressure remains constant, but temperature decreases? iii. temperature remains constant, but pressure increases? iv. temperature remains constant, but pressure decreases?

Syntenic genes can assort independently. Explain this observation.

Each of the two links has a mass of 2 kg and a centroidal radius of gyration of 60 mm. The slider at B has a mass of 3 kg and moves freely in the vertical guide. The spring has a stiffness of 6 kN/m. If a constant torque determine the angular velocity $\omega$ of OA(200 mm) when $\theta$ = 0.

The region between the curve $y=1 /(2 \sqrt{x})$ and the $x$-axis from $x=1 / 4$ to $x=4$ is revolved about the $x$-axis to generate a solid. Find the volume of the solid.

Described the relationship of the two graphed lines.

Rewrite each of the following division problems in base eight using the missing-factor approach, and find the answer in the table.

i. $61_{\text {eight }} \div 7_{\text {eight }}$

ii. $17_{\text {eight }} \div 3_{\text {eight }}$

iii. $30_{\text {eight }} \div 6_{\text {eight }}$

iv. $16_{\text {eight }} \div 2_{\text {eight }}$

v. $44_{\text {eight }} \div 6_{\text {eight }}$

vi. $25_{\text {eight }} \div 7_{\text {eight }}$

Suppose that on a very busy day, your bank is running short of available cash. Why would your bank prefer to borrow from another commercial bank instead of from the Federal Reserve?

Verify the Divergence Theorem for the vector field and region.

$$\mathbf { F } ( x , y , z ) = \langle x , 0,0 \rangle,$$

the region

$$x ^ { 2 } + y ^ { 2 } \leq z \leq 4$$

The most rigorous test of a firm's ability to pay its short-term obligations is its

a. current ratio
b. quick ratio
c. debt-to-assets ratio
d. times-interest-earned ratio

Integrate f over the given region.

$$f ( x , y ) = x ^ { 2 } + y ^ { 2 }$$

over the triangular region with vertices (0, 0), (1, 0), and (0, 1)

A solid wheel accelerates at $3.25 \mathrm{rad} / \mathrm{s}^{2}$ when a force of 4.5 N exerts a torque on it. If the wheel is replaced by a wheel with all of its mass on the rim, the moment of inertia is given by $I=m r^{2}$. If the same angular velocity were desired, what force would have to be exerted on the strap?