Evaluate for a = 4 and b = - 6 . Write in simplest form.

$$\frac { 3 a + b } { 24 }$$

Express the surface integral as an iterated double integral by using a projection on S on the yz-plane. $\iint_{S} x y^{2} z^{3} d S$; S is the first-octant portion of plane 2x+3y+4z=12.

You must use a resistor, a capacitor, or an inductor to fill a gap in a circuit. You want to have as much current as possible through this circuit element to ensure that it can be easily detected. Which element should you use if the current through it is (a) very high frequency (VHF), (b) very low frequency (VLF), (c) DC, (d) time-varying so that it is sometimes VHF and other times VLF?

Multiply. 22. -2 1/4 x ( -1 1/3 )

Simplify.

$$\frac { 5 x ^ { 2 } y ^ { 2 } } { x y ^ { 3 } }$$

Write each fraction or mixed number as an equivalent decimal. $15 \frac { 7 } { 12 }$

Round to the place of the underlined digit:

$$30.623 \underline{5} 5$$

In the gas phase, phosphorus pentachloride exists as separate molecules. In the solid phase, however, the compound is composed of alternating PC4+ and PCl6- ions. What change(s) in molecular shape occur(s) as PCI5 solidifies? How does the Cl-P-Cl angle change?

Find the coordinates of the point at which the tangent to the curve

$$y = x ^ { 3 } - 3 x ^ { 2 }$$

at x = 2 meets the curve again.

Water is released from a 0.8-m-deep reservoir into a 4-m-wide open channel through a sluice gate with a 0.1-m-high opening at the channel bottom. The flow depth after all turbulence subsides is 0.5 m. The rate of discharge is $(a) 0.92 m^3/s\ (b) 0.79 m^3/s\ (c) 0.66 m^3/s\ (d) 0.47 m^3/s\ (e) 0.34 m^3/s$

A music download website charges its non-members a $2.50 fee to download plus$1.25 for every song. The total download fee (f) for non-members is a function of the number of downloads (n):

$$f = \$ 2.50 + \$ 1.25 n$$

. Create a table of prices for the first 6 downloads.

A salesperson in a large bicycle shop is paid a bonus if he sells more than 4 bicycles a day. The probability of selling more than 4 bicycles a day is only .40. If the number of bicycles sold is greater than 4, the distribution of sales is as shown in Table 20. The shop has four different models of bicycles. The amount of the bonus paid out varies by type. The bonus for model A is $10; 40% of the bicycles sold are of this type. Model B accounts for 35% of the sales and pays a bonus of$15. Model C has a bonus rating of $20 and makes up 20% of the sales. Finally, model D pays a bonus of$25 for each sale but accounts for only 5% of the sales. Develop a simulation model to calculate the bonus a salesperson can expect in a day. TABLE 20:

$$\begin{matrix} \text{No. of Bicycles Sold} & \text{Probability}\\ \text{5} & \text{.35}\\ \text{6} & \text{.45}\\ \text{7} & \text{.15}\\ \text{8} & \text{.05}\\ \end{matrix}$$

Identify each variable as continuous or discrete: a. Number of people in line at a supermarket checkout counter b. Depth of a snowfall c. Length of time for a driver to respond when faced with an impending collision d. Number of aircraft arriving at the Atlanta airport in a given hour

Find the following. a) $\left| \frac { 1 + 2 i } { - 2 - i } \right|$ b) $| ( \overline { 1 + i } ) ( 2 - 3 i ) ( 4 i - 3 ) |$ c) $\left| \frac { i ( 2 + i ) ^ { 3 } } { ( 1 - i ) ^ { 2 } } \right|$ d) $\left| \frac { ( \pi + i ) ^ { 100 } } { ( \pi - i ) ^ { 100 } } \right|$