In a particular set of experimental trials, students examine a system described by the equation

$$\frac{Q}{\Delta t}=\frac{k \pi d^2\left(T_h-T_c\right)}{4 L}$$

We will see this equation and the various quantities in it in Chapter 20. For experimental control, in these vials all quantities except $d$ and $\Delta t$ are constant. (a) If $d$ is made three times larger, does the equation predict that $\Delta t$ will get larger or smaller? By what factor?

What internal control procedure(s) would best prevent or detect the following problems?

a. A production order was initiated for a product that was already overstocked in the company’s warehouse.

Major League Baseball Rule $1.09$ states that "the baseball shall weigh not less than 5 or more than $51 / 4$ ounces" (www.mlb.com). Use these values as the lower and the upper control limits, respectively. Assume the centerline equals $5.125$ ounces. Periodic samples of 50 baseballs produce the following sample means:

$$\begin{array}{|l|l|l|l|l|l|} \hline 5.05 & 5.10 & 5.15 & 5.20 & 5.22 & 5.24 \\ \hline \end{array}$$

a. Construct an $\bar{x}$ chart. Plot the sample means on the $\bar{x}$ chart.

b. Are any points outside the control limits? Does it appear that the process is under control? Explain.

The researchers also performed control treatments. Suggest two controls they might have used, and explain how each would be helpful in interpreting the results described

One of the buffer systems used to control the pH of blood involves the equilibrium between $\mathrm{H}_2 \mathrm{PO}_4{ }^{-}$and $\mathrm{HPO}_4{ }^{2-}$. The $\mathrm{p} K_{\mathrm{a}}$ for $\mathrm{H}_2 \mathrm{PO}_4^{-}$is 7.21. (a) Write the Henderson-Hasselbalch equation for this buffer system. (b) What $\mathrm{HPO}_4{ }^{2-}$ to $\mathrm{H}_2 \mathrm{PO}_4{ }^{-}$ratio is needed to maintain the optimum blood pH of 7.40?

Let i represent a displacement 1 km due east and j represent a displacement 1 km due north.The control tower of an airport is at (0, 0). Aircraft within 100 km of (0, 0) are visible on the radar screen at the control tower. At 12 : 00 noon an aircraft is 200 km east and 100 km north of the control tower. It is flying parallel to the vector b = -3i - j with a speed of $40\sqrt{10}$ km $\mathrm{h}^{-1}$. Write a vector equation for the path of the aircraft using t to represent the time in hours that have elapsed since 12 : 00 noon.

To control an agricultural pest called the medfly (Mediterranean fruit fly), $N$ sterilized male flies are released into the general fly population every day. If $s$ is the proportion of these sterilized flies that survive a given day, then $Ns^k$ will survive for $k$ days. If $s=$ 0.9 and 10,000 sterilized males are needed to control the medfly population in a given area, how many should be released every day?

An electron initially located at the origin of a coordinate system is projected horizontally into a uniform electric field with magnitude $E$ and directed upward. If the initial speed of the electron is $v_0$, then its trajectory is

$$x=v_0t\hspace{6pt}y=-\frac{1}{2}\left(\frac{eE}{m}\right)t^2$$

where $e$ is the charge of the electron and $m$ is its mass. Show that the trajectory of the electron is a parabola.

Note:The deflection of electrons by an electric field is used to control the direction of an electron beam in an electron gun.

The situation below reveals an internal control weakness:

• A purchasing agent for Sampson Manufacturing is responsible for buying diamonds for use in the company’s manufacturing process, approving the invoices for payment, and signing the checks. No supervisor reviews the purchasing agent’s work.

Requirements

1. Identify the missing internal control characteristic in each situation.

2. Identify each organization’s possible problem.

3. Propose a solution to the problem.

What internal control procedure(s) would provide protection against the following threats?

n. The company’s website is unavailable for seven hours because of a power outage.

A waveform is measured on the oscilloscope and its amplitude covers two vertical divisions. If the vertical control is set at 1 V/div, what is the total amplitude of the waveform?

A federal agency has put you in charge of responding to the zebra mussel invasion. How would you try to control the mussel's spread and impact?

Managers at some companies face an ongoing systems development crisis: IS departments develop systems that businesses cannot or will not use. At the heart of the problem is a "great divide" that separates the world of business and the world of IS. Few departments seem able or ready to cross this gap.

One reason for the crisis is that many companies are looking for ways to improve existing, out-of-date systems or to build new ones. Another is the widespread use of PC-based systems that have spawned high user expectations that IS departments are not meeting. Users seek more powerful applications than are available on many older systems.

The costs of the great divide can be devastating. An East Coast chemical company spent over $1 million on a budgeting and control system that was never used. The systems department's expertise was technical excellence, not budgets. As a result, the new system completely missed the mark when it came to meeting business needs. A Midwestern bank used an expensive computer-aided software engineering (CASE) tool to develop a system that users ignored because there had been no design planning. A senior analyst for the bank said, "They built the system right; but unfortunately they didn't build the right system."

d. Who plays the most vital role in the effective development of the system?

“Admiral” may be seen as a story about cloning, class, money, or control. Ultimately, what would you say “Admiral” is a story about? Why?