The birth control shot is one of the most effective methods of birth control available, and it works best when you get the shot regularly, every 12 weeks. Under ideal conditions, only 1 % of women taking the shot become pregnant within one year. In typical use, however, 3% become pregnant. 7 Choose at random 20 women using the shot as their method of birth control. We count the number who become pregnant in the next year.

(a) Explain why this is a binomial setting.

(b) What is the probability that at least one of the women becomes pregnant under ideal conditions? What is the probability in typical use?

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.

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?

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.

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

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?

When a government gives cash to an industry to support an activity of the industry, this is known as a. a tax break. b. a subsidy. c. a green tax. d. command-and-control.

In a control system, an accelerometer consists of a 4.70-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 0.800g, the object should be at a location 0.500 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.

Write an argument ether for or against compulsory population control. Support your argument with reasons and evidence form this textbook and form your own experience.

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.

Red Valve Co. of Carnegie, Pennsylvania, makes a control pinch valve that provides accurate, repeatable control of abrasive and corrosive slurries, outlasting gate, plug, ball, and even satellite coated valves. How much can the company afford to spend now on new equipment in lieu of spending $75,000 four years from now? The company’s rate of return is 12% per year.

$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline \# 1 & \# 2 & \# 3 & \# 4 & \# 5 & \# 6 & \# 7 & \text { \#8 } \\ \hline 162.2 & 165.8 & 156.4 & 165.3 & 168.6 & 167.0 & 186.8 & 178.3 \\ \hline 159.8 & 166.2 & 156.4 & 173.3 & 175.8 & 171.4 & 160.4 & 163.0 \\ \hline \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \hline 160.3 & 160.6 & 152.2 & 166.4 & 168.2 & 168.4 & 176.8 & 171.3 \\ \hline \end{array}$$

Prepare a control chart that specifies a centerline as well as an upper control limit (UCL) and a lower control limit (LCL).

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.

Air flows through the tapered duct, and during this time heat is being added that changes the density of the air within the duct. The average velocities are indicated. Select a control volume that contains the air in the duct. Indicate the open control surfaces, and show the positive direction of their areas. Also, indicate the direction of the velocities through these surfaces. Identify the local and convective changes that occur. Assume the air is incompressible.