Summarize the ways in which families may suffer as a result of illegal drug abuse.

The closing price (in dollars) per share of the stock of Tempco Electronics on the $t$th day it was traded is approximated by

$$P(t)= 20+12 \sin \left(\frac{\pi t}{30}\right)-6 \sin \left(\frac{\pi t}{15}\right)+4 \sin \left(\frac{\pi t}{10}\right)-3 \sin \left(\frac{2 \pi t}{15}\right) \qquad 0 \leq t \leq 20$$

where $t=0$ corresponds to the time the stock was first listed on a major stock exchange. What was the rate of change of the stock's price at the close of the fifteenth day of trading? What was the closing price on that day?

Describe the interface between the ICP torch and the mass spectrometer in an ICPMS instrument.

The general solution of a first-order linear differential equation is $y(t)=C e^{-10 t}-13$. What solution satisfies the initial condition y(0)=4?

In a normal distribution with mean

$$\mu = 30$$

, the data value x=-6 has a z-value of -3. Find the standard deviation

$$\sigma$$

.

The true solution Ax = b is slightly different from the elimination solution to LU x₀ = b; A - LU misses zero because of roundoff. One strategy is to do everything in double precision, but a better and faster way is iterative refinement: Compute only one vector r = b - Ax₀ in double precision, solve LU y = r, and add the correction y to x₀. Problem: Multiply x₁ = x₀ + y by LU, write the result as a splitting Sx₁ = Tx₀ + b, and explain why T is extremely small. This single step brings us almost exactly to x.

What are the natural tolerance limits of this process? The thickness of a metal part is an important quality parameter. Data on thickness (in inches) are given here, for 25 samples of five parts each.

$$\begin{matrix} \text{Sample Number} & x_1 & x_2 & x_3 & x_4 & x_5\\ \text{1} & \text{0.0629} & \text{0.0636} & \text{0.0640} & \text{0.0635} & \text{0.0640}\\ \text{2} & \text{0.0630} & \text{0.0631} & \text{0.0622} & \text{0.0625} & \text{0.0627}\\ \text{3} & \text{0.0628} & \text{0.0631} & \text{0.0633} & \text{0.0633} & \text{0.0630}\\ \text{4} & \text{0.0634} & \text{0.0630} & \text{0.0631} & \text{0.0632} & \text{0.0633}\\ \text{5} & \text{0.0619} & \text{0.0628} & \text{0.0630} & \text{0.0619} & \text{0.0625}\\ \text{6} & \text{0.0613} & \text{0.0629} & \text{0.0634} & \text{0.0625} & \text{0.0628}\\ \text{7} & \text{0.0630} & \text{0.0639} & \text{0.0625} & \text{0.0629} & \text{0.0627}\\ \text{8} & \text{0.0628} & \text{0.0627} & \text{0.0622} & \text{0.0625} & \text{0.0627}\\ \text{9} & \text{0.0623} & \text{0.0626} & \text{0.0633} & \text{0.0630} & \text{0.0624}\\ \text{10} & \text{0.0631} & \text{0.0631} & \text{0.0633} & \text{0.0631} & \text{0.0630}\\ \text{11} & \text{0.0635} & \text{0.0630} & \text{0.0638} & \text{0.0635} & \text{0.0633}\\ \text{12} & \text{0.0623} & \text{0.0630} & \text{0.0630} & \text{0.0627} & \text{0.0629}\\ \text{13} & \text{0.0635} & \text{0.0631} & \text{0.0630} & \text{0.0630} & \text{0.0630}\\ \text{14} & \text{0.0645} & \text{0.0640} & \text{0.0631} & \text{0.0640} & \text{0.0642}\\ \text{15} & \text{0.0619} & \text{0.0644} & \text{0.0632} & \text{0.0622} & \text{0.0635}\\ \end{matrix}$$

$$\begin{matrix} \text{Sample Number} & x_1 & x_2 & x_3 & x_4 & x_5\\ \text{16} & \text{0.0631} & \text{0.0627} & \text{0.0630} & \text{0.0628} & \text{0.0629}\\ \text{17} & \text{0.0616} & \text{0.0623} & \text{0.0631} & \text{0.0620} & \text{0.0625}\\ \text{18} & \text{0.0630} & \text{0.0630} & \text{0.0626} & \text{0.0629} & \text{0.0628}\\ \text{19} & \text{0.0636} & \text{0.0631} & \text{0.0629} & \text{0.0635} & \text{0.0634}\\ \text{20} & \text{0.0640} & \text{0.0635} & \text{0.0629} & \text{0.0635} & \text{0.0634}\\ \text{21} & \text{0.0628} & \text{0.0625} & \text{0.0616} & \text{0.0620} & \text{0.0623}\\ \text{22} & \text{0.0615} & \text{0.0625} & \text{0.0619} & \text{0.0619} & \text{0.0622}\\ \text{23} & \text{0.0630} & \text{0.0632} & \text{0.0630} & \text{0.0631} & \text{0.0630}\\ \text{24} & \text{0.0635} & \text{0.0629} & \text{0.0635} & \text{0.0631} & \text{0.0633}\\ \text{25} & \text{0.0623} & \text{0.0629} & \text{0.0630} & \text{0.0626} & \text{0.0628}\\ \end{matrix}$$

(a) Using all the data, find trial control limits for $\overline{X}$ and R charts, construct the chart, and plot the data. Is the process in statistical control? (b) Use the trial control limits from part (a) to identify out-of control points. List the sample numbers of the out-of-control points. Continue eliminating points and revising control limits until the charts are based only on in-control observations.

Determine whether the trinomial is a perfect square trinomial. If so, factor it.

$$4 x ^ { 2 } - 3 x + 9$$

Combine like terms whenever possible.

$$3 x^3+5 x^3$$

Approximate the value of the given expression to three decimal places by using three terms of the appropriate binomial series. Check using a calculator.

$$\sqrt[3]{1.045}$$

Five percent of people in the United States eligible to donate blood actually do. You randomly select four eligible blood donors and ask if they donate blood.

a) construct a binomial distribution,

b) graph the binomial distribution using a histogram,

c) describe the shape of the histogram,

d) find the mean,

e) find the variance,

f) standard deviation of the binomial distribution,

g) interpret the results in the context of a real-life situation. What values of the random variable $x$ would you consider unusual? Explain your reasoning.

Baseballs used in the major leagues in the United States must adhere to strict standards. One such standard is that the weight must be between 5 and $5.25$ ounces. One could look at this standard as a target weight of $5.125$ ounces with a tolerance of $+/-0.125$ ounces. The given data were taken from a random sample of 50 baseballs from a large production batch. The actual weight and deviation from the target weight are listed.

Using the specification limits as the control limits,

b) Is the process for producing baseballs in control?

The height of a punted football can be modeled with the quadratic function $h=-0.01 x^{2}+1.18 x+2 .$ The horizontal distance in feet from the point of impact with the kicker's foot is x, and h is the height of the ball in feet. a. Find the vertex of the graph of the function by completing the square. b. What is the maximum height of the punt? c. The nearest defensive player is 5 ft horizontally from the point of impact. How high must the player reach to block the punt? d. Suppose the ball was not blocked but continued on its path. How far down field would the ball go before it hit the ground? e. The linear equation $h=1.13 x+2$ could model the path of the football shown in the graph. Why is this not a good model?

If a penguin (an endotherm) on an ice floe rather than an iguana (an ectotherm) on a rock, would any of the arrows point in a different direction? Explain.