A direct-mail company assembles and stores paper products (envelopes, letters, brochures, order cards, etc.) for its customers. The company estimates the total number of pieces received in a shipment by calculating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton or whether it is worth the extra time required to pull a few pieces from several cartons. To aid management in making a decision, eight brochures were removed from each of the five cartons of a typical shipment and weighed. The weights (in pounds) are displayed in the table.

Carton 1	Carton 2	Carton 3	Carton 4	Carton 5
$.01851$	$.01872$	$.01869$	$.01899$	$.01882$
$.01829$	$.01861$	$.01853$	$.01917$	$.01895$
$.01844$	$.01876$	$.01876$	$.01852$	$.01884$
$.01859$	$.01886$	$.01880$	$.01904$	$.01835$
$.01854$	$.01896$	$.01880$	$.01923$	$.01889$
$.01853$	$.01879$	$.01882$	$.01905$	$.01876$
$.01844$	$.01879$	$.01862$	$.01924$	$.01891$
$.01833$	$.01879$	$.01860$	$.01893$	$.01879$

b. Do these data provide sufficient proof to show differences in the mean weight per brochure among the five cartons?

Your weight M on Mars varies directly with your weight E on Earth. If you weigh 116 pounds on Earth, you would weigh 44 pounds on Mars. Which equation relates E and M? A. M=E-72 B. 44M=116E C. M=29/11E D. M=11/29E

A $10-\text{lb}$ weight is hung on the lower end of a coil spring suspended from the ceiling, the spring constant of the spring being $20\,\,\text{lb}/\text{ft}$. The weight comes to rest in its equilibrium position, and beginning at $t=0$ an extrernal force given by $F(t)=10\cos 8t$ is applied to the system. The medium offers a resistance in pounds numerically equal to $5x'$, where $x'$ is the instantaneous velocity in feet per second. Find the displacement of the weight as a function of the time.

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Create a 95% confidence interval for the mean weight of such bags of chips.

Write a function rule for these table.

$$\begin{array}{|c|c|}\hline \text { Weight on } & {\text { Weight on }} \\ {\text { Earth (lb) }} & {\text { Moon (lb) }} \\ \hline 96 & {16} \\ \hline 123 & {20.5} \\ \hline 144 & {24} \\ \hline 171 & {28.5} \\ \hline\end{array}$$

Mrs. Munson is interested to know how her son's height and weight compare with those of other boys his age. She uses an online calculator to determine that her son is at the 48th percentile for weight and the 76th percentile for height. Explain to Mrs. Munson what these values mean.

The weight of potato chips in a medium size bag is stated to be 10 ounces. The amount that the packaging machine puts in these bags is believed to have a Normal model with mean 10.2 ounces and standard deviation 0.12 ounces. What's the probability that the mean weight of the 3 bags is below the stated amount?

An 8-lb weight attached to a spring exhibits simple harmonic motion. Determine the equation of motion if the spring constant is 1 lb/ft and if the weight is released 6 in. below the equilibrium position with a downward velocity of $\frac{3}{2} \mathrm{ft} / \mathrm{s}.$ Express the solution.

A heavy ball suspended by a cable is pulled to the side by a horizontal force $\overrightarrow{\mathbf{F}}$ as shown in Fig. 12-46. If angle $\theta$ is small, the magnitude of the force $F$ can be less than the weight of the ball because: (a) the force holds up only part of the ball's weight. (b) even though the ball is stationary, it is not really in equilibrium. (c) $\overrightarrow{\mathbf{F}}$ is equal to only the $x$ component of the tension in the cable. (d) the original statement is not true. To move the ball, $\overrightarrow{\mathbf{F}}$ must be at least equal to the ball's weight.

The official weight ofa nickel is 5 g, but the actual weight can vary from this amount by up to 0.194 g. Suppose a bank weighs a roll of 40 nickels. The wrapper weighs 1.5 g. a. What is the range of possible weights for the roll of nickels? b. Reasoning if all of the nickels in the roll each weigh die official amount, then the roll's weight is $40(5)+1.5=201.5$ g. Is it possible for a roll to weigh 201.5 g and contain nickels that do notweigh the official amount? Explain.

In a study to compare two different corrosion inhibitors, specimens of stainless steel were immersed for four hours in a solution containing sulfuric acid and a corrosion inhibitor. Forty-seven specimens in the presence of inhibitor A had a mean weight loss of 242 mg and a standard deviation of 20 mg, and 42 specimens in the presence of inhibitor B had a mean weight loss of 220 mg and a standard deviation of 31 mg. Find a 95% confidence interval for the difference in mean weight loss between the two inhibitors.

(a) As you ride on a Ferris wheel, your apparent weight is different at the top than at the bottom. Explain. (b) Calculate your apparent weight at the top and bottom of a Ferris wheel, given that the radius of the wheel is 7.2 m, it completes one revolution every 28 s, and your mass is 55 kg.

Suppose a 32-lb weight stretches a spring 2 ft. If the weight is released from rest at the equilibrium position, determine the equation of motion if an impressed force $f(t)=\sin t$ acts on the system for $0 \leq t<2 \pi$ and is then removed. Ignore any damping forces.

Calculate the pressure a $10 \mathrm{~N}$ block exerts on the table it rests on if its area of contact is $50 \mathrm{~cm}^2$.

Pressure $=$ weight density $\times$ depth

(Use $10,000 \mathrm{~N} / \mathrm{m}^3$ for the weight density of water, and ignore the pressure due to the atmosphere in the calculations below.)