A food company manufactures five types of 8 oz Trail mix packages using different mixtures of peanuts, almonds, walnuts, raisins, and M&Ms. The mixtures have the following compositions: $$ \begin{matrix} \text{ } & \text{Peanuts (oz)} & \text{Almonds (oz)} & \text{Walnuts (oz)} & \text{Raisins (oz)} & \text{M&Ms(oz)}\\ \text{Mix 1} & \text{3} & \text{1} & \text{1} & \text{2} & \text{1}\\ \text{Mix 2} & \text{1} & \text{2} & \text{1} & \text{3} & \text{1}\\ \text{Mix 3} & \text{1} & \text{1} & \text{0} & \text{3} & \text{3}\\ \text{Mix 4} & \text{2} & \text{0} & \text{3} & \text{1} & \text{2}\\ \text{Mix 5} & \text{1} & \text{2} & \text{3} & \text{0} & \text{2}\\ \end{matrix} $$ How many packages of each mix can be manufactured if 128 lb of peanuts, 118 lb of almonds, 112 lb of walnuts, 112 lb of raisins, and 104 lb of M&Ms are available? Write a system of linear equations and solve.

Four hundred people were selected from each of the four geographic regions (Midwest, Northeast, South. West) of the United States, and they were asked which form of camping they prefer. Pop-up camper/trailer, family-style (tenting with restrooms), rustic (tenting, no restrooms), or none were the options. The following table displays the survey's findings.

$$\begin{array}{lcccr} \hline & \text { Midwest } & \text { Northeast } & \text { South } & \text { West } \\ \hline \text { Camper/trailer } & 132 & 129 & 129 & 135 \\ \text { Family style } & 180 & 175 & 168 & 146 \\ \text { Rustic } & 46 & 50 & 59 & 68 \\ \text { None } & 42 & 46 & 44 & 51 \\ \hline \end{array}$$

Can you conclude that the distributions of preferred camping types are different for at least two of the regions based on the evidence from these samples? Use $\alpha=.01$.

A model airplane descends in a vertical dive through air at standard conditions ( 1 atmosphere and $20^{\circ} \mathrm{C}$ ). The majority of the drag is due to skin friction on the wing (like that on a flat plate). The wing has a span of $1 \mathrm{~m}$ (tip to tip) and a chord length (leading edge to trailing edge distance) of $10 \mathrm{~cm}$. The leading edge is rough, so the turbulent boundary layer is "tripped." The model weighs $3 \mathrm{~N}$. Find the speed (in meters per second) at which the model will fall.

The tractor-trailer unit is moving down the incline with a speed of 5 mi/hr when the driver brakes the tractor to a stop in a distance of 4 ft. Estimate the percent increase n in the hitch-force component which is parallel to the incline, compared with the force present at steady speed. The cart and its load combined weigh 500 lb. State any assumptions.

A typical tractor-trailer will move $18$ tons of air per mile at $55 \mathrm{~mph}$. Air resistance increases with speed, causing fuel efficiency to decrease at higher speeds. At highway speeds, a certain truck's fuel efficiency $t$, in miles per gallon ($\mathrm{mpg}$), can be approximated by

$$t=-0.1 s+13.1,$$

where $s$ is the speed of the truck, in miles per hour ($\mathrm{mph}$). Graph the equation and then use the graph to estimate the fuel efficiency at $66 \mathrm{~mph}$.

A tractor-trailer truck is coasting freely, with no brakes, down an $8^{\circ}$ slope at $1000$-$\mathrm{m}$ standard altitude. Rolling resistance is $120 \mathrm{~N}$ for every $\mathrm{m} / \mathrm{s}$ of speed. Its frontal area is $9 \mathrm{~m}^2$, and the weight is $65\ \mathrm{kN}$. Compute the terminal coasting velocity, in $\mathrm{mi} / \mathrm{h}$, for $(a)$ no deflector and (b) a deflector installed.

Here are three situations in which consumers might need some protection. A motorist asks for a tow rope 'strong enough for my trailer'. It breaks the first time he tries to use it. Do you think the consumer needs some legal protection in these cases? For each example. identify which part of UK consumer protection laws have broken by the business selling the goods.

A model airplane has a wing span of $6\ \mathrm{ft}$ and a chord (leading edge-trailing edge distance) of $4.5 \mathrm{in}$. The model flies in air at $60^{\circ} \mathrm{F}$ and atmospheric pressure. The wing can be regarded as a flat plate so far as drag is concerned. (a) At what speed will a turbulent boundary layer start to develop on the wing? (b) What will be the total drag force on the wing just before turbulence appears?

A food trailer serves chicken and records the order size and sides on their orders, as shown in the table.

Green Salad: 2 pieces 33 and 3 pieces 13 Macaroni & Cheese: 2 pieces 22 and 3 pieces 55 French Fries: 2 pieces 52 and 3 pieces 65 Cole Slaw: 2 pieces 35 and 3 pieces 55

Explain how to find the experimental probability that the next order is two pieces of chicken with a green salad.

Fission tracks are trails found in uranium-bearing minerals, left by fragments released during fission events. The article “Yo-yo Tectonics of the Nigde Massif During Wrenching in Central Anatolia” reports that fifteen tracks on one rock specimen had an average track length of $13\mu m$ with a standard deviation of $2 \mu \mathrm{m}.$ Assuming this to be a random sample from an approximately normal population, find a 99% confidence interval for the mean track length for this rock specimen.

A tractor-trailer truck has a drag area $C_D A=8 \mathrm{~m}^2$ bare and $6.7 \mathrm{~m}^2$ with an aerodynamic deflector (Fig. $7.18 \mathrm{~b}$ ). Its rolling resistance is $50 \mathrm{~N}$ for each mile per hour of speed. Determine the total horsepower required at sea level with and without the deflector if the truck moves at (a) $55\ \mathrm{mi} / \mathrm{h}$ and (b) $75\ \mathrm{mi} / \mathrm{h}$.

For elliptic curves, there are nice ways of finding points with rational coordinates (see Ezra Brown’s article “Three Fermat Trails to Elliptic Curves” in the May 2000 College Mathematics Journal). Show that the points (−3, 0) and (0, 3) are on the elliptic curve defined by $y^{2}=x^{3}-6 x+9$. Find the line through these two points and showthat the line intersects the curve in another point with rational (in this case, integer) coordinates.

Andy Tedesco is interested in buying a small pickup with a base price of $31,100. It has these options: stereo/CD player /navigation system,$1,445; power sunroof, $850; security package,$640; aluminum wheels, $545; tubular side steps,$525; heated front seats, $250; trailer tow group,$525; pearl coat paint, $225; and all-terrain tires,$100. Its destination charge is $645. Determine its sticker price.

Suppose that you are driving an 18-wheeler tractor-trailer truck along the highway. A car pulls up alongside your truck and then moves ahead very slowly. As it passes, the combined sound of the car and truck engines pulsates louder and softer. The combined sound can be either a sum of the two sinusoids or a product of them.

At what rate is the car's engine rotating?