A purse that originally cost $\$29.99$ is on sale for $50\%$ off. About how much is the sale price of the purse?

At an accident scene on a level road, investigators measure a car's skid mark to be $88$ m long. It was a rainy day and the coefficient of friction was estimated to be $0.42$. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the car's mass not matter?)

The population of raccoons in a state park satisfies a logistic growth model with $P_0=160$ in 2007 and $P(1)=190$ in 2008. A park ranger has estimated the carrying capacity of the park to be 1100 raccoons. Determine the logistic growth model for the raccoon population where $t$ is the number of years after 2007.

Draw the solid. octagonal pyramid

Draw a free-body diagram of the pedal-arm assembly from a bicycle with the pedal arms in the horizontal position and dimensions as shown in the figure. (Consider the two arms, pedals, and pivot as one piece.) Assuming a rider-applied force of $1500 \mathrm{~N}$ at the pedal, Find the torque applied to the chain sprocket and the maximum bending moment and torque in the pedal arm.

Bacteria Growth. A colony of bacteria is growing exponentially. Initially $500$ bacteria were in the colony. The growth rate is $20$ per hour. (a) How many bacteria should be in the colony in $12$ hours? (b) How many in one day? Use the formula $N = N_0e^{rt}$, where $N$ represents the number of bacteria.

An elite runner can run 100 m in 10 s. What is his average speed?

Tuition at a major university rose from $1,500/yr in 1962 to$20,000/yr in 1995. (a) What exponential rate of growth characterized that period of time? (b) If that growth rate were to continue for another 25 years (enough time for current students to have children in college!) what would the tuition be?

The hydraulic cylinder $C F$, which partially controls the position of rod $D E$, has been locked in the position shown. Knowing that $P=400 \mathrm{N}$ and $\theta=75^{\circ}$, determine $(a)$ the force in link $A B$, $(b)$ the corresponding force exerted on member $B C D$ at point $C$.

For each annual rate of change, find the corresponding growth or decay factor. -55%

Describe the distinctions between holding money for transactional purposes and holding it for speculative purposes.

Manuela found a great deal on pens at 3 for $0.99. It was such a good deal that she decided to buy two-dozen pens. How much did she pay for all of the pens?

An experimental bicycle wheel is placed on a test stand so that it is free to turn on its axle. If a constant net torque of $7.00 \mathrm{~N} \cdot \mathrm{m}$ is applied to the tire for $2.00 \mathrm{~s}$, the angular speed of the tire increases from 0 to $100 \mathrm{~rev} / \mathrm{min}$. The external torque is then removed, and the wheel is brought to rest by friction in its bearings in $125 \mathrm{~s}$. Compute $(a)$ the moment of inertia of the wheel about the rotation axis; $(b)$ the friction torque; $(c)$ the total number of revolutions made by the wheel in the $125 \mathrm{~s}$ time interval.

A hollow steel shaft with an outside diameter of $100 \mathrm{~mm}$ and a wall thickness of $10 \mathrm{~mm}$ is subjected to a pure torque of $T=5,500 \mathrm{~N}-\mathrm{m}$. (a) Determine the maximum shear stress in the hollow shaft. (b) Determine the minimum diameter of a solid steel shaft for which the maximum shear stress is the same as in part (a) for the same torque $T$.