For $f(x,y)=10e^{x^3-y^2}$, find $f_x(x,y),f_y(x,y)$ and $f_{yx}(x,y)$.

The county tax rate is 18 mills per $1 of assessed value. Find the tax due on property assessed at$62,500.

Each week a suburban railway company has a long-run $\operatorname{cost} C=a Q_1+b Q_2+c Q_1^2$ of providing $Q_1$ passenger kilometres of service during rush hours and $Q_2$ passenger kilometres during offpeak hours. As functions of the regulated fares $p_1$ and $p_2$ per kilometre for the rush hours and off-peak hours respectively, the demands for the two kinds of service are $Q_1=A p_1^{-\alpha_1} p_2^{\beta_1}$ and $Q_2=B p_1^{\alpha_2} p_2^{-\beta_2}$, where the constants $A, B, \alpha_1, \alpha_2, \beta_1, \beta_2$ are all positive. Assuming that the company runs enough trains to meet the demand, find expressions for the partial derivatives of $C$ w.r.t. $p_1$ and $p_2$.

The Madison County tax assessor determined the market value of a home to be $595,000. The rate of assessment in Madison County is 40% of market value. The tax rate is 42.73 mills. Calculate the real estate tax.

The CPI index number for Apparel was $130.5$ in 1994 and $118.3$ in 2007. What might be some reasons for the decrease in Apparel compared to other categories?

What does "creditworthiness" mean?

If each cell phone subscriber pays an average monthly rate of $\$ 50$ for the service and an additional $\$ 25$ per month in roaming charges, extra minutes, text messaging, and other fees, how much was spent in the year 2008 for cell phone service plans?

Minimizing material. A rectangular box with no top and six compartments is to have a volume of $96$ cubic inches. Find the dimensions that will require the least amount of material.

The following exercises describe the results of a hypothesis test in terms of the probability of obtaining a particular sample. In each case, use the given context to formulate the null and alternative hypotheses. Then discuss whether the sample provides evidence for rejecting or not rejecting the null hypothesis.

A Roper poll used a sample of $100$ randomly selected car owners. Within the sample, the mean time for ownership of a single car was $7.01$ years. Assuming that the actual mean ownership time is $7.5$ years, the probability of selecting a sample with a mean time of ownership of $7.01$ or less is $0.10$.

Your auto insurance has an annual premium of $\$ 500$, or you can pay 12 monthly payments of $\$ 45$. Is it cheaper to make one annual payment or the 12 monthly payments? Which option would you choose and why?

Solve the application problem. Round stock turnover to the nearest hundredth.

Jumbo Market has an average canned-fruit inventory of $\$ 4484$ at retail. Retail sales of canned fruit for the year were $\$ 98,669$. Find the stock turnover at retail.

Which investment will earn more money, a $\$ 1000$ investment for $5$ years at $8 \%$ compounded annually or a $\$ 1000$ investment for $5$ years compounded continuously at $7 \%$?

A satellite television provider charges $\$ 39.99$ per month for service. If you commit to a 2 -year contract, they will waive the $\$ 40$ set-up fee and charge $\$ 30.00$ per month. How much money will you save by committing to a 2 -year contract?

Use a graphing calculator to graph the region $R$ bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe $R$ in set notation with double inequalities, and evaluate the indicated integral correct to two decimal places.

$$y=\sqrt[3]{x},y=1-x,y=0;\quad \displaystyle\iint\limits_{R}24xy\ dA$$