Butane $(C_4H_{10})$ burns completely with 160% of theoretical air at $20^\circ C,$ 1 atm, and 90% relative humidity. Determine a. the balanced reaction equation. b. the dew point temperature, in $^\circ C,$ of the products, when cooled at 1 atm.

The yield V (in millions of cubic feet per acre) for a forest at age years is given by $V=6.7 e^{-48.1 / t}$. Use a graphing utility to graph the function.

How many tons of $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ are necessary to prepare 5.0 tons of phosphorus if the yield is 90%?

A rancher has 300 feet of fencing to enclose two adjacent pastures. (b) Graph the area function and estimate the dimensions that yield the maximum amount of area for the pastures.

Ethane is burned with 150% theoretical air in a gas-turbine combustor. The products exiting consist of a mixture of CO2, H2O, O2, N2, and NO in chemical equilibrium at 1800 K, 1 MPa. Determine the mole fraction of NO in the products. Is it reasonable to ignore CO in the products?

Suppose we stock an island with 250 rabbits and find that the population is 450 after one year (with no harvesting). After a number of years, the population stabilizes at what we think must be the carrying capacity of the island, 3,500 rabbits. Assume growth has followed a logistic curve. (a) We now want to start harvesting the rabbits to sell, with the objective of harvesting the most rabbits possible per year from the island. What population size should be maintained to achieve the maximum sustainable yield and what would be the maximum sustainable rabbit yield? (b) If the population is maintained at 1,200 rabbits, what would be the sustainable yield?

You flip a coin three times. It lands on heads twice and on tails once. Your friend concludes that the theoretical probability of the coin landing heads up is P(heads up) = 2/3. Is your friend correct? Explain your reasoning.

Compare the interlamellar spacing and the yield strength when a eutectoid steel is isothermally transformed to pearlite at (a) $700^{\circ} \mathrm{C}$; and (b) $600^{\circ} \mathrm{C}$

A certain brand of freezer is advertised to use $730 \mathrm{~kW} \cdot \mathrm{h}$ of energy per year.
($c$) What is the theoretical maximum amount of ice this freezer could make in an hour, starting with water at $20.0\degree \mathrm{C}?$

Lime, $\mathrm{CaO}$, can be produced in two steps as shown in the equations below. If the percentage yield of the first step is $83.5 \%$ and the percentage yield of the second step is $71.4 \%$, what is the expected overall percentage yield for producing $\mathrm{CaO}$ from $\mathrm{CaCl}_2$ ?

$$\begin{gathered} \mathrm{CaCl}_2(a q)+\mathrm{CO}_2(g)+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{CaCO}_3(s)+2 \mathrm{HCl}(a q) \\ \mathrm{CaCO}_3(s) \stackrel{\text { hat }}{\longrightarrow} \mathrm{CaO}(s)+\mathrm{H}_2 \mathrm{O}(g) \end{gathered}$$

Use the spinner below. Find the theoretical probability of landing on the given section(s) of the spinner.

$P($ greater than 4)

Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probability. If you use the subjective method, explain your reasoning. Randomly meeting someone born in a month beginning with a vowel (assume $365$ days in a year)

Austin deposits $2,250 into a 1-year CD at an interest rate of 2.3% compounded daily. What is the annual percentage yield? Round to the nearest hundredth of a percent.

A solid sample of Rb2SO3 weighing 6.24 g reacts with 1.38 L gaseous HBr, measured at 75°C and 0.953 atm pressure. The solid RbBr, extracted from the reaction mixture and purified, has a mass of 7.32 g. (a) What is the limiting reactant? (b) What is the theoretic al yield of RbBr, assuming complete reaction? (c) What is the actual percenta ge yield of product?