Ethane $(C_2H_6)$ gas at $77^\circ F,$ 1 atm enters a well-insulated reactor operating at steady state and burns completely with air entering at $240^\circ F,$ 1 atm. Determine the temperature of the products, in $^\circ F.$ Neglect kinetic and potential energy effects.

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions.

$$a = 28 , \quad b = 15 , \quad \angle A = 110 ^ { \circ }$$

Evaluate the given integral along the indicated contour. $\int_{C} \operatorname{Im}(z-i) d z$, where C is the polygonal path consisting of the circular arc along $|z|=1$ form $z=1$ to $z=i$ and the line segment from $z=i$ to $z=-1$.

Fill in the blank(s). If a zero of a polynomial function f is of even multiplicity, then the graph of f _______ the x-axis, and if the zero is of odd multiplicity, then the graph of f _______ the x-axis.

Liquid methanol $\left(\mathrm{CH}_3 \mathrm{OH}\right)$ at $25^{\circ} \mathrm{C}, 1$ atm enters an insulated reactor operating at steady state and burns completely with air entering at $100^{\circ} \mathrm{C}, 1 \mathrm{~atm}$. If the combustion products exit at $1256^{\circ} \mathrm{C}$, determine the percent excess air used. Neglect kinetic and potential energy effects.

What are government's purposes?

A random variable $X$ takes values between 0 and 4 with a cumulative distribution function

$$F(x)=\dfrac{x^2}{16}$$

for $0 \le x \le 4$. $\mathbf{(a)}$ Sketch the cumulative distribution function. $\mathbf{(b)}$ What is $P(X \le 2)$? $\mathbf{(c)}$ What is $P(1 \le X \le 3)$? $\mathbf{(d)}$ Construct and sketch the probability density function.

What gives the government the power to regulate mergers between firms? Give a good reason and a bad reason (from the perspective of society’s welfare) that two firms might want to merge.

If the random variables $X$ and $Y$ are related through the expression

$$Y=aX+b$$

show that they have a correlation of 1 if $a > 0$ and of −1 if $a < 0$.

Graph the system of inequalities. x+y<5, 2x-y>0,-x+5y>-20

Given

$$1 \text { acre } \approx 0.4 \text { hectare }$$

use dimensional analysis to find the area of a property measured at 16 hectares.

Nancy biked 2.65 miles in the morning and 3.19 miles in the afternoon. What total distance did she bike?

Demonstrate how to analyze a marketplace for a foodservice business.

Express each rational number as a decimal. Then insert either < or > in the shaded area between the rational numbers to make the statement true.

$$- \frac { 1 } { 125 } \ ? \ - \frac { 3 } { 500 }$$