A coal from Texas which has an ultimate analysis (by mass) of 39.25 percent C, 6.93 percent $H_{2},$ 41.11 percent $O_{2},$ 0.72 percent $N_{2},$ 0.79 percent S, and 11.20 percent ash (non-combustibles) is burned steadily with 40 percent excess air in a power plant boiler. The coal and air enter this boiler at standard conditions, and the products of combustion in the smokestack are at $127^{\circ} \mathrm{C}.$ Calculate the heat transfer, in kJ/kg fuel, in this boiler. Include the effect of the sulfur in the energy analysis by noting that sulfur dioxide has an enthalpy of formation of -297,100 kJ/kmol and an average specific heat at constant pressure of $c_{p}=41.7\ \mathrm{kJ} / \mathrm{kmol} \cdot \mathrm{K}.$

Solve the equation. Check your solution.

$$10 + a^2 = -7a$$

(a) Two protons in a molecule are separated by $3.80 \times$ $10^{-10} \mathrm{~m}$. Find the electric force exerted by one proton on the other. (b) How does the magnitude of this force compare to the magnitude of the gravitational force between the two protons? (c) What If? What must be the chargeto-mass ratio of a particle if the magnitude of the gravitational force between two of these particles equals the magnitude of electric force between them?

Police estimate that 80% of drivers now wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. If they stop 30 cars during the first hour, find the mean and standard deviation of the number of drivers expected to be wearing seatbelts.

Solve the inequality, if possible. Graph your solution.

$$2 m - 1 \geq 5 \text { or } 5 m > - 25$$

What characteristics of family and village life shaped Indian society?

find two systems of linear equations that have the ordered triple as a solution. (There are many correct answers.) (-6, -1/2, -7/4)

Fill in the blanks with an appropriate word, phrase, or symbol(s). If an operation is performed on any two elements of a set and the result is always an element of the set, we say that the set is _ under that given operation.

What frequencies do large particles scatter?

By rewriting each unit in terms of kilograms, meters, seconds, and coulombs, show that 1 N/C=1 V/m.

Find the slope of the line that passes through (3, -1) and (-2, -4).

Use mental math to solve. Then write the quotient. $- 3000 \div 30 \div - 10 \div - 10$

Simplify the expression. $\sqrt { \left( \frac { 36 } { 121 } \right) }$

Consider a setting where a Poisson approximation should work well: let $A_1, . . . , A_n$ be independent, rare events, with $n$ large and $p_j = P(A_j)$ small for all $j$. Let $X = I(A_1) + \cdots + I(A_n)$ count how many of the rare events occur, and let $\lambda = E(X)$. (a) Find the MGF of $X$. (b) If the approximation $1 + x \approx e^x$ (this is a good approximation when $x$ is very close to 0 but terrible when $x$ is not close to 0) is used to write each factor in the MGF of $X$ as $e$ to a power, what happens to the MGF? Explain why the result makes sense intuitively.