Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. x+2y=6, x=-1/3y+5

Consider the following equilibrium for which

$$\Delta H < 0$$

$$2 \mathrm { SO } _ { 2 } ( g ) + \mathrm { O } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { SO } _ { 3 } ( g )$$

How will each of the following changes affect an equilibrium mixture of the three gases:

$$SO_3(g)$$

is removed from the system?

Find the sum.

$$\sum _ { n = 0 } ^ { 4 } n ^ { 3 }$$

Suppose that you are purchasing cases of wine (12 bottles per case) and that, periodically, you select a test case to determine the adequacy of the bottles’ seals. To do this, you randomly select and test 3 bottles in the case. If a case contains 1 spoiled bottle of wine, what is the probability that this bottle will turn up in your sample?

Graph the inequality. y > 1

Show the commutative property of addition, A+B=B+A, holds for matrices A and B.

$$A = \left[ \begin{array} { r r r } { 4 } & { - 2 } & { 9 } \\ { 6 } & { - 1 } & { 0 } \\ { - 3 } & { 5 } & { 7 } \end{array} \right] , \quad B = \left[ \begin{array} { r r r } { - 11 } & { 2 } & { - 7 } \\ { 2 } & { 0 } & { - 5 } \\ { 1 } & { - 4 } & { 10 } \end{array} \right]$$

Calculate the ratio of $[Ca^{2+}]$ to $[Fe^{2+}]$ in a lake in which the water is in equilibrium with deposits of both $CaCO_3$ and $FeCO_3.$ Assume that the water is slightly basic and that the hydrolysis of the carbonate ion can therefore be ignored.

Use the given information to find the total cost. Original price: $49, Sales tax: 7%

HOW can I use a data model to predict an outcome?

Use an algebraic method to convert the polar coordinates to rectangular coordinates. Approximate exact values with a calculator when appropriate.

$$(-2.5,25°)$$

Simplify.

$$\sqrt [ 4 ] { 81 }$$

The logistic model $P(t)=\frac{95.4993}{1+0.0405 e^{0.1968 t}}$ represents the percentage of households that do not own a personal computer t years since 1984. In what year did the percentage of households that do not own a personal computer reach 10%?

A certain species of ionized atoms produces an emission line spectrum according to the Bohr model, but the number of protons Z in the nucleus is unknown. A group of lines in the spectrum forms a series in which the shortest wavelength is 22.79 nm and the longest wavelength is 41.02 nm. Find the next-to-the-longest wavelength in the series of lines.

If U is a subspace of

$$\mathbb { R } ^ { n }$$

, show that

$$U ^ { \perp \perp } = U$$

.