Fill in the blanks. The direct variation model y=kx^n can be described as “y varies directly as the nth power of x” or “y is ________ ________ to the th power of x”.

Factor each expression.

$$w ^ { 2 } - 144$$

Find the prime factorization of the number. 3190

An entertainment system has n speakers. Each speaker will function properly with probability p, independent of whether the other speakers are functioning. The system will operate effectively when at lest 50% of its speakers are functioning. For what values of p is a 5-speaker system more likely to operate than a 3-speaker system?

Solve each equation. Check your answer. 4x² + 1 = 0

Determine whether the statement is true or false, and justify your answer. If A is an n x n matrix with a nonzero determinant, then A has a QR-decomposition.

Draw a line to match the situation with the appropriate equation or proportion: 27 MP3s is what percent of 238 MP3s? (a). n = 27·2.38 (b) 27/100 = p/238 (c) 27/238 = n/100

Expand and simplify. a)

$$4 x ( x + 5 ) ( x - 5 )$$

b)

$$- 2 a ( a + 4 ) ^ { 2 }$$

c)

$$( x + 2 ) ( x - 5 ) ( x - 2 )$$

d)

$$( 2 x + 1 ) ( 3 x - 5 ) ( 4 - x )$$

e)

$$( 9 a - 5 ) ^ { 3 }$$

f)

$$( a - b + c - d ) ( a + b - c - d )$$

Illustrate the computation 8 - 5 with both continuous and discrete drawings for each of the three generic situations for subtraction. a. take-away b. comparison c. missing-addend. Notice how the drawings differ.

Use your school’s library, the Internet, or some other reference source to write a paper describing John Napier’s work with logarithms.

Rewrite each equation as a system of equations, and then use a graph to solve. 5x² = 3x - 7

Phosgene (COCl2) is an important intermed iate in the manufacture of certainplastics . It is produced by the reaction

$$CO(g) + Cl2(g) ↔ COCI2(g)$$

(a) Use the law of mass action to write the equilibrium expression for this reaction. (b) Ar 600°C, the equilibrium constant for chis reaction is 0.20 . Calculate the partial pressure of phosgene in equilibrium with a mixture of CO (at 0.0020 arm) and Cl2 (at 0.00030 atm).

In the interval

$$[ 0,2 \pi )$$

the solutions of

$$\sin x = \cos 2 x$$

are

$$\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \text { and } \frac { 3 \pi } { 2 }$$

Explain how to use graphs generated by a graphing utility to check these solutions.

Explain how you could use slope to show that the points A(-1, 5), B(3, 7), and C (5, 3) are the vertices of a right triangle.