A probability experiment consists of selecting a chip at random from a box that contains 40 chips. There are 30 red chips in the box and 10 green chips in the box. Allan plans to carry out a simulation of this probability experiment. He will use a random digit to represent a selection and if the digit is a 1, 2 or 3, the simulated outcome is red. If the random number is not 1, 2 or 3, the simulated outcome will be green. Is Allan’s plan a good one? Explain why or why not.

Write the $b_3$ of

$$\begin{equation*}B=\begin{bmatrix}1&&0&&1&&-3&&-1&&4\\2&&-1&&3&&-8&&-1&&9\\-1&&1&&-2&&5&&1&&-6\\ 0&&1&&-1&&2&&1&&-3\end{bmatrix}\end{equation*}$$

as a linear combination of the pivot columns of B.

Write a quadratic equation that has integer coefficients and has the given pair of solutions. -5 and -4

Test for symmetry and then graph each polar equation.

$$r = \sin \frac { \theta } { 2 }$$

Draw a digraph that has the given adjacency matrix.

$$\left[ \begin{array} { l l l l } { 0 } & { 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 1 } \\ { 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 1 } & { 0 } \end{array} \right]$$

A business sold $x ^ { 2 } + 6 x + 5$ items. The profit for each item sold is $\frac { x ^ { 2 } } { 100 x }$ dollars. a. What is the profit in terms of x? b. What is the profit (in dollars) if x = 50 ?

Rewrite the expression in terms of a single trigonometric function.

$$\frac { 1 } { \cos ( - \theta ) }$$

Use a reference angle to find the exact value of the sine, cosine, and tangent of the angle.

$$120 ^ { \circ }$$

Find general solutions of the systems. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.

$$\mathbf { x } ^ { \prime } = \left[ \begin{array} { r r r } { - 3 } & { 0 } & { - 4 } \\ { - 1 } & { - 1 } & { - 1 } \\ { 1 } & { 0 } & { 1 } \end{array} \right] \mathbf { x }$$

Find the original price, discount, sale price, or selling price. 5. Original price: ?, Discount: 75%, Sale price: $74.75

Evaluate the following integrals.

$$\int _ { 1 } ^ { e ^ { 2 } } \frac { ( \ln x ) ^ { 5 } } { x } d x$$

Six people attend the theater together and sit in a row with exactly six seats. a. How many ways can they be seated together in the row? b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat? c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?

A two-bedroom house in Seattle was worth $400,000 in 2005. If it appreciates at a rate of 3 .5 % each year: a. How much will it be worth in 2015? b. When will it be worth$800,000? c. In Jacksonville, houses are depreciating at 2% per year. If a house is worth $200,000 now, how much value will it have lost in 10 years?

Simplify each expression. $|12-30|$