Identify the verb or verb phrase in each sentence. State whether the writer has used the active or the passive voice. The wine bottles were stacked in the crypt.

This problem will show why steady-state probabilities are sometimes referred to as stationary probabilities. Let π1, π2, …, πs be the steady-state probabilities for an ergodic chain with transition matrix P. Also suppose that with probability πi, the Markov chain begins in state i. a. What is the probability that after one transition, the system will be in state i? b. For any value of n(n = 1, 2, …), what is the probability that a Markov chain will be in state i after n transitions? c. Why are steady-state probabilities sometimes called stationary probabilities?

Distinguishing Between Active and Passive Voice. On the line at the right identify the verb in each sentence as active or passive. The decorator removed the painting from the wall.

In each of the following sentences, identify the voice of the verb by writing above it A for active or P for passive.

Example 1. The ballad $\overset{\textit{\color{#c34632}{P}}}{{\underline{\text{was sung}}}}$ by Tiffany.

The dogwood blossoms $\underline{\text{were surrounded}}$ by bumblebees.

Use the most precise name for each figure described. a quadrilateral with exactly one pair of parallel sides.

Show that

$$\operatorname { det } \left[ \begin{array} { c c c c } { 0 } & { 1 } & { 1 } & { 1 } \\ { 1 } & { 0 } & { x } & { x } \\ { 1 } & { x } & { 0 } & { x } \\ { 1 } & { x } & { x } & { 0 } \end{array} \right] = - 3 x ^ { 2 }$$

.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Diversification is like saying "don 't put all your eggs in one basket."

Claire and Richard are both artists who use square canvases. Claire uses the polynomial $50x^2+250$ to decide how much to charge for her paintings, and Richard uses the polynomial $40x^2+350$ to decide how much to charge for his paintings. In each polynomial, x is the height of the painting in feet. When both Claire and Richard charge the same amount for a painting, how much does each charge?

Estimate to the nearest integer.

$$\sqrt { 40 }$$

(a) What is the unit circle, and what is the equation of the unit circle? (b) Use a diagram to explain what is meant by the terminal point P(x, y) determined by t. (c) Find the terminal point for

$$t = \frac { \pi } { 2 }$$

. (d) What is the reference number associated with t? (e) Find the reference number and terminal point for

$$t = \frac { 7 \pi } { 4 }$$

.

Let $S$ be an infinite set and let $M \subset A ( S )$ be the set of all elements $f \in A ( S )$ such that $f ( s ) \neq s$ for at most a finite number of $s \in S .$ Prove that: (a) $f , g \in M$ implies that $f g \in M$ (b) $f \in M$ implies that $f ^ { - 1 } \in M$

find the midpoint of the line segment joining the points. (-1, 2), (5, 4)

A bag of potting soil contains

$$4 \frac { 1 } { 4 }$$

pounds of soil. Each flower that Mr. Henderson plants will need

$$\frac { 1 } { 8 }$$

pound of soil. How many flowers will he be able to plant? F 16 G 28 H 32 J 34

Ballco manufactures large softballs, regular softballs, and hardballs. Each type of ball requires time in three departments: cutting, sewing, and packaging, as shown in Table 65 (in minutes). Because of marketing considerations, at least 1,000 regular softballs must be produced. Each regular softball can be sold for $3, each large softball, for$5; and each hardball, for $4. A total of 18,000 minutes of cutting time, 18,000 minutes of sewing time, and 9,000 minutes of packaging time are available. Ballco wants to maximize sales revenue. If we define RS = number of regular softballs produced LS = number of large softballs produced HB = number of hardballs produced then the appropriate LP is

$$\begin{aligned} \max z &=3 R S+5 L S+4 H B \\ \text { s.t. } & 15 R S+10 L S+8 H B \leq 18,000 \quad \text{(Cutting constraint)} \\ & 15 R S+15 L S+4 H B \leq 18,000 \quad \text{(Sewing constraint)}\\ 3 R S+4 L S+2 H B & \leq 9,000 \quad \text{(Packaging constraint)}\\ R S & \geq 1,000 \quad \text{(Demand constraint)}\\ R S, L S, H B & \geq 0 \end{aligned}$$

The optimal tableau for this LP is shown in Table 66. a. Find the dual of the Ballco problem and its optimal solution. b. Show that the Ballco problem has an alternative optimal solution. Find it. How many minutes of sewing time are used by the alternative optimal solution? c. By how much would an increase of 1 minute in the amount of available sewing time increase Ballco’s revenue? How can this answer be reconciled with the fact that the sewing constraint is binding? d. Assuming the current basis remains optimal, how would an increase of 100 in the regular softball requirement affect Ballco’s revenue? TABLE 65:

$$\begin{matrix} \text{Bills} & \text{Cutting Time} & \text{Sewing Time} & \text{Packaging Time}\\ \text{Regular softballs} & \text{15} & \text{15} & \text{3}\\ \text{Large softballs} & \text{10} & \text{15} & \text{4}\\ \text{Hardballs} & \text{8} & \text{4} & \text{2}\\ \end{matrix}$$

TABLE 66:

$$\begin{matrix} \text{z} & \text{RS} & \text{LS} & \text{HB} & \text{s1} & \text{s2} & \text{s3} & \text{e4} & \text{a4} & \text{rhs}\\ \text{1} & \text{0} & \text{0} & \text{0} & \text{0.5} & \text{0} & \text{0} & \text{4.5} & \text{M − 4.5} & \text{4,500}\\ \text{0} & \text{0} & \text{0} & \text{1} & \text{0.19} & \text{−0.125} & \text{0} & \text{0.94} & \text{−0.94} & \text{187.5}\\ \text{0} & \text{0} & \text{1} & \text{0} & \text{−0.05} & \text{0.10} & \text{0} & \text{0.75} & \text{−0.75} & \text{150}\\ \text{0} & \text{0} & \text{0} & \text{0} & \text{−0.17} & \text{−0.15} & \text{1} & \text{1.88} & \text{1.88} & \text{5,025}\\ \text{0} & \text{1} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{−1} & \text{1} & \text{1,000}\\ \end{matrix}$$