On January 1 Carol Farmer and Jim Romans formed a partnership, Research Consultants. Each partner invested $50,000 in cash on that date. The partnership agreement stated that the partners would share net income or loss equally. During the year Farmer invested an additional$2,000 and withdrew $7,500 for personal use. Romans invested an additional$1,500 and withdrew $8,500. Net income for the first year was$33,176. In your working papers, prepare a statement of changes in partners’ equity for the year ended December 31.

In $(\mathbb{Z}_{25}^*,\otimes)$ the set H={1,6,11,16,21} is a subgroup. Find the equivalence classes of the congruence mod H relation.

Match the term with its definition.

$$\begin{matrix} \text{Definition} & \text{Term}\\ \text{Containing genes from another species} & \text{A. transgenic}\\ \text{ } & \text{B. clone}\\ \text{ } & \text{C. gene therapy}\\ \text{ } & \text{D. DNA microarray}\\ \text{ } & \text{E. DNA fingerprinting}\\ \text{ } & \text{F. forensics}\\ \text{ } & \text{G. genetic marker}\\ \end{matrix}$$

On October 15 Martinez and Royka decide to end their partnership. Their assets consist of $10,000 in cash and inventory that cost$105,000 and was sold for $95,000. Their only liability is a note payable for$10,000 that will be paid in full. Their capital balances are Martinez, $60,000 and Royka,$45,000. They share profits and losses equally. In your working papers, prepare the journal entries to record the liquidation of the partnership.

On January 1, Dora purchases 175 of the $1,000, 7%, 15-year bonds issued by Splash City, with interest receivable semiannually on June 30 and December 31 each year. Assuming the market interest rate on the issue date is 8%, Dora will purchase the bonds for$159,869. 1. Complete the first three rows of an amortization table for Dora. 2. Record the purchase of the bonds by Dora on January 1 and the receipt of the first two semiannual interest payments on June 30 and December 31.

On January 1, Lifestyle Pools purchased 25% of Marshall Fence's common stock for $700,000 cash. By the end of the year, Marshall Fence reported net income of$160,000 and paid dividends of $60,000 to all shareholders. For Lifestyle Pools, record the initial purchase and its share of Marshall Fence's net income and dividends for the year.

The Gregorian epact is the number of days between January $1^{s t}$ and the previous new moon. This value is used to figure out the date of Easter. It is calculated by these formulas (using int arithmetic):

$$\begin{array}{c}{C=y e a r / / 100} \\ {\text {epact}=(8+(C / / 4)-C+((8 C+13) / / 25)+11(y e a r \% 19)) \% 30}\end{array}$$

Write a program that prompts the user for a 4 digit year and then outputs the value of the epact.

Generators provide the electricity for the Cassini spacecraft. The total output of the generators in watts (W) is modeled by

$$P ( t ) = 870 e ^ { - \frac { t } { 127 } },$$

where t is the time in years since the manufacture date. Describe how the model has been transformed from its parent function. Suppose the instruments on Cassini require at least 600 W to function. Use the model to predict how long the instruments on Cassini will function. Explain how you can use estimation to check your prediction.

Make a table that lists the characteristics of seedless vascular plant groups.

On February 1, 2008, there were 1615 High Definition radio stations broadcasting a digital signal alongside their analog signal. On February 1, 2009, there were 1877 such stations. Assume the rate of increase is constant.

$$\$$

(a) Find an equation to express the number N of High Definition radio stations in terms of x, the number of days after February 1, 2008. Use 365 days in a year.

$$\$$

(b) Find the point of intersection of the graph of this equation with the graph of to predict the date on which the 2000th HD radio station began broadcasting.

If

$$\overrightarrow{\mathrm{AB}}=\left( \begin{array}{c}{-1} \\ {3} \\ {2}\end{array}\right), \overrightarrow{\mathrm{AC}}=\left( \begin{array}{c}{2} \\ {-1} \\ {4}\end{array}\right)$$

, and

$$\overrightarrow{\mathrm{BD}}=\left( \begin{array}{c}{0} \\ {2} \\ {-3}\end{array}\right)$$

, find: $\overrightarrow{\mathrm{CD}}$

Imagine you are a molecular-sized reporter and are able to witness a chemical reaction achieve chemical equilibrium. Write down what you observe. Be sure to describe the actions of the reactants and products, and the setting!

What are three ways the body loses water?

If $\cos \theta=-\frac{3}{4}, \frac{\pi}{2}<\theta<\pi$ find the exact value of: $\sin (\theta+\pi)$