The table shows the projected numbers of hours H of television usage in the United States from 2003 through 2011.

$$\begin{array}{|c|c|} \hline \text { Year } & \text { Hours, } \boldsymbol{H} \\ \hline 2003 & 1615 \\ 2004 & 1620 \\ 2005 & 1659 \\ 2006 & 1673 \\ 2007 & 1686 \\ 2008 & 1704 \\ 2009 & 1714 \\ 2010 & 1728 \\ 2011 & 1742 \\ \hline \end{array}$$

Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t=3 corresponding to 2003.

Find f'(x) and state the domain of f'. f(x) = 1n (x + 2)

Write each percent as a decimal and as a fraction. 87.2%

Wendy and Peter each made up a new "Guess My Decimal" game just for you. Use their clues to determine the number. a. Wendy gives you this clue: "My decimal is seven-tenths greater than 46%. What is my decimal?" Show your work. b. Peter continues the game with the following clue: "My decimal is sixhundredths less than five-tenths." Use pictures and/or words to show your thinking.

Approximate to three decimal places

$$\cos 0.68$$

Find the sum of each infinite geometric series, if it exists. $\\$$0.27+0.0027+0.000027+\cdots$

Air enters the compressor of a Brayton refrigeration cycle at $100\ \mathrm{kPa}, 260 \mathrm{~K}$, and is compressed adiabatically to $300\ \mathrm{kPa}$. Air enters the turbine at $300\ \mathrm{kPa}, 300 \mathrm{~K}$, and expands adiabatically to $100\ \mathrm{kPa}$. For the cycle (a) determine the net work per unit mass of air flow, in $\mathrm{kJ} / \mathrm{kg}$. and the coefficient of performance if the compressor and turbine isentropic efficiencies are both $100 \%$. (b) plot the net work per unit mass of air flow, in $\mathrm{kJ} / \mathrm{kg}$, and the coefficient of performance for equal compressor and turbine isentropic efficiencies ranging from $80$ to $100 \%$.

The power at Ice Station Lion is supplied via solar cells. Once a year, a plane flies in and sells solar cells to the ice station at a price of $20 per cell. Because of uncertainty about future power needs, the ice station can only guess the number of cells that will be required during the coming year (see probability distribution in Table 6). If the ice station runs out of solar cells, a special order must be placed at a cost of$30 per cell. a. Assuming that the news vendor problem is relevant, how many cells should be ordered from the plane? b. In part (a), what type of cost is being ignored? TABLE 6:

$$\begin{matrix} \text{No. of Cells} & \text{Probability}\\ \text{50} & \text{.20}\\ \text{60} & \text{.15}\\\text{70} & \text{.30}\\ \text{80} & \text{.10}\\ \text{90} & \text{.15}\\\text{100} & \text{.10}\\ \end{matrix}$$

Write as a decimal. 4$\frac{1}{4}$

Approximate to three decimal places,

$$\cot 1.13$$

A person pulls a toboggan for a distance of 35.0 m along the snow with a rope directed

$$25.0 ^ { \circ }$$

above the snow. The tension in the rope is 94.0 N. (a) How much work is done on the toboggan by the tension force? (b) How much work is done if the same tension is directed parallel to the snow?

Describe the relationship between the values of the independent and dependent variables.

A person working on the transmission of a car accidentally drops a bolt into a tray of oil. The oil is 5.00 cm deep. The bolt appears to be 3.40 cm beneath the surface of the oil, when viewed from directly above . What is the index of refraction of the oil?

state the domain of the function,

$$f(x) = 1-x^2/x$$