The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food; RM, raw materials; $M$, manufacturing; F, fuels industry; U, utilities; SI, service industries)

Use this matrix

$$\overset{\textbf{A$\&$F}\qquad\ \textbf{RM}\qquad\quad \textbf{M}\qquad\quad \textbf{F}\qquad\ \textbf{U}\qquad\ \textbf{SI}}{\left[\begin{array}{cr} 0.410 & 0.008 & 0 & 0.002 & 0 & 0.006 \\ 0.025 & 0.493 & 0.190 & 0.024 & 0.030 & 0.150 \\ 0.015 & 0.006 & 0.082 & 0.009 & 0.001 & 0.116 \\ 0.097 & 0.096 & 0.040 & 0.053 & 0.008 & 0.093 \\ 0.028 & 0.129 & 0.039 & 0.058 & 0.138 & 0.409 \\ 0.043 & 0.008 & 0.010 & 0.012 & 0.002 & 0.095 \end{array}\right]}\begin{array}{c}\text{A$\&$F}\\\text{RM}\\\text{M}\\\text{F}\\\text{U}\\\text{SI}\end{array}$$

Which three industries would be most affected by a rise in the cost of raw materials?

The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food; RM, raw materials; $M$, manufacturing; F, fuels industry; U, utilities; SI, service industries) Use this matrix

$$\overset{\textbf{A$\&$F}\qquad\ \textbf{RM}\qquad\quad \textbf{M}\qquad\quad \textbf{F}\qquad\ \textbf{U}\qquad\ \textbf{SI}}{\left[\begin{array}{cr} 0.410 & 0.008 & 0 & 0.002 & 0 & 0.006 \\ 0.025 & 0.493 & 0.190 & 0.024 & 0.030 & 0.150 \\ 0.015 & 0.006 & 0.082 & 0.009 & 0.001 & 0.116 \\ 0.097 & 0.096 & 0.040 & 0.053 & 0.008 & 0.093 \\ 0.028 & 0.129 & 0.039 & 0.058 & 0.138 & 0.409 \\ 0.043 & 0.008 & 0.010 & 0.012 & 0.002 & 0.095 \end{array}\right]}\begin{array}{c}\text{A$\&$F}\\\text{RM}\\\text{M}\\\text{F}\\\text{U}\\\text{SI}\end{array}$$

For each $1000$ units of raw materials produced, how many units of agricultural and food products were required?

A survey of students in a large Introductory Statistics class asked about their birth order (1 = oldest or only child) and which college of the university they were enrolled in. Here are the data:

$$\begin{array}{c} \begin{array}{c} \text{Birth Order} \end{array} \\ \begin{array}{l|cc|c} \hline \text{College}& \text { 1 or Only } & \text { 2 or More } & \text { Total } \\ \hline \text {Arts \& Sciences } & 34 & 23 & \mathbf{5 7} \\ \text {Agriculture } & 52 & 41 & \mathbf{9 3} \\ \text {Human Ecology } & 15 & 28 & \mathbf{4 3} \\ \text {Other } & 12 & 18 & \mathbf{3 0} \\ \hline \text {Total } & \mathbf{1 1 3} & \mathbf{1 1 0} & \mathbf{2 2 3} \end{array} \end{array}$$

Suppose we select a student at random from this class. What is the probability that the person is

a firstborn student?

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is finite and strongly skewed, with standard deviation 0.7.

(a) What are the mean and standard deviation of the average number of moths $\bar{x}$ in 50 traps?

(b) Use the central limit theorem to find the probability that the average number of moths in 50 traps is greater than 0.6.

The summer monsoon rains bring 80% of India's rainfall and are essential for the country's agriculture. Records going back more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution that is approximately Normal with a mean of 852 millimeters (mm) and a standard deviation of 82 mm. Use the 68- 95- 99. 7 rule to answer the following questions.

(a) Between what values do the monsoon rains fall in 95% of all years?

(b) How small are the monsoon rains in the driest 2.5% of all years?

The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection for fecal contamination (Tampa Tribune, Mar. 31, 2000). You found the probability that a randomly selected slaughtered chicken passes inspection for fecal contamination. Now find the probability that, in a random sample of 5 slaughtered chickens, at least one passes inspection for fecal contamination.

The United States Department of Agriculture reported in Vegetables and Melons Outlook in 2007 that the average American consumes about $7.4 \times 10^{3}$ potato chips in a year. Since Idaho had about $1.5 \times 10^{6}$ people in 2007, how many potato chips would Idaho residents have consumed in 2007? Without using a calculator, make an exact computation and record your answer in scientific notation.

Use an inequality and the five-step process to solve the problem.

Following the guidelines of the U.S. Department of Agriculture, Dale tries to eat at least 5 half-cup servings of vegetables each day. For the first six days of one week, she had $4,6,7,4,6$, and 4 servings. How many servings of vegetables should Dale eat on Saturday, in order to average at least 5 servings per day for the week?

The table shows the number of people employed in agriculture in the United States from the year 1940 to the year 2000.

U.S. Agricultural Employment

Use the equation for the line of best fit to estimate the population in the year 2010. Round the answer to the nearest half million.

The table shows the number of people employed in agriculture in the United States from the year 1940 to the year 2000.

U.S. Agricultural Employment

Find the equation for a line of best fit using a graphing calculator. Round the values for a and b to the nearest thousandth.

Steam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 800 psia and $900^{\circ} \mathrm{F}$ and leaves as saturated vapor. Steam is then reheated to $800^{\circ} \mathrm{F}$ before it expands to a pressure of 1 psia. Heat is transferred to the steam in the boiler at a rate of $6 \times 10^{4}$ Btu/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at $45^{\circ} \mathrm{F}.$ Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the pressure at which reheating takes place. (b) the net power output and thermal efficiency, and (c) the minimum mass flow rate of the cooling water required.

Why is it so important that the face of commercial paper bear the words “payable to order” or “payable to bearer”?

Lamb's-quarter is a common weed that interferes with the growth of corn. An agriculture researcher planted corn at the same rate in 16 small plots of ground, then weeded the plots by hand to allow a fixed number of lamb's-quarter plants to grow in each meter of cornrow. No other weeds were allowed to grow. Here are the yields of corn (bushels per acre) in each of the plots:

Use your calculator or software to analyze these data. Make a scatterplot and find the least-squares line. What percent of the observed variation in corn yield can be explained by a linear relationship between yield and weeds per meter?

Solve the given problem.

American River College has plans to construct a rectangular parking lot on land bordered on one side by a highway. There are $640$ feet of fencing available to fence the other three sides. Let $x$ represent the length of each of the two parallel sides of fencing.

(a) Express the length of the remaining side to be fenced in terms of $x$.

(b) What are the restrictions on $x$ ?

(c) Determine a function $\mathscr{A}$ that represents the area of the parking lot in terms of $x$.

(d) Graph the function $\mathscr{A}$ from part (c) in a viewing window of $[0,320]$ by $[0,55,000]$. Determine graphically the values of $x$ that will give an area between $30,000$ and $40,000$ square feet.

(e) What dimensions will give a maximum area, and what will this area be? Determine analytically and support graphically.