91Ó°ÊÓ

The following data represent the width (in yards) and length (in miles) of various tornadoes. $$ \begin{array}{|cc|} \hline \text { Width (yards), } \boldsymbol{w} & \text { Length (miles), } \boldsymbol{L} \\ \hline 200 & 2.5 \\ \hline 350 & 4.8 \\ \hline 180 & 2.0 \\ \hline 300 & 2.5 \\ \hline 500 & 5.8 \\ \hline 400 & 4.5 \\ \hline 500 & 8.0 \\ \hline 800 & 8.0 \\ \hline 100 & 3.4 \\ \hline 50 & 0.5 \\ \hline 700 & 9.0 \\ \hline 600 & 5.7 \\ \hline \end{array} $$ (a) Draw a scatter plot of the data, treating width as the independent variable. (b) What type of relation appears to exist between the width and the length of tornadoes? (c) Select two points and find a linear model that contains the points. (d) Graph the line on the scatter plot drawn in part (a). (e) Use the linear model to predict the length of a tornado that has a width of 450 yards. (f) Interpret the slope of the line found in part (c).

A linear function is given. (a) Find the slope and y-intercept of each function. (b) Use the slope and y-intercept to graph each function. (c) What is the average rate of change of each function? (d) Determine whether each function is increasing, decreasing, or constant. $$ h(x)=-\frac{2}{3} x+4 $$

The data at the top of the next column represent the atmospheric pressure \(p\) (in millibars) and the wind speed \(w\) (in knots) measured during various tropical systems in the Atlantic Ocean. (a) Use a graphing utility to draw a scatter plot of the data, treating atmospheric pressure as the independent variable (b) Use a graphing utility to find the line of best fit that models the relation between atmospheric pressure and wind speed. Express the model using function notation. (c) Interpret the slope. $$ \begin{array}{|cc|} \hline \begin{array}{c} \text { Atmospheric Pressure } \\ \text { (millibars), } \boldsymbol{p} \end{array} & \begin{array}{c} \text { Wind Speed } \\ \text { (knots), } \boldsymbol{w} \end{array} \\ \hline 993 & 50 \\ \hline 994 & 60 \\ \hline 997 & 45 \\ \hline 1003 & 45 \\ \hline 1004 & 40 \\ \hline 1000 & 55 \\ \hline 994 & 55 \\ \hline 942 & 105 \\ \hline 1006 & 40 \\ \hline 942 & 120 \\ \hline 986 & 50 \\ 983 & 70 \\ \hline 940 & 120 \\ \hline 966 & 100 \\ \hline 982 & 55 \\ \hline \end{array} $$ (d) Predict the wind speed of a tropical storm if the atmospheric pressure measures 990 millibars. (e) What is the atmospheric pressure of a hurricane if the wind speed is 85 knots?

(a) find the vertex and axis of symmetry of each quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. \(f(x)=(x-3)^{2}-2\)

(a) find the vertex and axis of symmetry of each quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. f(x)=-2(x-3)^{2}+5

(a) find the vertex and axis of symmetry of each quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. \(f(x)=2(x-6)^{2}+3\)

Determine whether each function is linear or nonlinear. If it is linear, determine the slope. $$ \begin{array}{|rc|} {\boldsymbol{x}} & \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \\ \hline-2 & 0 \\ -1 & 1 \\ 0 & 4 \\ 1 & 9 \\ 2 & 16 \\ \hline \end{array} $$

(a) find the vertex and axis of symmetry of each quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. \(f(x)=-(x+5)^{2}\)

The relationship between the height \(H\) of an adult male and the length \(x\) of his humerus, in centimeters, can be modeled by the linear function \(H(x)=2.89 x+78.10\). (a) If incomplete skeletal remains of an adult male include a humerus measuring 37.1 centimeters, approximate the height of this male to the nearest tenth. (b) If an adult male is 175.3 centimeters tall, approximate the length of his humerus to the nearest tenth.

The relationship between the height \(H\) of an adult female and the length \(x\) of her femur, in centimeters, can be modeled by the linear function \(H(x)=2.47 x+54.10\). (a) If incomplete skeletal remains of an adult female include a femur measuring 46.8 centimeters, approximate the height of this female to the nearest tenth. (b) If an adult female is 152.4 centimeters tall, approximate the length of her femur to the nearest tenth.