A student calculates a function's average rate of change on an interval and finds that it is 0. The student concludes that the function is constant on the interval. Explain the students error, and give an example to support your explanation.

Write and solve an inequality for each problem.
To cover his rectangular backyard, Will needs at least 170.5 square feet of sod. The length of Will's yard is 15.5 feet. What are the possible widths of Will's yard?

Suppose we are working with a min problem and increase the right-hand side of a ≥ constraint. What can happen to the optimal z-value?

Hummingbird wing beat rates are much higher than those in other birds. The table gives data about the mass and the frequency of wing beats for various species of hummingbirds.

$$\begin{array}{} {Mass (g)}&{3.1}&{2}&{3.2}&{4}&{3.7}&{1.9}&{4.5}\\ {\text{Frequency of Wing Beats (beats per second)}}&{60}&{85}&{50}&{45}&{55}&{90}&{40}\\ \end{array}$$

a. Using a graphing calculator, find the linear regression model and state its domain. b. Predict the frequency of wing beats for a Giant Hummingbird with a mass of 19 grams. 6. Comment on the reasonableness of the prediction and what, if anything, is wrong with the model.

The following describes the unemployment rate in the United States from 2003 to 2013. In 2003, the unemployment rate was at 6.3% . The unemployment rate began to fall over the years and reached a minimum of about .4% in 2007 . A recession that began in 2007 caused the unemployment rate to increase over a two-year period and reach a maximum of about 10% in 2009 . The unemployment rate then decreased over the next four years to about 7.0% in 2013 . Sketch a graph of the function.

The model a=0.25 t+29 represents the median age a of females in the United States as a function of time t (in years since 1970 ) . a. Predict the median age of females in 1995. b. Predict the median age of females in 2015 to the nearest tenth.

Solve each equation for exact solutions over the interval $[0,2 \pi)$. $\cos 2 x=-\frac{1}{2}$

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument’s symbolic form to a standard valid or invalid form. If Tony plays, the team wins. The team won. $\therefor$. Tony played.

A room contains air in which the speed of sound is 343 m/s. The walls of the room are made of concrete, in which the speed of sound is 1 850 m/s. “A bare concrete wall is a highly efficient mirror for sound.” Give evidence for or against this statement.

Write each fraction in simplest form. 12/48

Perform the indicated operations Give the answers in standard form. (1+5i)(3+i)

Some chemists believe that satisfaction of the octet rule should be the top criterion for choosing the dominant Lewis structure of a molecul e or ion. Other chemists believe that achieving the best formal charges should be the top criterion. Consider the dihydrogen phosphate ion ,

$$\mathrm { H } _ { 2 } \mathrm { PO } _ { 4 } ^ { - }$$

in which the H atoms are bonded to O atoms. What is the predicted dominant Lewis structure if achieving the best forma l charges is the top criterion?

Anthropologists who study skeletal remains can predict a woman's height just from length of her humerus, the bone between the elbow and the shoulder. The table gives data for humerus length and overall height for various women.

$$\begin{array}{} {humerus length (cm)}&{35}&{27}&{30}&{33}&{25}&{39}&{27}&{31}\\ {height(cm)}&{167}&{146}&{154}&{165}&{140}&{180}&{149}&{155}\\ \end{array}$$

Using a graphing calculator, find the linear regression model and state its domain. Then predict a woman's height from a humerus that is 32 cm long, and tell whether the prediction is an interpolation or an extrapolation.

The table shows some values of a function. On which Intervals is the functions average rate of change positive? Select all that apply.

$$\begin{array}{} {x}&{0}&{1}&{2}&{3}\\ {f(x)}&{50}&{75}&{40}&{65}\\ \end{array}$$

a. From x=0 to x=1 b. From x=0 to x=2 c. From x=0 to x=3 d. From x=1 to x=2 e. From x=1 to x=3 f. From x=2 to x=3