Determine whether the statement is true or false. Justify your answer. The equation $\sin ^{2} \theta+\cos ^{2} \theta=1+\tan ^{2} \theta$ is an identity, because $\sin ^{2}(0)+\cos ^{2}(0)=1$ and $1+\tan ^{2}(0)=1$

(a) sketch the curve represented by the parametric equations (indicate the orientation of the curve). Use a graphing utility to confirm your result. (b) Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. Adjust the domain of the resulting rectangular equation, if necessary. $x=\sqrt{t}, y=1-t$

The times from a 100 meter race in seconds were: 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center best represents the data? Explain.

Determine whether each relation is a function. $\{(1,1),(2,2),(3,5),(4,10),(5,15)\}$

Which contains more chemical energy, 1 kmol of $\mathrm{H}_{2}$ or 1 kmol of $\mathrm{H}_{2} \mathrm{O}$?

Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

$$\sum ( - 1 ) ^ { k } \frac { k ( x - 4 ) ^ { k } } { 2 ^ { k } }$$

Evaluate the expression.

$$- \sqrt { 9 }$$

Find the inverse function of f informally. Verify that $f\left(f^{-1}(x)\right)=x$ and $f^{-1}(f(x))=x$. $f(x)=(x-1) / 2$

One kmol of $CO_2$ in a piston-cylinder assembly, initially at temperature T and 1 atm, is heated at constant pressure until a final state is attained consisting of an equilibrium mixture of $CO_2,$ CO, and $O_2$ in which the amount of $CO_2$ present is 0.422 kmol. Determine the heat transfer and the work, each in kJ, if T is (a) 298 K, (b) 400 K.

Simplify to a trigonometric function of a single angle. Do not evaluate.

$$\frac { \tan 50 ^ { \circ } - \tan 40 ^ { \circ } } { 1 + \tan 50 ^ { \circ } \tan 40 ^ { \circ } }$$

According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47.

Suppose a random sample of 200 Americans is asked to disclose whether they can order a meal in a foreign language. Is the response to this question qualitative or quantitative? Explain.

In each part, use the information to calculate the appropriate standard error of the mean.

The mean height for a sample of n = 25 children is $\overline{x} = 36$ inches, and the standard deviation is s = 1.0 inch

The value V of a Chevy Cobalt that is t years old can be modeled by $V(t)=16,500(0.82)^{t}$. According to the model, when will the car be worth $2000?

Convert the improper fraction to either a whole number or a mixed number: 12/5