Decide whether the statement is true or false. Give an explanation for your answer. If f(x) is a positive periodic function, then $\int _ { 0 } ^ { \infty } f ( x ) d x$ diverges.

Find each unknown number. Check your work.

$$\frac { b } { 4 } = 12$$

Federal regulations set standards for the size of the quarters of marine mammals. A pool to house sea otters must have a volume of ''the square of the sea otter's average adult length (in meters) multiplied by 3.14 and by 0.91 meter." If x represents the sea otter's average adult length and f(x) represents the volume (in cubic meters) of the corresponding pool size, this formula can be written as $f(x)=0.91(3.14) x^{2}$. Find the volume of the pool for each adult sea otter length (in meters). Round answers to the nearest hundredth. (a) 0.8, (b) 1.0, (c) 1.2, (d) 1.5.

Simplify using the index laws: a. $a^{4} b^{5} \times a^{2} b^{2}$ b. $6 x y^{5} \div 9 x^{2} y^{5}$ c. $\frac{5\left(x^{2} y\right)^{2}}{\left(5 x^{2}\right)^{2}}$

What do the symbols

$$\mu _ { \overline { x } } \text { and } \sigma _ { \overline { x } }$$

represent?

Evaluate the following derivatives. Express your answers in terms of f, g, f', and g'. $\frac { d } { d x } \left( \frac { x f ( x ) } { g ( x ) } \right)$

Suppose that $T$ is linear and

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}4\\-2\end{bmatrix}\end{pmatrix}= \begin{bmatrix}-6\\16\end{bmatrix}.\end{equation*}$$

Determine

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}-2\\1\end{bmatrix}\end{pmatrix}\text{ and } T\begin{pmatrix}\begin{bmatrix}8\\-4\end{bmatrix}\end{pmatrix}.\end{equation*}$$

Use your book or dictionary to define each term. Chitin _____.

Define hematocrit, and explain how it is determined.

Find the magnitude and direction angle for u. $\langle-7, 24 \rangle$

Solve each equation by completing the square. Express square roots in simplest form. $x^{2}-6 x=-6$ _____.

How can the subjunctive be used to give advice using the phrase in parentheses and the information given? Vamos a tener que entrar en nuestra habitación. Entonces es importante que (no perder la llave).

Convert. Where necessary, round to the nearest tenth. ? L $\approx$ 212 pt

Tell whether each function is linear or not. 7 - y = 5x + 11