A water bottle in the shape of a cylinder has a volume of 500 cubic centimeters. The diameter of a base is 7.5 centimeters. What is the height of the bottle? Justify your answer.

Find the area of a dodecagon (12 sides) with a side length of 9 inches.

A strain of E. coli Beu 397-recA441 is placed into a nutrient broth at $30^{\circ}$ Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured.

$$\begin{matrix} \text{Time (hours), x} & \text{Population, y}\\ \text{0} & \text{0.09}\\ \text{2.5} & \text{0.18}\\ \text{3.5} & \text{0.26}\\ \text{4.5} & \text{0.35}\\ \text{6} & \text{0.50}\\ \end{matrix}$$

Using a graphing utility, build an exponential model from the data.

Find the surface area of a right cone with a diameter of 10 feet and a height of 12 feet.

Choose the correct letter. A carpenter is cutting a 2 by 4 for the framing of a roof. The length needs to be 5 feet. He allows 0.1 foot possible variation for the length of the cut. What values of l represent the acceptable lengths for the board, in feet? A. l = 5, B. l ≤ 5.1, C. l ≥ 4.9, D. 4.9 ≤ l ≤ 5.1

An objective function and a system of linear inequalities representing constraints are given. Find the value of the objective function at each corner of the graphed region. Objective Function

$$z = x + 6 y$$

Constraints

$$\left\{ \begin{array} { l } { x \geq 0 , y \geq 0 } \\ { 2 x + y \leq 10 } \\ { x - 2 y \geq - 10 } \end{array} \right.$$

Compute the indicated row of the given product without computing the entire matrix.

$$\begin{equation*}A=\begin{bmatrix}1&&2&&3\\2&&-1&&4\\-3&&-2&&0\end{bmatrix}, C=\begin{bmatrix}2&&1&&-1\\4&&3&&-2\end{bmatrix}\end{equation*}$$

Row 2 of CA.

The difference of cubes is an expression of the form

$$a^3-b^3$$

. It can be factored according to the rule

$$a ^ { 3 } - b ^ { 3 } = ( a - b ) \left( a ^ { 2 } + a b + b ^ { 2 } \right)$$

. For each binomial, identify a and b, and factor using the rule.

$$27 y ^ { 3 } - 64$$

Graph of the equalities or inequalities. $7 \leq x \leq 10$

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.60 m and 1.02 m, respectively. The respective rotational speeds are 450 rev/min and 4 138 rev/min. Calculate the speeds of the tips of both rotors. Compare these speeds with the speed of sound, 343 m/s.

A biometric pad measures the speed, rhythm, and pressure of your handwriting.

Fill in the blank. The equation $\tan ^{2} x-5 \tan x+6=0$ is an equation of _______ type.

Write an equation for each parabola described below. Then graph the equation.

$$vertex (0, 1), focus (0, 4)$$

Evaluate the function at the indicated values.

$$h ( x ) = \frac { x ^ { 2 } + 4 } { 5 }$$

$$h ( 2 ) , h ( - 2 ) , h ( a ) , h ( - x ) , h ( a - 2 ) , h ( \sqrt { x } )$$