Classify each number as one or more of the following: integer, rational number, irrational number, real number, prime number, composite number.

3

For real numbers a, b, and c, identify the property that is illustrated by (a + b)c = ac + be.

Find the GCF of the expressions.

$9 x^2 y^3$ and $12 x y^4$

For real numbers a, b, and c, identify the property that is illustrated by (a + b)c = ac + be.

For real numbers a, b, and c, identify the property that is illustrated by (a + b)c = ac + be.

Evaluate expression.

$$-5^3$$

Convert the following base-10 numbers to hexadecimal and binary:

$$\begin{array}{lllll}\text { a. } 401 & \text { b. } 273 & \text { c. } 15 & \text { d. } 38 & \text { e. } 56\end{array}$$

Use an incremental approximation to estimate the function at the values given.

$$f(1.01,0.98), \text { where } f(x, y)=e^{x y}$$

A mass–spring–dashpot system with external force $f(t)$ is described. Under the assumption that $x ( 0 ) = x ^ { \prime } ( 0 ) = 0$, find the transient and steady periodic motions of the mass. Then construct the graph of the position function $x(t)$. If you would like to check your graph using a numerical DE solver, it may be useful to note that the function

$$f ( t ) = A [ 2 u ( t - \pi ) ( t - 2 \pi ) ( t - 4 \pi ) ( t - 3 \pi ) ( t - 5 \pi ) ( t - 6 \pi ) ) - 1 ]$$

has the value $+ A \text { if } 0 < t < \pi , \text { the value } - A \text { if } \pi < t < 2 \pi$, and so forth, and hence agrees on the interval $[ 0,6 \pi ]$ with the square-wave function that has amplitude $A$ and period $2 \pi$.

$$\begin{array} { l } { m = 1 , k = 10 , c = 2 ; f ( t ) \text { is a square-wave function with } } \\ { \text { amplitude } 10 \text { and period } 2 \pi . } \end{array}$$

Six employees at Larry's T-Shirt Palace received $1000 bonuses for their superb work Another three employees received$700 bonuses for their great artistry. What was the overall average bonus that Larry distributed?

The distance between eyepiece and objective lens in a certain compound microscope is $23.0 \mathrm{~cm}$. The focal length of the eyepiece is $2.50 \mathrm{~cm}$, and that of the objective is $0.400 \mathrm{~cm}$. What is the overall magnification of the microscope?

This problem involves the design of a circuit that finds the integer part of the square root of an 8-bit unsigned binary number N using the method of subtracting out odd integers. To find the square root of N, we subtract 1, then 3, then 5, etc., until we can no longer subtract without the result going negative. The number of times we subtract is equal to the integer part of the square root of N. For example, to find $\sqrt{27: 27-1}=26 ; 26-3=23 ; 23-5=18 ; 18-7=11 ; 11-9=2 ; 2-11$ (cannot subtract). Because we subtracted five times, $\sqrt{27}:=5$. Note that the final odd integer is $11_{10}=1011_{2}$, and this consists of the square root $\left(101_{2}=5_{10}\right)$ followed by a 1.

When is the absolute value of a number equal to the number?

For each of the following pairs of elements, state whether the binary compound they form is likely to be ionic or covalent. Write the empirical formula and name of the compound: (a) $\mathrm{B}$ and $\mathrm{F}$, (b) $\mathrm{K}$ and $\mathrm{Br}$.