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Corequisite for Statistics
Definitions, Order of Operations, Simplifying Expressions, and Sets

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Example 1

Write each of the following in symbols:

The sum of \(x\) and \(5\) is less than \(2\).
The product of \(3\) and \(x\) is \(21\).
The quotient of \(y\) and \(6\) is \(4\).
Twice the difference of \(b\) and \(7\) is greater than \(5\).
The difference of twice \(b\) and \(7\) is greater than \(5\).

Example 2

Expand and multiply: \(5^2\)

Example 3

Expand and multiply: \(2^5\)

Example 4

Expand and multiply: \(4^3\)

Example 5

Simplify: \(\; 5+3(2+4)\)

Example 6

Simplify: \(\; 5\cdot 2^3-4\cdot 3^2\)

Example 7

Simplify: \(\; 20-(2\cdot 5^2-30)\)

Example 8

Simplify: \(40-20 \div 5+8\)

Example 9

Simplify the expression \(\dfrac{72-68}{5}\)

Example 10

Evaluate the expression \(\dfrac{23.6+16.3+18.9}{7-1}\)

Example 11

Evaluate \(a^2+8a+16\) when \(a\) is \(0, 1, 2, 3,\) and \(4\)

Example 12

Evaluate \(\dfrac{x-\overline{x}}{s}\) if \(x=186\), \(\overline{x}=135.8\), and \(s=35.2\).

Example 13

Evaluate \(\dfrac{s^2}{n}\) for the given values of the variables.

  1. \(s=12\) and \(n=10\)

  2. \(s=4.3\) and \(n=100\)

Example 14

If \(A=\{\text{all college students in the United States}\}\) and \(B=\{\text{all college students in Boston}\}\), then which of the following is true?

  1. \(A\subset B\)

  2. \(B\subset A\)

Example 15

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cup B\).

Example 16

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap B\).

Example 17

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap C\).

Example 18

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(B\cup C\).

Example 19

If \(A=\{1,2,3,4,5,6\}\), find \(C=\{x \mid x\in A \text{ and } x\geq4\}\).

Mini Lecture
Simplify.

  1. \(4\cdot 2^2+5\cdot 2^3\)

  2. \(40-10\div 5+1\)

  3. \(3\left[2+4(5+2\cdot 3)\right]\)

  4. Translate into symbols: The sum of \(x\) and \(y\) is less than the difference of \(x\) and \(y\).

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