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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 $$5$$.

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Cynthia
(Spanish)

Example 2

Expand and multiply: $$5^2$$

Cynthia
(Spanish)

Example 3

Expand and multiply: $$2^5$$

Cynthia
(Spanish)

Example 4

Expand and multiply: $$4^3$$

Cynthia
(Spanish)

Example 5

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

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Anthony
(Spanish)

Example 6

Simplify: $$\; 5\cdot 2^3-4\cdot 3^2$$

Julieta
(Spanish)

Example 7

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

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Anthony
(Spanish)

Example 8

Simplify: $$40-20 \div 5+8$$

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Anthony
(Spanish)

Example 9

Simplify the expression $$\dfrac{72-68}{5}$$

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Julieta
(Spanish)

Julieta
(Spanish)

Example 10

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

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Julieta
(Spanish)

Example 11

Evaluate $$a^2+8a+16$$ when $$a$$ is $$0, 1, 2, 3,$$ and $$4$$

Edwin
(Spanish)

Example 12

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

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Julieta
(Spanish)

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 $$n=100$$

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Julieta
(Spanish)

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. $$B\subset A$$

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Example 15

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

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Edwin
(Spanish)

Example 16

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

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Julieta
(Spanish)

Example 17

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

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Edwin
(Spanish)

Example 18

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

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Julieta
(Spanish)

Example 19

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

Edwin
(Spanish)

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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