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 \(5\).

Expand and multiply: \(5^2\)

Expand and multiply: \(2^5\)

Expand and multiply: \(4^3\)

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

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

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

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

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

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

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

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

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

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

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

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

1. \(A\subset B\)

2. \(B\subset A\)

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

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

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

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

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 \(y\).