Chapter 2

Using the results of a student lunch survey, you determine that the probability that a randomly chosen student likes green beans is 0.38 . Is this probability theoretical or experimental?

In the expression \(4 x^{2}-7 y-8,\) what is the coefficient of the \(x^{2}\) -term? What is the coefficient of the \(y\) -term?

Would a business represent profits or losses with negative numbers?

Multiplying \(-12\) by \(-97\) produces the same result as multiplying \(-97\) by \(-12 .\) What property is this?

How many rows are there in the matrix at the right? How many columns? $$ \left[\begin{array}{rrr} 5 & -7 & 3 \\ 2 & -2 & -4 \end{array}\right] $$

Is \(7 x\) a term of the expression \(4 y^{2}-7 x-9 ?\) Explain.

Write an inequality for the sentence: Three is greater than negative five.

The probability that an event will occur is \(0.4 .\) Is it more likely that the event will occur, or is it more likely that the event will \(n o t\) occur?

Is dividing by a number the same as multiplying by the opposite of the number? Explain your reasoning.

What are the like terms in the expression \(-6-3 x^{2}+3 y+7-4 y+9 x^{2} ?\)

Is the order in which you add two numbers important? Make a sketch to help explain your answer. What property does this illustrate?

Is the product of an odd number of factors always a negative number?

Use the number line to complete: \(-2-5=?\)

The odds that an event will occur are 3 to \(4 .\) Is it more likely that the event will occur, or is it more likely that the event will not occur?

Is the reciprocal of a negative number sometimes, always, or never positive?

Show how to model the sum of \(-3,2,\) and \(-1\) in two ways. Make a sketch to illustrate both ways.

Is the product of an even number of factors always a positive number?

Explain the steps you would take to evaluate the expression \(5-7-(-4)\)

Use a counterexample to show that the following statement is false. The opposite of a number is never positive.

The probability of rain is \(80 \%,\) or 0.8 .

A friend tells you that \(-\frac{a}{b}=\frac{-a}{b}=\frac{a}{-b} .\) Is your friend correct? Use examples or counterexamples to support your answer.

Write a matrix to organize the information about a video store's movies. Label each row and column. Comedy: 25 new releases, 215 regular selections Drama: 30 new releases, 350 regular selections Horror: 26 new releases, 180 regular selections

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 4-5 $$

Complete the statement using \(>\) or \(<\). \(-3 \underline{?}-5\)

The odds in favor of winning a race are \(\frac{1}{3}\).

Find the sum. $$-2+0$$

Use the distributive property to rewrite the expression without parentheses. $$ 5(w-8) $$

Find the product. $$8 \cdot(-1)$$

Find the sum and the difference of the matrices. $$ \left[\begin{array}{rr}= -3 & 0 \\ -6 & 4 \\ 1 & -4 \end{array}\right],\left[\begin{array}{rr} 2 & -4 \\ 1 & -3 \\ -1 & 9 \end{array}\right] $$

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 3-(-8) $$

Complete the statement using \(>\) or \(<\). \(-3 \underline{?}0\)

The odds of being chosen for a committee are 1 to 1 .

Find the sum. $$4+(-3)$$

Use the distributive property to rewrite the expression without parentheses. $$ (y+19) 7$$

Find the reciprocal of the number. $$34$$

Find the product. $$-3 \cdot 0$$

Find the sum and the difference of the matrices. $$ \left[\begin{array}{rrr} 1 & 8 & -2 \\ -4 & -5 & 6 \end{array}\right],\left[\begin{array}{rrr} -1 & 9 & 2 \\ 3 & 3 & -5 \end{array}\right] $$

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 0-7 $$

Complete the statement using \(>\) or \(<\). $$-2 \underline{?}-\frac{1}{2}$$

Find the sum. $$-2+(-3)$$

Use the distributive property to rewrite the expression without parentheses. $$ (12-x) y $$

Find the reciprocal of the number. $$-8$$

Find the product. $$-5 \cdot(-7)$$

Tell whether the matrices can be added. $$ \left[\begin{array}{rr} 4 & -1 \\ 7 & 5 \end{array}\right],\left[\begin{array}{rr} 2 & -2 \\ 5 & -6 \end{array}\right] $$

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 2-(-3)-6 $$

Complete the statement using \(>\) or \(<\). $$-8 \underline{?}7$$

Find the sum. $$-7+7$$

Use the distributive property to rewrite the expression without parentheses. $$ -4(u+2) $$

Find the reciprocal of the number. $$-\frac{3}{4}$$

Find the product. $$-7 \cdot(-5)$$