91Ó°ÊÓ

Suppose you select a number at random from the sample space \(\\{1,2,3,4,5,6,7,8,9\\} .\) Find each theoretical probability. \(P\)(the number is less than 5)

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In \(\triangle A B C, B C=4\) and \(A C=8-A B\) . What can you conclude about \(A B ?\)

Justify each step by identifying the property used. \(\begin{aligned} 3 x & \leq 4(x-1)-8 \\ 3 x & \leq 4 x-4-8 \\ 3 x & \leq 4 x-12 \\\\-x & \leq-12 \\ x & \geq 12 \end{aligned}\)

Justify each step by identifying the property used. \(\begin{aligned} \frac{1}{2}(y+3) &>\frac{1}{3}(4-y) \\ 3(y+3) &>2(4-y) \\ 3 y+9 &>8-2 y \\ 5 y+9 &>8 \\ 5 y &>-1 \\ y &>-0.2 \end{aligned}\)

Solve each compound inequality. Graph the solutions. \(-6<2 x-4<12\)

Assume that an event is neither certain nor impossible. Then the odds in favor of the event are the ratio of the number of favorable outcomes to the number of unfavorable outcomes. a. If the odds in favor of the event are \(a\) to \(b\) or \(\frac{a}{b},\) what is the probability of the event? b. If the probability of the event is \(\frac{a}{b},\) what are the odds in favor of the event? c. Would you rather play a game where your odds of winning are \(\frac{1}{2},\) or a game where your probability of winning is \(\frac{1}{2} ?\) Explain.

Name the property of real numbers illustrated by each equation. $$ \frac{4}{7} \cdot \frac{7}{4}=1 $$

The random number table simulates an experiment where you toss a coin 90 times. Even digits represent heads and odd digits represent tails. What is the experimental probability, to the nearest percent, of the coin coming up heads? Random Number Table $$\begin{array}{lll}{31504} & {51648} & {40613} \\ {79321} & {80927} & {42404} \\ {15594} & {84675} & {68591} \\ {34178} & {00460} & {31754} \\\ {49676} & {58733} & {00884} \\ {85400} & {72294} & {22551}\end{array}$$ A. 45\(\%\) B. 50\(\%\) C. 54\(\%\) D. 56\(\%\)

Simplify by combining like terms. $$ x(3-y)+y(x+6) $$

Simplify by combining like terms. $$ 4(2 x+y)-2(2 x+y) $$