5. what is the exact area of a circle whose circumference is 18π meters? 6. andrea can walk 4 1/2 miles in 1…

5.

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=18\pi$, we have $2\pi r=18\pi$. Dividing both sides by $2\pi$, we get $r = 9$ meters.

Step2: Calculate the area of the circle

The formula for the area of a circle is $A=\pi r^{2}$. Substituting $r = 9$ into the formula, we have $A=\pi\times9^{2}=81\pi$ square - meters.

Answer:

$81\pi$ square meters

6.

Explanation:

Step1: Recall the speed - formula

The formula for speed $v$ is $v=\frac{d}{t}$, where $d$ is the distance and $t$ is the time. Here, $d = 4\frac{1}{2}=\frac{9}{2}$ miles and $t = 1\frac{1}{2}=\frac{3}{2}$ hours.

Step2: Calculate the speed

$v=\frac{\frac{9}{2}}{\frac{3}{2}}=\frac{9}{2}\times\frac{2}{3}=3$ miles per hour.

Answer:

3 miles per hour

7.

A. P(white)

Explanation:

Step1: Calculate the total number of marbles

The total number of marbles is $6 + 7+11 + 1=25$.

Step2: Calculate the probability

$P(\text{white})=\frac{\text{Number of white marbles}}{\text{Total number of marbles}}=\frac{6}{25}=0.24 = 24%$

Answer:

Fraction: $\frac{6}{25}$, Decimal: $0.24$, Percent: $24%$

B. P(pink)

Explanation:

Since there are no pink marbles in the bag, the number of favorable outcomes is 0. $P(\text{pink})=\frac{0}{25}=0 = 0%$

Answer:

Fraction: $\frac{0}{25}$, Decimal: $0$, Percent: $0%$

C. P(not blue)

Explanation:

Step1: Calculate the number of non - blue marbles

The number of non - blue marbles is $6 + 11+1=18$.

Step2: Calculate the probability

$P(\text{not blue})=\frac{18}{25}=0.72 = 72%$

Answer:

Fraction: $\frac{18}{25}$, Decimal: $0.72$, Percent: $72%$

D. P(red or blue)

Explanation:

Step1: Calculate the number of red or blue marbles

The number of red or blue marbles is $11 + 7=18$.

Step2: Calculate the probability

$P(\text{red or blue})=\frac{18}{25}=0.72 = 72%$

Answer:

Fraction: $\frac{18}{25}$, Decimal: $0.72$, Percent: $72%$

8.

A number cube has 6 possible outcomes ${1,2,3,4,5,6}$, and each coin has 2 possible outcomes ${H,T}$. For the first coin, when the number cube shows 1:

• If the first coin is $H$, and the second coin can be $H$ or $T$ (2 branches).
• If the first coin is $T$, and the second coin can be $H$ or $T$ (2 branches). Repeat this for each of the 6 outcomes of the number cube. In total, there are $6\times2\times2 = 24$ possible outcomes. The tree - diagram starts with 6 branches for the number - cube outcomes, and from each of those branches, there are 2 branches for the first - coin outcomes, and from each of those new branches, there are 2 branches for the second - coin outcomes.

9.

A. $\frac{x}{3}-4\geq - 11$

Explanation:

Step1: Add 4 to both sides

$\frac{x}{3}-4 + 4\geq-11 + 4$, which simplifies to $\frac{x}{3}\geq - 7$.

Step2: Multiply both sides by 3

$3\times\frac{x}{3}\geq3\times(-7)$, so $x\geq - 21$. To check, substitute a value greater than or equal to - 21 into the original inequality. For example, if $x=-21$, $\frac{-21}{3}-4=-7 - 4=-11$, and the inequality holds. To graph on a number line, draw a closed circle at - 21 (because $x$ can equal - 21) and draw an arrow to the right.

Answer:

$x\geq - 21$

B. $-5n-6\lt - 11$

Explanation:

Step1: Add 6 to both sides

$-5n-6 + 6\lt-11 + 6$, which simplifies to $-5n\lt - 5$.

Step2: Divide both sides by - 5 and reverse the inequality sign

$\frac{-5n}{-5}>\frac{-5}{-5}$ (when dividing by a negative number, the inequality sign flips), so $n > 1$. To check, substitute a value greater than 1 into the original inequality. For example, if $n = 2$, $-5\times2-6=-10 - 6=-16\lt - 11$. To graph on a number line, draw an open circle at 1 (because $n$ cannot equal 1) and draw an arrow to the right.

Answer:

$n > 1$