17. a bag contains ten blue marbles and five ...
17. a bag contains ten blue marbles and five yellow marbles. you randomly select two marbles from the bag. what is the probability that both marbles are yellow when you do not replace the first marble before selecting the second marble?\n① $\frac{1}{9}$\n② $\frac{4}{45}$\n③ $\frac{2}{21}$\n④ $\frac{5}{42}$\n18. you are building a rectangular chest. you want the length to be 8 inches, the width to be 6 inches, and the volume to be 432 cubic inches. what should the height be?\n① 9 inches\n② 14 inches\n③ 54 inches\n④ 72 inches\n19. what is the radius of a circle with a circumference of 74 centimeters?\n① 5.9 centimeters\n② 11.8 centimeters\n③ 23.6 centimeters\n④ 37.0 centimeters
Answer
### 17.
# Explanation:
## Step1: Calculate total marbles initially
There are $10 + 5=15$ marbles initially.
## Step2: Calculate probability of first - yellow marble
The probability of selecting a yellow marble first is $\frac{5}{15}=\frac{1}{3}$.
## Step3: Calculate probability of second - yellow marble
Since the first marble is not replaced, there are now $4$ yellow marbles and $14$ total marbles. So the probability of selecting a yellow marble second is $\frac{4}{14}=\frac{2}{7}$.
## Step4: Calculate probability of both events
By the multiplication rule for dependent events, the probability that both marbles are yellow is $\frac{1}{3}\times\frac{2}{7}=\frac{2}{21}$.
# Answer:
R. $\frac{2}{21}$
### 18.
# Explanation:
## Step1: Recall volume formula for rectangular prism
The volume formula for a rectangular prism is $V = l\times w\times h$, where $V$ is volume, $l$ is length, $w$ is width, and $h$ is height.
## Step2: Substitute given values
We know $V = 432$, $l = 8$, and $w = 6$. So $432=8\times6\times h$.
## Step3: Solve for $h$
First, $8\times6 = 48$. Then $h=\frac{432}{48}=9$.
# Answer:
A. 9 inches
### 19.
# Explanation:
## Step1: Recall circumference formula
The formula for the circumference of a circle is $C = 2\pi r$, where $C$ is circumference and $r$ is radius.
## Step2: Solve for $r$
We know $C = 74$, so $r=\frac{C}{2\pi}$. Substituting $C = 74$ and taking $\pi\approx3.14$, we have $r=\frac{74}{2\times3.14}=\frac{74}{6.28}\approx11.8$.
# Answer:
P. 11.8 centimeters