Question

a bowl contains 6 red beads, 8 black beads, and a number of green beads. there are no other beads in the bowl. the probability to randomly choose a black bead is 1/3. how many green beads are in the bowl? 4 7 10 24 28 a rectangular solid is 13 inches wide, 10 inches long and 5 inches tall. what is the volume of this rectangular solid, in cubic inches? 28 63 135 195 650

Explanation:

Step1: Define variable for green beads

Let $g$ = number of green beads.

Step2: Calculate total beads

Total beads = $6 + 8 + g = 14 + g$

Step3: Set up probability equation

Probability of black bead: $\frac{8}{14+g} = \frac{1}{3}$

Step4: Solve for $g$

Cross-multiply: $8 \times 3 = 1 \times (14 + g)$
$24 = 14 + g$
$g = 24 - 14 = 10$

Step5: Recall volume formula

Volume of rectangular solid: $V = l \times w \times h$

Step6: Substitute values and calculate

$V = 10 \times 13 \times 5 = 650$

Answer:

1. 10
2. 650