Question

Molly is at the carnival and wants to win a large stuffed animal for her sister. The game she wants to

play is a dart game consisting of 4 concentric circles. To get the large stuffed animal she must get the
dart in the outermost ring. The center ring is 8 inches in diameter and the diameter of each ring
increases by 2 inches.
Step 1: Draw the circles and label each ring's radius.
Step 2: What is the probability of her winning on the first throw?
Step 3: Assign each ring point values, 15 for the center and 5 points more for each ring.

Answer 1

Step 1: Drawing the circles and labeling each ring's radius:

To represent the game, we can draw four concentric circles. Let's label the radius of each ring:

- The center ring: radius = 4 inches (half of the diameter, which is 8 inches).

- The second ring: radius = 6 inches (center ring's radius + 2 inches).

- The third ring: radius = 8 inches (second ring's radius + 2 inches).

- The outermost ring: radius = 10 inches (third ring's radius + 2 inches).

Step 2: Calculating the probability of winning on the first throw:

To calculate the probability of winning on the first throw, we need to determine the area of the outermost ring and divide it by the total area of all four rings.

- The area of a circle is calculated using the formula: A = πr^2, where r is the radius.

- The area of the outermost ring is: A_outermost = π(10^2) = 100π square inches.

- The total area of all four rings is: A_total = π(4^2 + 6^2 + 8^2 + 10^2) = π(16 + 36 + 64 + 100) = π(216) square inches.

Now we can calculate the probability:

Probability of winning on the first throw = A_outermost / A_total = (100π) / (216π) = 100 / 216 ≈ 0.463 or 46.3%.

Step 3: Assigning point values to each ring:

We assign the following point values to each ring:

- Center ring: 15 points.

- Second ring: 20 points (15 points for the center ring + 5 additional points).

- Third ring: 25 points (20 points for the second ring + 5 additional points).

- Outermost ring: 30 points (25 points for the third ring + 5 additional points).

By assigning point values, the game rewards higher points for hitting the smaller and more challenging rings.

In summary, to win the large stuffed animal in the dart game, Molly needs to get the dart in the outermost ring. The probability of winning on the first throw is approximately 46.3%. Additionally, the center ring is assigned 15 points, with each subsequent ring increasing by 5 points, culminating in the outermost ring being worth 30 points.

your welcome have a good daaay <33

Answer 2

Step 1:

To draw the circles and label each ring's radius, we start with the center circle. The diameter of the center circle is 8 inches, so the radius is half of that, which is 4 inches.

The next ring will have a diameter that is 2 inches larger than the center circle. So its diameter will be 8 + 2 = 10 inches. Its radius is half of that, which is 5 inches.

The third ring will have a diameter that is 2 inches larger than the second ring. So its diameter will be 10 + 2 = 12 inches. Its radius is half of that, which is 6 inches.

The outermost ring will have a diameter that is 2 inches larger than the third ring. So its diameter will be 12 + 2 = 14 inches. Its radius is half of that, which is 7 inches.

So, the radii of the four concentric circles are as follows:

Center circle: 4 inches

Second circle: 5 inches

Third circle: 6 inches

Outermost circle: 7 inches

Step 2:

To find the probability of winning on the first throw, we need to know the total area of the dartboard and the area of the outermost ring.

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

The area of the dartboard is the sum of the areas of all four rings. Using the formula, we can calculate the areas:

Area of center circle = π(4^2) = 16π square inches

Area of second circle = π(5^2) = 25π square inches

Area of third circle = π(6^2) = 36π square inches

Area of outermost circle = π(7^2) = 49π square inches

To find the probability of winning on the first throw, we divide the area of the outermost ring by the total area of the dartboard:

Probability = Area of outermost ring / Total area of dartboard

Probability = 49π / (16π + 25π + 36π + 49π)

Probability = 49π / 126π

Probability = 49 / 126

Step 3:

Now let's assign point values to each ring. The center circle is worth 15 points. Each ring after that is worth 5 points more than the previous ring.

So, the point values for each ring are as follows:

Center circle: 15 points

Second circle: 20 points

Third circle: 25 points

Outermost circle: 30 points

Explanation:

<3