you spin the spinner twice and record the sum of the numbers you get. complete the array with the possible outcomes.
1 2 3
1 A 3 B
2 3 C D
3 E F 6
complete the array
A -
B -
C -
D -
E -
F -
A - 2
B - 5
C - 4
D - 5
E - 2
F - 3
To complete the array with the possible outcomes, we need to find the sum of each possible combination of numbers on the spinner when spun twice.
By looking at the rows and columns, we can deduce the following:
1. A + 3 = 4
Therefore, A = 1 (since 4 - 3 = 1)
2. 3 + C = 4
Therefore, C = 1 (since 4 - 3 = 1)
3. 3 + D = 5
Therefore, D = 2 (since 5 - 3 = 2)
4. E + F = 6
Therefore, E = 1 (since 6 - F = 1) and F = 5 (since 6 - E = 5)
Now we can update the completed array:
1 2 3
1 1 3 1
2 3 1 2
3 1 5 6
A = 1
B = 1
C = 1
D = 2
E = 1
F = 5
To complete the array with the possible outcomes, we need to consider the results of spinning the spinner twice and recording the sum of the numbers.
Based on the given information, let's examine the possible outcomes step by step.
1. Start with the first row, first column (A). To determine the possible values for A, we need to consider all possible sums that can be obtained by spinning the spinner twice. The numbers on the spinner range from 1 to 3.
When spinning the spinner twice, the potential sums are:
- If both spins result in 1, the sum is 1 + 1 = 2.
- If the first spin is 1 and the second is 2, the sum is 1 + 2 = 3.
- If the first spin is 2 and the second is 1, the sum is 2 + 1 = 3.
Therefore, A can be either 2 or 3.
2. Move to the first row, third column (B). To determine the possible values for B, we again need to consider all possible sums that can be obtained by spinning the spinner twice.
The potential sums are:
- If both spins result in 1, the sum is 1 + 1 = 2.
- If the first spin is 1 and the second is 3, the sum is 1 + 3 = 4.
- If the first spin is 3 and the second is 1, the sum is 3 + 1 = 4.
Therefore, B can be either 2 or 4.
3. Proceed to the second row, second column (C). To determine the possible values for C, we only need to analyze the specific sum mentioned for (2, 2). According to the given array, the sum of spinning two 2s is 3.
Therefore, C must be 3.
4. Proceed to the second row, third column (D). To determine the possible values for D, we need to consider all possible sums that can be obtained by spinning the spinner twice.
The potential sums are:
- If the first spin is 2 and the second is 1, the sum is 2 + 1 = 3.
- If the first spin is 2 and the second is 3, the sum is 2 + 3 = 5.
- If the first spin is 3 and the second is 2, the sum is 3 + 2 = 5.
Therefore, D can be either 3 or 5.
5. Proceed to the third row, first column (E). To determine the possible values for E, we need to consider all possible sums that can be obtained by spinning the spinner twice.
The potential sums are:
- If both spins result in 1, the sum is 1 + 1 = 2.
- If the first spin is 1 and the second is 3, the sum is 1 + 3 = 4.
- If the first spin is 3 and the second is 1, the sum is 3 + 1 = 4.
Therefore, E can be either 2 or 4.
6. Finally, we have F in the bottom-right cell, which is specified as the sum of spinning two 3s. According to the given array, F is 6.
So, the completed array is:
1 2 3
1 A 3 B
2 3 C D
3 E F 6
A - 2 or 3
B - 2 or 4
C - 3
D - 3 or 5
E - 2 or 4
F - 6