Let's break down the questions regarding the outcomes of spinning a spinner divided into 4 equal sections labeled with the numbers 1 through 4.
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Total possible outcomes: When you spin the spinner twice, each spin has 4 possible outcomes. Thus, for two spins, the total number of outcomes is: \[ 4 \times 4 = 16 \] So, "There are a total of 16 possible outcomes."
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Possible outcomes for spinning two numbers that have a sum greater than 5: The possible sums from two spins can range from 2 (1+1) to 8 (4+4). We need to identify the combinations where the sum is greater than 5. The combinations with sums greater than 5 are:
- (2, 4) → 2 + 4 = 6
- (3, 3) → 3 + 3 = 6
- (3, 4) → 3 + 4 = 7
- (4, 2) → 4 + 2 = 6
- (4, 3) → 4 + 3 = 7
- (4, 4) → 4 + 4 = 8 Counting these outcomes, we have the following pairs: (2, 4), (3, 3), (3, 4), (4, 2), (4, 3), and (4, 4), which gives us a total of 6 outcomes. Therefore, "There are 6 possible outcomes for spinning two numbers that have a sum greater than 5."
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Possible outcomes for spinning the same number twice: The outcomes where both spins result in the same number are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4) This gives us 4 outcomes: (1, 1), (2, 2), (3, 3), (4, 4). Therefore, "There are 4 possible outcomes for spinning the same number twice."
Now you can fill in the statements accordingly:
- "There are a total of 16 possible outcomes."
- "There are 6 possible outcomes for spinning two numbers that have a sum greater than 5."
- "There are 4 possible outcomes for spinning the same number twice."