5/54 or approximately 0.092592593
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
r = 4, y = 2, b = 1, so n = 3 + 1 = 4
r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
r = 5, y = 2, b = 1, so n = 9 + 1 = 10
And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
r = 6, y = 3, b = {2,1}, so n = 17 + 2 = 19
r = 6, y = 2, b = 1, so n = 19 + 1 = 20
And the pattern holds. So there are 20 possible rolls that meet the desired criteria out of 216 possible rolls. So 20/216 = 5/54.
the answer is The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
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22. Okay. What we need to do for this one is subtract fraction.l, because we are looking for how much more the second container holds than the first. We need to covert them to like denominators, which in this case is 8 5 3/4 = 5 6/8. Because 6/8 is less than 7/8, we need to regroup by adding 8 and turning the 5 into a 4. The problem would become like this: 4 14/8 - 1 7/8. When you subtract both numbers, you get 3 7/8. There. The second container holds 3 7/8 more gallons of water than the first.
23.
a. 15 student speeches will last 1 1/2 minutes each. In this case, we just simply multiply the fractions by multiply straight across. Multiply the top numbers together and the bottom numbers together. 1 1/2 is 3/2 a an improper fraction. Make 15 have a denominator of 1. 15/1 * 3/2 is 45/2 or 22 1/2 as a mixed number. It will take 22 1/2 minutes to give the speeches.
b. Okay. The teacher makes a 15 minute intro. Let’s add the time it takes to make the speeches and the teacher’s intro. 22 1/2 + 15 0/2 is 37 1/2. Yes. There is enough time to record everyone.
c. There are 60 minutes in 1 hour. Subtract the total amount taken on the camera from 60. 0/2 is less than 1/2. Again, regroup by adding 2 to make 2/2, and crossing out 60, so it becomes 59. 59 2/2 - 37 1/2 is 22 1/2. There are 22 1/2 minutes left on the digital camera.
