An ice-cream shop uses the following ingredients to make one sundae.
2 answers:
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Answer:
The expected sum of the numbers on the upward faces of the two dice is 7.
Step-by-step explanation:
Consider the provided information.
If two pair of dice tossed the possible out comes are:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)
Now we need to find the expected sum of the numbers on the upward faces of the two dice.
The expected sums can be:
Sum: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Prob: 1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36
As we know that the expectation of experiment can be calculated as:
Here S represents the numerical outcomes and P(S) is the respective probability.
Substitute the respective values in the above formula.
Hence, the expected sum of the numbers on the upward faces of the two dice is 7.
Answer:
It would take Henry 3 hours to clean the office carpets if Mary were not there to help
Step-by-step explanation:
Assume that it takes Henry t hours to clean the carpets
∵ Henry takes 3 hours less than Mary to clean the carpets
∵ Henry takes t hours
- That means add 3 to t to find Mary time
∴ Mary takes t + 3 hours
∵ The rate of Henry is
∵ The rate of Mary is
∵ Working together, they can clean the carpets in 2 hours
- Add the two rates and equate the answer by (their rate together)
∴
Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side
∵
∴
- Add the two fractions in the left hand side
∴
∴
Use the cross multiplication
∵ (t² + 3t)(1) = 2(2t + 3)
∴ t² + 3t = 4t + 6
- Subtract 4t from both sides
∴ t² - t = 6
- Subtract 6 from both sides
∴ t² - t - 6 = 0
- Factorize it into two factors
∴ (t - 3)(t + 2) = 0
Equate each factor by 0 to find t
∵ t - 3 = 0
- Add 3 to both sides
∴ t = 3
OR
∵ t + 2 = 0
- Subtract 2 from both sides
∴ t = -2 ⇒ reject this answer because there is no - ve time
∴ t = 3
∴ Henry would take 3 hours to clean the carpets alone
It would take Henry 3 hours to clean the office carpets if Mary were not there to help