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It is not clear whether the Happiness Index of the different years is compared based on the height of the smiley faces or the area of the smiley faces.
Depending on which criteria are used to compare the happiness index of the different year, the data can have a different interpretation.
s is directly proportional to the square of v. It is known that s = 36 for a particular value of v.
Find the value of s when this value of v is halved.
Nine gifts, three of which are identical, and the rest are distinct, are distributed among five people without restrictions on the number of gifts a person can have. By first considering the number of ways to distribute the distinct gifts or otherwise, find the number of ways that the nine gifts can be distributed.
First, consider the number of ways to distribute the 6 distinct gifts:
Gift A can be given to either Person P, Q, R, S or T: 5 ways
Gift B can be given to either Person P, Q, R, S or T: 5 ways
Gift C: 5 ways, Gift D: 5 ways, Gift E: 5 ways, Gift F: 5 ways
So, for 6 distinct gifts, number of ways to distribute to 5 persons = 56
Next, consider the number of ways to distribute the 3 identical gifts:
Case 1: 3 of the persons get 1 of these gifts each = 5C3 = 10
Case 2: 1 of the persons gets 1 of these gifts, another person gets 2 of these gifts:
5C2 x 2 = 20
*The “x 2” is for the permutation for 1st person gets 2 gifts and the 2nd gets 1 gift, OR the 1st person gets 1 gift and the 2nd gets 2 gifts.
Case 3: 1 of the persons get all 3 of these gifts = 5C1 = 5
Total number of ways = (10 + 20 + 5) x 56
= 546 875
The work done at the barrel is equal to the work done at the nozzle.
Word Done = Force x Distance.
The force at the barrel > the force at the nozzle, so for equal work done,
distance moved by water leaving barrel per second < distance moved by water leaving the nozzle per second.
This results in a greater speed of the water leaving the nozzle.
Alternative Answer:
Volume of water leaving the barrel per second = Volume of water leaving the nozzle per second.
The cylindrical volume = Base area x distance moved by the water.
Since base area of barrel > base area of nozzle, so for equal volumes,
distance moved by water leaving barrel per second < distance moved by water leaving nozzle per second.
This results in a greater speed of the water leaving the nozzle.