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1208.9
7days
To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.
The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.
There are 24 primes in S, so the product of S is:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97
We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.
5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.
25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.
Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros
Circular Track sis of 11 km
Speed of Mens are
4 , 5.5 , 8 km/hr
Time at Which they are at starting Points again
11/4 , 11/5 , 11/8
11/4 , 2.2 , 11/8
We need to find LCM of these
to find at what time they Meet again at starting point
LCM 11 * 2 = 22
After 22 Hrs they will meet at starting point
877.4
if am standing on a ballconi so i see the people what they
are doing and how they are handling with the people and
what they are taking to each and everybody.
c
37 SEATS….
because if passengers will occupy 3 seats, per head amount
payable will be 26.89.80.67 can not be divisible other than
3 and 26.89. so the,
Number of occupied seats will be 3
Number of unoccupied seats will be 40-3=37
(a) 29.12 (actual)
first year rate of paper (inflation rate) : 25 + 25 *
6.5/100 = 26.625
paper rate in first year is 1.5 % more . ..thr4
inflated cost in 1 yr = 26.625 + 1.5 / 100 * 26.625 =
27.024.
second year : 27.024 + 27.024 * 6.5 / 100 = 28.78
paper cost : 1.5 /100 * 28.78 + 28.78 = 29.12 ( approx..)
72
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