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12.9
2+3+5+7+11+13+17+19+23+29=129
129/10=12.9
190.85
1
6=1x2x3
24=2x3x4
60=3x4x5
120=4x5x6
210=5x6x7
336=6x7x8
b
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
Very exited
Solution:
As given, we have,
The cost of one pen = 36 Rs.
So, the cost of 15 pens = 36 × 15 = 540 Rs.
The cost of one book = 45 Rs.
So, the cost of 12 books = 45 × 12 = 540 Rs.
The cost of one pencil = 8 Rs.
So, the cost of 10 pencils = 8 × 10 = 80 Rs.
Now,
the cost of each eraser is 40 Rs. less than the combined costs of pen and pencil.
So,
Combined costs of pen and pencil = 36 + 8 = 44 Rs.
Cost of one eraser = 44 – 40 = 4 Rs.
So, the cost of 5 erasers = 4 × 5 = 20 Rs.
Hence,
The total amount spent is
Hence, the total amount spent is 1180 Rs.
I think the answer is: 16
the woman faster *1.5 from the man, every day.
because that, the exersize is:
24/1+1.5+x=6
x=1.5
24/1.5=16!
5
307,311,313,317,319
Clarke is 80 years old
After the mixing, 1lt of the mixture has 0.8lt of milk and 0.2lt of water. 1lt of milk costs Rs.12 so 0.8lt of milk costs 0.8 x 12 = 9.6
He sells the mixture at Rs.15,
so profit%=(15-9.6)/9.6 x 100 = 56.25%
Rs.265.80
Here is the solution to the given version of the puzzle (9 balls, one is heavier, need to identify oddball), where we label the balls A, B, …, I:
1. Weigh ABC versus DEF.
Scenario a: If these (1) balance, then we know the oddball is one of G, H, I.
2. Weigh G versus H.
Scenario a.i: If these (2) balance, the oddball is I.
Scenario a.ii: If these (2) do not balance, the heavier one is the oddball.
Scenario b: If these (1) do not balance, then the oddball is on the heavier side. For simplicity, assume the ABC side is heavier, so the oddball is one of A, B, C.
2. Weigh A versus B.
Scenario b.i: If these (2) balance, the oddball is C.
Scenario b.ii: If these (2) do not balance, the heavier one is the oddball.
answer is maximum of 2.
Let three consecutive even numbers be 2n,2n+2,2n+4
product=2n(2n+2)(2n+4)
If n=1,
product =2(4)(6)=48.
So, all the numbers will be divisible by 48 if change n.
area is given by Area of Rectangle = Length of Rectangle*(sqrt((Diagonal of Rectangle^2)-(Length of Rectangle^2)))
so substituting we get area=4*(sqrt((25-16)))
area=4*(sqrt(9))
since area cannot be negative hence we take sqrt of 9 as 3 (as sqrt of 9 is 3 and -3 as well)
area=4*3=12m^2