) A wierd number is a number that is the product of two consecutive primes, such as 7x11=77 . What is the least common multiple of the 5 smallest wierd number
7) According to an ancient belief, when a friend visits a sick person, 1/70 of his sickness is taken away. What is the least amount of friends that need to visit to take away at least 81% of a person's illness?
can any one get the answer
I don't really understand the first one.
But for the 2nd one. 1/70 = 0.01%. So 81/0.01 = 8100. Therefore, at least 8100 friends need to visit to take the illness away.
1. the first 5 'wierd' numbers are:
2x3=6
3x5=15
5x7=35
7x11=77
11x13=143
Now find the LCM of 6,15,35,77,143 which would of course be 2x3x5x7x11x13= .....
2. Raj's answer is not correct.
Look at it this way:
After the first friend 69/70 of the sickness is still there.
After the second friend visits 69/70 of the previous 69/70 of the sickness remains, or (69/70)^2 remains.
you want 81% of the sickness taken away, which means 19% remains.
So you are solving (69/70)^n = .19
an exponential equation that can be solved using logs.
I got n = log .19 / log(69/70) = 115.4
(verification: (69/70)^115 = .805...
To find the least common multiple (LCM) of the 5 smallest weird numbers, we need to find the LCM of 6, 15, 35, 77, and 143. Let's break down the process step by step:
1. List the 5 smallest weird numbers:
- 2 x 3 = 6
- 3 x 5 = 15
- 5 x 7 = 35
- 7 x 11 = 77
- 11 x 13 = 143
2. Prime factorize each of these numbers:
- 6 = 2 x 3
- 15 = 3 x 5
- 35 = 5 x 7
- 77 = 7 x 11
- 143 = 11 x 13
3. Identify the highest power of each prime factor:
- 2 is raised to the power of 1
- 3 is raised to the power of 1
- 5 is raised to the power of 1
- 7 is raised to the power of 1
- 11 is raised to the power of 1
- 13 is raised to the power of 1
4. Multiply all the prime factors together, each raised to its highest power:
LCM = (2^1) x (3^1) x (5^1) x (7^1) x (11^1) x (13^1)
= 2 x 3 x 5 x 7 x 11 x 13
= 30,030
So, the LCM of the 5 smallest weird numbers is 30,030.
Now, let's move on to the second question:
To determine the least number of friends needed to take away at least 81% of a person's illness, we can use the concept of exponential decay. Here's how to solve it:
1. Convert 81% to decimal form: 81% = 0.81
2. Set up an exponential equation using the formula for decay: (69/70)^n = 0.81
3. Take the logarithm of both sides of the equation to solve for n:
log((69/70)^n) = log(0.81)
n * log(69/70) = log(0.81)
n = log(0.81) / log(69/70)
≈ 115.4
Rounding up to the nearest whole number, we find that at least 116 friends need to visit to take away at least 81% of a person's illness.
I hope this explanation helps! If you have any further questions, feel free to ask.