on the right side there are 3 pink and 3 blue
on the left side, there are 2 pink and 3 blue plus 5 green
Therefore the 5 green are equivalent to 1 pink.
On the bottom left, we can see that 1 pink = 2 green + 1 blue
so since 1 pink is 5 green and also 2 green + 1 blue,
5 green = 2 green + 1 blue
so 3 green = 1 blue or 1 blue = 3 green
Looking at the right hand side, we have 3 blue + 3 pink = 1/2(144)
If we replace blue and pnk in terms of green,
3 (3 green) + 3 (5 green) = 72
9 green + 15 green = 72
24 green = 72
1 green = 3
1 blue = 3 green = 3(3) = 9
1 pink = 5 green = 5(3) = 15
Thanks to https://solveme.edc.org/mobiles/
Q: A traffic light has a cycle through green, yellow, red, green, yellow, red, etc.
Red and green are each 30 seconds with a 3 second yellow inbetween.
What is the probability that while Amir is watching during a random 3 second interval that the color changes?
9/63 = 1/7
It is a 63 second cycle.
The light changes at t=30, t = 33 and t = 63 given three three second intervals:
[27,30] and [30, 33] and [60,63] is a total of 9 seconds out of the 63 second interval
Factoring out 2^2016 from both the numerator and the denominator:
results in 5/3.
Q: Two coins are flipped and you cannot see the outcome but are told that at least one is a head. What is the probability that the other coin also landed on heads?
This is a classic probability question. Once you know that one coin is a head, there are 3 possible outcomes for the two coins with at least one head.
Since you know that one is a heads, and there are 3 possible outcomes, the probability is 1/3.
Q: Write down all the integers from 1 through 60 to form the number
Now delete 100 digits from this number.
Without rearranging the digits, what is the largest number possible?
A: Writing down all integers from 1 through 60 gives you a number 111 digits long:
9 numbers at 1 digit apiece: 9 digits
51 numbers at 2 digits apiece: 102 digits
Total: 111 digits.
So deleting 100 digits leaves us with 11 digits. It’s be best to have as many 9’s as we can as far to the left as we can. But there’s only 6 of those, and one of them is already in the hundreds place before we do any deleting.
If we’re not allowed to rearrange the digits, the largest number is:
99 999 785 960.