Q: How can you add eight 4s together so that the total adds up to 500?

A: 444 + 44 + 4 + 4 + 4 = 500

Q: How can you add eight 4s together so that the total adds up to 500?

A: 444 + 44 + 4 + 4 + 4 = 500

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?

A:

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?

A: 1/3

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.

HH

HT

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.

HH

HT

TH

Since you know that one is a heads, and there are 3 possible outcomes, the probability is 1/3.