Answer: The constant proportionality is 5/4
Step-by-step explanation: The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
If your equation is

, the only thing you need to do to get x by itself is to get rid of the denominator, the

. To get rid of a denominator, you multiply both sides by it, so you're left with

so
Answer: 0.0052
Step-by-step explanation:
Total number of times experiment was performed (n)= 12
Probability of the event (that one key out of a total of 12 opens the door) = 1/12 = 0.083
Hence, p = 0.83
q = 1 - p = 11/12 = 0.917
x = 3
Since the experiment was performed n number of times, a binomial probability distribution can defined the experiment.
P(x=r) = nCr ×p^r × q^n-r
P(x=3) = 12C3 × (0.083)⁴ × (0.917)^8
P(x=3) = 220 × (0.083)⁴ × (0.917)^8
P(x=3) = 0.0052