An absentminded professor does not remember which of his 12 keys will open his ocedoor. Suppose he tries them at random and with replacement. Find the probability that heopens his oce door after three tries.

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

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.

image result for what is another name for consecutive interior angles? ​

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation: