About 25% of those called for jury duty will find an excuse to avoid it. If 12 people are called what is the probability that all 12 will be available. (Binomial distribution)

Approximately (or, equivalently, ,) assuming that the availabilities of the jurors are independent from one another.

Step-by-step explanation:

The question states that the probability that a given juror is unavailable is approximately .

For the complement of that event, the probability that this particular juror is available would be .

Assume that the availabilities of the jurors are independent from one another. The number of available jurors would be a binomial variable with and ( independent observations, each with a probability of being "available".)

Hence, the probability that all jurors are available would be:

.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17