The amount of time needed for a certain machine to process a job is a random variable with mean EXi = 10 minutes and Var(Xi)=2 minutes2. The times needed for different jobs are independent from each other. Find the probability that the machine processes less than or equal to 40jobs in 7hours.

0.98732

Step-by-step explanation:

Given that :

Mean = 10 minutes

Variance = 2 minutes

For less than equal 40 jobs

Mean (m) = 40 * 10 = 400 minutes

Variance = 2 * 40 = 80 minutes

Standard deviation (s) = √variance = √80

Converting hours to minutes

X = 60 * 7 = 420 minutes

P(X≤ 420) :

Z = (x - m) / s

P(X≤ 420) :

Z = (420 - 400) / √80

Z = 20 / √80 = 20 / 8.9442 = 2.236

P(Z ≤ 2.236) = 0.98732

180 square centimeters

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet