Answer:
95% confidence interval for the mean number of months is between a lower limit of 6.67 months and an upper limit of 25.73 months.
Step-by-step explanation:
Confidence interval is given as mean +/- margin of error (E)
Data: 5, 15, 12, 22, 27
mean = (5+15+12+22+27)/5 = 81/5 = 16.2 months
sd = sqrt[((5-16.2)^2 + (15-16.2)^2 + (12-16.2)^2 + (22-16.2)^2 + (27-16.2)^2) ÷ 5] = sqrt(58.96) = 7.68 months
n = 5
degree of freedom = n-1 = 5-1 = 4
confidence level (C) = 95% = 0.95
significance level = 1 - C = 1 - 0.95 = 0.05 = 5%
critical value (t) corresponding to 4 degrees of freedom and 5% significance level is 2.776
E = t×sd/√n = 2.776×7.68/√5 = 9.53 months
Lower limit of mean = mean - E = 16.2 - 9.53 = 6.67 months
Upper limit of mean = mean + E = 16.2 + 9.53 = 25.73 months
95% confidence interval is (6.67, 25.73)
Answer:
Rounded to the nearest tenth, the length of the missing side is 5.4 in.
Step-by-step explanation:
According to the Pythagorean theorem, 
, where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides. We can use this to solve for the length of the hypotenuse of the right triangle shown in your question (the missing side):
This simplifies to 
. Now to solve for c (the length of the hypotenuse), we just take the square root of both sides of the equation and solve like so:
This simplifies to c≈5.4 in.
Answer:
Zero, based on the information provided.
Step-by-step explanation:
The output rate of the teller machine is (1 transaction/6 minutes). The input rate is (1 customer/10 minutes). This means that the machine completes a cycle faster than the customers arrive, on the average. I don't know how an average can be calculated without more information. If we assume customers arrive every 10 minutes, and no one screws up the machine, that there should be no waiting line. Is there more information about when the customers arrive? E.g., 50 arrive in the first hour the machine is open.
Solution
Step 1
The opposite angles of a parallelogram are equal:
Step 2
The equation is made true by the opposite angles theorem is
85 + y = 3y - 15
or
y = 50
I’m pretty sure the answer would be 116
