Answer: -2.10
Step-by-step explanation:
Given : 

Sample size : n= 50, since the sample size is greater than 30 , so we apply z-test.
Sample mean : 
Standard deviation : 
The test statistic for population mean :-

i.e. 
Hence, the value of the test statistic = -2.10
X represents (smaller) angle 1, y represents (larger) angle 2:
180 = x + y
y = 6x + 5
180 = x + y
180 = x + (6x + 5)
180 = 7x + 5
175 = 7x
25 = x
180 = 25 + y
155 = y
the smaller angle (x) is 25 degrees.
Answer:
0.2384 = 23.84% probability that 3 were laser printers.
Step-by-step explanation:
The printers will be chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:

In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:
20 orders means that 
8 were laser printers, which means that 
Sample of 5 means that 
What is the probability that 3 were laser printers?
This is P(X = 3).


0.2384 = 23.84% probability that 3 were laser printers.
Answer: 1) V≈1244.07 in 2) V≈54286.72 ft 3) V≈23816.41 yd
Step-by-step explanation:
Answer:
See step by step explanations to get answer.
Step-by-step explanation:
Given that:
Our linear approximation will be of the form y = c + mx. Use the values of f at the point a and the nearby point a h to find a good approximation. (You will need to set up a linear system involving c, m,a, h, f(a), f(a+ h), where c and m are the variables. You should also be able to solve this linear system exactly for the vector.