Solve the system 2x + 2y = −6 and 3x − 2y = 11 by using graph paper or graphing technology. What is the solution to the system?
2 answers:
Answer:
The solution of the system is:
(1,-4)
Step-by-step explanation:
We have to solve the system of equations:
and
using the graphing calculator.
As the graph are linear hence the solution of the system of equations is the intersection points of the graph of the two equations i.e. the point where the two lines meet.
Hence after plotting the graph of the system of equations we get the intersection point as:
(1,-4)
Hence, the solution of the system is:
(1,-4)
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Answer:
a) The standard deviation of x must be 0.25 inches.
b) We need a sample of 125 to reduce the standard deviation of x⎯⎯⎯ to the value you found in part(a).
Step-by-step explanation:
The 68-95-99.7 states that:
68% percent of the measures of a normally distributed sample are within 1 standard deviation of the mean.
95% percent of the measures of a normally distributed sample are within 2 standard deviations of the mean.
99.7% percent of the measures of a normally distributed sample are within 3 standard deviations of the mean.
The standard deviation of the population is 2.8. This means that .
(a) What standard deviation must x⎯⎯⎯ have so that 95% of all samples give an x⎯⎯⎯ within one-half inch of μ?
We want to have a sample in which 2 standard deviations are within 0.5 inches of the mean.
So, the standard deviation of the sample must be:
The standard deviation of x must be 0.25 inches.
(b) How large an SRS do you need to reduce the standard deviation of x⎯⎯⎯ to the value you found in part(a)?
We have that the standard deviation of a sample of length n is given by the following formula:
.
We want and we have
. So
We need a sample of 125 to reduce the standard deviation of x⎯⎯⎯ to the value you found in part(a).