The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set α = 0.05. The conclusion for this hypothesis test would be that because the test statistic is .

Step-by-step explanation:

information given

represent the sample mean  

represent the population standard deviation

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

z would represent the statistic

represent the p value for the test

Hypothesis to test

We want to test if the true mean is less than 12, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing the info given we got:

We can replace in formula (1) the info given like this:  

stops on an even number.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18