Answer:
It does not show variation
Step-by-step explanation:
Given

Required
Determine if there's direct variation between x and y
The general form of direct variation is:

Make y the subject of formula in the given parameters;


Compare
to 
<em>Since they are not of the same form, then the given equation do not show direct variation</em>
Answer:
E. -0.723
Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.
Step-by-step explanation:
Information provided
represent the sample mean for the length
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level
t would represent the statistic
represent the p value for the test
System of hypothesis
We need to conduct a hypothesis in order to check if the lathe is in perfect adjustment (6cm), then the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
since we don't know the population deviation the statistic is:
(1)
Replacing in formula (1) we got:
E. -0.723
P value
The degrees of freedom are given by:
Since is a two tailed test the p value would be:
Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.
The sample space has 36 possible pairs from 1,1 1,2 1,3 up to 6,5 and 6,6
(a). Three pairs add to 4 1,3 2,2 and 3,1 so P(4) = 3/36 = 1/12
(b). 6 pairs add to 7 so P(7) = 6/36 = 1/6
(c) 15 pairs add to less than 7 so P(<7) = 15/36 = 5/12