Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data in
1 answer:
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Answer:
It is proved that exixts at (0,0) but not differentiable there.
Step-by-step explanation:
Given function is,
- To show exixtance of
we take,
exists.
And,
exists.
- To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,
where m is a variable.
which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).
Answer:
a)
b) We are uncertain
c) It will change significantly
Step-by-step explanation:
a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.
Since we assume that the variances are equal, we use the pooled variance given as
,
where .
The mean difference .
The confidence interval is
b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.
c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.