Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume
1 answer:
Answer:
Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:
B.t
Step-by-step explanation:
Notation
represent the mean for male king penguins
represent the mean for the female king penguins
represent the sample standard deviation for the sample male
represent the sample standard deviation for the sample female
sample size for the male penguins
sample size for the female penguins
t would represent the statistic
Hypothesis
We need to conduct a hypothesis in order to check if the male king penguins weigh more than female king penguins, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:
B.t
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Answer:
8
Step-by-step explanation:
The median is the segment from vertex B to the midpoint of AC. That midpoint (D) is ...
D = (A + C)/2 = ((-6, 7) +(-2, -9))/2 = (-8, -2)/2
D = (-4, -1)
The length of the midpoint is the length of the segment DB between (-4, -1) and (4, -1). These points both have the same y-coordinate, so the length is the difference of x-coordinates: 4 -(-4) = 8.
Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>Step-by-step explanation:
Given the function j(x) = 11.6 and k(x) =
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) =
are inverse functions.