Answer:
D.
Step-by-step explanation:
The point-slope form of a line is given by:
The line given to us has equation; .
The slope of this line is -4. The of the line perpendicular to this line is the negative reciprocal of the slope of the given line.
Our slope of interest is therefore;
Since the point goes through (-2,7), we have .
We plug in the slope and the point into the point-slope formula to obain;
The required equation is:
Answer:
a) S = {1, 2, 3}
b) P(odd number) =
c) No
d) Yes
Step-by-step explanation:
a) The sample space is the set of all possible outcomes. By definition, the elements of a set should not be repeated. Hence, the sample space S = {1, 2, 3}
However, the sample is not equiprobable because each element has different probabilities.
b) P(odd number) =
Note that the odd numbers are 1 (on three faces) and 3 (on one face).
c) The fact the die has been biased does not change the possible outcomes. It only changes the probability of getting any given number.
d) Because the 3-face has been loaded, this probability changes. In fact, it is calculated thus:
Let's assume the probability for 1 or 2 is . Then that of 3 is
(because it is twice the others). The sum of probabilities must be 1.
P(odd number) = Prob(1) + Prob(3)
= =
Answer:
C) H0:μd=0 and Ha:μd≠ 0
Null hypothesis:
Alternative hypothesis:
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=value for the first shop , y = value for the second shop
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
Or equivalently :
Null hypothesis:
Alternative hypothesis:
Since we define the difference and we obtain this:
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
The 4 step is calculate the statistic given by :
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a two tailed test the p value is given by:
C) H0:μd=0 and Ha:μd≠ 0