if one letter is chosen at random from word "combed" what is the probability that the letter chosen will be a "d"
2 answers:
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There is a missing content in the question.
After the statements and before the the options given; there is an omitted content which says:
Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?
Answer:
C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).
Step-by-step explanation:
From the given question:
The resulting regression equation can be represented as:
where;
the estimated number of contracts in a quarter X is the coded quarterly value with X = 0
the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise
Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise
Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise
Our null and alternative hypothesis can be stated as;
Null hypothesis :
The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)
A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is 
. We have
so this vector field is not conservative.
- - -
Another way of determining the same result: We want to find a scalar function
such that its gradient is equal to the given vector field, 
:
For this to happen, we need to satisfy
From the first equation, integrating with respect to
yields
Note that
*must* be a function of 
only.
Now differentiate with respect to
and we have
but this contradicts the assumption that
is independent of . So, the scalar potential function does not exist, and therefore the vector field is not conservative.
so this vector field is not conservative.
- - -
Another way of determining the same result: We want to find a scalar function
For this to happen, we need to satisfy
From the first equation, integrating with respect to
Note that
Now differentiate with respect to
but this contradicts the assumption that