Answer: 8
Step-by-step explanation:
The degree of freedom for t-distribution of testing the differnce between the two population mean is given by :-
, where 
= Size of first sample.
= Size of second sample.
As per given ,
Veterinarian selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths.
i.e. 
and 
Now , If she calculates a two-sample confidence interval by hand for the difference in the mean number of flakes fed to horses with and without enteroliths the degrees of freedom she should use are
Hence, the correct answer is 8.
ANSWER
EXPLANATION
The given expression is;
We factor to obtain;
Multiply by the reciprocal of the second fraction
Cancel out common factors to get,
In order to construct this equation, we will use the variables:
V to represent mixture volume (40 ml)
C to represent mixture concentration (0.32)
v₁ to represent volume of first solution (40 / 4 = 10 ml)
c₁ to represent concentration of first solution (0.2)
v₂ to represent the volume of the second solution (40 * 3/4 = 30 ml)
c₂ to represent the concentration of the second solution
We know that the total amount of substance, product of the volume and concentration, in the final solution is equal to the individual amounts in the two given solutions. Thus:
VC = v₁c₁ + v₂c₂
40(0.32) = 10(0.2) + 30c
C=90°, A=75°, b=AC=19, x=AB
Without a figure, we see AC is adjacent to angle A, so
cos A = AC/AB = b/x
x = b/cos A = 10 / cos 75° ≈ 38.637
Answer: 38.6
