To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint 
that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling 
at the 8 points,
(1/2, 1/2, 1/2)
(1/2, 1/2, 3/2)
(1/2, 3/2, 1/2)
(3/2, 1/2, 1/2)
(1/2, 3/2, 3/2)
(3/2, 1/2, 3/2)
(3/2, 3/2, 1/2)
(3/2, 3/2, 3/2)
which are captured by the sequence
with each of 
being either 1 or 2.
Then the integral of 
over 
is approximated by the Riemann sum,
(compare to the actual value of about 4.159)
To find the x-int., let y = 0 and solve for x: 13x = 6, so x = 6/13: (6/13, 0)
To find the y-int., let x =0 and read off the y-int: (0, -6)
The answer is 19/27
51x19=969
51x27=1377
969/1377=19/27
Answer:
The probability of selecting a students that drinks sugar free red bull is <em><u>0.1</u></em>
Step-by-step explanation:
In this question, we are concerned with calculating probability that out of the 120 students interviewed, a student chosen at random drinks sugar free red bull.
Mathematically, the probability is = number of students that drinks sugar free red bull/Total number of students interviewed
We know the total number of students interviewed, but we do not know the number of students that drink sugar free red bull.
Now looking at the question, we can see that all the students interviewed has the choice of having only to drinks, monster or red bull.
Since 72 students drink monster, the number of students that take red bull = 120 - 72 = 48
Now from this 48, we have a ratio. The ratio of regular type to sugar free is 3:1. The number taking sugar free is thus 1/4 × 48 = 12 students
The probability of choosing a student that drinks sugar free red bull is thus 12/120 = 1/10 = 0.1
