Answer:
Step-by-step explanation:
Total number of students = 68
Let history = H
Maths = M
English = E
n(H) = 25
n(M) = 25
n(E) = 34
n(HnMnE) = 3
Total = n(H) + n(M) + n(E) - people in exactly two groups + 2(people in exactly 3 groups) + people in none of the groups
68 = 25 + 25 + 34 - people in exactly two groups - 6 +0
68 = 84 -6 - people in exactly two groups
68 = 78 - people in exactly two groups
People in exactly two groups = 78 - 68
= 10
OR
From the venn diagram, people in exactly two groups are represented by x, y and z
Total = 25 - x - y - 3 + 25 - x - z - 3 + 34 - y - z - 3 + x + y + z + 3
68 = 50 - x - 3 + 34 - y - z - 3
68 = 84 - 6 - x - y - z
68 = 78 - x - y - z
68 - 78 = - x - y - z
-10 = -(x + y + z)
x+y+z = -10/-1
x+y+z = 10
The number of students that registered for exactly two courses = 10
Answer:
Step-by-step explanation:
There were 9 other people there. First you would subtract how much marcus paid from the total (134.03-20.45=113.58). After that you just divide the remaining cost with 12.62 (113.58/12.62=9)
9514 1404 393
Answer:
3/(x +1) -4/(x +1)^2
Step-by-step explanation:
The partial fraction expansion will be of the form ...
A/(x+1)^2 +B/(x+1)
We can find the values of A and B by writing the sum of these terms:
= (A +B(x +1))/(x +1)^2
Then we require ...
B = 3
A +B = -1 ⇒ A = -4
So, the desired expansion is ...
3/(x +1) -4/(x +1)^2
Answer:
the first one is right but the second one is -2 , not 2.
Step-by-step explanation:
9514 1404 393
Answer:
- late only: 15
- extra-late only: 24
- one type: 43
- total trucks: 105
Step-by-step explanation:
It works well when making a Venn diagram to start in the middle (6 carried all three), then work out.
For example, if 10 carried early and extra-late, then only 10-6 = 4 of those trucks carried just early and extra-late.
Similarly, if 30 carried early and late, and 4 more carried only early and extra-late, then 38-30-4 = 4 carried only early. In the attached, the "only" numbers for a single type are circled, to differentiate them from the "total" numbers for that type.
__
a) 15 trucks carried only late
b) 24 trucks carried only extra late
c) 4+15+24 = 43 trucks carried only one type
d) 38+67+56 -30-28-10 +6 +6 = 105 trucks in all went out
