Answer:
B.
Step-by-step explanation:
a) {1,5,6,7,8}
b) {5}
c) {1,2,4}
d) {} = empty set
Step-by-step explanation:
- It is based on set theory.
- To find "a" first simplify within brackets.
- A' = everything apart from A which is {5,6,7,8} even universal.
- B'= everything apart from B which is {1,2,7,8}
- C'= everything apart from C which is {1,4,5,8}
- The notation "n" is intersection anything that is common in both.
- The notation "U" is "Union" everything within both.
- Rule if Union has more than one common it would still be mentioned.
- As one won't be written as twice.
- (B'nC') apart from B and apart from C the common in both is {1,8}
- A' U {1,8} apart from A union all in (B'nC')= {1,5,6,7,8}
- (BnC') same all of B intersection everything apart from C.
- A'n(BnC') = {5}
- (B'UC') = everything apart from B and C common in A n(B'UC') ={1,2,4}
- (AUBUC)' union all ABC but a complement gives 8.
- (AUBUC) union all ABC but not universal number{1,2,3,4,5,6,7}
- Intersection between them gives empty set as both are not common.
<h2><u>Part A:</u></h2>
Let's denote no of seats in first row with r1 , second row with r2.....and so on.
r1=5
Since next row will have 10 additional row each time when we move to next row,
So,
r2=5+10=15
r3=15+10=25
<u>Using the terms r1,r2 and r3 , we can find explicit formula</u>
r1=5=5+0=5+0×10=5+(1-1)×10
r2=15=5+10=5+(2-1)×10
r3=25=5+20=5+(3-1)×10
<u>So for nth row,</u>
rn=5+(n-1)×10
Since 5=r1 and 10=common difference (d)
rn=r1+(n-1)d
Since 'a' is a convention term for 1st term,
<h3>
<u>⇒</u><u>rn=a+(n-1)d</u></h3>
which is an explicit formula to find no of seats in any given row.
<h2><u>Part B:</u></h2>
Using above explicit formula, we can calculate no of seats in 7th row,
r7=5+(7-1)×10
r7=5+(7-1)×10 =5+6×10
r7=5+(7-1)×10 =5+6×10 =65
which is the no of seats in 7th row.
Answer:
27 hours
Step-by-step explanation:
180 divided by 20 is 9. Multiply 9 by 3 to get the hours
Answer:
L. W = 60. 30.
Step-by-step explanation:
Perimeter = 2L + 2W where W = width and L = the length, and L = 2W.
We have the following system:
2L + 2W = 180
L = 2W
Substituting L = 2W in the first equation we have:
2(2W) + 2W = 180
4W + 2W = 180
6W = 180
W = 180/6 = 30.
So L = 2*30 = 60.