Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
= 3·4ⁿ + 51
= 3·4ⁿ⁺¹ + 51
- = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
- = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ - is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since - is divisible by 9, we have;
- 
= 
- is divisible by 9
Therefore is divisible by 9 and is divisible by 9 for all positive integers n
Step-by-step explanation:
the answer to this question would be 12 and 1/8
Answer:
This would be a regular polygon.
Step-by-step explanation:
A regular polygon has congruent sides and interior angles.
An irregular polygon does not have congruent sides and all interior angles.
A convex polygon does not have a interior angle greater than 180°.
Lastly, a concave polygon has only one interior angle greater than 180°.
Using the process of elimination, it would not be a convex or concave polygon. Now we have either a regular or irregular polygon. This polygon can not be a irregular polygon because all the sides are congruent. This means that this polygon is a regular polygon!
So these are decmials of the accutal total so
.32=32%
what makes this question easy is that there are 200 members so to convert the percents into accutall numbers so like .32=32%=64 people (since 200 is 2 times of 100)
A. fiction of 31-40 compared to 21-30
fiction 31-40=.38=38%=76 readers
fiction 21-30=.32=32%=64 readers
76-64=12
A is FALSE
B. so we want to know how many people are 31-40 and prefer fiction
so .38=38% and 38% of 200=76
B is FALSE
C 43 members are 21-30
so we look at the total row for the 21-30 people and see that .43 or 43% or 86 people are in the 21-30 age group
C is FALSE
D. 140 members prefer fiction
look at the total column for fiction and see that .70 like fiction .70=70%=140 people
D is TRUE
so A,B,C are FALSE
D is TRUE
