Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
Answer:
∠2 = 18°
Step-by-step explanation:
∠WXZ = ∠1 + ∠2 ← substitute ∠1 = 3∠2
∠WXZ = 3∠2 + ∠2, that is
72 = 4∠2 ( divide both sides by 4 )
18 = ∠2, that is
∠2 = 18°
The volume is 508.94 cm^3
Answer:
$3.293
Step-by-step explanation:
You would multiply your total amount, 21.95, by your tip divided by 100, so 0.15. It would look like this: 21.95 x 0.15 = 3.293. Therefore, you would give the waitress a $3.293 tip. I Hope This Helps :)
Answer:
788.13 to the nearest hundredth.
Step-by-step explanation:
Let A be the total amount in the account after 3 years.
The formula is A = P(1 + x/100)^t .
Here P = 5000, x = 5 % and the time t = 3. years.
Amount after 3 years = 5000(1 + 5/100)^3
= 5788.13
So the Interest is 5788.13 - 5000
= 788.13.
