First, 27 = 3³, so 27¹⁵ = (3³)¹⁵ = 3⁴⁵.
So we have
27¹⁵ ≡ 3⁴⁵ (mod 33)
and
3 ≡ 3 (mod 33)
3² ≡ 9 (mod 33)
3³ ≡ 27 (mod 33)
3⁴ ≡ 81 ≡ 15 (mod 33)
3⁵ ≡ 3 • 15 ≡ 45 ≡ 12 (mod 33)
From here, the cycle continues:
3⁶ ≡ 3 • 12 ≡ 36 ≡ 3 (mod 33)
3⁷ ≡ 3 • 3 ≡ 9 (mod 33)
and so on.
This is to say that, for each power of 3, where the power is a multiple of 5, the remainder will always be 12, i.e. for any positive integer <em>k</em>,
Answer:
New price 3.10
Step-by-step explanation:
Answer:
The length of the rectangular field is 12 ft and the width is 5 ft.
Step-by-step explanation:
The area of a rectangle is:
The area of a rectangular field is, <em>A</em> = 60 ft.
The length of the field is:
l = w + 7
Compute the width of the field as follows:
Factorize the last equation by splitting the middle term as follows:
Now, since the width of rectangular field cannot be negative, the width is 5 ft.
Compute the length as follows:
l = w + 7
= 5 + 7
= 12
The length of the rectangular field is 12 ft.
The probability should be 1/60
N; n+1; n+2 - three consecutive whole number
n + (n + 1) + (n + 2) = 195
n + n + 1 + n + 2 = 195
3n + 3 = 195 |subtract 3 from both sides
3n = 192 |divide both sides by 3
n = 64
Answer: 64; 65; 66.