What is the interquartile range for the data set? 241, 230, 201, 245, 209, 211, 242, 201, 204, 228, 242, 243
melomori [17]
Answer:
What is the interquartile range for the data set?
241, 230, 201, 245, 209, 211, 242, 201, 204, 228, 242, 243
THE ANSWER IS 35.5
Neither of those two graphs do the trick, but if I saw the rest of the answer choices, then I would be happy to assist you.
Answer:
Answer below
Step-by-step explanation:
3x+7 + 3x+6 + 3x = 3x + 3x +4x+2
x= 11
(a) This is the same as computing 4⁵⁵ (mod 11). We have
4² ≡ 16 ≡ 5 (mod 11)
4³ ≡ 4 • 5 ≡ 20 ≡ 9 (mod 11)
4⁴ ≡ 4 • 9 ≡ 36 ≡ 3 (mod 11)
4⁵ ≡ 4 • 3 ≡ 12 ≡ 1 (mod 11)
Then from here,
4⁵⁵ ≡ (4⁵)¹⁰ • 4⁵ ≡ 1¹⁰ • 1⁵ ≡ 1 (mod 11)
(b) Each term in the sum
4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴
has a common factor of 4ⁿ, so this sum is the same as
4ⁿ (1 + 4 + 16 + 64 + 256) = 4ⁿ • 341 = 4ⁿ • 11 • 31
So the sum is indeed divisible by 11 for all integers <em>n</em>.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when <em>a</em> = 2.