Max used 1.6 liters of gasoline each hour moving lawns. How much gas does he use in 5.9 hours?
2 answers:
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This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.
∴N(c₁) =
N(c₂) =
∴N(c₁c₂) =
∴ Number of positive integers that are not divisible by 4 or 6,
N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.
∴N(c₁) =
N(c₂) =
∴N(c₁c₂) =
∴ Number of positive integers that are not divisible by 4 or 6,
N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
Answer:
The sequence aₙ = -15 +5n
The fifth term of the sequence
a₅ = 10
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given sequence
-10,-5,0,5,10,15,20,.....
The first term = -10
The difference of two terms in the given sequence is equal
d = -5-(-10) = -5 + 10 = 5
d = 0 -(-5) = 5
The given sequence is in arithmetic progression
<u><em>Step(ii):-</em></u>
The sequence
aₙ = -10 +(n-1) 5
aₙ = -10 + 5n -5
aₙ = -15 +5n
<u><em>Step(iii):-</em></u>
The sequence aₙ = -15 +5n
put n = 5
a₅ = -15 + 5(5) = -15 +25 = 10
<u><em>Final answer:-</em></u>
The sequence aₙ = -15 +5n
The fifth term of the sequence
a₅ = 10
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