Challenge A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the
1 answer:
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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:
D.
Step-by-step explanation:
Mass of Jupiter is given as 1,898,000,000,000,000,000,000,000,000 kg
Estimating this to the nearest whole number would be = 2,000,000,000,000,000,000,000,000,000 kg (rounding up the the "1,898")
To express this in scientific notation form, simply count how many zeros we have to the nearest whole number, 2.
We have 27 zeros there.
Therefore, we would multiply the whole number, 2, by 10 raise to the power of 27.
An estimate of the mass of Jupiter =