Ben is 12 years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was 4

Use the principle of inclusion and exclusion to find the number of positive integers less than 1,000,000 that are not divisable

wel

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) = $\frac{999,999}{6} = 166666$
N(c₂) = $\frac{999,999}{4} = 250000$
∴N(c₁c₂) = $\frac{999,999}{24} = 41667$
∴ 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

8 0

3 years ago

Butter and flour are mixed in the ratio 2 : 3.Chris has 640 grams of butter and 880 grams of flour.How much more flour does he n

VMariaS [17]

he need 1000 grams of all

3 0

3 years ago

A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose 1/10 degree every 1/4 hour for

klio [65]

Answer:

The rate is $\frac{2}{5}$ degree per hour.

Step-by-step explanation:

Given : A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose $\frac{1}{10}$ degree every $\frac{1}{4}$ hour for a limited time.

To find : What was the rate, in degrees per hour that the temperature of the compound rose ?

Solution :

In every $\frac{1}{4}$ hour the temperature of a compound rose $\frac{1}{10}$ degree

To get the rate, in degrees per hour,

In every 1 hour the temperature of a compound rose is

$r=\dfrac{\frac{1}{10}}{\frac{1}{4}}$ degree

$r=\dfrac{4}{10}$ degree/hr

$r=\dfrac{2}{5}$ degree/hr

Therefore, the rate is $\frac{2}{5}$ degree per hour.

5 0

3 years ago

Alan and Margot drive from City A to City B a distance of 147 miles. They take the same route and drive at constant speeds. Alan

S_A_V [24]

If one of them got there faster, who will it be?? 147 Miles keep that in mind ok. If they go on the Same route and Drive at Constant Speed. And Alan will start at 1:45 to 4:15. You will see the Difference of, 1:45 = 4:15 The 1 Has switched into the tens and the 4 Has Switched into The 100's. Alan Got there Fast. Margot Got there Faster. If you can Solve The Equation y=64x It will be 36y. 36 Miles speed. Well they need gas? we will find out later. Margot Got to City a To City B. so the Answer is. Margot Got there Fast Before Alan.

5 0

3 years ago

Which equation show you how to find 16-9?

Setler79 [48]

16-9=-7 nhbjjkljlhgcfgdfcjjjklhgfch;ljkhgfdfchk;klhjgf

6 0

3 years ago