All categories

3 years ago

How many of the first million positive integers share no common factors greater than 1 with 2020

Mathematics

1 answer:

Bingel [31]3 years ago

4 0

9514 1404 393

Answer:

396,040

Step-by-step explanation:

Factors of 2020 are 2, 5, 101.

There are 1,000,000 / 1010 = 990 multiples of 2 and 5 and 101.

There are 1,000,000 / 505 -990 = 990 multiples of 5 and 101 only.

There are 1,000,000 / 202 -990 = 3,960 multiples of 2 and 101 only.

There are 1,000,000 / 10 - 990 = 99,010 multiples of 2 and 5 only.

There are 1,000,000 / 101 -990 -990 -3960 = 3,960 multiples of 101 only.

There are 1,000,000 / 5 -990 -990 -99,010 = 99,010 multiples of 5 only.

There are 1,000,000 / 2 -990 -3960 -99,010 = 396,040 multiples of 2 only.

So, the total number of multiples of any factor of 2020 is ...

990 +990 +3960 +99,010 +3960 +99010 +396040 = 603960

Then the number of integers in the first million that do not share any common factors greater than 1 with 2020 is ...

1,000,000 -603,960 = 396,040

You might be interested in

Audrey, an astronomer is searching for extra-solar planets using the technique of relativistic lensing. Though there are believe

Stolb23 [73]

Answer:

Step-by-step explanation:

The model $N (t)$ , the number of planets found up to time $t$ , as a Poisson process. So, the $N (t)$ has distribution of Poison distribution with parameter $(\lambda t)$

The mean for a month is, $\lambda = \frac{1}{3}$ per month

$E[N(t)]= \lambda t\\\\=\frac{1}{3}(24)\\\\=8$

(Here. t = 24)

For Poisson process mean and variance are same,

$Var[N (t)]= Var[N(24)]\\= E [N (24)]\\=8$

(Poisson distribution mean and variance equal)

The standard deviation of the number of planets is,

$\sigma( 24 )] =\sqrt{Var[ N(24)]}=\sqrt{8}= 2.828$

For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter $\lambda$ . The sum of $K$ of these independent exponential has distribution Gamma $(K, \lambda)$ .

From the given information, $k = 6$ and $\lambda =\frac{1}{3}$

Calculate the expected value.

$E(x)=\frac{\alpha}{\beta}\\\\=\frac{K}{\lambda}\\\\=\frac{6}{\frac{1}{3}}\\\\=18$

(Here, $\alpha =k$ and $\beta=\lambda$ )

Calculate the probability that she will become eligible for the prize within one year.

Here, 1 year is equal to 12 months.

P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)

$=\frac{1}{Г (6)(\frac{1}{3})^6}(12)^{6-1}e^{-36}\\\\=0.2148696\\=0.2419\\=21.49%$

Hence, the required probability is 0.2149 or 21.49%

5 0

3 years ago

Find the equation of the line that goes through the point

Yuliya22 [10]

Answer:

y=-4x-8

Step-by-step explanation:

use the equation y-y1=m(x-x1) and solve for y

7 0

3 years ago

Read 2 more answers

Pls answer 18 20 and 22 show your work

Svetlanka [38]

Answer:

18- 300

20- 1,500

22- 300

Step-by-step explanation:

You can easily find the answer like this:

18. Multiply 60 and 100 together. The hundred is from 100%. After that, divide it by 20 because of the percent. After doing this, you should get 300.

20. 360*100=36,000 36,000/24= 1,500

22. 9*100=900 900/3=300

I hope this is what you were looking for. If you need more out of this, ask me to answer it again. :)

5 0

3 years ago

20.41312<br> (a) The given number truncated to four decimal places is

Ivanshal [37]

Answer:

20.4131

Step-by-step explanation:

You need to have only 4 decimal places after , last decimal being approximated

8 0

3 years ago

You can make small 20 small frames in 4 days or 21 large frames in 3 days. A customer has just place a order with you for 40 sma

cupoosta [38]

Answer:

I got 17.

Step-by-step explanation:

Because it takes 4 days to make 20 small frames, it takes 8 days to make 40. And because it takes 3 days to make 21 frames, and 21 multiplied by 3 is 63 (one less than 64), it would take 9 days (3 times the amount for 21) to make 64 large frames. In all, it would take APPROXIMATELY 17 days (9 +8 is 17)

6 0

3 years ago