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

Answers

Answer 1

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


Related Questions

Greg went to Bed Bath and Beyond to buy Christmas gifts for his family this year. In his first trip he bought 4 candles, 5 wallflowers, and 6 lotions for a total of $123. Greg forgot some people on his list the first time so he makes a second trip and spent $48 to buy 2 candles, 3 wallflowers, and 1 lotion. The price of a lotion is 2 less than 2 times the price of a wallflower. How much does each item cost?

Answers

Answer:

Price of Candle: 12.5

Price Wallflower: 5

Price of Lotion: 8

Step-by-step explanation:

Let cost of a candle = [tex]x[/tex]

Let cost of a wallflower = [tex]y[/tex]

Let cost of a lotion = [tex]z[/tex]

Cost of 4 candles = 4[tex]x[/tex]

Cost of 5 wallflowers = 5[tex]y[/tex]

Cost of 6 lotions = 6[tex]z[/tex]

Cost of 2 candles = 2[tex]x[/tex]

Cost of 3 wallflowers = 3[tex]y[/tex]

Cost of 1 lotion = [tex]z[/tex]

As per question statement:

[tex]4x+5y+6z=123 .... (1)\\2x+3y+z=48 ...... (2)\\z=2y-2 ..... (3)[/tex]

Using equation (3) in (1) and (2), the equations get reduced to :

[tex]\Rightarrow 4x+17y = 135 ..... (4)\\\Rightarrow 2x+5y = 50 ..... (5)[/tex]

Multiplying (5) with 2 and subtracting from equation (1):

[tex]7y = 35\\\Rightarrow y = 5[/tex]

By equation (3):

[tex]\Rightarrow z =8[/tex]

By equation (4):

[tex]\Rightarrow x = 12.5[/tex]

Therefore, the answer is:

Price of Candle: 12.5

Price Wallflower: 5

Price of Lotion: 8

Rachel is buying school supplies. She needs to buy a binder for $4.50, whiteboard markers for $7.00 and some mechanical pencils for $0.29 each. She can spend up to $13.00. Which inequality can be used to find m, the number of mechanical pencils she can buy?

Answers

0.29m + 4.50 + 7 < or equal to 13 ;)

The
table shows the lengths of four
trails at a horseback riding camp.
Estimate the total length of all the
trails. Show your work.
A. 2.6 B. 1.8 C. 4.2 D. 3.3

Answers

Answer:

Its not possible to solve without the actual table.

Step-by-step explanation:

Solve -103 = 6x + 17.

Answers

Answer: x=-20

-103= 6x + 17

-120=6x

-20=x

I Need Hellp! With this!!

Answers

Answer:

1/14

Step-by-step explanation:

slope = difference of y over difference of x

= (-3-(-4)) /(8 -(-6)) = 1/14

y = -0.25x – 4
When x=0, y = -4
When y=0, x = -16

Pls help me ASAP I have other homework to do and I don’t have time for this. It also detects if it’s right or wrong:(

Answers

Answer:

y = 25x + 50

Step-by-step explanation:

please help!!
(dont steal points pls)

Answers

Answer:

i think its 8.7  miles but i might be wrong please correct me if i am

Step-by-step explanation:

Well main street is 5.6 and there is a gab in between main street and highway 1 and its a big gab but not that big it is asking what the length and they are asking what the distance from highway 1 to main street is and that may not seem so far way but its asking from the begining of highway one. I THINK THAT IS CORRECT BUT I'M NOT VERY SURE  

It’s b .......................

helppppp pleaseeeeeee

Answers

Use Photomath it will help:)!!!!!!!............
answer:

step by step explanation:

yeah what they said^^^^^^^

Pls someone help me!

Answers

Answer:

When present,outliers will have an effect of the range since one of the outliers will either be highest or lowest number in a given data set and the range is found by finding the difference of the highest and lowest numbers.

The equation f = V + at represents the final velocity of an object, f, with an initial velocity, w, and an acceleration rate,
a, over time, t. Which is an equivalent equation solved for a?
Of-v=a
Of-vra
1
Of+V = a
o+v=a

Answers

Answer:

hey

Step-by-step explanation:

the answer is 5

How many tables that seat eight are required to provide places for 62 people at a banquet

Answers

Answer:

8

Step-by-step explanation:

62 divided by 8 is 7.75

you can't cut people so round it up and you get 8

Noya needs to determine the number of books that will fit into a box. If the box has a length of 18 inches and each book is StartFraction 2 Over 9 EndFraction of an inch thick, which expression can be used to determine the number of books that will fit into the box? 18 2/9 18 times 2/9 2/9 divided by 18 9/2 divided by 18

Answers

Answer:

A. 18÷2/9

Step-by-step explanation:

A. 18÷2/9

B. 18×2/9

C. 2/9÷18

D. 9/2÷18

Let

Total length of box = 18 inches

Thickness of each book = 2/9 inches

Number of books that will fit into the box = x

Number of books that will fit into the box = Total length of box ÷ Thickness of each book

x = 18 ÷ 2/9

= 18 × 9/2

= 162/2

= 81 books

The correct answer is A. 18÷2/9

Solve the equation for a.

K = 4a + 9ab

a = K(4 + 9b)
a = 4(K + 9b)
a = a equals StartFraction 4 plus 9 b Over K EndFraction equals h.
a = a equals StartFraction K Over 4 plus 9 b EndFraction equals h.

Answers

Answer:

[tex]a= \frac{k}{9b+4}[/tex]

Step-by-step explanation:

In this question, you would solve for "a".

Solve:

K = 4a + 9ab

Since we have our "a" on the same side, we can factor it out from the variables:

K = a(9b + 4)

To get "a" by itself, we would have to divide both sides by 9b + 4:

K/9b+ 4 = a

Your answer would be K/9b+ 4 = a

It would look like this: [tex]a= \frac{k}{9b+4}[/tex]

Answer:

it's a = K / 4 + 9b

Step-by-step explanation:

i just took the test & got it right .

PLEASE HELP FAST ITS TIMED! I Will Give Brainlist And Extra Points!

Answers

Answer:

-8, -5

Step-by-step explanation:

the answer to number one is -8. For functions, you just plug in the number in the parenthesis for x and then you solve. For number two, it is -5.

Answer:

-8, -5

Step-by-step explanation:

What number is 25% of 160? (worth lots of points because why not lol) help me-

Answers

Answer:

40

Step-by-step explanation:

This can be solved by changing the percentage to a decimal number, then multiplying by 160.

0.25×160=40

anybody knows the best way to get rid of a migraine or to make it feel better
it k1lls so bad it's so painful. don't say got to the doctor's cuz there medicine doesn't rlly help

Answers

Answer:

The best way to help is to get some water or get some sleep.It is either because you didn't get enough sleep or that you are dehydrated.

Step-by-step explanation:

Answer:

Drink a soda the instant you feel one coming on- sugar and caffeine tend to help.

If you can, try a good chiropractor- they can do adjustments that help with so many things including splitting headaches.

Try an OTC medicine.

sleep, dark, quiet, calm- try not to think too much and stay hydrated. maybe try carbonated water.

try to massage your neck yourself. it could help.

try to use a cold or a hot compress on your head.

Bananas. A tried and true natural headache reliever, bananas have potassium, magnesium, B vitamins, and complex carbohydrates, all components that contribute to headache relief.

The taste and smell of green apples have shown to help dim or lessen the intensity of migraines.

Hot packs and heating pads can relax tense muscles. Warm showers or baths may have a similar effect. Drink a caffeinated beverage. In small amounts, caffeine alone can relieve migraine pain in the early stages or enhance the pain-reducing effects of acetaminophen (Tylenol, others) and aspirin.

Step-by-step explanation:

avoid blue light from screens.

The graph of f (x) = x + 5 is a vertical translation 5 units
up of the graph of f(x) = x. How can you obtain the graph of
f(x) = x + 5 from the graph of f (x) = x using a horizontal
translation?

Answers

Answer:

A horizontal translation of 5 units to the left.

Step-by-step explanation:

Given the parent linear function:

[tex]\displaystyle f(x)=x[/tex]

To shift vertically n units, we can simply add n to our function. Hence:

[tex]f(x)=x+n[/tex]

So, a vertical shift of 5 units up implies that n=5. So:

[tex]f(x)=x+5[/tex]

As given.

However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:

[tex]f(x-n)=(x-n)[/tex]

Where n is the horizontal shift.

For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:

[tex]f(x-1)=(x-1)[/tex]

Or:

[tex]f(x)=x-1[/tex]

We notice that this is also a vertical shift of 1 unit downwards.

Therefore, we want a number n such that -n=5.

So, n=-5.

Therefore, it we shift our function 5 units to the left, then n=-5.

Then, our function will be:

[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]

Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.

The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
(3x-9)°
(x+15)

Answers

Answer:

318.6

Step-by-step explanation:

(3x-9) + (x+15) = 180

3x (x+15) -9 (x+15)

4x + 45x - 9x + 6 = 180

40x + 6 = 180

40x = 180 - 6

40x = 174

x = 4.34

(3x-9) = 4.34 * 3x-9 = 4.02

(x+15) = 4.34 + 15 = 19.34

180 - (4.02 + 19.34)

= 180 - 23.36

= 156.64

hope this answer helps!!

A freezer can be bought on hire purchase by making a desposiy of 15% of the cash price which is $2975 the interest which is 20% of the outstanding balance is charged the amount payable is paid in 12 monthly instalements.Calculate the freezer

Answers

Answer: See explanation

Step-by-step explanation:

a. The deposit

= 15% × $2975

= 15/100 × $2975

= 0.15 × $2975

= $446.25

b. The hire purchase price

Outstanding balance = $2975 - $446.25 = $2528.75

20% of outstanding balance

= 20% × $2528.75

= 0.2 × $2528.75

= $505.75

Hire purchase price

= $2975 + $505.75

= $3480.75

c. The difference the hire purchase price and cash price

= $3480.75 - $2975

= $505.75

d. The difference as a percentage of the cash price.

= ($505.75 / $2975) × 100

= 0.17 × 100

= 17%

I NEED HELP ASAP PLSSSSSSS

Answers

Answer:

53 degrees

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

180-127=53

what does x equal and what are the angle measures?? help Asap

Answers

all triangles are 180 always. make a equation 2x+x+x+8 then combine like terms so it will be 4x+8 then divide by 4 on bith sides x=2

Do any body know the summary for The Christmas carol act 2 scene 2?

Answers

Answer:

Act 2 of the Christmas Carol begins with Scrooge getting a visit from the ghost of Christmas present. This spirit is a jolly man filled with happiness and laughter. ... Scrooge sees Bob Cratchit's crippled son, Tiny Tim, who shows so much kindness towards everyone that it warms Scrooge's heart.

Step-by-step explanation:

your welcome

The number of students that enrolled in a new school club as a function of time can be represented by the function as shown in the graph.

What is the average rate of change in the number of students that enrolled between hours 1 and 2?​

Answers

Answer:

I think it is 1 student per 15 min

Step-by-step explanation:

What is the cube root of 27x^18?
A)3x^6
B)3x^9
C)9x^6
D)9x^9


Answers

it’s most likely a :)

Answer:

It’s B

Step-by-step explanation:

just answered question

what isvequivalent to y=23x−6?

Answers

Answer:

Slope = 46.000/2.000 = 23.000

x-intercept = 6/23 = 0.26087

y-intercept = -6/1 = -6.00000


Helpppp meeeeeeeeeee

Answers

The answer is A.

Explanation: You look at the x axis to see where the line is and look at that. The line goes from -4 to 3 on the x axis. On the y axis is the same but on the y axis. You see it goes from 0 to 5. This is least to greatest.

hello can anyone help me ? here the question

Answers

Answer:

A. 1/5k - 2/3j and -2/3j +1/5k

Step-by-step explanation:

A. 1/5k - 2/3j and -2/3j +1/5k

B. 1/5k - 2/3j and -1/5k +2/3j

There is a change in the signs of each term

1/5k changed to -1/5k

-2/3j changed to +2/3j

Not equivalent

C. 1/5k - 2/3j and 1/5j - 2/3k

There is a change in the variables

1/5k changed to 1/5j

-2/3j changed to -2/3k

D. 1/5k - 2/3j and 2/3j - 1/5k

The is a change in the signs of each term

1/5k changed to -1/5k

-2/3j changed to +2/3j

The only equivalent expression is

A. 1/5k - 2/3j and -2/3j +1/5k

Solve for z. 2z − 3 = 1

Answers

Answer:

z = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

2z - 3 = 1

Step 2: Solve for z

Add 3 on both sides:                    2z = 4Divide 2 on both sides:                z = 2

if the circumference of the greatest circle of a sphere is
[tex]\pi \: cm \: find \: its \: volume[/tex]

Answers

Answer:

hlo buddy

Step-by-step explanation:

The formula for the volume of a sphere is V = 4/3 πr³.

Which statement explains one way that ponds and lakes differ?

Ponds are shallower than lakes.

Ponds are larger than lakes.

Pond water moves more than lake water.

Lakes have more plants at the bottom than ponds.

Answers

Answer:

Ponds are shallower than lakes.

Step-by-step explanation:

The statement that explains one way that ponds and lakes differ is: Ponds are shallower than lakes.

Ponds and Lakes

The major difference between ponds and lakes are ponds are :

Pond are depth or shallower and smaller than lakes while lakes are larger or bigger.

Lakes are more deeper compare to ponds which inturn means that  ponds are not deeper than lakes.

Inconclusion the statement that explains one way that ponds and lakes differ is: Ponds are shallower than lakes.

Learn more about ponds and lakes here:https://brainly.com/question/131190

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