the set $s = \$ contains the first $50$ positive integers. after the multiples of 2 and the multiples of 3 are removed, how many integers remain in the set $s$?

Answers

Answer 1

Clearly, |S| = 50.

Count the multiples of 2 between 1 and 50:

⌊50/2⌋ = ⌊25⌋ = 25

(where ⌊x⌋ denotes the "floor of x", or the largest integer that is smaller than or equal to x; in other words, round down to the nearest integer)

Count the multiples of 3 between 1 and 50:

⌊50/3⌋ ≈ ⌊16.667⌋ = 16

Since LCM(2, 3) = 6, the sets of multiples of 2 and multiples of 3 have some overlap. Count the multiples of 6 between 1 and 50:

⌊50/6⌋ ≈ ⌊8.333⌋ = 8

Then by the inclusion/exclusion principle, we remove from S

25 + 16 - 8 = 33

elements, so that the new set S contains 50 - 33 = 17 elements.


Related Questions

Please help asap! I will mark brainliest for correct answer!!
a softball player hits a pitched ball when it is 4 feet above the ground. the initial velocity is 75 feet per second. Use the formula: h=-16t^2+vt+s. How long will it take for the ball to hit the ground?

Answers

Answer: Do the math, the positive solution

t = 5.0495 seconds (If it's wrong sorry, I havent done a problem like this one in awhile!)

Step-by-step explanation:

empat angka setelah angka tiga

Answers

Answer:

hindi ko po gets

yan sorry

Question 1
Without solving, what can you tell about the solution to
this equation?
b + 14
(b + 14)
2
1 / 116
There is no solution.
There are infinitely
many solutions.
b is equal to 1 only.
b is equal to 0 only.

Answers

Answer:

there are infinitely many solutions

Step-by-step explanation:

1/2(b+14) is the same as (b+14)/2, so no matter what number you plug in for b, both sides will always be equal. thus, there is infinitely many solutions.

hope this helps <3

Answer: there is no solution.

Step-by-step explanation:

We can see mentally that when we multiply both sides by 2, we will be left with b+14 on both sides which will cancel out ( “b” will cancel out) so there is no solution.

Describe the transformation

Answers

Answer:

6 to the right

Step-by-step explanation:

Yes, it might be scary at first sight bexause of the square mark. But it is no more special than any other graph transformation. The sqare mark here nly indicates that this graph is a parabola, and the 6 inside shifts the graph (be careful, it is negative so it moves the graph to the RIGHT, by 6 -- the square mark doesnt apply to that).

WILL GIVE BRAINLIEST

Answers

Answer:

  A) 1: linear; 2: exponential (see equations in part B)

  B) the value of 2 will be almost 15% greater

Step-by-step explanation:

Part A:

As is often the case with multi-part questions, later parts of the question answer earlier parts. The equations shown in Part B are linear for Option 1 and exponential for Option 2.

The table values for Option 1 have a common difference of (1200 -1100) = 100.

The table values for Option 2 have a common ratio of (1210/1100) = 1.10.

Linear functions produce sequential values with a common difference (the slope of the function). Option 1 is linear.

Exponential functions produce sequential values with a common ratio (the growth factor). Option 2 is exponential.

__

Part B:

The investment values after 7 years will be ...

  Option 1: f(7) = 100(7) +1000 = 1700

  Option 2: g(7) = 1000(1.1^7) ≈ 1948.72

The value of Option 2 will be about $248.72 higher, or 14.6% higher than the value of Option 1. Whether that is significant or not is in the eye of the beholder. Many people might consider that to be significantly better performance. (It would take another 2 1/2 years for Option 1 to have that value.)

the product of 20 and z

Answers

Answer:

20z

Step-by-step explanation:

just times 20*z which give you 20z

The graph below shows the
relationship between the distance a
car is driven and the number of
gallons of gas used. What is the slope
and what does it represent?

Answers

Answer:

The slope is 30 and it represents the distance the car can travel per gallon of gas used

Step-by-step explanation:

We just need to look at the x=1 and find the y in order to find the slope and here we see that when x=1, then the y=30 so, therefore, the slope is 30

It represents the number of miles the car can drive per gallons of gas used as we can see that we are comparing the gas used with the distance traveled, so therefore it is comparing the distance the car can travel based on the gas used.

Slope = rise/run
Slope = 60 mi/2 gal
Slope = 30 mi/gal

The slope represents the distance a car travels and the gas used.



S is a geometric sequence.

a) (1x + 1), 1 and (rootx - 1) are the first three terms of S.
Find the value of x.
You must show all your working.


b) The 5 term of S can be written in the form a V2 + b
where a and b are integers
Find the value of a and the value of b

Answers

Answer: your answer would be 2

Step-by-step explanation:

4/7 + 21/30 x ((21 x 4) + (23 x 8)) = n
need in simplest form

Answers

n= 340.36, 4/7 + 21/30 times (84 + 184)= 340.36

a store is having clearance sale where merchandise on the sales racks is reduced by 80% from the original price. if a jacket was originally priced at $76, what is the sale price?

Answers

Answer:

Sale price is [tex]15.2\$[/tex]

Step-by-step explanation:

Price is reduced by 80% from the original price.

Here original price is $76

Sale price is

[tex]=76-76\times\frac{80}{100}\\\\=0.2\times76\\\\=15.2\$[/tex]


Help asap pls!!! Put steps if possible 3

Answers

Answer:

i. 15.4

ii.45.2

Step-by-step explanation:

correct me if im wrong

tnx

if each quadrilateral below is a square,find the missing measures​

Answers

Answer:

∆EFG = 90°

∆GDH = 45°

∆FEG = 45°

∆DHG = 90°

The measure of the given angles are -

m ∠EFG = 90°

m ∠EFG = 45°

m ∠FEG = 45°

m ∠DHG = 45°

What is square?

A square is a quadrilateral with all sides congruent to one another.

Given is to find the measure of angles given in the question.

We can write the measure of angles as -

m ∠EFG = 90°

m ∠EFG = 45°

m ∠FEG = 45°

m ∠DHG = 45°

Therefore, the measure of the given angles are -

m ∠EFG = 90°

m ∠EFG = 45°

m ∠FEG = 45°

m ∠DHG = 45°

To solve more questions on angle measurements, visit the link-

brainly.com/question/29014197

#SPJ2

How many factors does 60 have? A)10 B) 8 C) 12 D) 4​

Answers

Answer:

60 have 12 factors :1,2,3,4,5,6,10,12,15,20,30,60

The number 60 has 12 factors :)

A map is drawn to a scale of 28 miles per inch. Fill in the table.
need some help

Answers

Answer:

inches: 0.5 miles: 14

inches: 1 miles 28

inches: 1.5 miles 42

Hope This Helps!!!

Which operation should you perform first when you simplify 63 − (2 + 54 × 6) ÷ 5? A division B multiplication C subtraction D addition

Answers

Answer:

start with what's inside the parenthesis so in this case do 54x6 first then solve (2+ whatever the answer was by multiplying 54 times 6  

Step-by-step explanation:

Answer A division

HELP ME PLEASE I NEED HELP WITH THIS

Answers

Answer:

V = 82,406.16 cm³

Step-by-step explanation:

Volume of a sphere

V = 4πr³/3

V = 4•3.14•27³/3

V = 247,218.48/3

V = 82,406.16 cm³

Please help me 87x89 PLEASE

Answers

The answer to 87x89 is 7,743.

Answer:

7743 :)

Step-by-step explanation:

The ratio of three number is 5:6:7. If the sum of the numbers is 54. What
are the numbers?

Answers

Let the numbers be 5x, 6x and 7x respectively.Therefore, by the problem

[tex]5x + 6x + 7x = 54 \\ = > 18x = 54 \\ = > x = 3[/tex]

So, the numbers are (5 × 3) i.e., 15, (6 × 3), i.e., 18, (7 × 3), that is 21.

Answer:

The numbers are 15, 18 and 21.

Hope you could get an idea from here.

Doubt clarification - use comment section.

if <4=<6 then ____=____​

Answers

Answer: #2 CD=CA

Step-by-step explanation:

So sorry if wrong but i think it may be right.

GOOD LUCK!!

Andrew washed 32 car windows in 4 hours. At this rate, how many windows did he wash in 8 hours?

Answers

8 hours is twice as many as 4:

Multiply the number of windows in 4 hours by 2:

32 x 2 = 64 windows in 8 hours

Answer:

64

Step-by-step explanation:

32÷4=8 8 car windows per hour. 8×8=64

Alexandra wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. How much will Option 2 be worth after 20 years?


A.

$6727.50


B.

$3000.00


C.

$7400.25


D.

$5604.41

Answers

d

$5604.41 will be worth after 20 years I think

Compound interest is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

Option 2 will be worth $7400.25 after 20 years.

Option C is the correct answer.

What is compound interest?

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

Option 2.

1st year.

Principal = 1100

2nd year.

Principal = 1210

3rd year.

Principal = 1331

(1210 - 1100) / 1100 x 100

= 110/1100 x 100

= 10%

This means,

It is increasing at a rate of 10% annually.

Now,

P = $1100

r = 10%

n = 1

t = 20

A = P [tex](1 + r/n)^{nt}[/tex]

A = 1,100 [tex](1 + 0.1)^{20}[/tex]

A = $7400.25

Thus,

Option 2 will be worth $7400.25 after 20 years.

Option C is the correct answer.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ2

if x+y=10 and x-y =6 what is the answer of x cube - y cube fast​

Answers

Answer:

x+y=10 which means that x=10-y

Replace 10-y in the other equation which gives you:

10-y-y=6

10-2y=6

-2y=-4

y=2

Replace 2 in any of the 2 equations same answer for both:

x+y=10

x+2=10

x=8

So,

[tex] {x}^{3} - y^{3} [/tex]

[tex] = {8}^{3} - {2}^{3} [/tex]

=512-8

=504

Hope this helps!

HURRYYYY MATH PEOPLE!!! I ONLY HAVE 3 MINUTES!!! ​

Answers

Answer:

x > -4

Step-by-step explanation:

- 16x < 64

Divide by -16 on both sides. (Remember you always do the opposite on these type of questions!)

x > -4

(When dividing or multiplying by a negative the inequality sign flips!)

Hope this helps and have a good day!

7L of an acid solution was mixed with 3L of a 15% acid solution to make a 29% acid solution. Find the percent concentration of the first solution.

Answers

Answer:

hypotenuse Pythagoras property

Let 7L acid solution concentration=x%
According to question

(7x+3*15)/10=29


7x+45=290


x=35%

A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is an hourly wage of ​$24. Option B is a commission rate of 10​% on weekly sales. How much does she need to sell this week to earn the same amount with the two​ options?

Answers

Answer: the answer is $9,600

Step-by-step explanation:

option A = 40(24)   =  option B = x (.1)       where x is her gross sales

40(24) = x(.1)

40(24)/.1 = x = sales = $9600

Need help on HS geometry

Answers

Answer:

RS = 46 , RT = 38

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle (mid segment) is half the length of the third side, then

RS = 2 × UW = 2 × 23 = 46

RT = 2 × VW = 2 × 19 = 38

Which of the following values could represent the probabilities of complementary events? StartFraction 1 over 7 EndFraction and StartFraction 2 over 7 EndFraction 28% and 82% Two-fifths and Three-fifths 10% and 80%

Answers

Answer:

a

Step-by-step explanation:

Answer:

2/5 and 3/5

Step-by-step explanation:

PLZZ HELP

Order these numbers from least to greatest. ​

Answers

7.1 ,7.109 ,7.1091 ,7.19
7.1, 7.109, 7.1091, 7.19

Write
48
:
132
:
84
in its simplest form.

Answers

Answer:

4:11:7

Step-by-step explanation:

Find the GCF, or greatest common factor of the 3 numbers. In this case it is 12. To simplify, divide each number by 12

Answer:

4:11:7

Step-by-step explanation:

please mark me as brainlest

what is the recriprocal of 8

Answers

the reciprocal of 8 is 1/8

Answer:

answer = 1/8

Step-by-step explanation:

answer = 1/8

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