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

Can someone plz help :(((((

What is the area, in square inches, of the rectangle?

Answers

Answer:

What are the side lengths?

how to find the perimeter of a triangle with vertices

Answers

Answer:

P = A + B + C

Step-by-step explanation:

Essentially, just add the length of each side. The sum is the perimeter.

Hit brainliest if this was helpful :)

add each side

hope ithelps you

3 In AABC, 2C = 90°, then which of the following is true? a) ABP = BCP + AC b) AC2 = AB? + BC2 c) BC2 = AB? + ACP d) AC = AB + BC ​

Answers

Answer:

a bit hard q

Step-by-step explanation:

becoz i am not good at algebra

Marty was renting a boat and wanted to get the best plan. Rental plan A charges a fee of
$50 plus $25 per hour. Plan B charges a fee of $10 plus $35 per hour.
Using systems of equations, answer the following questions. Show all your work.
Part A: Write a system of equations the represent the situation. (Be sure to identify the
variables.)

Answers

Answer:

?

Step-by-step explanation:

i'm sorry  i'm just trying to get points this is my test and i need to know the answer and then i found the " Add answer ( 5 points ) and it was like calling my name so i am here now...bye

The system of equations that represent the situation are as follows;

C = $50 + $25h

C = $10 + $35h.

According to the question;

Mary was trying to rent a boat and wanted to get the best plan.

Let C = Charged fees

and h = hours of rental

For Plan A:

Rental plan A charges a fee of$50 plus $25 per hour.

C = $50 + $25h

For Plan B:

Plan B charges a fee of $10 plus $35 per hour.

C = $10 + $35h.

Read more on rental charges;

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The blueprint for Moreno​'s living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new​ blueprint? (The width is 8)

Answers

Answer:

Part a) The scale of the new blueprint is      

Part b) The width of the living room in the new blueprint is  

Step-by-step explanation:

we know that

The scale of the original blueprint is

and

the width of the living room on the original blueprint is 6 inches

so

Find the actual width of the living room, using proportion

Find the actual length of the living room, using proportion

Find the scale of the new blueprint, divide the length of the living room on the new blueprint by the actual length of the living room

simplify  

     

Find the width of the living room in the new blueprint, using proportion

Identify the slope in the following equation: y= -x + 7
PLEASE HELP!!!!

Answers

Answer: The slope is -1 because this equation is already in y=mx+b so we dont have to apply the y2-y1 over x2-x1 formula you can easily identify the slope when its in y=mx+b because the slope always has a x after the number for example: 4x

Answer:

It is the coefficient of the x, when the y is isolated. In this case it is -1.

Express the perimeter of the following
rectangle in terms of n.
3n-7
n + 5
1. O 4n - 2
2. O 8n - 14
3. O 8n - 4
4. O 6n - 14

Answers

The perimeter would be

2(3n - 7) + 2(n + 5)

6n - 14 + 2n + 10

Simplify

8n - 4

So the answer would be C

6 O
Which function is graphed on the coordinate plane below?
Ty
x
f(x) = 2x - 6
Of(x) = 2x + 6
f(x) = -2x + 6
Mark this and retum
Save and Exit
Next
Submit

Answers

Step-by-step explanation:

we don't see all possible answer options.

but it does not matter.

the line is clearly

y = 2x - 6

why ?

the slope is always the factor of x.

and the slope is defined as ratio of "y coordinate change / x coordinate change".

and we can clearly see, for every change in x by +1, y changes by +2. zu, the slope is 2/1 = 2.

and when x = 0, the graph shows us the y-intercept with y = -6.

hence the above mentioned equation.

The Function is graphed on the coordinate plane is y= 2x- 6.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have points from the graph as (3, 0) and (0, -6).

So, the slope of line is

slope= (-6 -0)/ (0-3)

slope = -6/ (-3)

slope= 2

Now, using the slope intercept form

y= mx + b

y= 2x + b

Now, put x= 3 and y= 0 we get

0= 6 + b

b = -6

So, the required function is

y= 2x - 6.

Learn more about Slope here:

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Find the value of x.

Answers

Answer:

x = 12

Step-by-step explanation:

Angle Bisector Theorem:  PS / PQ = RS / QR

24/14 = x/7

cross-multiply:

14x = 168

x = 12

(-r-5)-(-2r-4) help me solve pls lol

Answers

answer:

[tex]r - 1[/tex]

Step by step explanation:

Step 1: Distribute

[tex]( - r - 5) - ( - 2r - 4) \\ ( - r - 5) + 2r + 4[/tex]

Step 2: Eliminate redundant parenthesis

[tex]( - r - 5) + 2r + 4 \\ - r - 5 + 2r + 4[/tex]

Step 3: Add numbers

[tex] - 3 \purple{ - 5} + 2r + \purple{4} \\ - r \purple{ - 1} + 2r[/tex]

Step 4:Combine like terms

[tex] \purple{ - r } - 1 + \purple{2r} \\ \purple{1r} - 1[/tex]

Step 5:Multiply by 1

[tex]1r - 1 \\ r - 1[/tex]

Hopefully it's help

I copy MissJoy2 answer cuz her/his answer is right

Asap?


Robert wrote two patterns. Pattern 1 started at 2 and followed the rule "add 4." Pattern 2 started at 1 and followed the rule "add 3." Pattern 1 is represented by x-coordinates, and Pattern 2 is represented by y-coordinates. Which table shows the ordered pairs for these two patterns?


X Y
1 2
4 6
8 10
12 14

X Y
2 1
6 4
10 7
14 10

X Y
1 2
2 6
3 10
4 14

X Y
2 1
4 4
6 7
8 10

Answers

Answer:

the 2nd one lol

Step-by-step explanation:

Answer:

number 2ᕙ(@°▽°@)ᕗStep-by-step explanation:

Need all answers a lot of points

Answers

F is the answer for the first one

The Y intercept is 3. Since it’s going up 3 over one, the fraction is 3/1 which can be simplified to 3. and the graph is going up since you go from left to right. So F [ y=3x+3] is the correct answer

What is the mean of 9, 8, -15 and -12?

The Mean is:

Answers

Answer:

-2.5

Step-by-step explanation:

add all the values and divide by the no of values present

Work out the difference between 38.3 and 1.72​

Answers

Answer:

36.58

Step-by-step explanation:

38.3-1.72=36.58

The value of the expression 38.3 - 1.72 will be 36.58.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

38.3 and 1.72​

Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have

⇒ 38.3 - 1.72

⇒ 36.58

The value of the expression 38.3 - 1.72 will be 36.58.

More about the Algebra link is given below.

https://brainly.com/question/953809

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What is the solution to the system of equations?
y = -2x – 6
4x - y = -36

A (15, 24)

B (-7, 8)

C (-5, 4)

Answers

It’s a i think I don’t know

The graph of y = f(x) is the solid black graph below. Which function represents the
dotted graph?
Submit Answer
O y = f(x + 3) - 5
O y = f(x - 3) - 5
O y = f(x - 3) + 5
O y = f(x + 3) + 5

Answers

Answer:First option, y=f(x+3)+5

Step-by-step explanation:

analyse the transformation first

From the dotted function, when compared to the solid black line, is moved 3 units to the left, and moved upwards by 5 units

Input transformation

In graphing, when a value is shifted horizontally, its transformation is equal to: -(x2-x1), and in this instance, we end up with a value of +3so, f(x+3) is the first componentWhen a function is shifted horizontally, it is proportiante to the distance it moves, so (y2-y1)in this instance, it is 0 - -5=5so the transformation vertically is +5

Final answer, when all values are added is y=f(x+3)+5

NEED HELP NOW PLEASE

Answers

Answer:

-33.24 degrees F, -33.625 degrees F, -33.833 degrees F

h(x) = 2x2 + x + -3
Find h(2)

Answers

7 the answer is 7 for this one
7 da the answer is 7 my broda

help please! a is wrong, that was my initial answer.

Answers

Answer:

D -1

Step-by-step explanation:

[tex]-6(3a+4)=3a-3[/tex]

[tex]-18a-24=3a-3[/tex]

[tex]-18a-3a=-3+24[/tex]

[tex]-21a=21[/tex]

a = [tex]\frac{21}{-21} =-1[/tex]

Hope this helps

An ice cream cup has 3 scoops of chocolate, 4 scoops of vanillas and 3 scoops of butter scotch ice cream. What is the probability that if you randomly sampled the ice cream that you will taste chocolate or vanilla ice cream?

Answers

Answer:

7 out of 10

Step-by-step explanation:

if you have 10 in the cup then you add

4 vanilla 3 chocolate = 7

and add all scoops together and you get 10

so your probability would be 7 out of 10

another way to say it is

the probability of getting chocolate or vanilla ice cream from the cup would be 7 out of 10

Which of the following points would be on the graph of
the equation y=-40 + 6?
-4, -10)
(-4, 22)
(1, -10)
(1, - 2)
О
-
о

Answers

Step-by-step explanation:

To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.

Pls explain how to solve it!

Answers

Answer:

a = jd

Step-by-step explanation:

We want to solve for a given that a/d = j

To do so we want to isolate a (get a by itself )

We can do this by using inverse operations.

We would want to get rid of the d

A is being divided by d.

The inverse of division is multiplication so to get rid of the d we multiply a/d by d but whatever we do to one side we must do to the other so we multiply both sides by d

a/d * d = a

j * d = jd

we are then left with a = jd

And we are done!

Answer:

a = jd

Step-by-step explanation:

We have to solve the equation for a - in other words, we have to find a in terms of d and j. Another way to think about this is that we need a by itself on one side, equal to the other two values in some sort of relationship.

So, how can we accomplish this? Well, currently a is being divided by d, so we should probably multiply both sides by d to get that d away from a. The process is shown below:

[tex]\frac{a}{d} =j[/tex]

[tex]\frac{a}{d} *\frac{d}{1} =j*d[/tex]

[tex]\frac{ad}{d} =jd[/tex]

[tex]a=jd[/tex]

And look at that! We've solved for a in terms of the other two values. If you need any more help or everything I just did was confusing or overwhelming, let me know so I can clarify. :)

Find x- and y-intercepts of 4x + 2y = 10

Answers

Answer:

Below is the graph

Hope This Helps!!!

Answer:

( 5/2 , 0 ) x- intercept , ( 0 , 5 ) y- intercept

Step-by-step explanation:

To find x- intercept , set y = 0

4x + 2(0) = 10

x = 5/2

To find y- intercept , set x = 0

4(0) + 2y = 10

y = 5

Calculate the average travel time for each distance, and then use the results to calculate. A 6-column table with 3 rows in the second, third, and fifth columns and 1 row in the other columns. The first column labeled Number of Washers has entry 1 washer mass = 4. 9 grams. The second column labeled Trial has entries trial number 1, trial number 2, trial number 3. The third and fourth columns labeled Time to travel 0. 25 meters t subscript 1 (seconds) have entries in the third column 2. 24, 2. 21, 2. 23 and average in the fourth column. The fifth and sixth columns labeled time to travel 0. 5 meters t subscript 2 (seconds) have entries in the fifth column 3. 16, 3. 08, 03. 15 and in the sixth column average. The average time that it takes for the car to travel the first 0. 25m is s. The average time to travel just between 0. 25 m and 0. 50 m is s. Given the time taken to travel the second 0. 25 m section, the velocity would be m/s.

Answers

The average travel time is simply the mean travel time between the given points

The average time that it takes for the car to travel the first 0.25m is 2.23s. The average time to travel just between 0.25m and 0.50m is 0.9s. Given the time taken to travel the second 0.25 m section, the velocity would be 0.28m/s.

(a) The average time to travel the first 0.25m

The time travel in the first 0.25m are: 2.24s, 2.21s and 2.23s.

So, the average time to travel is:

[tex]Time = \frac{2.24s + 2.21s + 2.23s}{3}[/tex]

[tex]Time = \frac{6.68s}{3}[/tex]

[tex]Time = 2.23s[/tex]

(b) The average time to travel just between 0.25m and 0.50m

The time travel in the 0.50m are: 3.16s, 3.08s and 3.15s.

So, the average time to travel this distance is:

[tex]Time = \frac{3.16s + 3.08s + 3.15s}{3}[/tex]

[tex]Time = \frac{9.39s}{3}[/tex]

[tex]Time = 3.13s[/tex]

The average time to travel between both distance is the difference between the average time of each distance.

So, we have:

[tex]Average = 3.13s - 2.23s[/tex]

[tex]Average = 0.9s[/tex]

(c) The velocity in the second 0.25m section

The distance and time are:

[tex]Distance = 0.25m[/tex]

[tex]Time = 0.9s[/tex]

So, the velocity is:

[tex]Velocity = \frac{Distance}{Time}[/tex]

This gives

[tex]Velocity = \frac{0.25m}{0.9s}[/tex]

[tex]Velocity = 0.28m/s[/tex]

Read more about distance, velocity and time at:

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determine whatever ABCD is a parallelogram by using the midpoint formula.
A(3,3) B (1.2) C(-3.1) D (-1.4)

Answers

Answer:

Not a parallelogram.

Step-by-step explanation:

By the midpoint formula, the midpoint of a segment between [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] is:

[tex]\begin{aligned} \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)\end{aligned}[/tex].

A quadrilateral is a parallelogram if and only if the midpoints of the two diagonals are the same.

The two diagonals of quadrilateral [tex]{\sf ABCD}[/tex] are segment [tex]\sf{AC}[/tex] and segment [tex]{\sf BD}[/tex], respectively.

Using the midpoint formula, the midpoint of segment [tex]{\sf AC}[/tex] (between [tex]{\sf A}\; (3,\, 3)[/tex] and [tex]{\sf C}\; (-3,\, 1)[/tex]) would be:

[tex]\begin{aligned} & \left(\frac{3 + (-3)}{2},\, \frac{3 + 1}{2}\right) \\ =\; & (0,\, 2)\end{aligned}[/tex].

Likewise, the midpoint of segment [tex]{\sf BD}[/tex] (between [tex]{\sf B}\; (1,\, 2)[/tex] and [tex]{\sf D}\; (-1,\, 4)[/tex] would be [tex](0,\, 3)[/tex].

Thus, quadrilateral [tex]{\sf ABCD}[/tex] would not be a parallelogram since the midpoints of its two diagonals are not the same.

Just a little help please ☺️
Simplify

(3^8/3^5)3

3^9
3^39
3^10
3^6

Answers

[tex]\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9[/tex]

Which statement about f ( x ) = x 2 + 5 x − 84 is true?

Answers

Answer:

It is False

Step-by-step explanation:

f(x)=x^2-25. Determine the value of x for the given function formula

Answers

Answer:

You can't really determine anything here, as we'd need to know also the value of F(x)! Check again if there misses anything in this question.

inverse of
f(x)=6x+5

Answers

Attached image is the answer

HELPPPPPPPPPPPPPppPPPPPPPPPPpppp

Answers

-5


A negative [-] times a positive [+] is a negative [-]
A negative [-] times a negative [-] is a positive [+]
A positive [+] and a positive [+] is a positive [+]

Since the quotient is a positive [+] 35, that means there had to have been two negatives [-] to make a positive. The answer is -5
ANSWER = -5

WORK:
35/ 7 = 5
~ Remember to add negative (-)
So the answer is -5
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