there are 24 baseball teams in a league. each team plays two matches against each of the other teams, work out the total number of matches played

The factor tree diagram is shown below.

========================================================

Explanation:

The first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

These numbers have factors of 1 and themself only.

Divide 405 over the smallest prime (2)

405/2 = 202.5

We don't get a whole number result, so 2 is not a factor of 405

Repeat for the prime next prime (3)

405/3 = 135

We get a whole number result. Therefore, 3 is a factor of 405

405 = 3*135

-------------------------

Now focus on 135.

Divide 135 over the smallest prime (2)

135/2 = 67.5

This rules out 2 as a factor of 135

Repeat for the prime number 3

135/3 = 45

So we can see that

135 = 3*45

which shows 3 is a factor of 135.

--------------------------

Now focus on 45. The prime 2 isn't a factor since 45/2 = 22.5 isn't a whole number

But 3 is a prime factor because 45/3 = 15 is a whole number. So 45 = 3*15 is the case.

Furthermore, 15/3 = 5 to show that 15 = 3*5

--------------------------

We can express all of this as a factor tree as shown below. The primes have been circled in red.

We have the primes of: 3, 3, 3, 3, 5

We can shorten the four '3's into 3^4

Therefore, 405 = 3^4 * 5

The product in terms of prime factor is  3*3*3*3*5.

The factors of a number are numbers that evenly divide into it. A prime factor is a factor that is only divisible by 1 and itself.

Given:

405

On performing prime factorization

405= 3*3*3*3*5

Hence, the prime factors are  3*3*3*3*5.

Learn more about prime factors here:

https://brainly.com/question/10454590

#SPJ2

Step-by-step explanation:

option b is the correct answer

Answer:

177

Step-by-step explanation:

All Done! Please mark as Brainliest :)

Answer:

177

Step-by-step explanation:

The tenth is 9 which means you round up so the correct answer is 177.

Hope It Helps Sorry If I'm Wrong

Answer: 1

Step-by-step explanation:

[tex]\displaystyle\\\frac{14}{33} *\frac{55}{8} *\frac{12}{35} =\\\\\frac{14*55*12}{33*8*35}=\\\\\frac{2*7*5*11*3*4}{3*11*2*4*5*7}=\\\\\frac{1}{1}=\\\\1[/tex]

The sum of n natural numbers is three digits number and all digits are the same. The same digits is 6 and the sum is 666.

A three-digit number with the same digits is the sum of n natural numbers.

Let's say the sum of n natural numbers is bbb.

Then,

n( n + 1) / 2 = bbb

n( n + 1) / 2 = b( 111 )

n( n + 1) / 2 = b ( 3 × 37 )

n( n + 1) = 6b × 37

Now, the left-hand side of the equation is the product of two consecutive natural numbers.

Therefore, the right-hand side of the equation is also the product of two consecutive natural numbers.

Hence, 6b = 36

b = 36/ 6

b = 6 and n = 36

As a result, 36 numbers have been added together, and their total is 666.

Learn more about natural numbers here:

https://brainly.com/question/2228445

Answer:

A: sf 2 or 1/2

Step-by-step explanation:

Answer:

Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent.

Step-by-step explanation:

Answer: 8oz of the 20% and 12oz of the 70%

Step-by-step explanation:

(20*x) + (70*(20-x)) / 20 = 50

(20x +1400-70x) / 20 =50

20x +1400-70x  = 1000

50x=400

x=8

20-8=12

The coordinates of A, B and C are (-1, -8), (0, -7) and (1, -6) respectively.

Here, we are given that A, B and C are coordinates on the line y = x − 7.

Also, we are given the following table for x and y values of A, B and C

x                    -1    0    1

y                    -8  -7   -6

coordinates   A  B  C

The coordinates of a point are written in (x, y) format where x and y are the values of the x and y axis respectively.

Thus, the coordinates of A are (-1, -8)

the coordinates of B are (0, -7)

and the coordinates of C are (1, -6)

Learn more about the coordinate system here-

https://brainly.in/question/4178855

#SPJ9

Functions and their domains of all the subparts are:

So,

(A) (fog)(x) and domain:

[tex](f \circ g)(x)=f(g(x))=(g(x))^2+g(x)=\left(x^2+14 x+2\right)^2+x^2+14 x+2\\=x^4+28 x^3+200 x^2+56 x+4+x^2+14 x+2=x^4+28 x^3+201 x^2+70 x+6[/tex]

The domain of (fog)(x) is the collection of domain values for g(x) with range values in the domain of f(x).

Because both functions are polynomials, the domain is [tex](-\infty, \infty)[/tex].

(b) (gof)(X) and domain:

[tex](g \circ f)(x)=g(f(x))=(f(x))^2+14(f(x))+2=\left(x^2+x\right)^2+14\left(x^2+x\right)+2\\=x^4+2 x^3+x^2+14 x^2+14 x+2=x^4+2 x^3+15 x^2+14 x+2[/tex]

The domain name is [tex](-\infty, \infty)[/tex] because this is a polynomial composition.

(c) (fof)(x) and domain:

[tex]\begin{aligned}&(f \circ f)(x)=f(f(x))=(f(x))^2+f(x)= \\&\left(x^2+x\right)^2+x^2+x=x^4+2 x^3+x^2+x^2+x=x^4+2 x^3+2 x^2+x\end{aligned}[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

(d) (gog)(x) and domain:

[tex](g \circ g)(x)=g(g(x))=(g(x))^2+14(g(x))+2=\left(x^2+14 x+2\right)^2+14\left(x^2+14 x+2\right)+2\\=x^4+28 x^3+200 x^2+56 x+4+14 x^2+196 x+28+2=x^4+28 x^3+214 x^2+252 x[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

Therefore, functions and their domains of all the subparts are:

Know more about functions here:

https://brainly.com/question/25638609

#SPJ4

The complete question is given below:
Find the functions and their domains. (enter the domains in interval notation.)

[tex]f(x)=x^2+1 x, g(x)=x^2+14 x+2[/tex]

(a) (fog)(x) and domain

(b) (gof)(X) and domain

(c) (fof)(x) and domain

(d) (gog)(x) and domain

Answer: -1

Step-by-step explanation:

      We will use the Order of Operations to solve;

Given:

-4 + (3)² ÷ (5 + 4) • 3

Addition in parentheses:

-4 + 9 ÷ (9) • 3

Raise to the power of 2:

-4 + 9 ÷ (5 + 4) • 3

Division:

-4 + 1 • 3

Multiplication:

-4 + 3

Addition:

-1

go ask God bro ain't nobody know that

Answer:

4

Step-by-step explanation:

[tex]\sqrt{x} 368640 = 1920[/tex]

The number of digits in 1920 is 4

The number of digits in the square root of 3686400 is 4.

In mathematics, the square root is a component that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.

The square root of 3686400 is,

√3686400 = ±1920

The number of digits in 1920 is 4.

Only four digits make up 4-digit integers; the first digit must be one or higher, and the other three can be any number between 0 and 9. Examples of four-digit numbers include 5693, 1023, and 9825.

Thus, the number of digits in the square root of 3686400 is 4.

Learn more about the square root here,
https://brainly.com/question/3120622

#SPJ2

As  given Chole and Tinos age , the present age of Tino is equal to 15 years.

As given,

Let x and y be the present age of Chole and Tino. respectively.

Combined age = 48

Given condition,

x + y = 48 _______(1)

Three years ago

x - 3 = 2y

⇒x =2y +3 _______(2)

Substitute the value of x in (1),

2y+3 +y =48

⇒ 3y = 45

⇒ y = 15years

Therefore , as given Chole and Tinos age , the present age of Tino is equal to 15 years.

Learn more about age here

brainly.com/question/3023145

#SPJ4

The solution of the expression for a is a = -1 9/40

The expression is given as:

negative a minus five eighths equals three fifths for a.

Rewrite the expression properly as:

-a - 5/8 = 3/5

Collect the like terms in the above expression

So, we have:

a = -5/8 - 3/5

Evaluate the like terms in the above expression

So, we have:

a = -1 9/40

Hence, the solution of the expression for a is a = -1 9/40

Read more about expression at

https://brainly.com/question/723406

#SPJ1

Answer:

x = 2

Step-by-step explanation:

Equation: 5x = 10

--- Divide 5 on both sides

x = 2

This means that each apple can make 2 cakes.

Answer: 2

Step-by-step explanation: because  if u divide both sides by 5

The area of the rectangular-shaped building is 2448 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular-shaped building that is 34 feet wide and 72 feet long. The area of the rectangle will be calculated as below:-

Area of rectangle = Length x width

Area of rectangle = 34 x 72

Area of rectangle = 2448 square feet

Therefore, the area of the rectangular-shaped building is 2448 square feet.

To know more about the area follow

https://brainly.com/question/25292087

#SPJ4

Answer:

Divisible rule of 11

If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number

Divisible rule of 5

Divisibility by 5 is easily determined by checking the last digit in the number.  If the last number is either 0 or 5, the entire number is divisible by 5.

First of all, the number 3456 is not divisible by 11 and 5.

But if we change position of digits then the numbers divisible by 11 are-

3564 / 11= 324

3465 / 11= 315

3465 / 5= 693

4356 / 11 = 396

4653 / 11 = 423

5346 / 11 = 486

5643 / 11 = 513

6534 / 11 = 594

6435 / 11 = 585

6435 / 5=1287

But the numbers 3465 and 6435 are also divisible by 5

So the numbers divisible by 11 but not with 5 are:

3564 , 4356, 4653, 5346, 5643 and 6534

Learn more about divisibility test here:

https://brainly.com/question/9462805

#SPJ9

Answer:

35/4

Step-by-step explanation:

8*4=32

32+3

=35

35/4

Answer:

111111111/200000000

Answer:

Graph in the picture

For a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53 m

For given question,

A particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s.

We can observe that, for t1 = 1.82 s and t2 = 3.81 s

object is moving from right to left along the x axis.

We know that, the displacement of a particle moving in a straight line is the change in its position.

so, d = 4.97 - 16.5

d = -11.53

The negative sign indicates that the object is moving from right to left along the x axis  for t1 = 1.82 s and t2 = 3.81 s

Therefore, for a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53m.

Learn more about the displacement here:

https://brainly.com/question/16965160

#SPJ4

Our standard linear slope equation is:

mx + b = y

We're told our slope is 1/2, so that's our m value.

When x = 0 our value is 5. If you need this visualized, then:

1/2 * 0 +b = 5

0 + b = 5

b = 5

So our equation looks like:

x/2 + 5 = y

Colton is approximately 3.9 feet apart from his  younger sister.

Pythagoras Theorem:

The statement o the Pythagoras theorem is, "if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. "

Then it can be written as,

BC² = AB² + AC²​​.

Where,

​​​​AB is the base,

AC is the altitude (height), and

BC is the hypotenuse.

Given,

Colton looks around at an assembly. he notices his younger sister to his right and his older brother 7 feet ahead of him.

And Colton's brother and sister are 8 feet apart.

Now, we need to find the distance between Colton and his younger sister.

Based on the given statement, we can draw their position like the following figure.

Here B represents the position of Colton, A represents the position of his older brother and C represents the position of his younger sister.

Now, we have to use the Pythagoras Theorem in order to solve it,

=> 8² = BC² + 7²​​.

=> 64 = BC² + 49

=> 64 - 49 = BC²

=> BC² = 15

=> BC = √15

Therefore,

=> BC ≈ 3.9 feet

Therefore, the distance between Colden and his younger sister is approximately 3.9 feet.

To know more about Pythagoras Theorem here.

https://brainly.com/question/343682

#SPJ4

Answer:

-20, -18

Step-by-step explanation:

let x = the smaller number

Let x + 2 = the larger number

3(x +2) -26 = 4x

3x + 6 -26 = 4x

3x -20 = 4x  Subtract 3x from both sides of the equation

-20 = x

x + 2

-20 + 2 = -18

Check:

3(-20 + 2) -26=  4(-20)

3(-18) - 26 = -80

-54 -26 = -80

-80 = -80

We get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.

We are given the sets as:

U= { 2, 4, 6, 8, 10, 12, 14, 16, 18}

A = {4, 10, 12, 14, 18}

B = { 2, 4, 6, 8, 10, 14, 16}

We first will find out A':

A' = U - A

A' = { 2, 4, 6, 8, 10, 12, 14, 16, 18}  - {4, 10, 12, 14, 18}

A' = { 2, 6, 8, 16}

Now, we will find B':

B' = U - B

B' = { 2, 4, 6, 8, 10, 12, 14, 16, 18}  - { 2, 4, 6, 8, 10, 14, 16}

B' = { 12, 18}

Now, we have to find:

(AUB)' = U - (AUB)

AUB = {4, 10, 12, 14, 18} U { 2, 4, 6, 8, 10, 14, 16}

AUB = { 2, 4, 6, 8, 10, 12, 14, 16, 18}  = U

(AUB)' = U - U = ∅.

Now, we will find A' U B':

A' U B' = { 2, 6, 8, 16} U { 12, 18}

A' U B' = {2, 6, 8, 12, 16, 18}

Therefore, we get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.

Learn more about sets here:

https://brainly.com/question/2166579

#SPJ9

Answer: 7.333

Step-by-step explanation:

first move the three over 47-3 = 6y

the divide by - 6 to get y by itself 44/-6 = y