3 Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How
many of each piece would each child need to build tracks that are equal in length?
Answer Statements:

Answers

Answer 1

Answer:

72

Step-by-step explanation:

The smallest number that is divisible by two given numbers is called the Least Common Multiple (LCM) of those numbers.

What's the smallest number that is a multiple of 8 and also a multiple of 18?

One way to find out is to start making lists of multiples:

Multiples of 8:  8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on,

Multiples of 18:  18, 36, 54, 72, 90, 108, and so on.

This method can be a bit tedious, but in this case, it's clear that 72 is the LCM of 8 and 18.

Another method is to use the prime factorization of the two numbers.

Write 8 and 18 as the product of prime numbers; each number has a unique prime factorization.

8 = 2 x 2 x 2 = 2^3

18 = 2 x 3 x 3 = 2^1 x 3^2

To form the LCM, build a product of primes using the highest exponent in either of the two numbers.

LCM = 2^3 x 3^2 = 8 x 9 = 72.


Related Questions

A submarine that is already at 605 feet below sea level ascends (rises up) 475 feet before descending (sinking down) another 255 feet.

Answers

Answer:

-350ft

Step-by-step explanation:

so basically 605 is negative and 255 is a negative then you add those two then it would be -860 then you subtract the positive 475 and that will equal -350

5x+2
2x
Perimeter:
PLEASE HELP

Answers

Answer:

14x + 4

Step-by-step explanation:

The perimeter of a rectangle is the sum of all its sides. The rectangle have two sides with length 5x + 2, so:

(5x + 2)×2 = 10x + 4

And it also have two sides with length 2x, so:

(2x)×2 = 4x

And now just add it:

10x + 4 + 4x = 14x + 4

Answer: Perimeter = 14x + 4

Concept:

Here, we need to know how to find the perimeter of a rectangle.

Perimeter (rectangle) = 2 (l + w)

l = length

w = width

If you are still confused, you may refer to the attachment below for a graphical explanation.

Solve:

Given information

l = 5x + 2

w = 2x

Given expression

Perimeter = 2 (l + w)

Substitute values into the expression

Perimeter = 2 (5x + 2 + 2x)

Combine like terms

Perimeter = 2 (7x + 2)

Expand parentheses and apply the distributive property

Perimeter = 2 · 7x + 2 · 2

Perimeter = 14x + 4

Hope this helps!! :)

Please let me know if you have any questions

Is the following irrational or rational?
ILL GIVE BRAINLIEST

6.4
2.178046372849
-2

Answers

6.4 is Rational. It ends in a decimalif the nine is the last number and it does not go on (indicated by ...) then the number is rational-2 is rational. It's an integer. All integers are rational.

The quotient of a number and three tenths decreased by 2 is 6

Answers

I believe the answer you are looking for is 2.4.

Solution:

n over 3/10-2=6

n over 3/10=8

Multiply 3/10 and 8

You will get 2.4.

graph of f(x)= -3x*2+12and g(x)=mx+6

Answers

Answer:

see the picture

Step-by-step explanation:

hope it helps you

please follow me please

Can someone help me out?

Answers

Answer:

I think it's D.................

2. Shelby and her two friends have 2 pies left after the bake sale after
school. They divide the pies evenly among themselves. How much pie did each
student receive?

Answers

Answer:

.67

Step-by-step explanation:

There are three friends and two pies. You are splitting the pies not the people so you divide 2 by 3 to get 0.66666667. Meaning each girl got .67 or around 6/10 of a pie.

f(x) = (x + 1)(x - 5). What is the vertex?
(1,5)
(5.1)
(2.-9)
(-9,2)​

Answers

Answer:

(2, -9)

Step-by-step explanation:

f(x) = (x + 1)(x - 5)

[tex] =f(x) = {x}^{2} - 5x + x - 5[/tex]

[tex] = f(x) = {x}^{2} - 4x - 5[/tex]

[tex] = f(x) = {1x}^{2} - 4x - 5[/tex]

[tex] = f(x) = {1x}^{2} + ( - 4x) - 5[/tex]

= a = 1, b = -4

[tex] = x = \frac{ - 4}{2 \times 1} [/tex]

[tex] = x = - \frac{ - 4}{2} [/tex]

[tex] = x - ( - 2)[/tex]

[tex] = x = 2[/tex]

= f(x) = (x + 1) x (x - 5); x = 2

= f(2) = -9

= (2, -9)

In a single throw of two coins,find the probability of getting each of the following:-)
i.)Tails on both
ii)Tails at least on one
iii)Tails on one
iv)No tails

Should be answered by:-)
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other best users

Answers

Step-by-step explanation:

1.) two tails :

total no. of outcomes possible is TT,TH,HT,HH

no. of outcomes with TT is 1

p( tails on both) = 1/4

2.) tails at least one:

no. of outcomes with one tails atleast is 3 (TT,th,ht,)

p( atelast one tails) = 3/4

3.) tails on one

no. of outcomes with one tails at most is 2 (th,ht)

p( atmost one tails) is 2/4= 1/2

4. no tails

no. of outcomes with no tails is 1(HH)

p( no tails) = 1/4

hope it's understandable.

Answer:

1.) two tails :

total no. of outcomes possible is TT,TH,HT,HH

no. of outcomes with TT is 1

p(tails on both) = 1/4

2.) tails at least one:

no. of outcomes with one tails atleast

is 3 (TT,th,ht,)

p(atelast one tails) = 3/4

3.) tails on one

no. of outcomes with one tails at most is 2 (th,ht)

p(atmost one tails) is 2/4= 1/2

4. no tails

no. of outcomes with no tails is 1(HH)

p(no tails) = 1/4

Yolanda has 3/4 of a cup of sugar. This is 3/5 of what she needs. How much sugar does Yolanda need?
Show your reasoning.

Answers

Answer:

[tex]1\frac{1}{4}[/tex] cups

Step-by-step explanation:

1. Info we have

3/4=3/5

2. Solving

3/4*1/3=3/5*1/3

1/4 = 1/5

1/4*5=1/5*5

5/4=5/5

5/4= 1 and 1/4 cups

Hope this helped! Please mark brainliest :)

~~ SUMMER ~~

The pages in a book are numbered starting with one. The book has 250 pages. How many digits did the printer use in numbering the pages of the book? A. 640 B. 642 C. 320 D. 321

Answers

Answer:

B)642

Step-by-step explanation:

Between 1 and 9 , it will use 9 letters

Between 10 and 99, there are 90 different numbers and every number have 2 digits so it will use 180 letters

Between 100 and 250 , there are 151 different numbers and every number have 3 digits so it will use 453 letters

Totally it used 9+180+453=642

Write a variable expression to represent the phrase. The difference of a number and 1

Answers

Answer:

[tex]x-1[/tex]

Step-by-step explanation:

Hi there!

Let [tex]x[/tex] represent "the number".

The difference of a number and 1

⇒ [tex]x-1[/tex]

I hope this helps!

Help with geometry please​

Answers

3x-10+42+58=180 because angles in a triangle add up to 180
X=30
Z is equal to 3x-10
So z=80
80+42= 122
180-122= 58 (angle C)
Y = 122 because angles on a straight line add up to 180

g(b)=5b-9
h(b)=(b-1)^2
(h*g)(-6) = ???

Answers

[tex](h \times \: g)(b) = (b - 1)^{2} (5b - 9) \\ = ( {b}^{2} - 2b + 1)(5b - 9) \\ = 5 {b}^{3} - 19 {b}^{2} + 23b - 9[/tex]

[tex](h \times \: g)( - 6) = 5( - 6) ^{3} - 19( { - 6}^{2}) + 23( - 6) - 9 \\ = 5( - 216) - 19(36) - 138 - 9 \\ = - 1080 - 684 - 138 - 9 \\ = - 1911[/tex]

I hope I helped you^_^

The value of function (h·g)(b) for x=-6 is -867.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(b)=5b-9 and h(b)=(b-1)².

Now, (h·g)(b)=h(b)×g(b)

= (b-1)²×5b-9

= (b²-2b+1)×(5b-9)

= b²(5b-9)-2b(5b-9)+1(5b-9)

= 5b³-9b²-10b²+18b+5b-9

= 5b³-10b²+23b-9

Now, (h·g)(-6)

= 5(-6)³-10(-6)²+23(-6)-9

= -1080+360-138-9

= -867

Therefore, the value of function (h·g)(b) for x=-6 is -867.

To learn more about the function visit:

https://brainly.com/question/28303908.

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Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

Answers

Answer: -1, 13

Step-by-step explanation:

mark me brainliest if you want plz

Midpoint formula:  (x2 + x1)/2, (y2 + y1)/2

(-6 + 4) / 2, (14 + 12) / 2

(-2) / 2, 26 / 2

(-1, 13)

Suppose the average yearly salary of an individual whose final degree is a​ master's is ​$50 thousand less than twice that of an individual whose final degree is a​ bachelor's. Combined, two people with each of these educational attainments earn ​$124 thousand. Find the average yearly salary of an individual with each of these final degrees.

Answers

Bachelor's degree salary = $53000

Master's degree salary = $66000

Step-by-step explanation:

Given that :

Let Salary of bachelor's degree holder = x

Salary of Master's degree holder = 2x - 40000

Master's salary + bachelor's salary = $119,000

Hence,

Master's salary + bachelor's salary = 119,000

2x - 40000 + x = 119,000

3x = 119000 + 40000

3x = 159000

x = 159000 / 3

x = $53,000

Bachelor's degree salary = $53,000

Master's degree salary ; 2x - 40000 ; 2(53000) - 40000 = $106,000 - $40,000 = $66000

The average yearly salary of an individual with a bachelor's degree is $58,000, and the average yearly salary of an individual with a master's degree is $66,000.

Let, the average yearly salary of an individual with a bachelor's degree as "B" and the average yearly salary of an individual with a master's degree as "M".

According to the information given:

The average yearly salary of an individual with a master's degree is $50 thousand less than twice that of an individual with a bachelor's degree:

M = 2B - $50,000

The combined yearly salaries of two people with each of these educational attainments earn $124 thousand:

B + M = $124,000

Now we can solve this system of equations to find the values of B and M.

Substitute the value of M from the first equation into the second equation:

B + (2B - $50,000) = $124,000

3B - $50,000 = $124,000

Now, solve for B:

3B = $174,000

B = $174,000 / 3

B = $58,000

Substitute the value of B back into the first equation to find M:

M = 2B - $50,000

M = 2 * $58,000 - $50,000

M = $116,000 - $50,000

M = $66,000

So, the average yearly salary of an individual with a bachelor's degree is $58,000, and the average yearly salary of an individual with a master's degree is $66,000.

To learn more on equation click:

https://brainly.com/question/14468218

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Solve the inequality for v. 40 ≤ 4v

please will mark brainiest.

Answers

Hi ;-)

[tex]40\leq4v\\\\4v\geq40 \ \ /:4\\\\v\geq10\\\\\huge\boxed{v\in\langle10;+\infty)}[/tex]

Answer:

[tex]v\geq 10\\[/tex]

Step-by-step explanation:

Divide both sides by 4.

Flip

Which expression is equivalent to -0.62u+u+ 0.89u?
0.51u
Ou + 0.27
Submit Answer
1.27u
O 1+ 0.27

Answers

Answer:

[tex]⚪ \: \: 1.27 \: u[/tex]

Step-by-step explanation:

[tex] - 0.62u + u + 0.89u \\ = ( - 0.62 + 1 + 0.89)u \\ = 1.27u[/tex]

What is the factored form of this expression x^3+3x^2-6x-18

Answers

Answer:

(x + 3) (x^2 - 6)

Step-by-step explanation:

Factor the following:

x^3 + 3 x^2 - 6 x - 18

Factor terms by grouping. x^3 + 3 x^2 - 6 x - 18 = (x^3 + 3 x^2) + (-6 x - 18) = x^2 (x + 3) - 6 (x + 3):

x^2 (x + 3) - 6 (x + 3)

Factor x + 3 from x^2 (x + 3) - 6 (x + 3):

Answer: (x + 3) (x^2 - 6)

what’s the equivalent multiplication statement to 9 divide 1/11

Answers

Answer: 9*11

When u divide any number by a fraction u can simply flip the denominator and numerator and multiply as u normally would.

So in this case:
1) First flip the denominator and numerator so that it looks like 11/1 instead of 1/11
2) Any number divided by 1 is just itself so 11/1 becomes 11
3) Now just multiply it with 9 and u get the expression: 9*11
If u wanted to solve it further 9*11 = 99

I hope this helps :)


Ju Chan solved the previous question by finding the expression 4(-15).

Which problem would give the same result? Select two options.

Answers

Answer:

-15(4) or -4(15) or 15(-4)

Step-by-step explanation:

As long as you stick with the same variables, you can change their position in the equation or change both of their signs. This should give you the same answer.

Let's say your equation was -2(6). This means you must multiply -2 and 6. This should give you -12. You could also phrase it as 2(-6) or -6(2) or 6(-2). They all give you -12 as a result.

Answer:

(-1)(15+15+15+15)

(-15)+ (-15)+ (-15)+ (-15)

Step-by-step explanation:

Which equation represents a line which is parallel to the y-axis?
x = 6
O y = -1
Submit Answer
O x = 4y
Oy= 2 +1
PLS HELP ASAP

Answers

Answer:

x=6

Step-by-step explanation:

when there is no 'y' in equation, the line is always

parallel to y-axis

In which of the following pairs of numbers is -6 larger than the first number, but smaller than the second number?

Answers

Answer:

-7, -6, -5

Step-by-step explanation:

-7 < -6

-5 > -6

-7 < -6 < -5

calculate the mean of the set of boys and girls below:

boys 21, 18, 20, 16, 16, 22, 28, 24, 26

girls 13, 16, 15, 14, 15, 19, 22, 26, 12

A-boys: 21.22 girls: 16.89

b-boys, 21 girls, 15

c-boys 18.5 girls 17

d-boys 18.5 girls 15

Answers

Answer:

Boys: 21.22 Girls: 16.89

Answer: A

Step-by-step explanation:

Add all the data points and divide it by the number of the data points.

Help! write the set of numbers in set-builder notation: the set of all real numbers except 100​

Answers

Answer:

Step-by-step explanation:

The set of all real numbers except for 100 in set builder notation (assuming the variable is x) is:

The very first x represents the variable.

The second with the R represents the number. Here, we want all real numbers.

And the third is the constraint. We want all real numbers except for 100.

Answer:

{ x | x ∈ R, x ≠ 100 }

Step-by-step explanation:

Real numbers (R) include all rational and irrational numbers.

Hence, If we need to write it in set-builder notation, we will write as:

{ x | x ∈ R, x ≠ 100 }

In words : "x such that x belongs to R, x is not equal to 100"

This shows that x is any real number except for 100.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!

is 5/3 an integer?

Answers

Answer:

No!

Step-by-step explanation:

An integer is a a whole negetive number. A few examples are 4, -4, or even 4/4.

What is the value of -2/3 x (-1/4)x(-24/4)

Answers

Answer:

-1

Step-by-step explanation:

In the figure, ABFG and CDEF are two
10
parallelograms such that the sum of their areas is
702 cm². If AB = CD = EF = FG =
BC , find the
area of the shaded region.
G
F
E
+

Answers

Answer:

[tex]A_{BCF}[/tex] = 351 cm²

Step-by-step explanation:

What is the prime factorization of 81?
Enter your answer as a product of prime numbers, like 2 x 3, or as a single prime number, like 17.

Answers

Answer:

[tex]3^{4}[/tex]

Step-by-step explanation:

                 81

               27    3

            9  3    

        3  3

3*3*3*3 = [tex]3^{4}[/tex]

janessa is playing a board game with two friends. using a single die, one friend rolled a four, and the other friend rolled a three. janessa needs to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. Is the probability of Janessa winning an independent event or dependent event

Answers

Answer:

It is a dependent event, because it depends of the number she'll get rolling the die

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