Given 64 / 108, what common factor would reduce this fraction to its lowest terms?

The work would be finished 2.25 times faster if they had been doing the work at the same time.

Assumption;

In essence, the total time required to finish the ditch by 2 workers is; 2 hours.

However, since they took 1 hour turns on the job, it follows that; The total time used is;

Hence they could have finished the work in;

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Answer:

5x + 20

Step-by-step explanation:

5(x+4)

5(x) + 5(4)

5x + 20

Hope this helps!

Answer:

Basic subtraction:

needed students: minimum required students - students signed up

needed students: 26 - 19

needed students: 7 students, the club needs.

Solution:

We know that the inequality form is x ≥ 26. If we subtract the number of students required by the number of students joined, we will obtain the required students to start the club.

Hence, the club needs 7 more students to have a club.

Answer:

28

Step-by-step explanation:

(((75+45) ÷5) - 10 )2 -> first add 75 and 45

((120 ÷ 5) - 10)2 -> Divide 120 by 5

(24 - 10)2 -> Subtract 24 by 10

(14)2 - > 28

Ans: 28

Answer:

Step-by-step explanation:

(a)

(b)

#a

Check IO bisects the FH at 90°.

#b

So the options are

1. We can measure the following two things:

(i) a person's height

(ii) the velocity required to reach Mars.

2. Everything involving a rocket launch needs to be extremely precise; otherwise, it could result in tragedy. However, anything involving a person's height won't result in disaster.

This can be solved using the concept of precision and uncertainty concept.

The accuracy of a material or substance is the distance or degree to which two or more measurements are near to one another. Every time a measurement is performed, a new result is obtained that falls within the uncertainty interval that surrounds the measured value.

1. We don't need to be very precise because we can measure a person's height with a modest degree of accuracy. The person hearing would get a notion of their height if we said, "That individual is roughly 5 feet tall."

On the other hand, if we estimate the rocket speed to Mars incorrectly, it would lead to tragedy in the future, hence we require great precision. In order to ensure that we strike the necessary objective in space, we apply intricate mathematics.

2.  Like we stated in problem 1, everything involving space travel needs extreme accuracy. The spaceship might crash and calamity could ensue if our estimates are incorrect. Engineers utilized the incorrect settings in the one instance where anything went wrong, causing the Mars lander to smash into the planet rather than securely land there.

Due to the enormous expense of these space exploration missions, it is imperative to obtain as many exact and accurate values as possible. Now, details like a person's height don't necessarily need to be accurate because we can just guesstimate a person's height depending on who we're speaking to.

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Answer:

x=−7

Step-by-step explanation:

(x+4)(2)−3(x+4)−3=0

(x)(2)+(4)(2)+(−3)(x)+(−3)(4)+−3=0(Distribute)

2x+8+−3x+−12+−3=0

(2x+−3x)+(8+−12+−3)=0(Combine Like Terms)

−x+−7=0

Answer:

Letter a is 6:38 and letter b is 2:17

Hope this helps!

Answer:

130 degrees

Step-by-step explanation:

The right top triangle is isosceles, so the supplementary angle of angle α is (180 - 80)/2 = 50 degrees.

Therefore, α = 180 - 50 = 130 degrees.

Step-by-step explanation:

f'(x)=-2sin(x)+2cos(2x)=0

as cos(2x)=2sin(x)cos(x),

-2sin(x)+4cos(x)sin(x)=0

sin(x)-2cos(x)sin(x)=0

(sin(x))(1-2cos(x))=0

-> x = 0, pi/3

testing these values along with the end points of the interval,

f(0)=2

f(pi/3)=1+(0.5sqrt(3))

f(pi/2)=0

so the min is 0 and the max is 2.

Answer:

A) 3.94

B) 12.40

Step-by-step explanation:

Refer to the work image. You also need the radius to calculate A and B.

Answer:

[tex]y= -\frac{8}{7} x - 7[/tex]

Step-by-step explanation:

Hope this helps! :)

Answer:

a) 36x-27y-207

b)12x-6y+2

c)300y-60x-195

d)-8x-96

d)8x+272y-576

Step-by-step explanation:

In all of these equations, you multiply the numbers on the outside of the parentheses to all of the terms inside the parentheses to get each of your different answers.

Hope this helps and please award brainliest if possible!

Line plots are used to express variables using markers

The total phone call for eight months is [tex]10\frac 34[/tex] hours

From the line plot, we have the following summation

[tex]Total = 1hr + 1\frac 12 hr * 2 + \frac 34 hr[/tex]

When the total hours of phone call for the 8th month is added, the summation equation becomes

[tex]Total = 1hr + 1\frac 12 hr * 2+ \frac 34 hr + 6 hr[/tex]

Add the expressions

[tex]Total = 10\frac 34[/tex]

Hence, the total phone call for eight months is [tex]10\frac 34[/tex] hours

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Answer:

56

Step-by-step explanation:

8C5 = 56

Answer:

  8C5 = 56

Step-by-step explanation:

The formula for nCk is ...

  nCk = n!/(k!(n-k)!)

Then the value of 8C5 is ...

  8!/(5!(8-5)!) = 8·7·6/(3·2·1) = 8·7

  8C5 = 56

_____

Additional comment

The larger of the denominator factorials will cancel most of the factors of the numerator. The remaining denominator factors can be factored from the remaining numerator values to simplify the problem of doing the math by hand. Most graphing calculators and all spreadsheets can compute this function for you.

  [tex]\dfrac{8!}{5!\cdot3!}=\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(5\cdot4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\dfrac{8\cdot7\cdot6}{3\cdot2\cdot1}=\dfrac{8\cdot7\cdot6}{6}=8\cdot7[/tex]

Prioritize meeting basic needs and invest in education and skill development, while supporting community projects for a fair distribution of funds.

Prioritize basic needs: I would recommend ensuring that everyone's basic needs are met first, such as food, shelter, and healthcare. This promotes fairness by addressing essential requirements for survival and well-being.

Invest in education and skill development: Allocating funds towards education and skill development programs can empower individuals to improve their future prospects and contribute to society. It promotes fairness by providing equal opportunities for personal growth and advancement.

Support community projects: Encouraging investments in community projects, infrastructure development, and social initiatives can benefit a broader range of people. It promotes fairness by aiming to uplift the community as a whole, rather than focusing solely on individual interests.

By following these principles, the recommended approach for spending money can ensure fairness by addressing basic needs, fostering personal development, and benefiting the community at large. Ultimately, the specific allocation of funds would depend on the context, priorities, and values of the individuals involved.

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Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

Hope that helps!

Answer:

288 inches

Step-by-step explanation:

24x12 =  288

each foot has 12 inches

Answer:

divide it, 5400 divided by 9 is 600.

Answer:

Step-by-step explanation:

Answer:

y=6.23 hope this Helps!

Step-by-step explanation:

Answer:

-2 (x+7)

-2x-14

hope it helps you

have a great day :)

Answer:

y = 2x - 3

Step-by-step explanation:

y - 9 = 2 ( x - 6 )

y - 9 = 2x - 12

Hi! I can help you with a smile! :)

Answer:

y=2x-3

Hope it helps!

~Nature~

Enjoy your day!

Answer:

57/6   60/6    22/6   26/6

Step-by-step explanation:

So the answers for the blanks are 57, 60, 22, 26.

Let me know if I am incorrect.

Answer:

20 years

Step-by-step explanation:

when the boy is 8 and half his sisters age his sister is 16

four years later the boy will be twelve, so if his sister was 16 four years later she will be 20

Answer:

20 years old

Step-by-step explanation:

Let n represent the age of the boy's sister then...

[tex]8=\frac{1}{2}n[/tex]

Multiply both sides by 2

[tex]n=16[/tex]

When the boy is 12, it will be 4 years from when he is 8 therefore...

16 + 4 = 20 years old

Answer:

c hope this hrlpe

Step-by-step explanation:

For any square matrix A, if it is invertible, its inverse is given by

[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A)[/tex]

where adj(A) is the so-called adjugate matrix, which is the transpose of the cofactor matrix of A. If you don't know what that is, that's not terribly important. What is important is that the inverse does not exist if the determinant, det(A), is zero.

We have

[tex]A=\begin{bmatrix}6&7\\-6&7\end{bmatrix} \implies \det(A) = 6\times7-7\times(-6)=84 \neq 0[/tex]

so the inverse does indeed exist. (And we eliminate D as an answer.)

From the given choices, it's quite clear that C must the correct answer, since we know det(A) = 84, and we can easily confirm that

[tex]\begin{bmatrix}7&-7\\6&6\end{bmatrix} \begin{bmatrix}6&7\\-6&7\end{bmatrix} = \begin{bmatrix}84&0\\0&84\end{bmatrix}[/tex]

so that multiplying by 1/84 recovers the identity matrix.

We are given with a square matrix and we are asked to find it's inverse if it exists . So , let's recall some important points first :-

Now , in this question let's assume that [tex]{\sf A=\begin{bmatrix}6 & 7 \\ -6 & 7\end{bmatrix}}[/tex]

Now , Calculating det(A) :-

[tex]{:\implies \quad \sf det(A)=\begin{vmatrix}6 & 7 \\ -6 & 7 \end{vmatrix}}[/tex]

[tex]{:\implies \quad \sf det(A)=42-(-42)}[/tex]

[tex]{:\implies \quad \sf det(A)=42+42}[/tex]

[tex]{:\implies \quad \sf det(A)=84}[/tex]

As , det(A) ≠ 0 . So , [tex]{\bf A^{-1}}[/tex] exists . Now , we need to find the matrix of cofactors first , but let's find cofactors first , so here ;

[tex]{\blacktriangleright \sf C_{11}=7,\: C_{12}=6,\: C_{21}=-7,\: C_{22}=6}[/tex]

Now , let's assume that matrix of cofactors is C , so putting the cofactors as elements of the matrix , C will be ;

[tex]{:\implies \quad \sf C=\begin{bmatrix}7 & 6 \\ -7 & 6\end{bmatrix}}[/tex]

Now , adj(A) will be found by interchanging it's rows by columns and vice versa.

[tex]{:\implies \quad \sf adj(A)=\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex]

Now as [tex]{\sf A^{-1}}[/tex] is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{A^{-1}=\dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}}}[/tex]

Hence , Option C) [tex]{\sf \dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex] is correct :D