Find the mean of these numbers:
2,6,9,56,63,68

Answer:

  gh280,854

Step-by-step explanation:

You want the total income after 3 and half years of a man and a woman who receive a monthly salary of gh3725 and gh2962 respectively.

You can add up the income from each of the months for each of them, or you can use multiplication to simplify the problem.

The total income each month is ...

  gh3725 +gh2962 = gh6687

The total received in 42 months is ...

  42 × gh6687 = gh280,854

Their total income after 3 1/2 years is gh280,854.

__

Additional comment

There are 12 months in a year, so ...

  3×12 +1/2×12 = 36 +6 = 42

months in 3 1/2 years.

[tex]2x+2y=-8 \implies x+y=-4 \implies y=-4-x[/tex]

We can substitufe this result into the second equation.

[tex]-10x-5(-4-x)=-5 \\ \\ -10x+20+5x=5 \\ \\ -5x+20=5 \\ \\ -5x=-15 \\ \\ x=3 \implies y=-4-3=-7[/tex]

[tex]\therefore[/tex] The solution is [tex](3,-7)[/tex].

Answer:

(10, 24)

Step-by-step explanation:

First equate both the equations,

2(x+2) = 4(x-4)

Then expand the brackets,

2x + 4 = 4x - 16

Collect like terms in each sides,

4 + 16 = 4x - 2x

Simplify and solve,

20 = 2x

20 ÷ 2 = x

x = 10

Then substitute 10 for x in one of the equations,

y = 2(x + 2)

y = 2(10 + 2)

y = 24

Therefore, the point of interssection is (10, 24).

you can solve this using the simultaneous equation

so y = y

4(x-4) = 2( x + 2)

4x - 16 = 2x +4

4x - 2x = 4+16

2x/2=20/2

therefore x=10

y=2 (x+2)

y=2(10+2)

y=2(12)

y=24

Answer:

6

Step-by-step explanation:

The number completes the sequence is 6

Answer:

Step-by-step explanation:

if the bars are similar, they are proportional.

make a proportion: length  =  30    =  10

                                width       12         x

cross multiply:     12 times 10 = 120

divide by the number that ids left - 120 ÷ 30  = 4 cm

The width of the smaller bar is 4 cm.

Answer:

Below

Step-by-step explanation:

You need to find the LCD of 12 16 and 20

Using Prime Factorization:

     12 = 2 * 2          * 3

     16 = 2 * 2 * 2 * 2

    20 = 2 * 2               * 5      

            2    2   2   2  3   5                  so LCD will be 2 * 2 * 2 * 2 * 3 * 5= 240

so she will need    240 / 12 = 20 packs of pencils

                               240 / 16 = 15  packs of notebooks

                                240 / 20 = 12 packs of pens

Answer:

Step-by-step explanation:

90

By solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.

It primarily consists of a variable, sometimes with a numerical constant in addition.

Take the following illustration into consideration to quickly grasp this idea. 3x – 4 = 5. It is a simple equation of class 7.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

So, we know that the ration is 6:11 and the perimeter is 510 units.

Then, form and solve the equation as follows:

510 = 2(6x + 11x)

510 = 12x + 22x

510 = 34x

x = 510/34

x = 15

Then, the length will be:
6x

6(15)

90 units

Therefore, by solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.

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Answer:

The correct equation you're looking for is the first choice: [tex]\frac{240 miles}{5 hours}[/tex] = 48 miles  per hour.

Step-by-step explanation:

The formula to show the relationship between rate, time, and distance is [tex]rt=d[/tex], where [tex]r[/tex] represents the rate of change, [tex]t[/tex] represents time, and [tex]d[/tex] represents the total distance. Since you are given the distance and time, and are looking for the rate of change, then you need to divide the total distance traveled by the time it took to travel that distance, so the correct equation is [tex]\frac{240miles}{5hours}[/tex] = 48 miles per hour.

Have a great day! Feel free to let me know if you have any more questions :)

He must sell 520 units from the second shipment in order to have sold 80 percent of all of the unit.

This is mathematical equations.

The salesman sold 75% of 800 units, so he sold 0.75 * 800 = 600 units from the first shipment.

The salesman wants to sell 80% of all the units, which is a total of 0.80 * (800 + 600) = 0.80 * 1400 = 1120 units.

To find out how many units he must sell from the second shipment, we subtract the number of units he has already sold from the number of units he wants to sell:

1120 units - 600 units = 520 units.

Therefore, the salesman must sell 520 units from the second shipment in order to have sold 80% of all the units.

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Answer:

248

Step-by-step explanation:

Find the volume of each box, then add them up.

Volume = l x w x h

Top:  5 x 2 x 5 = 50

Middle:  6 x 4 x 3 = 72

Bottom:  9 x 7 x 2 =126

Total = 50 + 72 + 126 = 248 cubic feet

Answer: -2

Step-by-step explanation: use the slope formula.

Answer:

10²

Step-by-step explanation:

assume you typed 10.4 million

so 10³/10.4 ≈ 10²

Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°

Explaining quadrilaterals?

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.

What is quadrilateral formula?

When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.

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The complete question is -

Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.

Step-by-step explanation:

what is the question ?

without an actual question I can only "daydream" things about this information.

EB is the diameter, FB is therefore the radius.

since FB = 3 units, EB = 2×FB = 2×3 = 6 units.

the arc angle AB = 120°.

if you need to express the angle in radians, remember :

360° (the full circle) = 2pi

120° = 360/3 = 2pi/3

the arc angle AE is the supplementary angle to AB (both together have 180° or 2pi/2 = pi).

180 = AB + AE = 120 + AE

AE = 180 - 120 = 60°

60° = 360/6 = 2pi/6 = pi/3

the arc angle BC = 45°.

45° = 360/8 = 2pi/8 = pi/4

the arc angle CD = 30°

30° = 360/12 = 2pi/12 = pi/6

the arc angle ED is the supplementary angle to BC and CD.

180 = ED + BC + CD = ED + 45 + 30 = ED + 75

ED = 180 - 75 = 105°

105° = pi - pi/4 - pi/6 = 12pi/12 - 3pi/12 - 2pi/12 = 7pi/12

the sum of

AB + BC + CD = 2pi/3 + pi/4 + pi/6 =

= 4×2pi/12 + 3pi/12 + 2pi/12 =

= 8pi/12 + 3pi/12 + 2pi/12 = 13pi/12

so, nothing fits to any of your answers.

again, I am not sure what problem you need to solve here.

maybe you can build your answer out of the various pieces I gave you here.

The correct answer is:

Function f is translated to the right 7 units.

Function f is translated down 4 units

$20

there is two ways to solve this.

ratio form:

80% / 100% = X / $25

---> 2000 / 100 = X

---> X = 20

Decimal form:

80% --- move decimal two places to the left.

80% = 0.8 --- now multiply decimal by total value

0.8 x 25 = 20

$20.

On solving the provided question, we can say that the area of the picture of the flyer in the newspaper is = 36 square inches.

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

he original flyer has an area of = 576 square inches.

The Picture Noah prints will be a dilation of the flyer using a scale factor of 1/4.

Scale factor k=1/4

So the area of the picture of the flyer in the newspaper is

A = 576 X k^2

A = 576*1/4*1/4

A = 36 sq in.

the area of the picture of the flyer in the newspaper is = 36 square inches.

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Answer:

4) 175

5) 2

6) 72

7) 48

8) 45

9) 5

10) 18

11) 3

12) 10

13) 30

14) 12

15) 1

16) 2

17) 2

18) 8

Step-by-step explanation:

The easiest way to do this is to cross-multiply.

Ans:

Q4. 175

Q5. 2

Q6. 72

Q7. 48

Q8. 45

Q9. 5

Q10. 18

Q11. 3

Q12. 10

Q13. 30

Q14. 12

Q15. 1

Q16. 2

Q17. 2

Q18. 8

Answer and Step-by-step explanation:

Let's call the angle between the roads on the south side "y" for simplicity. Since the two roads intersect, the sum of the two adjacent angles on one side must add up to 180 degrees. Therefore, we can set up an equation:

y + 69 = 180

Solving for y, we get:

y = 180 - 69 = 111

We also know that y is equal to 3x, so we can set up another equation:

3x = 111

Solving for x, we get:

x = 37

Therefore, the value of x is 37.

The expression to find the total number of stickers bought by Mark is x = 9s.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The number of sheets of stickers Mark bought is denoted by the variable = s.

The number of stickers on each sheet is = 9

Let the total number of stickers be x.

Use the arithmetic operation of multiplication.

Then the expression will be -

Total number of stickers = Number of sheets of stickers × Number of stickers on each sheet

Substitute the values into equation -

x = s × 9

x = 9s

Therefore, the expression is obtained as x = 9s

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Answer:

5.06%

Step-by-step explanation:

x = cost of living....then increase it 2 %

       1.02 x   = new cost of living      now increase this 3 %

           (1.03) 1.02x = 1.0506x     which equates to 5.06% increase in 2 years

The solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:

[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]

Let x(t) and y(t) be the solution of the linear system of differential equations:

[tex]$\frac{dx}{dt} = ax + by$[/tex]

[tex]$\frac{dy}{dt} = cx + dy$[/tex]

with initial conditions x(0)=5 and y(0)=3.

The general solution of the system of differential equations can be written as:

[tex]$x(t) = e^{at} (X0 \cos(bt) + Y0 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (X0 \sin(bt) - Y0 \cos(bt))$[/tex]

where X0 = 5 and Y0 = 3.

Therefore, the solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:

[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]

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Answer:

Step-by-step explanation:

Distribute.

4xb and 4x-0.17b

C. 4b - 0.68b

The three consecutive positive integers satisfying the statement are

9, 10, and 11.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The three numbers be n, (n + 1), and (n + 2).

Therefore, the numerical expression of the given statement is,

2(n)(n + 2) + 2 = 20(n + 1)

2n² + 4n + 2 = 20n + 20.

2n² - 16n - 18 = 0.

n² - 8n - 9 = 0.

n² - 9n + n - 9 = 0.

n(n - 9) + 1 (n - 9) = 0.

(n - 9)(n + 1) = 0.

n = 9 is the positive integer.

So, The numbers are 9, 10, and 11.

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The equivalent expression of 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 136/120a + 107/120b.

One common way to simplify an expression is to use the unitary method, which involves finding a common denominator and then canceling out like terms.

In this case, we'll use the unitary method to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.

To start, we'll find a common denominator for all the terms in the expression.

The least common multiple of 5, 3, 8, 6, and 5 is 120. Now, we can convert all the fractions to have a denominator of 120.

Next, we'll simplify each term by dividing the numerator and denominator by their greatest common factor.

96/120a can be simplified to 8/10a by dividing both the numerator and denominator by 8. 80/120b can be simplified to 2/3b by dividing both the numerator and denominator by 40. And so on.

Finally, we'll rearrange the terms and simplify them using the unitary method. We'll start by canceling out like terms, which have the same variable and the same sign.

So, 8/10a and 96/120a are both positive and have the variable a, so we can simplify them to 104/120a.

Similarly, we can simplify 2/3b and 105/120b to 107/120b. We'll then add up all the positive terms and subtract all the negative terms.

The final equivalent expression is

=> 104/120a + 107/120b + 15/120 - 90/120

=> (104 + 107 + 15 - 90)/120a + (107/120)b

=> 136/120a + 107/120b.

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Answer:

y = 3(2)^x

Step-by-step explanation:

If we look at the x and y values, we see that the xs' increase by 1 each time, while the ys' double (12*2 = 24, 24 *2 = 48 etc.).

Because the value doubles each time, we know that this is an exponential equation, and the base (b) is 2.

The general form (as shown) is y = a(b)^x, where a is the initial value (y-intercept or value of y when x = 0) and b is the base.

We can find a by plugging in one x and y coordinate and 2.

For example, we can use (1, 6) to solve for a:

[tex]y=a(b)^x\\6=a(2)^1\\6=a(2)\\3=a[/tex]

Time is 9:42 a.m. when they meet will at the starting point again.

We have, Cheko and Sharko started running at the same time and starting point. The shape of ground or stadium is circular. Time taken by Cheko to complete the one round of stadium

= 7 minutes

Time taken by Sharko to complete the one round of stadium = 6 minutes.

At 9.00 a.m, both are start running together. We have to calculate time they will meet at the starting point again. So, they will starting together after LCM ( 7, 6) minutes. LCM stands for least common multiple of 7 and 6. The factors of 7 and 6 are the following, 7 = 1×7

=> 6 = 2× 3 × 1

So, LCM (6,7 ) = 2×3×7×1 = 42 minutes

Thus, the again starting time = 9:00 a.m. + 42 minutes = 9: 42 a.m.

Hence, the required time is 9: 42 a.m.

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Answer:

9

Step-by-step explanation:

this is the explanation 6×3=18 18÷2=9