Is my answer correct?

Using proportions, it is found that:

A proportion is a fraction of a total amount.

In this problem, the directors share one-third of the profit, hence:

18000/3 = 6000

6000/2 = 3000.

That is, each director gets 6000.

The remaining 18000 - 6000 = 12000 will be shared equally by the 24 employees, hence:

12000/24 = 500

Each employee gets 500.

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Answer:

x = 5

y = 2

Step-by-step explanation:

multiply by -2 the second equation and add the first equation to eliminate "x"

[tex]4x+5y=30\\-4x-10y=-40[/tex]

_______________

            [tex]-5y=-10\\y=\frac{-10}{-5} =2[/tex]

To find "x", substitute the value of "y" in any equation. I do it in the first

[tex]4x+5(2)=30[/tex]

[tex]4x+10=30[/tex]

[tex]4x=30-10\\x=20/4=5[/tex]

Hope this helps

Answer:

i got you

Step-by-step explanation:

first you will make the easiest equation into y=mx+b

2x=5y=20

subtract 2x from it self and 20, you will eliminate the 5 but keep the y then you will get y=2x+20

then you will substitute it into the y in the other equation 4x+5(2x+20)=30

after doin that you will multiply 5 by both the number in the parenthesis

4x+15x+100=30 add like terms 4x+15x =

19x+100=30 subtract 100 fromm itself and 30 you will get -70

-70 divided by 19x then you will get your answer

Answer:

ok so we have to make it so we can get rid of one of the varibles by adding or subtracting

so lets multiply the first one by 4

120x+16y=4160

minus the second one so

108x=2160

divide by 108

x=20

then we just plug in

12(20)+16y=2000

240+16y=2000

-240

16y=1760

divide by 16

y=110

(20,110)

Hope This Helps!!!

Answer:

x = 54

Step-by-step explanation:

x/3 = x-36

x= 3x-36.3

2x= 36.3

x = 18.3

x = 54

Answer:

Step-by-step explanation:

The given age ratio is valid 12 years after the age at which Arnold was x years old. When Arnold was x, Ken was x-34.

  (x +12) = 3((x -34) +12) . . . . . the age relation in 2013

__

Solving for x, we have ...

  x +12 = 3x -102 +36

  78 = 2x . . . . . . . add 66-x

  39 = x

In 2001, Arnold was 39 years old.

_____

Additional comment

In 2001, Arnold was 39 and Ken was 5. Ken is 34 years younger.

In 2013, Arnold was 51 and Ken was 17. Arnold was 3 times Ken's age.

Using the z-distribution, it is found that the 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are given by:

[tex]n = 90, \pi = \frac{12}{90} = 0.1333[/tex]

Then, the bounds of the interval are found as follows:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 - 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.041[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 + 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.2256[/tex]

The 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.

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Answer: Square is a 17*17. Ok so its 121-25=96

Step-by-step explanation:

96

Answer:

8 inches

Step-by-step explanation:

You first divide 240 by 3 which is 80

Then you find what number is 2 less than the other number that is you multiplied together you get 80

And we know that 8 × 10 = 80

There for the :-

Width is 8 in

Length is 10 in

Hight is 3 in

The proof is if you multiply all of them you have to get 240

And if you multiply 8, 10, and 3 you get 240

Answer:

the scale factor is 6

scale factor:

length of image ÷ length of original

Here:

Answer:

y = 4

Step-by-step explanation:

because 5 x 4 = 20 and 20 × 4 = 80 and so on y is equal to four

              -the pentagon is a regular pentagon meaning all its side lengths

               are equal since all the sides have one tick mark which says all        

               the side lengths are equal

     2. Solve:

                   Perimeter: 6 + 6 + 6 + 6 + 6 = 30cm

                ⇒ distance between the base pentagon and the top pentagon

                         ⇒ Height is 6 cm

     ⇒ the non-base faces are the squares on the side of the figure

       ⇒ there are 5 squares

          ⇒ Lateral Area = 5 * (Area of Square) = 5 * (6 * 6) = 180 square cm

  The formula for the pentagon's area ⇒ [tex]\frac{5}{2}*s*a[/tex]

       *apothem is the distance from the center of the pentagon to any

         one of the sides

           Area = [tex]\frac{5}{2} *6*4.1 = 15 * 4.1 =[/tex] 61.5 square centimeters

        Surface Area = 2 * (Area of Base) + (Lateral Area)

                                = 2 *61.5 + 180 = 123 + 180 = 303 square centimeters

Hope that helps!

Step-by-step explanation:

must be at least 100m, and the rectangle width, also known as twice the circle radius, must be less than or equal to 60m. That would make for a relatively normal-shaped track

The perimeter of the track is 464 m

The length around an object is called its perimeter.

Given that, a rectangle with semicircles at two ends. there is a running track around the perimeter of the field.

The dimension of the rectangle are 100 m and 64 m

The distance between the outer an dthe inner track is 10 m,

The diameter of the outer semicircles is 64+10+10 = 84 m

Therefore, is radius = 42 m

The perimeter of the outer semicircle = 2×π×radius

= 2×3.14×42

= 264 m

The length of the two straight lines = 100 + 100 = 200 m

Therefore, total perimeter of the whole track = 200+264 =464 m

Hence, the perimeter of the track is 464 m

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The figure for this question is:

Answer:

800

Step-by-step explanation:

96/12=8

8 x 100= 800

Answer:

Your answer is 800

Step-by-step explanation:

When given three side lengths:

      --> the three sides lengths that can form a triangle are the ones where

      the sum of two side lengths of a triangle is always greater than the

      third side

Thus the choice that fits the requirement is choice (C).

Hope that helps!

Answer:

Step-by-step explanation:

The labels on the axes of the graph tell you the meaning of the coordinates of a point on the graph. The ordered pair lists the horizontal coordinate first. The horizontal axis is labeled hours, and the vertical axis is labeled miles.

The point (hours, miles) = (1.5, 75) means Kurt drove 75 miles in 1.5 hours.

__

You can find the miles driven in 1 hour by reading the graph at the horizontal coordinate 1 hour. You find that is 50 miles. The 1 represents 1 unit, so the "unit rate" is 50 miles in 1 hour. Such a rate is also called a "speed" of 50 miles per hour.

If Kurt had driven fewer miles in an hour, the points on the graph would all have smaller vertical coordinates. The unit rate (slope) would be less than 50 miles per hour.

Answer:

[tex]x * x + x * x * x * x = y[/tex]

The formula for finding exponents is multiply the number following the exponent by itself that number of times.

Answer:

c. 2x.

Step-by-step explanation:

16x2 - 14x

Common factor of 16 and 14 =  2'

for x2 and x it is x,

Answer: 2x.

The measure of arc RT in the circle S is about 60 degrees.

A circle is the locus of a point such that the distance from its fixed point is always constant.

The question is not complete. A similar question is attached.

From the diagram:

arc RT = 2 * ∠RUT(angle at circle center is twice angle at circumference)

arc RT = 2 * 30

arc RT = 60°

The measure of arc RT in the circle S is about 60 degrees.

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Answer:

270 Markers

Step-by-step explanation:

5 x 54 = 270

(sorry if I'm wrong)

Answer:

[tex]\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6 }=\frac{2}{6} =\frac{1}{3}[/tex]

Step-by-step explanation:

To complete the steps:

[tex]\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6 }=\frac{2}{6} =\frac{1}{3}[/tex]

I think the question you are answering a question that does not require simplification so ignore the last bit (= 1/3)

Answer:

187

Step-by-step explanation:

a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

The value of 36th term is 187.

An orderly sequence of numbers known as arithmetic progression (AP) has a constant difference between any two consecutive numbers. Additionally known as arithmetic sequence.

abbreviated as AP, a mathematical sequence in which the difference between two consecutive terms is always constant.

Given series

12, 17, 22,.....

since the series is in AP because the difference between any two consecutive numbers is equal,

17 - 12 = 5 and 22 - 17 = 5

for nth term of AP

aₙ = a₁ + (n - 1)d

where a₁ = 12, n = 36, d  =5

a₃₆ = 12 + (36 - 1)5

a₃₆ = 12 + 35 × 5

a₃₆ = 12 + 175

a₃₆ =  187

Hence 187 is the 36th term.

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The coordinates of Omega house is (3/2, 1)

Data;

To find the coordinates of Omega house, we can use the formula of midpoint of a line since Omega house falls between Forsyth Tech and Stadium

[tex]x,y = (\frac{x_1+ x_2}{2} , \frac{y_1+y_2}{2})[/tex]

We can substitute the values and solve for both x and y coordinates.

[tex]x = \frac{x_1+x_2}{2} \\x = \frac{7 + (-4)}{2} = \frac{3}{2}[/tex]

The value of the y-coordinate is

[tex]y = \frac{-5+ 3}{2} = 1[/tex]

The coordinates of Omega house is (3/2, 1)

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Using the given function, it is found that the projectile hits the ground after 20 seconds.

It hits the ground when it's height, given by h(t), is equals to zero.

In this problem, the function that models it's height is given by:

h(t) = -4.9t^2 + 98t.

Then:

h(t) = 0

-4.9t^2 + 98t = 0.

-4.9t(t - 20) = 0

t - 20 = 0 -> t = 20.

The projectile hits the ground after 20 seconds.

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Answer:

1,620

Step-by-step explanation:

L x W x H

L = 15

W = 12

H = 9

15 x 12 = 180

180 x 9 = 1620

Answer:

Given equation:

[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]

27 can be written as [tex]3^3[/tex]

Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]

[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]

Therefore, we can rewrite the given equation with base 3:

[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]

To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]

[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]

[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]

[tex]\implies -3x=-4x+6[/tex]

Add [tex]4x[/tex] to both sides:

[tex]\implies x=6[/tex]

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

We can add the same quantity to both sides of the equations, and still have an equivalent equation. Let's add [tex]x+2[/tex] to both sides, then sum like terms

[tex]5-x +x+2 = -2 +x+2\\5+2 = x\\7=x[/tex]

(this is the rule that allows us to move items from one side do the other of the equal sign by changing its sign)

At this point we have a solution, let's replace it to verify

[tex]5-(7) = -2\\-2=-2[/tex]

Answer:

k = 7

Step-by-step explanation:

To solve this, first, you need to find the slope of the line. To do this, you can convert it into point-slope form.

3y = -2x + 5

y = - 2/3x + 5/3

The slope is -2/3, so the perpendicular slope in 3/2

You find the difference between the x - values (2 - -2 = 4), then multiply that by the slope (4 x 3/2 = 6) finally, you add that to the y value of point one.

1 + 6 = 7