) 30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag and the third bag has twice as many as the first bag. If x is the number of marbles in the first bag, find the number of marbles in each bag.

Answer:

3

Step-by-step explanation:

Answer:

[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}=a^8[/tex]

Step-by-step explanation:

[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}\\\\= \frac{a^3a^9}{a^4}\\\\=a^3a^9\\\\=a^{3+9}\\\\=a^{12}\\\\=a^{12-4}\\=a^8[/tex]

Answer:

a⁸

Step-by-step explanation:

a³*a⁹/a⁴

Product law:Says that if the base of the number being multiplied is the same, then we can add the exponents

Therefore

a to the power of 3+9/a⁴

a¹²/a⁴

Quotient law:Says that when we divide two numbers with the same base,we can subtract the exponents

Therefore

a to the power of 12-4

a⁸

Answer:

Step-by-step explanation:

Its d

Answer:

(C) 10200m

Step-by-step explanation:

Dizem-nos na pergunta que um homem de negócios tem um espaço retangular de 100 m por 750 m para correr.

O primeiro passo é calcular o perímetro do retângulo.

Perímetro de um rectângulo = 2 (Comprimento × Largura)

Da pergunta,

Comprimento = 100m

Largura = 750m

Perímetro do rectângulo = 2 ( 100 + 750)

= 2(850)

= 1700m

Perímetro do rectângulo = 1700m

Somos questionados na pergunta para determinar quantos metros (Distância) um atleta viajou que tem apenas 6 voltas ao redor das extremidades do espaço.

A distância total percorrida pelo atleta ao correr é calculada como:

6 × perímetro do rectângulo.

= 6 × 1700

= 10200m

Quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço = 10200

Answer:

30.6

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 23°

Opposite = 13

Adjacent = y

The value of y can be obtained by using the following trig ratio:

Tan θ = Opposite /Adjacent

Tan 23° = 13/y

Cross multiply

y × Tan 23° = 13

Divide both side by Tan 23°

y = 13/Tan 23°

y = 30.6

Therefore, the value of y in the diagram above is 30.6

Answer:

4x - 2y = 2

Step-by-step explanation:

Given that (1, 1 ) is a solution then it must satisfy the equation

Consider the equations given

2x + y = 2 → 2(1) + 1 = 2 + 1 = 3 ≠ 2 ← not True

4x - 2y = 2 → 4(1) - 2(1) = 4 - 2 = 2 ← True

2x - 2y = 2 → 2(1) - 2(1) = 2 - 2 = 0 ≠ 2 ← not True

x + y = 4 → 1 + 1 = 2 ≠ 4 ← not True

Thus

4x - 2y = 2 completes the system.

Answer: 3 feet²

Step-by-step explanation:

Simply do 2*18 (In a rectangle A = l*w) to get 36 inches, or 36/12 feet, or 3 feet.

Hope it helps <3

Answer:

Width = 1.5 Inches

Step-by-step explanation:

Original Height: 24 Inches

Original Width: 18 Inches

Given Height: 2 inches

24 divided by 2 = 12. This means the poster was dilated by 12.

18 divided by 12 = 1.5

Answer:

x = [tex]\frac{22}{3}[/tex]

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 6 when x = 2, then

- 6 = 2k ( divide both sides by 2 )

- 3 = k

y = - 3x ← equation of variation

When y = - 22, then

- 22 = - 3x ( divide both sides by - 3 )

x = [tex]\frac{-22}{-3}[/tex] = [tex]\frac{22}{3}[/tex]

Answer:

Step-by-step explanation:

Hello

p(A∪B) = p(A) + p(B) - p(A∩B) = 0.5 + 0.4 - 0.15 = 0.9 - 0.15 = 0.75

hope this helps

[tex]i^5+i^{-25}+i^{45}[/tex]

Rewrite the term [tex]i^{-25}[/tex]

[tex]=i^5+\dfrac{1}{i^{25}}+i^{45}[/tex]

Expand each term so we have

[tex]=i(i^2)^2+\dfrac{1}{i(i^2)^{12}}+i(i^2)^{22}[/tex]

Use the fact that [tex]i^2=-1[/tex]

[tex]=i(-1)^2+\dfrac{1}{i(-1)^{12}}+i(-1)^{22}[/tex]

Use the fact that [tex](-1)^{a}=1[/tex] when a is an even number

[tex]=i+\dfrac{1}{i}+i[/tex]

Simplify

[tex]=i-i+i[/tex]

[tex]=i[/tex]

Let me know if you need any clarifications, thanks!

Answer:

1/i +2i

Step-by-step explanation:

i^5+i^-25+i^45    i^2=-1

i^4*i +i^-24*i^-1 +i^44 *i

(i²)² i+ (i²)^-12*i^-1+(i²)^22 *i     since i²=1

i+i^-1+i=

i+1/i +i=1/i +2i

Answer:

$307

Step-by-step explanation:

$2.00  + $100  + $100  + $100  + $5.00 = $307

Answer:

put it in a calculator, 8,000 times whatever number u need

Answer:

Ok, a system of equations means that we have a given number of equations with the same solutions.

If we only have tables, this means that we need to have one table for each equation:

For example, if we are working only with two variables, x and y, in those tables we can see the pints (x, y) that belong to each equation.

Now, a point (x, y) will be a solution of the system of equations only if it belongs to the data table for each equation

This would mean that if we graph those data sets, the graphs will intersect at the point (x, y) that belongs to all the tables of data.

Other way may be using the data in the tables to construct the equations, but you said that you only want to use the tables, so this method can be discarded.

Answer:

abd

Step-by-step explanation:

The true statements about the reflection shown in picture attached are :

M∠X'Z'Y' = 90°

M∠X'Z'Y' = 90°m∠MCY = 90°

M∠X'Z'Y' = 90°m∠MCY = 90°BZ' ≅ BZ

Reflection is a type of transformation that flips a shape in a mirror line (also called a line of reflection) so that each point is the same distance from the mirror line as its reflected point.

here, we have,

When reflection of a preimage occurs, the image produced is congruent to the preimage because reflection produces isometric images. This means that both the preimage and image are similar in shape and size.

Since m∠XZY = 90°, will be congruent with the angle m∠X'Z'Y' ; Hence, m∠X'Z'Y' = 90°

The segment MN and YY' are perpendicular, hence forming a right angle. m∠MCY = 90°

B is the midpoint between ZZ'. Hence, the distance between BZ' and BZ will be the same. BZ' ≅ BZ

From the image produced, XY and X'Y are not parallel

Learn more on reflection :

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Complete question:

Which statements must be true about the reflection of ΔXYZ across Line M N? Select three options. M∠X'Z'Y' = 90° m∠MCY = 90° XX' ≅ YY' BZ' ≅ BZ XY || X'Y

Answer:

We shall need to pick at least 4 balls to be sure that we are getting balls with the same color

Step-by-step explanation:

Here, we want to know the least number of balls to be taken out of the box to be sure that we have all the three colors represented.

We know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know we have all the colors of balls represented, we will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that we have taken all the colors since we would have exhausted picking other balls at this point.

So we shall be needing at least 4 balls picked to ensure that we have all the colors represented

Answer:

the answer is C. 180°clockwise

Answer:

[tex]x^2 + y^2 + 4x + 4y = -119/16[/tex]

Step-by-step explanation:

The axes x and y are calibrated in 0.25

If the circle is carefully considered, the radius r of the circle is:

r = -1.25 - (-2)

r = 0.75 units

The equation of a circle is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

The center of the circle (a, b) = (-2, -2)

Substituting  (a, b) = (-2, -2) and r = 0.75 into the given equation:

[tex](x - (-2))^2 + (y - (-2))^2 = (3/4)^2\\\\(x + 2)^2 + (y + 2)^2 = (3/4)^2\\\\x^2 + 4x + 4 + y^2 + 4y + 4 = 9/16\\\\x^2 + y^2 + 4x + 4y + 8 = 9/16\\\\16x^2 + 16y^2 + 64x + 64y + 128 = 9\\\\16x^2 + 16y^2 + 64x + 64y = -119\\\\x^2 + y^2 + 4x + 4y = -119/16\\[/tex]

Answer:

1196cm³

Step-by-step explanation:

Step 1

Find the volume of the Rectangular Prism = Length × Width × Height

Length = 12 cm

Width = 20 cm

Height = 5 cm

Volume of a Rectangular prism = 12 × 20 × 5

= 1200cm³

Step 2

Volume of the Eraser

The Eraser has the shape of a box.

Volume = Length × Width × Height

Length = 0.5 cm

Width = 2 cm

Height = 4 cm

Volume = 4cm³

Step 3

Find the volume of the art box not taken up by the eraser

Volume of the art box not taken up by the eraser = Volume of the Art box - Volume of the Eraser

= 1200cm³ - 4cm³

= 1196cm³

Therefore, volume of the art box not taken up by the eraser is 1196cm³

Answer:

560cm

Step-by-step explanation:

Volume = Length × Breadth × Height

= 10 × 8 × 7

= 560 cm³

Answer:

Step-by-step explanation:

Volume =length x breadth x height

10 x 8 x 7=560cm^3

Answer:

The Horizontal Asymptote is at x=3

Step-by-step explanation:

Here is a way to remember this

One way to remember this is the following pnemonic device: BOBO BOTN EATS DC

EABOBO -Exponents are bigger on bottom, y=0

EABOTN -Exponents are bigger on top, none

EATS DC - Exponents are the same, divide coefficients

3/x-2 the exponents are the same, divide leading coefficients

3/1 = 3 the horizontal asymtote is at x=3

Answer:

24

Step-by-step explanation:

90/7 ÷ 1 3/4

Change to an improper fraction

90/7 ÷ ( 4*1 +3 ) /4

90/7 ÷ 7/4

Copy dot flip

90/7 * 7/4

90/4

22.5

Best estimate is 24

Answer:

A:2

Step-by-step explanation:

A is the answer because 90 divided by 7 is 12.8 which would be 13, and the 1 and 3/4 would be 7. 13 divided by 7 would equal 1.85. When rounded your answer would be 2.

Answer:

The volume of the figure is approximately 1244 in³

Step-by-step explanation:

The figure is formed by a rectangular prism and a hemisphere, therefore its total volume is formed by the the sum of the volume of each of these forms. The volume of a rectangular prism can be found by using the expression:

[tex]V_{rect} = length*width*height[/tex]

While the volume of a hemisphere is given by:

[tex]V_{hemis} = \frac{2}{3}*\pi*r^3[/tex]

The radius of the hemisphere is the difference between the total length of the figure and the length of the prism, therefore:

[tex]r = 17 - 11 = 6 \text{ in}[/tex]

We can now find the volume of the figure:

[tex]V = V_{rect} + V_{hemis}\\V = 11*6*12 + \frac{2}{3}*\pi*(6)^3\\V = 792 + 144*\pi\\V = 792 + 452.39\\V = 1244 \text{ in}^3[/tex]

Answer:

[tex] Area = 112.1 m^2 [/tex]

Step-by-step Explanation:

Given:

∆WXY

m < X = 130°

WY = x = 31 mm

m < Y = 26°

Required:

Area of ∆WXY

Solution:

Find the length of XY using Law of Sines

[tex] \frac{w}{sin(W)} = \frac{x}{sin(X)} [/tex]

X = 130°

x = WY = 31 mm

W = 180 - (130 + 26) = 24°

w = XY = ?

[tex] \frac{w}{sin(24)} = \frac{31}{sin(130)} [/tex]

Multiply both sides by sin(24) to solve for x

[tex] \frac{w}{sin(24)}*sin(24) = \frac{31}{sin(130)}*sin(24) [/tex]

[tex] w = \frac{31*sin(24)}{sin(130)} [/tex]

[tex] w = 16.5 mm [/tex] (approximated)

[tex] XY = w = 16.5 mm [/tex]

Find the area of ∆WXY

[tex] area = \frac{1}{2}*w*x*sin(Y) [/tex]

[tex] = \frac{1}{2}*16.5*31*sin(26) [/tex]

[tex] = \frac{16.5*31*sin(26)}{2} [/tex]

[tex] Area = 112.1 m^2 [/tex] (to nearest tenth).

Answer:

a. y = 28,000×(1 - 0.07)^t

b. 20,945.46 acres

Step-by-step explanation:

a. The annual percentage decrease in in size of rainforest = 7%

The size of the rainforest in 2009 = 28,000 acres

The exponential decay formula is y = C×(1 - r)^t

Where:

y = Final Amount

C = Initial amount = 28,000 acres

r = Rate of Change = 0.07

t = Time

Which gives;

y = 28,000×(1 - 0.07)^t

b. In 2013 (year 4, t = 4), the amount of rainforest remaining is therefore;

y = 28,000×(1 - 0.07)^(4) = 28,000×0.93^4 = 20,945.46 acres

The size of the rainforest that remained in 2013 is 20,945.46 acres.

Answer:

20(-3)

Step-by-step explanation:

Examine the graph and the map.

On the left, a bar graph titled Deforestation Trend in the Amazon Rainforest. The x-axis is labeled Acres in kilometers squared of Rainforest Lost. The y-axis is labeled Year from 2004 to 2016. 2004 lost 27,772 acres. 2005 lost 19,014 acres. 2010 lost 7,000 acres. 2012 lost 4.571 acres. 2016 lost 7,989 acres. On the right, a map titled Deforestation of the Amazon Rainforest by 2016. The Amazon River is labeled. A key notes deforestation by 2016, amazon forest in 2016, and non-forest vegetation. Labeled clockwise are Roraima, Amapá, Maranhäo, Pará, Tocantins, Mato Grosso, Rondônia, Acre, and Amazonas. Acre, Amazonas, Roraima, Amapá, Maranhäo, Mato Grosso and Rondônia are deforested by 2016. Pará, Maranhäo, Tocantins, Mato Grosso, and Rondônia have the Amazon forest in 2016. Mato Grosso, Tocantins and Maranhäo have majority of non-forest vegetation.

Which is the best conclusion about the Amazon rainforest that can be drawn from these sources?

Deforestation in the Amazon has accelerated since 2004.

Deforestation in the Amazon is no longer an important issue.

Despite population growth, the Amazon rainforest is increasing in size.

Despite positive trends, the Amazon rainforest remains in danger of destruction.

Answer:

12π inches

Step-by-step explanation:

s = rθ

s = (21) (4π/7)

s = 12π

The length of the arc will be;

⇒ Arc = 37.68 inches

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The central angle = 4π/7

And, A circle has a radius of 21 inches.

Now,

We know that in circle;

⇒ Arc = Radius × Angle

Substitute all the values, we get;

⇒ Arc = 21 × 4π/7

⇒ Arc = 3 × 4 × 3.14

⇒ Arc = 37.68 inches

Thus, The length of the arc will be;

⇒ Arc = 37.68 inches

Learn more about the circle visit:

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Answer:

Area = 19.9 mm²

Step-by-step explanation:

Step 1: Find Angle V.

m < V = 180 - (131 + 27) (sum of angles in a triangle)

V = 22°

Step 2: Find UW using the law of sines.

[tex] \frac{UW}{sin(V)} = \frac{UV}{sin(W)} [/tex]

Plug in your values

[tex] \frac{UW}{sin(22)} = \frac{8}{sin(27)} [/tex]

Multiply both sides by sin(22) to solve for UW

[tex] \frac{UW*sin(22)}{sin(22)} = \frac{8*sin(22)}{sin(27)} [/tex]

[tex] UW = \frac{8*sin(22)}{sin(27)} [/tex]

[tex] UW = 6.6 mm [/tex]

Step 3: Find the area of ∆UVW

Area = ½*UW*UV*Sin(U)

Area = ½*6.6*8*sin(131)

Area = 3.3*8*sin(131)

Area = 19.9 mm² (to the nearest tenth)

Answer:

12 ÷ 4

Step-by-step explanation:

Let's try to solve the given expression to see if it matches with any of the options guven..

[tex] \frac{1}{4}*12 [/tex]

[tex] = \frac{1*12}{4} [/tex]

[tex] = \frac{12}{4} [/tex] (this is equivalent to 12 ÷ 4, which is given in the question)

Thus,

12 ÷ 4 equivalent to [tex] \frac{1}{4}*12 [/tex]

Answer:

a) 2a + 3c = $44.50

     a + 2c + $25.50

b) $19

Step-by-step explanation:

Simultaneous equations. A = adult. C = children

2a + 3c = $44.50 (EQUATION 1)

a + 2c = $25.50 (EQUATION 2)

Now solve this using the method of elimination:

2a + 3c = $44.50 (EQUATION 1)

a + 2c = $25.50 (EQUATION 2)

Multiply equation 2 by 2 so that both equations have the same a coefficient.

2a + 4c = $51 (NEW EQUATION 2)

Now subtract equation 1 from equation 2:

2a - 2a + 4c - 3c = $51 - $44.50 (2a cancels out)

c = $6.50

Now substitute c into one of the equation, in this case, I'm using original equation 2.

a + 2($6.50) = $25.50

a + $13 = $25.50

a = $12.50

Total cost of one adult and child = $6.50 + $12.50

                                                       = $19

Answer:

option d

Step-by-step explanation:

hope this helps

Answer:

The last graph

Step-by-step explanation:

This is because when there is a greater than sign, the line on the graph is dotted and the shaded area is facing upwards. I try to remember that when there is a greater than sign or a greater than or equal to sign, the shaded area faces up towards the sky.

Hope this helps. Please inform me if my answer is wrong.

Answer:

The last graph is correct

Step-by-step explanation:

Hello,

First of all, you need to identify the line y = -3x + 1

This is a line so two points are enough to identify it.

-3*0+1 = 1 so (0,1) is a point of this line and

-3*1 + 1 = -2 so (1,-2) is another point of this line.

I attached a graph of this line.

Now, the inequality is y > 1-3x

It means that we are looking for the part of the plan which is (strictly) above this line.

This is not ( [tex]\geq[/tex] ) inequality but a strict equality (  > ) so the points of the line are not included, so the last graph is the correct one.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you