Find the measure of

The number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, let we had:

R numbers of red counters, and G number of green counters originally.

Then, total counters in the bag originally = R +G

One counter out of R+G counters can be chosen in R+G ways. But one green counter out of R+G counters can be chosen in G ways.

Thus, probability of taking green counter out in one random picking is:

[tex]\dfrac{G}{R + G}[/tex]

It is given that this probability is 4/9. Therefore, we get:

[tex]\dfrac{G}{R+G} = \dfrac{4}{9}\\\\\\9G = 4R + 4G\\\\5G = 4R[/tex](first equation)

When 4 more red counters and 2 more green counters were added, then:

One counter out of R+G+6 counters can be chosen in R+G+6 ways. But one green counter out of R+G+6 counters can be chosen in G+2 ways (since there are G+2 green counters in the considered bag) ways.

Thus, probability of taking green counter out in one random picking is:

[tex]\dfrac{G+2}{R + G+6}[/tex]

It is given that this probability is 10/23. Therefore, we get:

[tex]\dfrac{G+2}{R+G+6} = \dfrac{10}{23}\\\\\\23G + 46 = 10R + 10G + 60\\\\13G = 10R + 14[/tex](second equation)

Thus, we got a system of two linear equations as:

[tex]5G = 4R\\13G = 10R + 14[/tex]

From first equation, getting the value of G in terms of R,

[tex]G = \dfrac{4R}{5}\\[/tex]

Now, substituting this with G in the second equation, we get:

[tex]\\13\left(\dfrac{4R}{5} \right) =10R + 20\\\\52R = 50R + 20\\2R = 20\\R = 10[/tex]

From this value of R, and the value of G in terms of R, we get:

[tex]G = \dfrac{4R}{5}\\\\ = \dfrac{4 \times 10}{5} = 8[/tex]

Thus, R = 10 and G = 8.

Thus, the number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.

Learn more about probability here:

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Answer:

The square root of 16 is rational.

Step-by-step explanation:

Answer:

Step-by-step explanation:

V10,000 20.5121/3 21. 41/2. 22. 11/3. 23.

Answer:

20 weeks

Step-by-step explanation:

If 20 kilograms of paper have already been recycled, and the goal is 40 kilograms, subtract the 20 kg from the 40 kg. You are left with a remaining 20 kg to recycle. If the new plan has the office recycling 1 kg a week, mulitply that by 20 kg to get 20 weeks.

It will take the office 20 weeks to reach the total 40 kg of recycled paper.

Answer:

$30

Step-by-step explanation:

1.5 x 20 = 30

Answer:

to determine whether the equation of the line parallel or perpendicular.we have to find there slope.

Step-by-step explanation:

3y=15-2x

y=15/3 -2x/3

y=5-2x/3

y=-2x/3 +5

4x+6y=-48

6y=-48-4x

y=-4x/6 -48/6

y=-4x/6 -8

now to say two lines are parallel there slope should be the same

-2/3 ≠ -4/6

to say two line are perpendicular with one another the product of there slope should be -1

-2/3 * -4/6

=8/18

=4/9 which is different from -1

Answer: around i believe 10:35

Step-by-step explanation:

Answer:

its 10:20

Step-by-step explanation:

Answer:

Area of the Rectangle is (length×breadth)

[tex]5 {x}^{5} {y}^{3} \times {(7 {x}^{3}y) }^{4} = 5 {x}^{5} {y}^{3} \times 2401 {x}^{12} {y}^{4} \\ = 12005 {x}^{17} {y}^{7} [/tex]

Third option is the right answer.

Answer:

Step-by-step explanation:

it is 12.5

Answer: the answer is 12.5%

Answer:

D

Step-by-step explanation:

Answer:

x > - 15

Step-by-step explanation:

Given

36 > - 2(x + 4) + 14 ← distribute and simplify right side

36 > - 2x - 8 + 14

36 > - 2x + 6 ( add 2x to both sides )

2x + 36 > 6 ( subtract 36 from both sides )

2x > - 30 ( divide both sides by 2 )

x > - 15

Answer:

(the last one)

Step-by-step explanation:

Hi there!

This looks like a diagnostic. I had to take one last week and it was horrible!

Anyway, the numerator is the product of 5 and the sum of x and y, which can be written as 5(x+y)

The denominator is the product of negative 8 and x, which can be written as -8x.

I hope this helped!

Answer:

630.

Step-by-step explanation:

Given the following data;

Dimensions for cube = ¼ inches

[tex] Volume \; of \; cube = \frac {1}{4} * \frac {1}{4} * \frac {1}{4} [/tex]

Volume = 1/64 cubic inches.

For rectangular box;

Length = 2½ = 5/2 inches.

Width = 2¼ = 9/4 inches.

Height = 1¾ = 7/4 inches.

[tex] Volume \; of \; cube = \frac {5}{2} * \frac {9}{4} * \frac {7}{4} [/tex]  

Volume = 315/32 inches

Therefore, to find the amount of cubes;

[tex] Number \; of \; cubes = \frac {Volume \; of \; box}{Volume \; of \; cube} [/tex]

Substituting into the equation, we have;

[tex] Number \; of \; cubes = \frac {\frac {315}{32}} {\frac {1}{64}} [/tex]

[tex] Number \; of \; cubes = \frac {315}{32} * 64 [/tex]

[tex] Number \; of \; cubes = 315 * 2 [/tex]

Number of cubes = 630

Answer: x = 5

Step-by-step explanation:

Based on the information, the number is x= 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Consider that the number be x.

Given that;

Tripling the number we get = 3x.

On subtraction from 28, the equation will be: 28 - 3x.

Now forming the equation for result. Twice the number will be 2x. Result = 2x + 3.

Now equating these two equations as;

28 - 3x = 2x + 3

Rewriting the equation as;

3x + 2x = 28 - 3

Now, addition on Left Hand Side and subtraction on Right and Side

5x = 25

x = 25 ÷ 5

Performing division on Right Hand Side, we get;

x = 5

Learn more about equations here;

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Answer:

Step-by-step explanation:

Change the 2/3 to 4/6

Now the ratio becomes 3:4:6

So the number of each is

3x + 4x + 6x = 520

13x = 520

x = 40

Red = 3*40 =      120

Yellow = 4*40 = 160

Blue = 6 * 40  = 240

Total =               520

Answer:

The equation of line with  slope: -3 and y-intercept: -6​ is [tex]\mathbf{y=-3x-6}[/tex]

Step-by-step explanation:

We need to write an equation of the line with the given slope and y-intercept. slope: -3 ,y-intercept: -6​

The general equation for slope-intercept form is: [tex]y=mx+b[/tex]

where m is slope and b is y-intercept.

We are given in the question:

slope: -3 y-intercept: -6​

So, we have slope m = -3 and y-intercept b = -6

Putting values in the slope-intercept form equation:

[tex]y=mx+b\\y=-3x-6[/tex]

So, The equation of line with  slope: -3 and y-intercept: -6​ is [tex]\mathbf{y=-3x-6}[/tex]

Answer: 6.7inch

Step-by-step explanation:

From the question, we are informed that Emma made a scale model of the Sam Houston's monument and that the monument's actual height is 67 ft tall but Emma is using a scale where 1 inch is 10 ft.

The height of Emma's model will therefore be 67ft divided by 10 since he's using a scale of 1:10. This will be:

= 67/10

= 6.7inch

Answer:

55 seconds

Step-by-step explanation:

Okay so, 1/12 of a minute would be 5 seconds. 10/12 would be 50 seconds. You go up 5 continuously.

Step-by-step explanation:

1book valume = 25cm×20cm×2cm=1000cm³

a packet valume = 6×1000cm³ = 6000cm³

Answer:

216000 cm3

Step-by-step explanation:

length of packet = 6 × 25 cm = 150 cm

breadth of packet = 6 ×20 cm = 120 cm

height of packet = 6 × 2 cm = 12 cm

Now,

volume of packet = l×b×h = 150 cm × 120 cm × 12 cm

= 216000 cm3

Answer:

AB = 12.5

Step-by-step explanation:

BX is an altitude and a median. That means that triangle ABC is isosceles.

AB = CB

AB = 12.5

9514 1404 393

Answer:

Step-by-step explanation:

Use the distributive property to distribute the outside minus sign to all terms inside parentheses.

1) 5.5x +1 -(1.5x +17) = 5.5x +1 -1.5x -17 = x(5.5 -1.5) +(1 -17)

  = 4x -16

__

2) x -3x -(-5x) = x -3x +5x = x(1 -3 +5)

  = 3x

Answer:

12x + 2

Step-by-step explanation:

4 ( 2x + 1 ) ⇔ 8x + 4

2 ( 2x - 1 )​ ⇔ 4x - 2

8x + 4 + 4x - 2 = 12x + 2

Answer:

f(x) = -100(1.05)^(x+5) + 50

Step-by-step explanation:

Here, we want to write an equation that represents the transformation

5 units right means 5 units on the positive x-axis

50 units up means we add this to the total y value

So the resulting equation will be;

f(x) = -100(1.05)^(x+5) + 50

Answer:

Look at explanation

Step-by-step explanation:

3x - y = 14

-3         -3

x=11

-------------------------------------------------

5x + 4y = 12

9xy=12

-9     -9

xy=3

x=1.5 y=1.5

--------------------------------------------------------

total= 14

Sorry if wrong btw

Answer:

[tex](4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = - 3 {n }^{2} + 4n + 1 \\ ( - 3 {n}^{2} - 3n) - (1n + 1) \\ - 3n(n + 1) - 1(n + 1) \\ (n + 1)( - 3n - 1) \\ n = - 1 \\ n= \frac{1}{ - 3} [/tex]

Answer:

[tex]f(n) - g(n) = (4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = \boxed{4n - 3 {n}^{2} + 1}[/tex]

Answer:

2. 260

3. 16

4. 71

5. 47

6. 137

8. 23

Step-by-step explanation: