there are only r red counters and g green counters in a bag. a counter is taken at random from the bag. the probability that the counter is green is 4/9 the counter is put back in the bag. 4 more red counters and 2 more green counters are put in the bag. a counter is taken from the bag. the probability that the counter is green is 10/23 find the number of red counters and the number of green counters that were in the bag originally. your final line must say, ... red and ... green counters.

There Are Only R Red Counters And G Green Counters In A Bag. A Counter Is Taken At Random From The Bag.

Answers

Answer 1

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

How to calculate the probability of an event?

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:

Number of red counters in modified bag = R + 4Number of green counters in modified bag = G + 2Number of total counters in modified bag = R + 4 + G+ 2 = R + G + 6

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:

brainly.com/question/1210781


Related Questions

favorite food pizza35 hotdog30 hamburger 200 whta percatage is all student's count

Answers

Answer:

265

Step-by-step explanation:

200+30=230

230+30=260

260+5=265

The access code for a car's security system consists of four digits. The second digit cannot be zero and the last digit must be odd. How many different codes are available?

Answers

Answer:

4,500 different codes.

4,500 codes your welcome

how do you solve it tho

Answers

Answer:

solve what

Step-by-step explanation:

there's no question

Answer:

you forgot the picture lol

c) The area of a rectangle is 80 cm² and it is 8 m broad.In process
(i) Find its length (ii) Find its perimeter
11​

Answers

Answer:

i) the length is 10cm

ii) the perimeter is 36 cm

Step-by-step explanation:

i) We know that Area of a rectangle can be found by using the following formula...

A = l x w

(where A is area of the triangle, l is the length of the triangle, and w is the width of the rectangle).

From this we know that

l = A/w

[tex]l = 80cm^{2} / 8cm = 10cm[/tex]

ii) Now that we know both the length and the width we know we can find the perimeter by using the following formula...

P = 2(l + w)

[tex]P = 2(10cm+ 8cm )\\P = 20cm + 16cm\\P = 36cm[/tex]

The half-life of a radioactive kind of iodine is 60 days. How much will be left after 240 days, if you start with 480 grams of it?

Answers

Answer:

30 grams

Step-by-step explanation:

half life is 60 days so every 60 days the amount 480 grams will be half

in 240 days will decay  240 /60 = 4 times

once 480 /2 = 240

twice 240 /2 = 120

trice 120 / 2 = 60

four times 60/2 = 30 grams will be left

NOBODY HAS HELPED ME TODAY ??? please help me !!!

Answers

AB/AD = BC/DE
28/20 = 2x+3/15
28(15)/20 = 2x+3 = 2x+3 = 21
2x=18
x=9

25% of a number is 8.
What is the original number?

Answers

Answer:

B. 32

Step-by-step explanation:

25% is 1/4 of 100%, so you multiply 8 by 4.

Graph y+9=−3x. please help me

Answers

Well, first thing we need to do is put this in slope intercept form of y.

Subtract 9 from both sides to isolate "y".

y= -3x-9

Now we can graph the equation

Graph the point (0,-9) since it is the y-intercept.

To get the x intercept, isolate the "x" variable instead of "y".

y+9 = -3x

(Divide every number on both sides of the equation by -3 to isolate "x".)

y/-3 -3= x

now that this is in slope intercept form of x, plug in 0 for y to get the number for x when y is 0.

0/-3 -3 = x

-3 = x.

Graph (-3, 0). Connect this point to the point (0,-9) and you get have successfully graphed the equation y+9= -3x.

I hope this helped.

Write an algebraic expression for s decreased by nine

Answers

Answer:s-9

Step-by-step explanation: Decreased means subtract . and you are subtracting s from 9.

Hope it helps

Please help, pic attached!

Answers

Answer:

(y − 9) (y − 2)

Step-by-step explanation:

Factor  y^2 − 11y + 18 using the AC method.

(y − 9) (y − 2)

The “AC” method or factoring by grouping is a technique used to factor trinomials. A trinomial is a mathematical expression that consists of three terms.

Please help me would be very appreciated.

Answers

Answer:

C

Step-by-step explanation:

Answer for this question is c

On the blueprints for a building, 8 inches represents 28 feet. If the blueprints show a distance of 16 inches
between the two walls, how many feet separate the walls?

Answers

Answer:

56 feet

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

{(1, 7.6) (2, 7.2) (3, 6.8) (4, 6.4) (5, 6) (6, 5.6)}

Is this a function or no?

Answers

Answer:

Yes

Step-by-step explanation:

Let's put them vertically because that helps me explain this

x, y

1, 7.6

2, 7.2

3, 6.8

4, 6.4

5, 6

6, 5.6

                                           

For this to be a function there should be one output for every input, the y coordinates are our outputs and as you can see none of them repeat so this is a function.

Which property is demonstrated by the equation (5 + a) + 3 = (a + 5) + 3?

Answers

Answer:

Communitive Property

Step-by-step explanation:

Commutative property = 2 + 3 = 3 + 2 or 2(3) = 3(2)

Associative Property = (2 x 3) 5 = 2 (3 x 5) or (2 + 3) + 5 = 2 + (3 + 5)

Inverse Property = 2 + (-2) = 0 or (2/1)(½) = 1

Basic Definitions:

Commutative Property - Gives you the ability to switch the order of the numbers in an expression.

Associative Property - Let's you move the parenthesis in an expression but not the numbers.

Inverse - Uses numbers like 0 and 1.

Using these basic definitions and examples, we can summarize that the best answer would be Communitive Property

i don't need the work just the answer!!

Answers

i believe that it’s y=5x

hi, can you please do these? thanks for helping!​

Answers

Answer:

i will answer you other if u rate me brainliest

Answer: (A) 1/10: 5 9/10 :5/6

(B) 3 3/4: -2 7/50

(C) 8 5/8 : 4/9

(D)2 2/5: 2 67/210: -2 2/3

(E)-1 1/2 : 81/128

Step-by-step explanation:

hopes this helps

Whos your favorite operator in rainbow six seige

Answers

Answer:

It has to be Maverick how about u

Step-by-step explanation:

Answer:

Niclas "Pengu" Mouritzen

Step-by-step explanation:

Find c.
Round to the nearest tenth:
2 cm
15°
105

Answers

Answer:

0.5cm

Step-by-step explanation:

Using the sine rule

Answer:

c = 0.5 cm

Step-by-step explanation:

Using the Sine rule in the triangle, then

[tex]\frac{c}{sin15}[/tex] = [tex]\frac{2}{sin105}[/tex] ( cross- multiply )

c × sin105° = 2 × sin15° ( divide both sides by sin105°

c = [tex]\frac{2sin15}{sin105}[/tex] ≈ 0.5 cm ( to the nearest tenth )

4/3=-6e-5/3

solve for "E" plz

Answers

Answer:

e=-1/2

Step-by-step explanation:

4/3=-6e-5/3

Multiply both sides by 3:

4=-18e-5

Add 18e to both sides:

18e+4=-5

Subtract 4 from both sides:

18e=-9

Divide both sides by 18:

e=-1/2

*You don't have to, but I am currently trying to reach the next level, and all I need is some more brainliest answers. If you think my answer was brainly enough, you can make my answer the brainliest, but no pressure. I just help people for fun! :) Thank you, have a great day!*

Write the slipe-intercept form of the equation of each line given the slope and y-intercept.

Please helppp!!!! i will give brainliest!!

Answers

Answer:

1. -1/2

2. 3/-2

3. 1/2/2

4. 7/2

Step-by-step explanation:

Hope it helped

Use the domain (1/2, 1, 2, 4, 8) to plot the points on the graph for the given equation. The grid marks represent one unit,
the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
y = log 2 x

Answers

According to values of a function we can plot the points on a graph.

What is domain?

Domain is the value which we used to enter in a function to get the value of a function.

How to plot the points on the graph?

We have been given the domain of the function and we have to plot the value in the graph.

F(1/2)=log1=0

F(1)=log2=0.3

F(2)=log4=0.6

F(4)=log8=0.9

F(8)=log16=1.2

Learn more about graphs at https://brainly.com/question/4025726

#SPJ2

(01.05)
What is the equation, in slope-intercept form, of the line that passes through (0, -2)
and has a slope of -3? (5 points)
O 1) y = -3x - 2
O 2 y=-3x+ 2
O3) y = –2x+3
O 4) y = -2x - 3

Answers

Answer:

O1

Step-by-step explanation:

Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

We are given a point: (0,-2) and a slope; -3.

we can substitute the numbers into the equation above, with what we know, to find b.

-2=-3(0)+b

multiply

-2=0+b

-2=b

so the y intercept is -2.

Since we know that the slope is -3, and the y intercept is -2, the equation is y=-3x-2

Therefore O1 is your answer

Hope this helps!

If DF=70, find the value of x.

Answers

Answer:

x = 12

Step-by-step explanation:

DE + EF = DF

2x - 1 + 5x - 13 = 70

7x - 14 = 70

7x = 70 + 14

    = 84

x = 84 ÷ 7

x = 12

Answer: x=12

Step-by-step explanation:

2x-1+5x-13=70

Combine like terms

7x-14=70

Add 14 to both sides

7x=84

Divide both sides by 7

X=12

An airplane prepares for landing. When it begins its descent towards the airport, the plane's
altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000
feet. Write an equation for the altitude of the plane. What will the altitude of the plane be after
descending for 12 minutes?

Answers

27,000 - 19,000 = 8,000
it descended 8,000 feet in 6 minutes

so in 12 minutes it would of descended 16,000 feet, it’s doubled

19,000-8000= 11,000

The required equation represents the descent motion of the airplane is y = 27000 - 1333.333x and 11000 feet.

Given that,
An airplane prepares for landing. When it begins its descent towards the airport, the plane's altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000 feet. Write an equation for the altitude of the plane.

What is the slope of the line?

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope of the motion of the airplane,
m = 27000 - 19000 / 6 = 1333.33
The equation of the plane is given as,
y - y₁ = m (x - x₁)
Substitute the value in the above equation,
y - 27000 = -1333.33[x - 0]
y = 27000 - 1333.33x

Now put x = 12 in above equation,
y = 27000 - 1333.33[12]
y = 11000

Thus, the required equation represents the descent motion of the airplane as y = 27000 - 1333.333x and 11000 feet.

Learn more about slopes here:
https://brainly.com/question/3605446

#SPJ2

Suppose there are 21 students in your class. If the teacher draws 2 names at random, what is the probability that you and your best friend will be chosen?


1/20

1/105

1/210

2/21​

Answers

Answer:

2/21

Step-by-step explanation:

Probability = expected outcome/ possible outcome

2/21 is ur answer because u got 2 people outta a 20 chance of drawing that student

Mmmm! I love apple cider punch this time of year, and so do all my neighbors. My recipe calls for two quarts of apple cyder, three teaspoon of cinnamon, and one pint of lemon-lime soda. This will make enough for 8 people to share. In my neighborhood, however, there are 36 people. How much do I need for each ingredient to make enough for everyone?​

Answers

Answer:

j

Step-by-step explanation:

Which function shows a fabric with a price of $1.25 per square yard?

Answers

Answer:

D

Step-by-step explanation:

Pls help it due in a hour and show workings...

Answers

I think 11 miles but I’m not 100% hope I helped ;)

Need help with explicit rule. Please help.

Answers

Answer:

An = 74(1.07)^n-1

Step-by-step explanation:

Here, we want to get the explicit rule

We are told that the sequence is geometric

At hour 4, we have that this is the 4th term

With conformance to the rule of geometric progression;

T4 = ar^3

90 = ar^3

for the 6th hour, this is the sixth term

103 = ar^5

dividing the 6th term by the 4th term, we have that

103/90 = ar^5/ar^3

103/90 = r^2

r = 1.07

To get a, we simply use any of the terms to substitute

using;

ar^3 = 90

a = 90/r^3

a = 90/1.07^3

a = 73.5 which is approximately 74

So the explicit rule is as follows;

An = 74(1.07)^n-1

PLEASE HELP URGENT!!

An irregular polygon is shown below:

A: 21 Square Inches

B: 22 Square Inches

C: 26 Square Inches

D: 29 Square Inches

Answers

Answer:

[tex]26\:\mathrm{in^2}[/tex]

Step-by-step explanation:

The irregular polygon is made of a large rectangle with two smaller rectangles cut out of it. Therefore, we can find the area of the large rectangle and subtract these two smaller rectangles:

[tex]10\cdot 5-2\cdot3\cdot4=50-24=\fbox{$26\:\mathrm{in^2}$}[/tex].

Other Questions
Write one sentence that contain past tense Please! Help! Me!The next question refers to the following passage. The sentences have been numbered to help you identify them more easily.(1) As she was driving to visit her twin, Jayla had a strange feeling that something bad was going to happen.(2) Meanwhile, Kayla had the same exact premonition.(3) Worried about her sister, Kayla called Jayla's cell phone.(4) Because she took her eyes off the road to answer the phone call, Jayla lost control of her car and crashed through the front of Kayla's house.What is the function of the introductory word in sentence 2? a. It refers to the person being addressed.b. It is a transition word.c. It provides a short answer.d. It creates a short delay. The following stemplot displays the number of forest fires (the stem is in tens of thousands) that occurred each year over the period from 1980 to 2012.4 | 0244778895 | 0012222344778886 | 023787 | 348How many data values are in this data set? HELP ME PLZZZ!!!!!!Complete the following sentence.The Copernican Revolution changed Europe's blank view. wilbur has sold 100, 42,87, and 66 appliances in the last four months, respectively. How many appliances will he need to sell this month to maintain an average of at least 72 sales per month? f(x)=3x-5 please help :> i need help with this !!!! What is an example of a beneficial mutation? The answer can't be:HIV ResistanceBone densityMalaria resistancePlease help, I have to get this assignment turned in by today Find the missing slant height An alpha particle has the same composition as a A) hydrogen nucleus B) deuterium nucleus C) beryllium nucleus D) helium nucleus Arianna buys computer games from an online store. Each game she orders costs $25, and shipping for her total order is $10. Arianna wants to spend $110. How many computer games can Arianna buy? Create an equation for the problem here. please help im so lost lol Ancient Greeks created works that expressed the ideals of a form, beauty, and harmony b beauty, reason, and balance c reason, balance, and harmony d harmony, balance, and beauty plzzz guys help I'm so confused At the beginning of a population study, a city had 320,000 people. Each year since, the population has grown by 4.8%. Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t. Even though Prince Prospero is the Protagonist, he isn't necessarily the "good guy." Why is he still considered the protagonist? Six rolls of fabric are used for making five dresses equally.How much fabric is used for each dress? An increase in aurora activity on Earth could be related to what activity on the Sun?O A decrease in prominenceB decrease in solar FaresOc decrease in speed of solar windD increase in speed of solar windE increase in sun spots Why is it important that charters and ordinances do not violate state and federal laws? Solve the following inequality:2. 4x + 6 < 38 Which professional has helped Jennifer in this example?Jennifer bought a new smart phone from a local store that sells electronic products. After a week, she started experiencing problems with thephone's display screen. She went back to the store and spoke to its ___representative, who replaced the product andapologized for the inconvenience.