The population of a rabbit colony triples each month.

The population started with 5 rabbits. How many

rabbits are there after 6 months?

Answers

Answer 1

Answer:

3645 rabbits after 6 months.

Step-by-step explanation:

The population of a rabbit colony triples each month.

This means that the population of the colony after t months is given by:

[tex]P(t) = P(0)(3)^t[/tex]

In which P(0) is the initial population.

The population started with 5 rabbits.

This means that [tex]P(0) = 5[/tex]

So

[tex]P(t) = 5(3)^t[/tex]

How many rabbits are there after 6 months?

This is P(6). So

[tex]P(6) = 5(3)^6 = 3645[/tex]

3645 rabbits after 6 months.


Related Questions

3p + 7q = 55
7p + 7q = 91
What is p and q

Answers

Step-by-step explanation:

3p + 7q = 55

7p + 7q = 91

(-)

-4p=-36

p=9

q=4

Answer:

p = 9 and q = 4

Step-by-step explanation:

3p + 7q = 55 -- (1)

7p + 7q = 91 -- (2)

(2) - (1) : 4p = 36

               p = 9 -- (3)

Substituting (3) into (1),

27 + 7q = 55

7q = 28

q = 4 -- (4)

Therefore, p = 9 and q = 4

If this helps you, please mark brainliest!

Have a nice day!

At the start of a month, Sasha and Natalia each have a certain amount of money.
Sasha has $400 and saves $20 each week. The graph below shows the amount of money in Natalia's account each week
Whose monthly activity shows a greater rate of change, and by how much?
A) Sasha, by $10/week
B)Sasha, by $19/week
C) Natalia, by $10/week
D) Natalia, by $19/week

Answers

Answer:

Option (A)

Step-by-step explanation:

Sasha has an amount of $400 and saves $20 per week.

If we graph the savings of Sasha, her savings per week will be defined by the slope of the line = $20 per week

Similarly, from the graph attached,

Slope of the line given in the graph = Per week savings of Natalia

Slope of line passing through (0, 190) and (2, 210) will be,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{210-190}{2-0}[/tex]

          = 10

Therefore, per week savings of Natalia = $10

Difference in savings of Sasha and Natalia = 20 - 10 = $10 per week

Here, Sasha shows the greater rate of change by $10 per week

Therefore, Option (A) will be the answer.

Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The length of side Y X is 9 centimeters.
The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Select two options.

YZ = 9 cm
XZ = 9 cm
XZ = 9 StartRoot 2 EndRoot cm
XZ = 2(XY)
YZ is the longest segment in △XYZ.

Answers

ANSWER: YZ=9 cm bc of the right angle

The side YZ=9 cm of the right angle

We have given that,

Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The length of side Y X is 9 centimeters.

The length of segment XY is 9 cm.

We have to determine the statements regarding triangle XYZ are correct.

What is the right angle triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular.

The right angle with angles 45-45-90 has two side same.

Therefore the side YZ=9 cm bc of the right angle

To learn more about the right-angle triangle visit:

https://brainly.com/question/64787

#SPJ5

3.) If y varies directly as x and y = 24 when x = 6, find the variation constant and the equation of variation.​

Answers

Problem:-

3.) If y varies directly as x and y = 24 when x = 6, find the variation constant and the equation of variation.

Solution:-

A. Express the statement “y varies directly as x”, as y = kx .

B. Solve for k by substituting the given values in the equation.

[tex]\sf\rightarrow{y = kx}[/tex]

[tex]\sf\rightarrow{24 = 6k}[/tex]

[tex]\sf\rightarrow{K = \frac{24}{6} }[/tex]

[tex]\sf\rightarrow{K={\color{magenta}{4}}}[/tex]

Answer:-Therefore, the constant of variation is 4.

C. Form the equation of the variation by substituting 4 in the statement y = kx. Thus , y = 4 x.

[tex]{\large{—————————————————————}}[/tex]

#CarryOnMath⸙

Raj is travelling to another country.
He flies for 5 hours at an average speed of 950 km/h on one plane.
He then flies for 6 hours 30 minutes at an average speed of 830 km/h on a second plane.
What is the total distance, in km, he travelled by plane?

Answers

Answer:

10145

Step-by-step explanation:

5 times 950 equals 4750

and 6.5 times 830 equals 5395

add first and second value

4750 + 5395 equals 10145

there is no arguing

Answer:

10145 km

Step-by-step explanation:

Time x speed = Distance

5 x 950 = 4750

6.5 x 830 = 5395

add together = 10145

As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 100 milligrams of Medication A with 80 milligrams of Medication B. However this week, the doctor said to only use 16 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?

Answers

Answer:

Step-by-step explanation:

20 milligrams

Written as a simplified polynomial in standard form, what is the result when
(2x + 4)^2 is subtracted from 7x^2-10x-10?

Answers

(7x^2 - 10x - 10) - (2x + 4)^2

(7x^2 - 10x - 10) - (4x^2 + 8x + 8x + 16)

(7x^2 - 10x - 10) - (4x^2 + 16x + 16)

(7x^2 - 4x^2) + (- 10x - 16x) + (- 10 - 16)

3x^2 - 26x - 26

The weights of a certain dog breed are approximately normally distributed with a mean of 49 pounds, and a standard deviation of 6 pounds. Use your graphing calculator to answer the following questions. Write your answers in percent form.

Required:
a. Find the percentage of dogs of this breed that weigh less than 53 pounds.
b. Find the percentage of dogs of this breed that weigh less than 49 pounds.
c. Find the percentage of dogs of this breed that weigh more than 49 pounds.

Answers

Answer:

a. 74.86%

b. 50%

c. 50%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 49 pounds, and a standard deviation of 6 pounds.

This means that [tex]\mu = 49, \sigma = 6[/tex]

a. Find the percentage of dogs of this breed that weigh less than 53 pounds.

The proportion is the p-value of Z when X = 53. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{53 - 49}{6}[/tex]

[tex]Z = 0.67[/tex]

[tex]Z = 0.67[/tex] has a p-value of 0.7486.

0.7486*100% = 74.86%, which is percentage of dogs of this breed that weigh less than 53 pounds.

b. Find the percentage of dogs of this breed that weigh less than 49 pounds.

p-value of Z when X = 49, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 49}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5

0.5 = 50% of dogs of this breed that weigh less than 49 pounds.

c. Find the percentage of dogs of this breed that weigh more than 49 pounds.

1 subtracted by the p-value of Z when X = 49, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 49}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5.

1 - 0.5 = 0.5 = 50% of dogs of this breed that weigh more than 49 pounds.

Answer the following: a) 2x32 =
b) (2 x 3)2 =

Answers

Answer:

a) 64 b) 12

Step-by-step explanation:

32 + 32 = 64

2*3 = 6

6*2 = 12

Answer:

a) 64 b) 12

Step-by-step explanation:

The answer for a is simple the answer is 64 just multipy 32 with 2 and the second one first you have to solve he answer iin the bracket then the answer you get from the bracket you will have to multiply with the number outside the bracket which is 2 and the answer you get will be 12.

If a obtuse triangle Has a base of 9in an 13in height what is the area triangle?

Answers

Multiple 9 and 13 after that

Which of the quadratic functions has the narrowest graph?

y = 2x^2
y = –x^2
y = 1/8x^2
y = 1/6x^2

Answers

A quadratic function's graph being wide or narrow is determined or depended on a-term:

[tex] \large{y = a {x}^{2} + bx + c}[/tex]

If |a| has a lot of value, for example a = 2 or a = 100. The graph will get narrower if increasing the value of |a|. On the other hand, If |a| has small value, for example a = 1/2 or a = 1/10000. The graph would be wide.

Also it does not matter if a-term is negative or not since a-term being positive or negative determines if a parabola is upward or downward. Only |a| determines how narrow/wide the graph is.

From the question, it is clear that the parabola y = 2x^2 is the narrowest graph since it has the highest |a| value out of all choices.

Answer

y = 2x^2

Help! 3-4 quick please!!

Answers

3: independent
4: dependent

Can I get some help with my homework

Answers

Answer:

1) 37

2) 23

3) 4

4) 58

5) 67

6) 7

7) x = 14

  BC = 27

  CD = 61

  BD = 88

Step-by-step explanation:

1) Add them

2) Subtract them

3) Add them and set equal to 36

6x + 1 + x + 7 = 36

4) Add them and set equal to 9x - 39

47 + 3x + 10 = 9x - 39

Substitute x into 3x + 10 to find EF

5) Add them and set equal to 6x - 35

19 + 4x - 20 = 6x - 35

Substitute x into 6x - 35 to find UW

6) Add them and set equal to 7x-27

3x - 5 + x - 1 = 7x - 27

7) Add them. Solve for x and substitute.

4x - 29 + 5x - 9 = 7x - 10

Find the value of 100-98+96-94+92-90+...+8-6+4-2

Answers

Answer:

10

solution

100-98 =2

96-94 = 2

92-90 = 2

8-6 = 2

4-2 =2

2+2+2+2+2=10✓

Assume that in a statistics class the probability of receiving a grade of A equals .30 and the probability of receiving a grade of B equals .30. The probability that a randomly selected student from this class will receive either an A or a B equals:________

a. 0.09
b. 9
c. 6
d. 3

Answers

Answer:

c. 0.6

Step-by-step explanation:

A student cannot receive an A or a B simultaneously, so [tex]P(A \cap B) = 0[/tex].

Grade of A equals .30 and the probability of receiving a grade of B equals .30.

This means that [tex]P(A) = P(B) = 0.3[/tex]

The probability that a randomly selected student from this class will receive either an A or a B equals:

This is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.3 + 0.3 - 0 = 0.6[/tex]

So the probability is 0.6, and the correct answer is given by option c.

write an equation for the line parallel to y=-3x+4 that contains P(1,4)

Answers

Answer:

y = -3x + 7

Step-by-step explanation:

If the line is parallel, it will have the same slope. So, this line will have a slope of -3.

Plug in the slope and given point into y = mx + b, and solve for b:

y = mx + b

4 = -3(1) + b

4 = -3 + b

7 = b

Plug in the slope and y intercept into y = mx + b

y = mx + b

y = -3x + 7

So, the equation is y = -3x + 7

Find the selling price of a $32 item after a 50% markup.
The selling price is $

Answers

Answer:

The new price is 48

Step-by-step explanation:

First find the markup

50% of 32

.5 * 32 = 16

Add the markup to the original price

16+32 = 48

The new price is 48

Answer:

$48

Step-by-step explanation:

32 * 0.50 = 16

32 + 16 = 48

Hope this is helpful

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = 1 + 2√t, y = t3 - t, z = t3 + t; (3,0,2)

Answers

Solution :

Given parametric equation for :

[tex]$x=1+2 \sqrt t$[/tex]

[tex]$y=t^3-t$[/tex]

[tex]z=t^3+t[/tex]

The point is (3, 0, 2)

The vector equation is equal to :

[tex]$r(t) = \left<1+2 \sqrt t, t^3 -t, t^3+t \right>$[/tex]

Solving for r'(t) by differentiating each of the components of r(t) w.r.t. to t,

[tex]$r'(t)= \left< \frac{1}{\sqrt t}, \ 3t^2-1, \ 3t^2+1 \right>$[/tex]

The parameter value corresponding to (3, 0, 2) is t = 1. Putting in t=1 into r'(t) to solve for r'(t), we get

[tex]$r'(1) = \left< \frac{1}{\sqrt 1}, \ 3(1)^2-1, \ 3(1)^2+1 \right>$[/tex]

We know that parametric equation for  line through the point [tex]$(x_0, y_0, z_0)$[/tex]  and parallel to the direction vector <a, b, c > are

[tex]$x=x_0+at$[/tex]

[tex]$y=y_0+bt$[/tex]

[tex]z=z_0+ct[/tex]

Now substituting the  [tex]$(x_0, y_0, z_0)$[/tex]   = (3, 0, 2) and  <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get:

[tex]$x=3+(1)t$[/tex]

x  = 3 + t

y = (0) + (2)t

y = 2t

z = (2) + (4)t

z = 2 + 4t

question 7.
identify the zeros of the graphed function
A) -2,2
B)-2,0,2
C)-2
D)2

Answers

Answer:

-2,0 0,-8 , 2,0 hope that helps

Gerald is thinking of a number n, and he wants his sister to guess the number. His first clue is that 7 more than 3 times his
number is at least 10 and at most 28. Write a compound inequality that shows the range of numbers that Isabella might be
thinking of.
Write your answer in interval notation. For example-3

Answers

Answer:

(1, 7)

Step-by-step explanation:

The number is n.

7 more than 3 times his

number is at least 10 and at most 28.

Thus;

10 ≤ 3n + 7 ≤ 28

Let's solve individually;

10 ≤ 3n + 7

10 - 7 ≤ 3n

n ≥ 3/3

n ≥ 1

Also,

3n + 7 ≤ 28

3n ≤ 28 - 7

3n ≤ 21

n ≤ 21/3

n ≤ 7

Thus, since n cannot be more than 7 or less than 1, it means in interval Notation, the answer is;

(1, 7)

Zoe draws ABC on the coordinate plane.
ТУ
B
5
4
3
2.
1
А
ol
1
12
13
4
5
What is the approximate perimeter of AABC to the nearest hundredth?
O A 8.47 units
o
B
12 units
C 12.94 units
O D. 15.31 units

Answers

Answer:

12.94 units

Step-by-step explanation:

Perimeter of ∆ABC = AB + BC + AC

✔️Distance between A(1, 1) and B(3, 5):

[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] A(1, 1) = (x_1, y_1) [/tex]

[tex] B(3, 5) = (x_2, y_2) [/tex]

[tex] AB = \sqrt{(3 - 1)^2 + (5 - 1)^2} [/tex]

[tex] AB = \sqrt{(2)^2 + (4)^2} [/tex]

[tex] AB = \sqrt{4 + 16} [/tex]

[tex] AB = \sqrt{20} [/tex]

AB = 4.47 units

✔️Distance between B(3, 5) and C(5, 1)

[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] B(3, 5) = (x_1, y_1) [/tex]

[tex] C(5, 1) = (x_2, y_2) [/tex]

[tex] BC = \sqrt{(5 - 3)^2 + (1 - 5)^2} [/tex]

[tex] BC = \sqrt{(2)^2 + (-4)^2} [/tex]

[tex] BC = \sqrt{4 + 16} [/tex]

[tex] BC = \sqrt{20} [/tex]

BC = 4.47 units

✔️Distance between A(1, 1) and C(5, 1):

AC = |1 - 5| = 4 units

✅Perimeter of ∆ABC = 4.47 + 4.47 + 4 = 12.94 units

a number is 2 more than 3 times the other number if the is 26 then the number are​

Answers

Answer:

80

Step-by-step explanation:

more in math means add

if you multiply three by 26 is 78 + 2 would be 80  

PSA im not great in math

Can you solve this problem

Answers

Answer:

x = 18

Step-by-step explanation:

8 x 18 - 3 = 141

The answer is to your question is 18

Point A has coordinates (-24, -54)
Point B has coordinates (40, -46)
Find the equation of the perpendicular bisector of line AB.
ANSWER ASAP

Answers

Answer:

[tex]y=-8x+14[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

A perpendicular bisector of a line segment is 1) perpendicular to the line segment and 2) passes through the midpoint of the line segmentPerpendicular lines always have slopes that are negative reciprocals (ex. -2 and 1/2)Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of  when x is 0)

1) Determine the midpoint of the line segment

Midpoint: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] where the coordinates of the endpoints are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the endpoints (-24, -54) and (40, -46)

[tex](\frac{-24+40}{2} ,\frac{-54+(-46)}{2} )\\(\frac{-24+40}{2} ,\frac{-54-46}{2} )\\(\frac{16}{2} ,\frac{-100}{2} )\\(8 ,-50)[/tex]

Therefore, the midpoint of line AB is (8,-50).

2) Determine the slope of the line segment

This will help us find the equation of the perpendicular bisector.

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the endpoints (-24, -54) and (40, -46)

[tex]= \frac{-46-(-54)}{40-(-24)}\\= \frac{-46+54}{40+24}\\= \frac{8}{64}\\= \frac{1}{8}[/tex]

Therefore, the slope of line AB is [tex]\frac{1}{8}[/tex].

3) Determine the slope of the perpendicular bisector

Because perpendicular lines always have slopes that are negative reciprocals, the slope of the perpendicular bisector is -8 (the negative reciprocal of 1/8). Plug this slope into [tex]y=mx+b[/tex]:

[tex]y=-8x+b[/tex]

4) Determine the y-intercept (b) of the perpendicular bisector

[tex]y=-8x+b[/tex]

Recall that we found the midpoint of line AB, (8,-50). The perpendicular bisector passes through this point. Plug (8,-50) into [tex]y=-8x+b[/tex] and solve for b:

[tex]-50=-8(8)+b\\-50=-64+b[/tex]

Add 64 to both sides to isolate b

[tex]-50+64=-64+b+64\\14=b[/tex]

Therefore, the y-intercept of the line is 14. Plug this back into [tex]y=-8x+b[/tex]:

[tex]y=-8x+14[/tex]

I hope this helps!

Consider this as a simultaneous-move (static) game:
Player B
Left Right
Top 2, 2 3, 2
Player A
Bottom 1, 3 1, 4
1a) Write down the Best Response Correspondence for each of the two players.
1b) Does any player have a dominant strategy in this game? Explain.
1c) Find all Nash Equilibria in pure strategies of this game.
1d) Is there any Nash Equilibria in mixed strategies?

Answers

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

For point a:

When Player A selects Top, Player B selects Left or Right.

Player B selects Right when player A selects Bottom

Thus, player B's best statement is correct.

When player B selects the left, then game A selects the top

When player B selects the right, player A selects the top

Hence, Player A's right response is Top.

For point b:

The main strategy inside the game is Player A, which would be Top. Since he won't choose Below except under situations since the payment to Bottom is below his payoff for Top irrespective of player B.

For point c:

Player A will purely pick Top & Player B right and player A also will pick Top and player B is right. Game A will's pattern. In this case, neither player has the motive to move away. There are two Nash balances since player B is paid the same amount, irrespective of what he's playing any strategy, as player A is always at the top.

For point d:

Consider if player B plays left with "q" probability and right with "1-q" probability. We're done

[tex]2q + 2(1-q) = 3q+4(1-q) \\\\2(1-q) - 4(1-q) = 3q - 2q \\\\-2(1 - q) = q \\\\-2 + 2q = q \\\\2q-q= 2 \\\\q= 2\\[/tex]

It is not possible since q is a chance that really can exceed 1. Hence, for this game, there is no mixed strategy nash balancing.

HELPPPPPPPPPPPP PLEASEEEEEEEEEEE I NEEEEEDDDDDDDD HELP IM BEGGING SOMEONE PLEASEEEEEEEEEEEE​

Answers

Answer:

49.13

Step-by-step explanation:

1/2×6×8=24 3.14×4²/2=23.15

24+23.15=49.13

Which of the following is next in the series

Answers

Answer:

a

Step-by-step explanation:

blue red blue red like this

Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.

If she continues to read at the same rate, will she be able to complete this book in under 1 hour?
[ Select ]
If so, how much time will she have left? If not, how much more time is needed?
[ Select ]

Answers

Answer:

no

22.25 minutes

Step-by-step explanation:

First determine how long it will take her to read the entire book

20 pages          47 pages

--------------  = ----------------

35 minutes         x minutes

Using cross products

20x = 35*47

20x=1645

Divide by 20

20x/20 = 1645/20

x =82.25 minutes

This is more than 1 hour ( 1 hour = 60 minutes)

82.25 minutes - 60 minutes = 22.25 minutes

She will need 22.25 more minutes

a garden pond is in the shape of a rectangle that measures 5 m by 3 m. a stone path is built all around the pond. this path is the same width all the way around. the area of the pond and the path together is 39 m². how wide is the path?​

Answers

Answer:

1.16 m (approximately)

Step-by-step explanation:

Let x be the width of the path.

Total area  = (5+2x)(3+2x) = 39

Expand and simplify

4x²+ 16x+15-39 = 0

4x² + 16x - 24 = 0

Simplify

x² + 4x -6 = 0

Rational factoring does not work, so use quadratic formula

x = +/- sqrt(10) -2

= 1.16 or -5.16 (reject)

= 1.16 m (approximately)

In a game, there are 12 identical balls of which seven are red and five are green.

Five red balls and two green balls have number ‘2’ written on them. The rest of the

red balls have number ‘1’ written on them, and the rest of the green balls have the

number ‘3’ written on them. A random sample of three balls is selected without

replacement. Let denotes the event that all the balls selected are red and

denotes that the sum of numbers of the three balls is equal to 6. Calculate:

(i) P(A) ,

(ii) P(B),

(iii)P ( A∩ B),

(iv)P(A|B).​

Answers

Answer:

its number 2 and if its a mutable answers writ 3 also

The probabilities are: (i) P(A) = 1/6

(ii) P(B) = 38/55

(iii) P(A ∩ B) = 1/110

(iv) P(A|B) ≈ 0.00152

To calculate the probabilities, let's first find the total number of ways to choose 3 balls out of the 12 balls.

Total number of ways to choose 3 balls out of 12 = 12C3 = (12 * 11 * 10) / (3 * 2 * 1) = 220

(i) P(A): Probability that all three balls selected are red.

Number of ways to choose 3 red balls out of 7 red balls = 7C3 = (7 * 6 * 5) / (3 * 2 * 1) = 35

P(A) = Number of favorable outcomes / Total number of outcomes = 35 / 220 = 1/6

(ii) P(B): Probability that the sum of the numbers on the three balls is equal to 6.

The possible combinations that sum up to 6 are: (2, 2, 2), (2, 2, 1), and (1, 1, 3).

Number of ways to choose 3 balls such that their sum is 6:

- For (2, 2, 2), we have 1 choice for each color, so 1 * 1 * 1 = 1 way.

- For (2, 2, 1), we have 1 choice for each color, so 1 * 1 * 1 = 1 way.

- For (1, 1, 3), we have 6 choices for the first red ball (all are labeled '1'), 5 choices for the second red ball (since one '1' is already taken), and 5 choices for the green ball labeled '3', so 6 * 5 * 5 = 150 ways.

Total number of ways to choose 3 balls with sum 6 = 1 + 1 + 150 = 152

P(B) = Number of favorable outcomes / Total number of outcomes = 152 / 220 = 38/55

(iii) P(A ∩ B): Probability that all three balls selected are red and the sum of their numbers is equal to 6.

From the above calculations, we know that there are 1 way to choose (2, 2, 2) and 1 way to choose (2, 2, 1) such that all three balls are red and the sum is 6.

P(A ∩ B) = Number of favorable outcomes / Total number of outcomes = 2 / 220 = 1/110

(iv) P(A|B): Probability that all three balls selected are red, given that the sum of their numbers is equal to 6.

P(A|B) = P(A ∩ B) / P(B) = (1/110) / (38/55) = (1/110) * (55/38) ≈ 0.00152 (rounded to five decimal places).

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