There are 10 pens in a box. There are x red pens in the box. All the other pens are blue. Jack takes at random two pens from the box. Find an expression, in terms of x, for the probability that Jack takes one pen of each colour. Give your answer in its simplest form.​

Answers

Answer 1

The probability that one of each color is selected is [tex]\frac{10x - x^2}{45}[/tex]

Probabilities

The probability of an event is the chances of the said event

The given parameters are:

Total  = 10Red = xBlue = 10 - x

Calculating the required probability

The probability that one of each color is selected is calculated as follows:

[tex]P = P(Blue) \times P(Red) + P(Red) \times P(Blue)[/tex]

So, we have:

[tex]P = \frac{10 - x}{10} \times \frac{x}{9} + \frac{x}{10} \times \frac{10 - x}{9}[/tex]

This gives

[tex]P = \frac{x(10 - x)}{90} +\frac{x(10 - x)}{90}[/tex]

Take LCM

[tex]P = \frac{2x(10 - x)}{90}[/tex]

Simplify the above expression

[tex]P = \frac{x(10 - x)}{45}[/tex]

Expand

[tex]P = \frac{10x - x^2}{45}[/tex]

Hence, the probability that one of each color is selected is [tex]P = \frac{10x - x^2}{45}[/tex]

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Related Questions

What is the surface area of the rectangular prism below?

Answers

Answer:

is 736 units

Step-by-step explanation:

my explanation is that I got it wrong because of the answer above of me an the right answer was 736 not 706

The surface area of the rectangular prism below with height as 8 units, length as 19 units and breadth as 8 units is A) 736 square units.

The surface area of a rectangular prism is the total area of all the faces of the prism. The rectangular prism below has 6 faces, each of which is a rectangle.

The area of a rectangle is given by:

area = length * breadth

The surface area of the rectangular prism is then given by:

surface area = 2 * (length * breadth + breadth * height + height * length)

Plugging in the values for the length, breadth, and height, we get:

surface area = 2 * (19 * 8 + 8 * 8 + 19 * 8) = 2 * (152 + 64 + 152) = 2 * 368 = 736 square units

Therefore, the surface area of the rectangular prism is A) 736 square units.

Here is a breakdown of the surface area of each of the faces:

Front face: 19 * 8 = 152 square units

Back face: 19 * 8 = 152 square units

Top face: 8 * 8 = 64 square units

Bottom face: 8 * 8 = 64 square units

Left face: 19 * 8 = 152 square units

Right face: 19 * 8 = 152 square units

The total surface area is the sum of the areas of all 6 faces, which is 736 square units.

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Darrian creates caricatures for an initial fee of $5 then charges $2 each minute it takes him to complete the drawing.Write an equation to match the situation.

Answers

Answer:

2x+5

Step-by-step explanation:

Equation  y = 3x + 5  correctly represents the situation.

What is an equation?

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Darrian creates caricatures for an initial fee of $5 then charges $2 each minute.

Let x be the number of each extra minutes.

And y be the total fees.

So, the equation;

The total fee = Charges of x minutes + initial fee.

y = 3x + 5

Therefore, the equation is  y = 3x + 5.

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Please help me thank you :)

Answers

Answer:The equation is y = -x/2 - 3Step-by-step explanation:

We know the equation.

=> y = mx + b

We also know the y-intercept, which is -3.

=> b = -3.

All we need to find is the slope. Once the slope is found, our equation is set.

=> Slope = Rise/Run=> -1/2 = SlopeConclusion:

Since the slope has been found, the equation is y = -x/2 - 3.

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

At a glass vase factory, 2 out of the last 10 vases produced were chipped. What is the experimental probability that the next vase will be chipped?

Answers

Answer:

there is a 20% chance that a vase will be cracked

Step-by-step explanation:

Answer:

2/10 = 1/5 = 0.2 = 20%

Step-by-step explanation:

how many solutions are there for 2x−5=8x+7−6x

Answers

Answer:62

Step-by-step explanation:

2 times 5=10-5=5

8 times 7=56+7= 63-6=57+5=62!

No solution. hope this helps

3q+3.97=7.57 please help im stuck on ixl

Answers

Answer:

1.2

Step-by-step explanation:

3q+3.97=7.57

3q=7.57-3.97

3q=3.6

q=3.6/3

q=1.2

please help!
the subject is 9th-grade geometry honors

I need help finding the length for this problem.

Answers

Ya is = 10x-28 see the picture for explanation

This graph represents the design of a child’s slide what is the slope of the slide

Answers

Answer:

I think it is 1/2 because it goes up 1 over 2

Explain with examples of your own how to find the domain and range of a function.

Answers

Step-by-step explanation:

hope it will help you....

Determine the intercepts of the line.

Answers

Answer:

x = 5/3 or 1.67 and y= 2.5 or 5/2

Step-by-step explanation:

Firstly to find the x intercept make y= 0 meaning put zero at where ever you find y to help eliminate the y

so

3x + 2y =5

3× + 2 (0)=5

3×=5

×=5/3 or 1.67

Secondly for the y intercept make x = 0 meaning put zero at where ever you find x to help eliminate the x leaving you with y

3x + 2y =5

3 (0) + 2y = 5

2y=5

y= 5/2 or 2.5

Evaluate.

(−16+0.6(−13)+1)2

What is the value of the expression?

Enter your answer as a simplified fraction in the box.

Answers

-56, this one was difficult so let me know if you need me to explain

The diagram shows a rectangle 15cm long and 13cm wide.It has been split into four smaller rectangles. write the area of each small rectangle on the diagram.

Answers

Answer:The Answer is in the explanationStep-by-step explanation:

length of the rectangle = 15 cmBreadth of the rectangle = 13 cmArea of the rectangle = length × breadthArea of the rectangle = length × breadth = 15cm × 13cm =

[tex]195 cm^{2}[/tex]

Area of each splited rectangles =

[tex] \frac{195cm{}^{2} }{4} [/tex]

=

[tex]48.75 {cm}^{2} [/tex]

!! PLEASE MARK ME THE BRAINLIEST!!

AND I'M REALLY VERY SORRY IF MY ANSWER IS WRONG

Gia started to solve the equation 3(x − 10) − 5x = 2x − 26 below. They want to move the variables to the left side of the equation for their next step.



Fill in Line 4 and give the property.


Line 1: 3(x − 10) − 5x = 2x − 26 Original Problem
Line 2: 3x − 30 − 5x = 2x − 26 Distributive Property
Line 3: -2x − 30 = 2x − 26 Collect Like Terms

Line 4:


please helpp

Answers

Answer:

Subtract 2x from each side, Subtraction Property

Step-by-step explanation:

Maci is saving money to go to Disney world for spring break. She has saved $570 so far. She works at Walmart and makes $9.20 per hour. How many more hours must work ur she needs a total of $800 to go to Disney world?

Answers

Answer:

25 hours

Step-by-step explanation:

subtract 800 from 570 to find out how much more she needs to save

divide your answer by 9.20

hope you understand

Explain whether the pairing is a function

Answers

NOT a function because it has one to many

it would’ve been a function if it had many to one

simplify and factor if necessary​

Answers

Answer:

[tex]\frac{1}{x}[/tex]

Step-by-step explanation:

[tex]\frac{3x - 12}{3x^{2} - 12x}[/tex]

[tex]\frac{3x - 12}{x(3x-12)}[/tex]          Factor out x.

[tex]\frac{1}{x}[/tex]                    Simplify.


A music store purchases a grand
piano, wholesale, for $5,000.
They markup the retail price 65%.
What is the retail price?

Answers

Answer: 8250

Step-by-step explanation:

Answer:

8548

Step-by-step explanation:

If y is a positive integer, for how many different values of y is RootIndex 3 StartRoot StartFraction 144 Over y EndFraction EndRoot a whole number?.

Answers

The value of y will be 18 or 144.

Given information:

The given expression is [tex]\sqrt[3]{\frac{144}{y} }[/tex].

It is required to find the values of y which are whole numbers.

Now, factorize 144 as,

[tex]144=2\times2\times2\times2\times3\times3\\144=2^3\times2\times3\times3[/tex]

So, for the value of given expression to be a whole number, the value of y should be,

[tex]2\times3\times3=18[/tex] or 144.

For the above values of y, the given expression will be,

[tex]\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{18} }\\=\sqrt[3]{8} =2\\\sqrt[3]{\frac{144}{y} }=\sqrt[3]{\frac{144}{144} }\\=\sqrt[3]{1} \\=1[/tex]

Therefore, the value of y will be 18 or 144.

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Answer:

Its B. 2

Step-by-step explanation:

Edge

HELPPPPP!!!!!!!!!!!!!!!!!!!! THIS IS DUE IN 17 MINUTES AND THIS IS THE LAST QUESTION I NEED THE ANSWER TO! (((PLEASE ACTUALLY GIVE ME THE ANSWER AD NOT THE LINKY PLEASE!!)))

Answers

Answer:

689/1000

hope this helped

F(x) = -4x + 3, find f(-3)

Answers

[tex]f(x) = -4x +3\\\\f(-3) = -4(-3) +3 = 12 +3 = 15[/tex]

the numbers 1 to 9 are randomly arranged to form a 9-digit number. what is the probability that the number obtained is divisible by 18?
(please write the solution)

Answers

Answer:

Hence the probability that the number is divisible by 18 is 4/9 or approx. 0.4444. or even 44.4%

Step-by-step explanation:

If we have 9 digits 1–9 placed randomly to form a 9-digit number without repetition and we want the probability of that number is divisible by 18, then we only need to look at the fact if it is divisible by 18, then it is also divisible by 2 and 9. Adding the digits 1–9 would give us the following (including checking for divisibility by 9):

(9 x 10)/2 =90/2 = 45

45÷9=5

By divisibility of 9, if the sum of the digits is divisible by 9, then the original number itself is divisible by 9. Since the number 45 is divisible by 9, we know that all the possible 9-digit numbers will be as well. The only thing we would have to look at is if it is even since the number has to be divisible by 2. 

There are 9 digits of which 4 are even (2, 4, 6 or 8).

So the probability that the number is divisible by 2 is 4/9.

Hence the probability that the number is divisible by 18 is 4/9 or approx. 0.4444.

pleaseeee help me ………

Answers

Answer:

number 2

Step-by-step explanation:

Will give brainliest
No need to give explanation.
No links!!

The system of equations has

Answers

Answer:

One Solutions I think

Step-by-step explanation:

what is the probability​

Answers

Answer:

1/4

Step-by-step explanation:

the probability on getting blue on spinner is 1/2

1/2 x 1/2 =1/4

Problem Solving
4. A school club sells 43 raffle tickets on Monday and
39 raffle tickets on Tuesday. How many more raffle
tickets did it sell on Monday than on Tuesday?

Answers

Answer:

They sold 4 more raffle tickets on monday than they did on tuesday.

Step-by-step explanation:

Answer: they sold 4 more raffle tickets on monday than tuesday.-

Step-by-step explanation:

The perimeter of an equilateral triangle is 14.4 cm. Find out the length of the side of that triangle in decimal fraction.​

Answers

Answer:

4.8 cm

Step-by-step explanation:

Given,

Perimeter of an equilateral triangle = 14.4 cm

As we know,

Perimeter of an equilateral triangle = 3 × sides (s) = 3s

Therefore,

By the problem,

=> 3s = 14.4 cm

[On dividing both sides with 3]

[tex] = > \frac{3s}{3} = \frac{14.4}{3} [/tex]

[On Simplification]

=> s = 4.8 cm

Hence,

The required side of the given equilateral triangle is 4.8cm(Ans)

What is the equation of the line?

Answers

Answer: x=0

Step-by-step explanation:

The line has an undefined slope and has infinitely many solutions as it passes through the y-axis

Therefore the equation of the line is x=0

3х + 4y= 4
12х + 16y = 8

Answers

Answer:

No Solution.

Step-by-step explanation:

3x+4y=4

12x+16y=8

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

-4(3x+4y)=-4(4)

12x+16y=8

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

-12x-16y=-16

12x+16y=8

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

0=-8

no solution

Simplify x⁷y⁹ ÷ x³y⁶

Answers

X^4 y^3
...............

A number is les than or equal to -11

Answers

Answer:

-12 is the answer for this question

Step-by-step explanation:

make me as brainlist

Answer:

[tex]x\leq-11[/tex]

Step-by-step explanation:

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