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

PLEASE HELP QUICKLY Determine the equivalent system for the given system of equations: 5x + 3y = 1 4x − 5y = 4

Answers

Answer:

x = 32/67 y = 36/67

Step-by-step explanation:

5x+3y = 4 ------1

14x-5y = 4 -------2

1×5 ; 25x+15y = 20 --------3

2×3 ; 42x-15y = 12 -------4

3+4 ; 67x = 32

x = 32/67

5×(32/67)+3y = 4

y = 36/37

Answer:

2x + 3y = 7

9x − 2y = 4

Step-by-step explanation:

i did the quiz on flvs

The exchange rate at the post office is £1 = €1.17. How many euros do I get for £280?

Answers

Answer:

327.21 euros.

Step-by-step explanation:

(789+890)=(2992) answer it and i give u a taco

Answers

Answer:

False

Step-by-step explanation:

789+890 = 1679

Answer:

789+890+1313=2992

Step-by-step explanation:

Plz, Help Me Quickly!!!
What is the equation of a horizontal ellipse with a major axis = 12 and a minor axis = 10?

Answers

The equation of the horizontal ellipse is [tex]\frac{x^2}{144}+\frac{y^2}{100}=1[/tex]

Ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

The standard form of an ellipse with horizontal major axis is:

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where a > b

since a = 12, b = 10, hence:

[tex]\frac{x^2}{12^2}+\frac{y^2}{10^2}=1\\\\\frac{x^2}{144}+\frac{y^2}{100}=1[/tex]

The equation of the horizontal ellipse is [tex]\frac{x^2}{144}+\frac{y^2}{100}=1[/tex]

Find out more on ellipse at: https://brainly.com/question/19507943

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-2x-4) + 1.

Answers

Using translation concepts, it is found that the parent function was:

Reflected over the x-axis.Horizontally compressed by a factor of 2.Shifted right 4 units.Shifted up 1 unit.

The parent function is:

[tex]f(x) = \log{x}[/tex]

The first transformation is:

[tex]\log{x} \rightarrow \log{-x}[/tex]

Which means that it was reflected over the x-axis.

Then, [tex]\log{-x} \rightarrow \log{-2x}[/tex], which means that it was horizontally compressed by a factor of 2.

Then, [tex]\log{-2x} \rightarrow \log{-2x - 4}[/tex], which means that it was shifted right 4 units.

Finally, 1 was added to the function, which means that it was shifted up 1 unit.

To learn more about translation concepts, you can take a look at https://brainly.com/question/4521517

what is the sum of 4 and -5​

Answers

Answer:

-1

Step-by-step explanation:

its like subtracting 5 and 4

Which exponential expression is equivalent to the product shown 2/3×2/3×2/3×2/3×2/3×2/3×2/3?

Answers

Answer:

B. (2/3) x (2/3) x (2/3)

C. 8/27

D. 2^3 /3^3

hope this helps

The art club in Northwestern middle school is selling candy bars as a fundraiser. each art club member....

Answers

28.2 students would be able to sell candy.
150 -9=141
Divide that by 5 to find out how many students would be able to sell candy

Molly O'Rourke assembles computers for Radius Computer. She works 8 hours per
day less 2 breaks at 15 minutes per break. She spends 45 minutes on each
computer. How many computers should she be able to assemble in one day?

Answers

Answer:

10

Step-by-step explanation:

I converted 8 hours to minutes so solve the equation easily

8 hours = 480 minutes

I subtracted the amount of time she takes for a break

480- (15+15) = 450

To find the number of computers she could repair I divided 450 by the number of minutes she spends repairing one computer.

[tex]\frac{450}{45}[/tex]= 10

Therefore, she could fix 10 computers during her 8 hours of work.

__________________________________________________________

Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

which inequality is a true statement select each correct answer

Answers

Answer:

A. False

B. True

C. False

D. False

E. True

Hope This Helps!!!


Jenna has 38 coins. She uses 19 coins to buy a notebook. How many coins does she have left?
Explain how you can solve and check this problem.

Answers

Answer: 19 coins

Step-by-step explanation:

38-19=19

To check, take any one of the nubers and replace it with x, and when you solve for x. you'll get that number back. For example:

Let x represent the amount used to buy a notebook

19+x=38

x=38-19

x=19

38 coins - 19 coins = 19 coins

You solve the problem by subtracting how many coins she used by how many coins she has

Please help :)

Chloe is an acrobat in a local circus. Her job is to move across a tightrope from point A to point B while blindfolded! She can only move using the distances that you tell her to move in your instructions. Chloe may go past the ladder. However, if she does, make sure she turns around and goes back toward the ladder.

Use the link: Link

Your Task: Work with your partner to find different combinations of the lengths given in parts (a) through (d) below that will allow Chloe to move from point A and end at point B (the end of the tightrope). You may use each length as many times as you like. .

1. For each crossing, look for at least three different ways to get the acrobat across. *Draw a diagram on your paper that shows the solution with the least amount of steps. *For the neither 2 write a number sentence/equation.​

Answers

Explanation:

We'll let you draw the diagram. Here are some possible equations. We have listed the shortest sequence first.

(a) 24 = (10 + 10 + 4) = (8 + 8 + 8) = (10 + 8 + 4 + 2)

(b) 17 = (10 + 3 + 2 + 2) = (10 + 3 + 3 + 3 - 2) = (3 + 3 + 3 + 3 + 3 + 2)

(c) 15 = (11 + 4) = (6 + 6 + 3) = (4 + 4 + 4 + 3)

(d) 27 = (19 + 8) = (19 + 12 - 4) = (19 + 12 + 4 - 8)

A plant food company recommends mixing a teaspoon of food with every gallon of water and only adding a
teaspoon when the water level goes above the next whole gallon
Which graph models the number of teaspoons of food depending on the amount of water?

Answers

Answer:

The answer is A. Edge 2022. Hope this helps

Step-by-step explanation:

The next closest one would've been C. But they asked for the teaspoons based on the amount of water not over a constant period of time. So A is right.

Answer:

A

Step-by-step explanation:

HELPPPPPPP PLSSSSS!!!!!! 100 points
Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S

Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.

Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because

of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.

Answers

Answer:

B.of the AAS congruence theorem.

Step-by-step explanation:

hope this helps!

What is the largest power of 2 that is a divisor of 13^4 - 11^4?

Answers

Answer:

[tex]2^5[/tex]

Step-by-step explanation:

Given:

[tex](13^4 - 11^4)(13^2+11^2)[/tex]

add all together with exponents

=48*290

= Then turn into a smaller exponent

= [tex]2^4 * 3 * 2*145[/tex]

combine like terms

[tex]2^4 *2[/tex]

=[tex]2^5[/tex]

Answer:

5

Step by step explanation :

13^4-11/4=13920

2^5=32

13920÷32=435

Therefore largest power = 5

Please mark me as the brainliest answer

Thank you ☺

please help with geometry problems

Answers

Answer:

put your  best gees

Step-by-step explanation:

The solution set of inqulity 4>-2x in R is …

Answers

[tex]4>-2x\\\\\implies -\dfrac{4}2 <\dfrac{-2x}{-2}\\\\\implies -2<x\\\\\implies x >-2\\\\\text{Interval, }~ (-2, \infty)[/tex]

PLEASE HELP ME

Solve 2x^2-x>15

Show your work

Answers

Answer:

  x < -5/2  or  3 < x

Step-by-step explanation:

Subtracting 15 puts the relation into a more standard form:

  2x^2 -x -15 > 0

  (2x +5)(x -3) > 0 . . . . . factor

The zeros of these factors are x = -5/2 and x = 3.

For values of x between those values (-5/2 ≤ x ≤ 3), the product of these factors will be negative or zero. In order for the product to be positive, x must not be in that range.

The solution is ...

  x < -5/2  or  3 < x

_____

Additional comment

Several methods are taught for factoring a quadratic expression. One of my favorite is using a graphing calculator to find the zeros. If p is a zero, then (x-p) is a factor.

Another way to approach the factoring of ax^2 +bx +c is to find factor pairs of the product (ac) that have a total of b. Here, that means finding factors of 2(-15) = -30 that have a sum of -1. Consider ...

  -30 = (1)(-30) = 2(-15) = 3(-10) = 5(-6)

The sums of these pairs are -29, -13, -7, -1. With the values 5 and -6, you can rewrite the quadratic expression as 2x^2 +5x -6x -15. This can be factored by grouping pairs of terms:

  x(2x +5) -3(2x +5)

  (2x +5)(x -3) . . . . . . . the factorization we show above.

__

You can see on the graph that the quadratic is greater than 0 when x < -2.5 or x > 3.

sooooooooooooooooooooooooooooo easy

Answers

Answer:

11/12..................

Answer:

J) 11/12

Step-by-step explanation:

Which three points are collinear?

Answers

according to defination of collinear points :Three or more points are said to be collinear if they all lie on the same straight line.

therefore, A,B,C points are collinear.

Scientists say we should sleep 3/8 of a day.How about many hours is this

Answers

Answer:

9 hours

Step-by-step explanation:

Answer:

[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer ☘}}[/tex]

number of hours in a day = 24

according to scientists ,

we should sleep number of hours = 3/8

therefore ,

[tex] \frac{3}{8} \: of \: 24 \: hours = \frac{3}{8} \times 24 \\ = > 9 \: hours[/tex]

hope helpful~

Can someone plz help Me?

Answers

Answer:

D

Step-by-step explanation:

As the y value doesn't change between the  points that means  that it would be reflected over the y axis

Please answer these questions.(please include work/explanation)(1)

Answers

Answer:

Hi there!

I will help you answering the questions, if you do not understand what I'm working about, you can ask me on comment section.

Number 1

First of all, we need to multiple the separated function.

[tex] \sf2(3x + 4)(x - 1)(x - 3) \\ = \sf(6x + 8)(x - 1)(x - 3) \\ \tt multiple \: the \: first \: equation \\ \tt(6x + 8) \: with \: (x - 1) \\ \sf = (6x \times x + 6x \times - 1 + 8 \times x + 8 \times - 1)(x - 3) \\ = \sf({6x}^{2} + 2x - 8)(x - 3) \\ \tt then \: multiple \: the \: last \: one \\ \tt (6 {x}^{2} + 2x - 8) \: with \: (x - 3) \\ \sf = \boxed{ \bold{ \red{ {6x}^{3} - 16x {}^{2} - 14x + 24}}}[/tex]

So the right answer is A

━━━━━━━━━━━━━━━━━

Number 2

the graph has four zeros at :

-4-2/309

After that we make them equal with 0, here is the thing:

x = -a is equal with x + a = 0

So we can conclude that :

-4 → x + 4 = 0-2/3 → 3x + 2 = 00 → x = 09 → x - 9 = 0

Then we substitute them to a function :

x(x + 4)(3x + 2)(x - 9) = 0

3x⁴ - 13x³ - 118x² - 72x = 0

Then we looking on the option which one is equal with the answer above.

The right answer is B

━━━━━━━━━━━━━━━━━

Hope It Helps!

What is an equivalent expression to 7x - 3y + 8x ?

Answers

Answer:

15x-3y

Step-by-step explanation:

Ok, this question might seem hard but its not! theres only 2 varibles here, x and y. In this problem we add the 2 numbers that are x which gives us 15x and then the -3y gets added to the rephrasment.

can anyone help me pls ??

Answers

Answer:

A

Step-by-step explanation:

Volume of a cylinder= πr² *height.height=volume÷πr²height=250÷π(which in this case we are using 3.14)3²height=8.85=A

Find the domain and range of the function represented by the graph . What’s the domain an range

Answers

b, remember the domain is the x values, and the range is the y values

An account earns 8.4% interest compounded monthly. If 12,000 is invested in the account initially, how much
interest is earned in this account over a 25 year period?

Answers

Answer:

$30,2400

Step-by-step explanation:

First, we need to find how much interest he earns in a month

8.4% of $12,000 = $1,008

Next, we multiply the amount of interest per month by the number of months in 25 years

25 years = 300 months

Now we can multiply the two values to get our final answer

1,008 x 300 = $30,2400

A plane travels 460 miles per hour. how many miles does the plane travel in feet per second?

Answers

Answer:

674.667 feet per second

If 60% of a KNOWN NUMBER is 180, what is the 40% of that UNKNOWN NUMBER?

Answers

Step-by-step explanation:

I think you mean you want to find out 40% of a number,, when 60% of it is 180, so I'll answer that:

60% = 180

÷6

10% = 30

x4

40% = 120

(if you want to find 100%, multiply 30 by 10)

Hopefully this helps :)

While shopping at his local home improvement store, Chen noticed that the directions for an extension ladder state, “This ladder is most stable when used at a 60° angle with the ground.” He wants to buy a ladder to paint a two-story house. How long does his ladder need to be in order to reach the top of the house if the house is 27 feet tall?

Answers

The length of the ladder needed to reach the top of the house is 31.2 feet.

Trigonometric ratio is used to show the relationship between the sides and the angles of a right angled triangle.

Let d represent the length of the ladder. Using trigonometric ratio:

[tex]sin(60)=\frac{27}{d} \\\\d=\frac{27}{sin(60)} =31.2\ feet[/tex]

The length of the ladder needed to reach the top of the house is 31.2 feet.

Find out more at: https://brainly.com/question/4326804

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