There are 6 yellow, 9 blue, and 4 orange balls inside an urn. 8 balls are chosen from the urn without replacement. Let X, Y , and W denote the number of yellow, blue, and orange balls selected, respectively.

(a) Find P{X + W = 1}.
(b) Find P{X = 2, Y = W}

Answers

Answer 1

Using the probability concept, it is found that:

a) P{X + W = 1} = 0

b) P{X = 2, Y = W} = 0.0667

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, the order in which the balls are chosen is not important, hence, the combination formula is used to find the number of outcomes.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In total, 8 balls are chosen from a set of 19, hence:

[tex]T = C_{19,8} = \frac{19!}{8!11!} = 75582[/tex]

Item a:

1 from a set of 15.7 from a set of 4.

Not possible, hence:

P{X + W = 1} = 0

Item b:

2 from a set of 6.3 from a set of 9.3 from a set of 4.

Hence:

[tex]D = C_{6,2}C_{9,3}C_{4,3} = \frac{6!}{2!4!} \times \frac{9!}{3!6!} \times \frac{4!}{3!1!} = 5040[/tex]

Then, the probability is:

[tex]p = \frac{D}{T} = \frac{5040}{75582} = 0.0667[/tex]

P{X = 2, Y = W} = 0.0667

A similar problem is given at https://brainly.com/question/15536019

Related Questions

What is the median of these figure skating ratings? 5.0 6.0 7.0 7.5 8.0 9.0 10.0

Answers

to find the median, line the numbers up from smallest to largest
5.0, 6.0, 7.0, 7.5, 8.0, 9.0, 10.0
then, go from outside in, alternating from left and right, crossing out numbers until you have 1 number left.
Example:
6.0, 7.0, 7.5, 8.0, 9.0, 10.0
6.0, 7.0, 7.5, 8.0, 9.0
7.0, 7.5, 8.0, 9.0
7.0, 7.5, 8.0
7.5, 8.0
7.5 is the median

Which methods of evaluating a capital investment project ignore the time value of money?

Answers

Answer: Varies

Step-by-step explanation:

It involves any that is not concerned with making a profit.

A patients IV bag contains 750mL. Four hours later, the IV bag contains 450mL.

a) Determine the rate at which the bag is draining.
b) Use your answer from (a) to predict how many mL of IV fluid are left in the bag after 6 hours.

Answers

Answers:
a) 75ml/hr
b) 0ml left

Explanation:
a) 750ml - 450ml = 300ml (This is how much we know the bag drained within 4hrs)

300ml/4=75ml

so now we know the rate of drain is 75ml/hr

b) since rate is 75ml/hr:
75*6=450
450-450=0

Hence there will be no fluid left for the patient.

(a) The rate at which the bag is draining is 75mL/h.

(b) After 6 hours, the remaining fluid is =0 mL.

What is rate?

Rate is a measurement of change of a quantity with respect to another quantity.

Given that,

Initial volume of bag=750 mL,

After 4 hours later, the volume of bag= 450.

(a)

To determine the rate of draining,

The change of volume in 4 hours= 750-450=300

The change of volume in 1 hour = 300/4=75

So, the rate of draining= 75mL

(b)

To determine the remaining volume of bag after 6 hours,

The volume drains in 1 hour=75 mL

The volume drains in 6 hours = 75×6=450

The remaining fluid = 450-450=0

The fluid remains after 6 hours is 0mL.

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The graph of y = (x -k)? is shown below.
у
61
5
لما له
1
-3-2-1
1 2 3 4 5 6 7
X
1
-2
-3
What is the value of k?

Answers

Answer:

(7) 3 2 2x 23 xy y - 10 0 Solution The equation 2x2 23xyy2-100 has A2,B 23, and (1 13) as p3 (Example 2). 13: 271279. 2 m) long and 6 ft Step-by-step explanation:

Select the table of values that you would use to graph f(x) = 3x2 – 4.
Hello Please help.

Answers

The the table of values that you would use to graph [tex]f(x) = 3x^{2} -4[/tex] is option "B"

What is point on graph?

A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph.

According to the question

Points on graph for equation :

[tex]f(x) = 3x^{2} -4.[/tex]

Now,

Table of points on graph

x y

-2 8

-1 -1

0 -4

1 -1

2 8

Hence, The the table of values that you would use to graph [tex]f(x) = 3x^{2} -4[/tex] is option "B" .

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For the given equation, what is the step to clear the fractions and who -- Multiply both sides by 6 to get 2-1 =7 Multiply both sides by 12 to get 2y - 1 = 7 Multiply both sides by 6 to get dy - 1 = 21 Multiply both sides by 18 to get 12y - 3 = 7

Answers

Step-by-step explanation:

you should add the equation for one to answer

Without graphing, describe the transformation from the parent function
f(x) = | x |.

1. y = 5| x |
2. y = 1/3 I x I
3. y = 3| x |

Answers

Answer:

1. y = 5|x| ⇒vertical stretch

2. y = ⅓|x| ⇒vertical compression

3. y = 3|x| ⇒vertical stretch

Step-by-step explanation:

Given the parent absolute value function, f(x) = |x|:

1) y = 5|x|

The transformed function, y = a|x|, where |a| > 1, represents the vertical stretch of the parent graph by a factor of a.

A vertical stretch is a transformation to the parent function where there is an increase in distance between corresponding points of a graph.

Therefore, the absolute value equation, y = 5|x|, represents a vertical stretch of the parent function by a factor of 5. The graph of y = 5|x| is narrower than the parent function, f(x) = |x|.

2) y = ⅓|x|

The transformed function, y = a|x|, where 0< |a| < 1, represents the vertical compression of the parent graph by a factor of a.

A vertical compression is a transformation to the parent function where there is a decrease in distance between corresponding points of a graph.

Therefore, the absolute value equation, y = ⅓|x|, represents a vertical stretch of the parent function by a factor of ⅓. The graph of y = ⅓|x| is wider than the parent function, f(x) = |x|.

3) y = 3|x|

Similar to question 1, the absolute value equation, y = 3|x|, represents a vertical stretch of the parent function by a factor of 3. The graph of y = 3|x| is narrower than the parent function, f(x) = |x|.

Attached are the graphs of the given absolute value functions, where it shows the transformations to the parent function, f(x) = |x|.

What is the name of the process you use to rewrite a quadratic function from standard form into vertex form?

Graphing the transformation
Completing the square
Creating vertex form
Transforming the parent function.

Answers

Answer:

completing the square

Step-by-step explanation:

You can change a quadratic equation from standard form to vertex form by completing the square!

5 1/8 - 3 2/3 =? ..............................

Answers

Answer:

1 11/24

Step-by-step explanation:

5 1/8= 41/8

3 2/3 = 11/3

41/8 -11/3 = (41*3)/(8*3) -(11*8)/(3*8)

=123/24 -88/24

= (123-88)/24

=35/24

=1 11/24

What is the density of the oak board? Show your work.

What is the density of the oak board? Show your work.

Answers

Answer:

it is 5.5 inches wide, 1.5 inches thick and 3 feet long

Answer: Im not really sure if this is correct but it's what I put so I hope it is. If it's incorrect please let me know.

Step-by-step explanation:

We first need to find its mass and volume.

Mass: 8.05

Volume: Turn 3 feet into inches: 36

36in × 1.5in × 5.5in =297

Density : 8.05lb ÷ 297 cubic inches = 0.027 cubic inches

Need some help!!!!! This is hard for me!

Answers

Answer:

X-intercept: (25,0)

Y-intercept: (0,55)

Step-by-step explanation:

Given m\parallel nm∥n, find the value of x. n m (8x+19)° 59°

Answers

(8x19) /5;6 to the newest rate

.........................

Answers

Answer:

[tex]2[/tex]

Step-by-step explanation:

Let [tex][n][/tex] denote the area of some polygon [tex]n[/tex].

The sum of the area of quadrilaterals BCDE and MNDE is equal to [tex][ABC]-([MBE]+[NDC]+AMN])[/tex] (big triangle subtracting the three smaller triangles that aren't part of BCDE or MNDE).

Let the area of triangle ABC be [tex]\alpha[/tex].

Triangle AMN is similar to triangle ABC. Because their side lengths are in ratio 1:2 respectively, the ratio of the area of triangle AMN to triangle ABC is [tex]1:2^2=1:4[/tex].

Therefore, [tex]\displaystyle [AMN]=\frac{1}{4}[ABC]=\frac{1}{4}\alpha[/tex].

Now for triangle NDC, NDC is similar to triangle AMC. Since M is the midpoint of AB, AMC is half the area of ABC. The ratio of the side lengths between triangle NDC and triangle AMC is [tex]1:2[/tex] because the D is the midpoint of MC, so it follows the ratio of their areas must be [tex]1:4[/tex], respectively.

Therefore, [tex]\displaystyle[NDC]=\frac{1}{4}[AMC]=\frac{1}{8}[ABC]=\frac{1}{8}\alpha[/tex].

We can use the same concept for triangle MEB. Triangle MEB is similar to triangle ANB, and the ratio of their sides is also [tex]1:2[/tex], since E is the midpoint of BN. Their areas are in the ratio [tex]1:2^2=1:4[/tex] and we have [tex]\displaystyle [MBE]=\frac{1}{4}[ANB]=\frac{1}{8}\alpha[/tex].

Thus,

[tex]\displaystyle \frac{[ABC]}{[BCDE]+[MNDE]}=\frac{\alpha}{\alpha-\frac{1}{4}\alpha-\frac{1}{8}\alpha-\frac{1}{8}\alpha}=\frac{\alpha}{0.5\alpha}=\frac{1}{\frac{1}{2}}=\boxed{2}[/tex]

Write 0.007 as a fraction.
Do not try to simplify your answer.
05
금
Х
5
?

Answers

Answer:

7/1000

Step-by-step explanation:

In BCD, BC = DB and mB = 139º. Find mD.

Answers

will be 139 = md=87 d\g

What is the equation of a line that passes through the points (3, 6) and (8, 4)?

Answers

To solve this problem you find the slope of the equation and then use that to plug in a given point to find b:

y=-2/5x+7.2

Answer:

[tex]y=-\frac{2}{5} x+\frac{36}{5}[/tex]

Step-by-step explanation:

→ Find the gradient

[tex]\frac{4-6}{8-3}= \frac{-2}{5} =-\frac{2}{5}[/tex]

→ Write into y = mx + c format

[tex]y=-\frac{2}{5} x+c[/tex]

→ Substitute in ( 3 , 6 )

[tex]6 = -\frac{6}{5} +c[/tex] ∴ [tex]c = 6+\frac{6}{5} =\frac{36}{5}[/tex]

→ Rewrite into y = mx + c format

[tex]y=-\frac{2}{5} x+\frac{36}{5}[/tex]

What is 4a I will give brainiest to whoever’s is first

Answers

4A is ( 4 times A )which will ultimately turn out to A being a number of some sort or cancelled out depending on the problem

Plz help me well mark brainliest! Only if u are right!

Answers

Answer:

[tex]x=-6\frac{1}{2}[/tex]

Step-by-step explanation:

I hope this help you

Answer:

B. x = -6 1/2

Step-by-step explanation:

13 3/4 + x = 7 1/4

55/4 + x = 29/4

x = -26/4 ~ -6 1/2

(HELP PLEASE 1!!!!!1!!) How can you tell if data is continuous or discrete

Answers

Answer:

Socratic app

Step-by-step explanation:

it will help you

Triangle DEF is dilated by a scale factor of 2/3 to form triangle D´E´F´. What is the measure of side DE?

Answers

Answer:

DE = 30

Step-by-step explanation:

Let X be the measure of side DE.

You can write this equation to represent the problem:

[tex]x *\frac{2}{3} =20[/tex]

The measure of DE (x) is multiplied by the scale factor of [tex]\frac{2}{3}[/tex] to become 20.

Solve for x:

[tex]x *\frac{2}{3} =20\\\frac{2x}{3} =20\\2x=60\\x=30[/tex]

DE = 30

Help!!! Show work!!!!!

Answers

Answer:

1. (-2,-5) (-1,-1) (0,3) (1,7) (2,11)

2. (-8,-4) (-4,-3) (0,-2) (4,-1) (8,0)

3. (-4,3) (-2,2) (0,1) (2,0) (4,-1)

4. (-2,-1) (-1,2) (0,5) (1,8) (2,11)

Step-by-step explanation:

1. Slope = (11-7)/(2-1) = 4/1 = 4/1

y-intercept: 7 - (4)(1) = 3

Start in the vertical line (y) on 3, 4 up and 1 to the right (you need to points to trace a line)

2. Slope = (0- - 2)/(8-0) = 1/4

y - intercept = -2-(1/4)(0) = -2

Start on -2 vertical line, 1 up and 4 to the right.

3. Slope = (1-0)/(0-2 = -1/2

y-Intercept: 0 - (-1/2)(2)=1

Start on 1 vertical line then 1 down and two to the right (the slope is negative, the line goes downhill)

4. Slope: (8-1)/(1-0) = 7/1

y-intercept = 1 - (7)(0) = 1

Start on 1 vertical line (y) , seven up and 1 to the right.

Harold and his brother collected 2019 cans a 1-year period. Each boy collected the same number of cans. About how many cans did each boy collect? Explain how you found your answer.

Answers

Answer:

1008.5 cans

Step-by-step explanation:

2019/2=1008.5

if you wanted per day, 1008.5/365=2017/730

pls help me i will mark as brilliant

Answers

Answer:

Step-by-step explanation:

[tex]45 \: min = 0.75 \: hour[/tex]

[tex]0.75 * 8 = 6 \: hours[/tex]

A metal rod is
7
8
meters long. It will be cut into pieces that are each
1
56
meters long. How many pieces will be made from the rod?

Answers

Answer:

Step-by-step explanation:

I'm not so sure with the number's you submited but I assume it's 7,8m and 1,56 m

1. convert them to cm (780 cm and 156 cm )

2. 780/156 = 5

Would appreciate the help

Answers

i dont know :))))))))))))))))))))))

[tex] \frac{25}{ \sqrt[3]{5} } [/tex]write ^ as a power of 5

Answers

Answer:

[tex]5^{\frac{5}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponent

[tex]\sqrt[3]{a}[/tex] = [tex]a^{\frac{1}{3} }[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

[tex]\frac{25}{\sqrt[3]{5} }[/tex]

= [tex]\frac{5^2}{5^{\frac{1}{3} } }[/tex]

= [tex]5^{\frac{6}{3}-\frac{1}{3} }[/tex]

= [tex]5^{\frac{5}{3} }[/tex]

How to divided 4 and 2/4

Answers

Answer:

Step-by-step explanation:

turn 2/4 into fraction by dividing 2 by 4 equals to 0.5 then divide 4 by 0.5 equals 8

There are 63 students in band. This represents 30% of the grade. How many students are in the entire grade

Answers

So, the question is 63 is 30% of what number?

That can translate to the equation

63 = 30% · x or 63 = 0.3x

Divide by 0.3 and you get x = 210.

There are 210 students in band.

Answer:

210 students

Step-by-step explanation:

210 x (3/10) = 63

(I am giving branlest) (plz help only if you understand )

Which expression has the sum of twenty six twentieths?

two fifths plus four tenths
four fifths plus two fourths
one half plus three tenths
three fourths plus two fifths

Answers

b. four fifths plus two fourths

Step-by-step explanation: Change the fractions to their equivalents in 20ths-- like finding the common denominator.

Divide the original denominator into 20, then multiply the result by the original numerator to get the new numerator.

4/5 20/5 = 4 4×4 = 16 so 4/5 is equivalent to 16/20

2/4 20/4 = 5 5×2 = 10 so 2/4 is equivalent to 10/20

Add: 16/20 + 10/20 = 26/20

brainliest me

525, 650, 539, 643, 764, 539, 687
What is the interquartile range of these numbers

Answers

Answer:

148

Step-by-step explanation:

sorry, im not sure how to solve it, but its 148

hope this kinda helped :)

mark me brainliest :D

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There are 6 yellow, 9 blue, and 4 orange balls inside an urn. 8 balls are chosen from the urn without replacement. Let X, Y , and W denote the number of yellow, blue, and orange balls selected, respectively. (a) Find P{X + W = 1}. (b) Find P{X = 2, Y = W}

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There are 6 yellow, 9 blue, and 4 orange balls inside an urn. 8 balls are chosen from the urn without replacement. Let X, Y , and W denote the number of yellow, blue, and orange balls selected, respectively.

(a) Find P{X + W = 1}.
(b) Find P{X = 2, Y = W}