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
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
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Related Questions
A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories. Determine how many calories 14 brownies would have. Round to the nearest calorie
Answers
The number of calories in 14 brownies is 233 calories.
The first step is to determine the average calorie in 1 brownie.
Average calorie = 50 calories / 3 = 16.667 calories
In order to determine the number of calories in 14 brownies, multiply the average calorie by 14 brownies.
Total calories = 16.67 x 14 = 233 calories
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IF YOU HELP ME WITH THIS YOU ARE AUTOMATICALLY MY FAVORITE PERSON
Determine the intercept of the line
Y-intercept ( , )
X- intercept ( , )
Answers
Answer:
Y-intercept: (0, 2.5)
X-intercept: (3.5, 0)
i need help on this math problem
Answers
Answer:
I think the first one goes with the second one
Step-by-step explanation:
here is the other question
Answers
Answer:
1. -3 × A1 + A2 --> B2
2. [tex]-\frac{1}{7}[/tex] × B2 --> C2
Step-by-step explanation:
1. -3 × A1 + A2 --> B2
(4x × -3) + 12x = -12x + 5x = -7x
(2y × -3) + 6y = -6y + 6y = 0y
(-10 × -3) + -9 = 30 - 9 = 21
2. [tex]-\frac{1}{7}[/tex] × B2 --> C2
-7x × [tex]-\frac{1}{7}[/tex] = 1x
21 × [tex]-\frac{1}{7}[/tex] = -3
Same process as last time
Write an explanation to help your friend understand why the expression 0.45x represents decreasing x by 55%.
Need the answer please and thank you!
Answers
Answer:
A variable is a letter that is used to represent a number. For instance, in this problem the variable x represents an unknown number that will equal 5 when added to 2.
Step-by-step explanation:
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
x - (55/100)x = 0.45x
The decreasing x by 55% is 0.45x
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Decreasing x by 55%.
This can be written as,
= x - (55/100)x
= x - 0.55x
= 0.45x
Thus,
The decreasing x by 55% is 0.45x
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In a raffle 1000 tickets are being sold, at $1 each. The first prize is $100, and there are 3 second prizes of $50 each. How much does the price of the ticket exceed the expected value
Answers
Answer:
The price of of the ticket exceeds its value by $ .75
If
x
=
2
and
y
=
6
, evaluate the following expression:
2
(
y
−
x
)
Answers
Answer:
8
Step-by-step explanation:
x =2, y=6
2(y-x)
#subsitute the variables with their values
2*(6-2)
2*4
8
Alternative(don't do it this way, it's unnecessary but it can be done):
x =2, y=6
2(y-x)
2y - 2x
(2*6) - (2*2)
12 - 4
8
1. What is the x-intercept for the equation -2x+5y =-10?
Answers
Answer:
2x-5y=10 in slope intercept form is y=2/5x-2. The x intercept would be 5 and the y intercept would be -2. The slope is 2/5.
Step-by-step explanation:
Think about the axis for a moment. You have the y-axis and the x-axis. The y-axis crosses the x-axis at y=0. Consequently the graph must also cross the x-axis when its equation has its y-value set to 0.
Likewise the graph will cross the y-axis when x=0
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solving your question
To find the x-intercept set y=0 giving
[tex] - 2x + 5(0) = - 10 \\ - 2x = - 1 |?| [/tex]
Multiply both sides by ( -1) giving
[tex]2x = 10[/tex]
Divide both sides by 2 giving
[tex] \frac{2}{2} \times x = \frac{10}{2} \\ [/tex]
But [tex] \frac{2}{2} = 1 \: \\ [/tex] giving
[tex]x = \frac{10}{2} \\ [/tex]- BRAINLIEST answerer
find the quotient please
Answers
The table below shows the number of classes offered at a fine arts school in New York.
Art: 45
Dance: 30
Music: 40
Theater: 35
What part-to-whole ratio represents the number of music classes offered at the school?
Answers
Answer:
40:140
Step-by-step explanation:
The explanation.is in the diagram above
Find the y-intercept of the following equation. Simplify your answer.
y = 9x - 3/7
y-intercept
Answers
Step-by-step explanation:
Find the slope? or what....
If the area of rectangular plot is 200 cm and its length is 10 m. find out its breadth.
Answers
Answer:
The area of a rectangle is A=l x w.
So, 200=10 x w
Divide both sides by 10.
20 = w
The width of the rectangle is 20 m.
:)
Write 5y to the 3rd power without exponents
Answers
Answer:
5y*5y*5y
Step-by-step explanation:
uhh no explanation cuz logic
The 3rd power of the term 5y without exponents is 125.y.y.y
What is power of any number?If a is any positive number and n is its power , then aⁿ means a is multiplied by itself n times
The given term is 5y,
To find the third power of 5y,
The cube of 5y = (5y)³
To write the 3rd power without exponents,
Simplify the term (5y)³.
(5y)³ = 5y x 5y x 5y
= 125 y.y.y
The required 3rd power of 5y without exponents is 125.y.y.y.
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Look at UVZ and WVZ in the image below.
Which of the following is the best description for this pair of angles?
A) supplementary
B) acute
C) straight
D) complementary
Answers
Answer:
A Supplementery
Step-by-step explanation:
they show on usa test prep
The best description for the given pair of angles is supplementary as shown in the figure. which is the correct answer would be an option (A).
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if you have two angles and you add their measures together, the sum will be 180 degrees if the angles are supplementary.
For example, consider the following pair of angles:
Angle A measures 80 degrees.
Angle B measures 100 degrees.
The sum of the measures of these two angles is 80 + 100 = 180 degrees, so angle A and angle B are supplementary angles.
As per the given figure, we have two angles UVZ and WVZ
As indicated in the image, the best description for the given pair of angles is supplementary.
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If Keegan has 15 nickels and quarters in his pocket, and they have a combined value of 195 cents, how
many of each coin does he have?
__quarters
__nickels
Answers
Answer:
7 Quarters and 4 Nickels
Step-by-step explanation:
basically, Since a Quarter is worth 25 cents and a Nickel is worth 5 cents, You can do 25x7=175 and 5x4=20 then add 175+20 and then you get 195.
Hope I could help! :)
In which quadrant would you find the graph of (-5, -6)?
O AT
O B) ||
O C) IUI
O D) IV
Answers
Answer:
Third quadrant
Step-by-step explanation:
To count quadrants, you do it counter-clockwise, so, since the point is in the (negative, negative) quadrant, it is the third one
To study the effects of a medication on migraines, every 10th adult from an alphabetized list of patients who suffer from migraines were selected. Then, the sample was surveyed about the number of migraines they have each month. The names of the 50 adults selected were written on equal sized tiles, placed in a bag, and mixed well. The people with names on the first 25 tiles selected were given the migraine medication. The remaining 25 people were given a placebo. After six months, all patients were surveyed again about the number of migraines they had each month. The change in the mean number of migraines between the two groups was compared. Which of the following is the best description of the randomization approach? random selection random assignment both random selection and random assignment neither random selection nor random assignment
Answers
Answer:
Random Assignment
Step-by-step explanation:
Please help me please!!!!!!!!!
Answers
Step-by-step explanation:
the radius is diameter divided by 2
7/2/2 =1 .75
circumference of a circle is 2πr
2*22/7*1.75=11
3.14*11 =34.54
what number is its own oppositie?
Answers
Answer:
0Step-by-step explanation:
what number is its own oppositie?
The number 0 is the only number that is its own opposite.
What’s 3 plus 3 please help I don’t the answer
Answers
Answer:
6
Step-by-step explanation:
3+3=6 lolzzz ik u already knew that but im taking dem points!!!
Determine whether the graphs of given pair of equations are parallel,
perpendicular, or neither. 2x+5y=15
3x+5y=15
Answers
Answer:
Neither because x can't equal 3 and equal 2 at the same time and 2x + 5y doesn't equal 3x + 5y. 3x is > 2x by one x
Step-by-step explanation:
Hope this answer works for you!
congruent or simular
Answers
First is similar
∆XYZ and ∆MNO are congruent
Polygons are similar
The square one is congruent
First one on right side is similar
Rugs are similar
rectangles are similar
Plz help!! Given: DE is a midsegment of ABC. Show all work.
Find the value of x and y.
And What is the length of AC? !Please show all work!
Incase photo is blurry
AE-y+6
EC-x-3
DE-x+2
BC-24
Answers
Answer:
AC=14
X=10
Y=1
Hoped this helped!
Step-by-step explanation:
DE is half of BC, therefore x=10. AE and EC have to be the same length, which is 7. SO, y=1 and x is 10.
Given 4(3x-8)=52 prove x=7
Answers
Answer:
4(3x-8)=52
divide both sides by 4
4/4(3x-8)=52/4
3x-8=13
add both sides by 8
3x-8+8=13+8
3x=21
divide both sides by 3
3x/3=21/3
x=7
Step-by-step explanation:
this question got asked three times =)
Answer:
52 is the answer
Step-by-step explanation:
You always work with your paratheses first. Work with your variable(s) to make things easier. Plug in the number given for your variable.
3(7)=21
Subtract the numbers in the paratheses once you have found the number with the variable.
21 - 8 = 13
Last step is to combine the number in the parentheses with the number(s) out of the parentheses. Depending on the equation, the number outside of the parentheses will have to be added/subtracted/multiplied/divided. In this equation, we have to multiply since there´s no given sign for multiplying. You automatically know you have to multiply because the number is right next to the parentheses.
4 * 13 = 54 or 13 * 4 = 54
I hope this helps u! :D
Solve the equation, 3/4x + 3 - 2x = -1/4 + 1/2x + 5
Answers
Answer:
I think x= -1
Step-by-step explanation:
after how many years will £6,000.00 yield a simple interest of £900.00 at 3%
Answers
Answer:
add 1 Century to divide £6 000 000
Answer:
the answer to your question is 105 I think sorry if it's not
Need some help!!!!! This is hard for me!
Answers
Answer:
X-intercept: (25,0)
Y-intercept: (0,55)
Step-by-step explanation:
find the degree of the polynomial 5ab^3-7a^5c^2-5
Answers
Answer:
7
Step-by-step explanation:
as -7a^5c^2 term has two cofficient a and b and each have power.by adding power of one term we get 7
vertex, maximum height, and axis of symmetry
Answers
Answer:
19 height
Step-by-step explanation:
sorry but thats all i know
hope it helps, have a nice day/night! :D
This table shows data collected by a runner.
A three column table with 7 rows. The first column, Time in minutes, has the entries, 1, 2, 3, 4, 5, 6. The second column, Distance in miles, has the entries, 0.19, 0.38, 0.57, 0.76, 0.95, 1.14. The third column, Elevation in meters, has the entries, 12, 28, 67, 98, 124, 145.
Which statement about the scenario represented in the table is true? Assume time is the independent variable.
The distance run is a nonlinear function because it does not have a constant rate of change.
The elevation is a nonlinear function because it does not have a constant rate of change.
Both the distance run and the elevation are nonlinear functions because they do not have constant rates of change.
Both the distance run and the elevation are linear functions because they have a constant rate of change.
Answers
Answer:
a
Step-by-step explanation:
Answer:
The correct answer is B, The elevation is a nonlinear function because it does not have a constant rate of change.
Step-by-step explanation: