An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (p.m.f.) of X.
Answers
Given: An urn contains 11 balls, 3 white, 3 red, and 5 blue balls.
You win $1 for each red ball you select and lose a $1 for each white ball you select.
Let X be the number of times you win.
The total number of ways to select 2 balls (order does not matter) =
The number of ways so that two balls are white (and \( X=-2):^3C_2=3 \)
\(P(X=-2)=\dfrac{3}{55}\)
The number of ways so that two balls are red (and \( X=2):^3C_2=3 \)
\(P(X=2)=\dfrac{3}{55}\)
The number of ways so that one ball is red, one is white (and \( X=0):^3C_1\times^3C_1=9 \)
The number of ways so that two balls are blue (and \( X=0 \) ): \( ^5C_2=(5 \cdot 4) / 2=10 \)
i.e. \(P(X=0)=\dfrac{10+9}{55}=\dfrac{19}{55}\)
The number of ways so that one ball is blue, one is white (and \( X=-1 \) ): \( ^5C_1\times^3C_1=15 \)
\(P(X=-1)=\dfrac{15}{55} =\dfrac{3}{11}\)
The number of ways so that one ball is blue, one is red (and \( X=1 \) ): \( ^5C_1\times^3C_1=15 \)
\(P(X=1)=\dfrac{15}{55} =\dfrac{3}{11}\)
Thus, the probability mass function (p.m.f.) of X would be ( in attachment) :
Related Questions
math math math math math math math
Answers
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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A 13 km 13km13, start text, k, m, end text stretch of road needs repairs. Workers can repair 3 1 2 km 3 2 1 km3, start fraction, 1, divided by, 2, end fraction, start text, k, m, end text of road per week. How many weeks will it take to repair this stretch of road?
Answers
you can start by dividing the total length of the road by the distance that can be repaired per week:
13 km ÷ 3 1/2 km/week = 3.71 weeks
Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.
Match each expression with A, B, C or D.
A=a^3
B=6a
C=12a
D=3a^2
i)3a x 4
ii)a^2xa
iii) 6 1/2 a^2
Answers
The matching expressions are:
\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)
i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.
ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.
iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.
To understand the matching expressions, let's break down each one:
i) 3a x 4:
This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).
ii) a^2 x a:
This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).
iii) 6 × 1/2 a^2:
This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).
Therefore, the matching expressions are:
i) 3a x 4 = C (12a)
ii) a^2 x a = A (a^3)
iii) 6 × 1/2 a^2 = D (3a^2)
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Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Select zero, 1, or more than 1. There is/are ? line(s) of symmetry.
Answers
Answer:
This Symbol has 4 lines of Symmetry
Dascha is making a decorative table to
sell at a fair. The cost of her materials is
$80. If the table sells for $150, what is
the percent of markup?
Answers
The required percent markup is 87.5%.
Here,
The markup is the difference between the selling price and the cost price, expressed as a percentage of the cost price.
Markup = ((Selling price - Cost price) / Cost price) x 100%
In this case, the cost of materials is $80 and the selling price is $150, so the markup is:
Markup = ((150 - 80) / 80) x 100%
Markup = (70 / 80) x 100%
Markup = 0.875 x 100%
Markup = 87.5%
Therefore, the percent markup is 87.5%.
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How do I solve this question?
Answers
Answer:
160 large blocks
Step-by-step explanation:
25 small blocks --- 40 large blocks
100 small blocks --- x large blocks
Making a proportion,
25/100 = 40/x
Cross multiplying,
25x = 4000
Dividing by 25 on both sides,
x = 160 large blocks
A laptop computer originally priced at $1,600 now sells for $1,800. What is the percent of increase?
Answers
Answer:
12.5%
Explanation:
The percent of increase can be calculated as:
\(\frac{v_f-v_i}{v_i}\times100\)Where vf is the final value and vi is the initial value.
So, replacing vf by $1800 and vi by 1600, we get:
\(\frac{1800-1600}{1600}\times100=\frac{200}{1600}\times100=12.5\text{ \%}\)Therefore, the percent of the increase is 12.5%
Select the sentence that has no punctuation or capitalization errors.
In the Summer, we will vacation at lake powell.
In the summer we will Vacation at Lake powell.
In the summer, we will vacation at Lake Powell.
Answers
Answer:
In the summer, we will vacation at Lake Powell.
Step-by-step explanation:
Here, summer is common noun and Lake Powell is a proper noun.
Proper noun should be capitalized.
Please helpppp. I keep getting the wrong answer for this problem and I don’t know why because I’m using PEMDAS like I’m supposed to!!!
[(-4) + (-2)]•(-4) - (-8) + (-2)
Answers
Answer:
I'm not sure what the dot means but I got -6 • 2
... me no like math...
Answers
Answer:
i got 61.27
Step-by-step explanation:
quater circumference \(=\frac{3.14 * 22}{4}\)
= 17.27
20+2+2+(20-11)+11+17.27 = 61.27
What is 6721 x 381 divided by 14 + 84
Answers
Let's break down the expression step by step:
1. Multiply: 6721 x 381 = 2,561,901.
2. Divide: 2,561,901 divided by 14 = 182,993.64 (rounded to two decimal places).
3. Add: 182,993.64 + 84 = 183,077.64 (rounded to two decimal places).
Therefore, the result of the expression 6721 x 381 divided by 14 + 84 is approximately 183,077.64.
Answer: 26129.6
Step-by-step explanation:
6721 x 381 = 2560701
14 + 84 = 98
2560701 / 98 = 26129.6
hey any help? (please make sure this is correct i'd appreciate it)
Answers
Answer:
Below
Step-by-step explanation:
Line AB is of the form y = mx + b where m is the slope = 2
Line BC is perpendicular to this and will have slope - 1/m = - 1/2 and includes the point C (0,6)
The point slope form of line BC will then be
( y-6) = - 1/2 ( x - 0) which can be re-arranged to
y = - 1/2x + 6 < ==== equation for line BC
Piecewise linear relations
Answers
The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = 2x + 4 if [-2, 0]
This the sub-function define between the interval [-2, 0].
f(x) = 4 if [0, 2)
This the sub-function define between the interval [0, 2).
f(x) = -2x + 8 if [2, 4)
This the sub-function define between the interval [2, 4).
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For what value of k are the graphs of y = 3x + 4 and 2y = kx + 9 parallel?
Answers
between 1993 and 1996 there were 6545 injured during horse races find the ratio of injured per year
Answers
First, we have to calculate the years passed between 1993 and 1996:
1996-1993 = 3 years
Now divide the number of injured during horse races (6545) by the number of years (3)
6545 /3
2,182 injured per year
In △JKL , if m∠ J < 90° , then ∠K and ∠L are _____
Answers
Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.
In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.
An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.
In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.
Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.
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i need a tutor who can answer more than 1 question.if not im sorry i have to end the session
Answers
Part A.
The area of a triangle is given by the product of its base and the height relative to that base.
Since these triangles have the same base b and same height h, they have the same area.
Part B.
The area of a rectangle or parallelogram is given by the product of base and height. Since these figures have the same base and height, they have the same area.
Part C.
These figures have different shapes, so we can't affirm that they have the same area.
Part D.
The height shown in the image is not the height relative to side b, therefore we can't affirm that the triangles have the same area.
What is the midpoint of EF If E has the coordinates of (2,4) and F has coordinates of (6,8)
Answers
Answer:
\(\boxed {\boxed {\sf (4,6) }}\)
Step-by-step explanation:
The midpoint formula is:
\((\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2} )\)
where (x₁, y₁) and (x₂, y₂) are the points are the endpoints.
We are given the points: (2,4) and (6,8). Therefore,
\(x_1=2\\y_1=4 \\x_2=6 \\y_2=8\)
Substitute the values into the formula.
\((\frac{2+6}{2},\frac{4+8}{2})\)
Find the x coordinate first.
Add 2 and 6: 2+6=8 Divide by 2: 8/2=4\((4, \frac{4+8}{2})\)
Find the y-coordinate next.
Add 4 and 8: 4+8= 12Divide by 2: 12/2=6\((4,6)\)
The midpoint of EF is (4,6)
\( \large\bf \underline{Given:-}\)
E has the coordinates of (2,4)F has coordinates of (6,8)\( \large\bf \underline{To \: Find:-}\)
The midpoint of EF.\(\large\bf \underline{ Solution:-}\)
\( \sf \: Here, \\ \sf (2,4) = ( x_{1}, y_{1}) \\ \sf (6,8) = ( x_{ 2}, y_{2})\)
We know that,
\( \sf \bigstar \: Formula \: to \: find \: the \: midpoint = ( \frac{ x_{1} + x_{2} }{2}, \: \frac{ y_{1} + y_{2} }{2} )\)
\( \sf \: Hence, \: The \: midpoint \: of \: EF \: is = ( \frac{2 + 6}{2} , \frac{4 + 8}{2} )\)
\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = ( \frac{8}{2} , \frac{12}{2} )\)
\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf =( 4,6)\)
\( \bf \: Therefore, the \: midpoint \: of \: EF \: is \: (4,6).\)
State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for the equation y'=(ycot(2t))/(t^2+y^2+1)
Answers
We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.
Where in the ty-plane the hypotheses of the existence and uniqueness theorem are satisfiedThe Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:
1. f(t, y) is continuous in the region.
2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.
then there exists a unique solution to the differential equation that passes through any point in the region.
In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:
f(t, y) = (y cot(2t)) / (t² + y² + 1)
This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.
To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:
∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²
Taking the absolute value and simplifying, we get:
|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|
= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|
Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:
1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1
Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.
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Find the coefficients of the polynomial with a leading coefficient of: one, and roots: zero, nine, and nine.
x^3+__x^2 +81x+__
Answers
\(zeros \begin{cases} x=0\implies &x=0\\ x=9\implies &x-9=0\\ x=9\implies &x-9=0 \end{cases}\qquad \implies a(x)(x-9)(x-9)=\stackrel{y}{0} \\\\\\ \stackrel{\textit{with a coefficient of 1}}{1(x)(x-9)(x-9)=y}\implies x(x-9)^2=y\implies x(x^2-18x+81)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^3-18x^2+81x=y \end{array}}~\hfill\)
After she pays her bills each month, Lana has $300 left. Based on the graph below, which is the best estimate of how much she will spend on movies and eating out? $180 $75 $160 $200 $90 Discretionary Spending 16- to 22-Year-Olds Shopping for Pleasure 34% Hobbies 12% Eating Out 30% Movies 24%.
Answers
The best estimate of how much she will spend on movies and eating out is given as follows:
$162.
How to obtain the best estimate?The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.
The percentages associated with movies and eating out are given as follows:
Eating out: 30%.Movies: 24%.The amount that she has left is given as follows:
$300.
Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:
(0.3 + 0.24) x 300 = 0.54 x 300 = $162.
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from least to greatest: 1/5, 7/8, 3/4
Answers
Answer:
1/5, 3/4, and 7/8
1/5, 3/4, 7/8
Yooooo HELPPP
with this question plz
Answers
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
What does 0 = 0 indicate about the solutions of the system?
Answers
Answer:
it indicates that it is infinitely many solutions
A group of students were in a disagreement about how to solve for x in the figure. Which
method could be used to solve? *
Use tan (30)
Use the Pythagorean Theorem
Use sin (30)
Use cos (30)
Answers
Answer:
use cos (30) because x is adjecent and 12 is the hypotenuse
Step-by-step explanation:
HELP I NEED THE ANSWER BY TODAY!!!!!!
1.Most snakes live where the temperature ranges from 75° to 90°, inclusive. Write a compound inequality to
represent temperatures where the snakes will NOT live.
2.Atlantic sea turtles that incubate below 23° or above 33° rarely hatch. Write a compound inequality to
represent the temperatures at which the eggs SHOULD be incubated.
3.A certain road has a speed limit of 65 mph and a minimum speed of 40 mph. Write a compound inequality that
represents the speed you should drive to avoid getting a ticket.
Answers
Answer:
What is his answer I'm just go with 90 c 75 equals +109 carry the nine and throw away the 100 and 9 plus 1000003333333368888886666666777777266666666222222266666 = 2222222222299999999996666666666822222222222666666666666633333333333333399999333333333333333888888888888 I'm in 5 e grade by the way (:
Step-by-step explanation:
so don't blame me if I'm
I will give u branlylist
Answers
Answer:
the other answer is a scam or virus they keep doing that
Step-by-step explanation:
if you already clicked on it welp hope
The graph shows the function f(x).
On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot
Answers
The equation that represents the given data is \(\RM \\f(x) = -\sqrt[3]{-x} ,\) Option D is the correct answer.
What is a Function ?It is a statement where two variables , one dependent and one independent are related.
It is given that
a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
The equation given in the options are
\(\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}\)
The function goes through (8,2)
Substituting the values
f(x) = -2
f(x) = \(\sqrt[3]{7}\)
f(x) = -3
f(x) = 2
The equation that represents the given data is
\(\RM \\f(x) = -\sqrt[3]{-x} ,\) Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
i don't get how to do this one
Answers
4. Each team in a youth soccer league pays $784 10
consists of 12 players and the fee is divided equally
does each player pay?
Show your work
Answer
Answers
Each player pays approximately $65.34 between all 12 players if the fee is divided equally.