You have a shuffled deck of thro cards: 2, 3, and 4, and you deal out the three cards. Let Er denote the event thitith card dealt is even numbered. (a) What is P(Ez E1), the probability the second card is even given that the firscard is even? b) What is the conditional probability that the first two cards are even givesthat the third card is even? (c) Let O; represent the event that the ith card dealt is odd numbered. What is P[E2 Oil, the conditional probability that the second card is even given thatthe first card is odd? (d) What is the conditional probability that the second card is odd given thatthe first card is odd?
Answers
There is only one possible outcome where the first card is odd and the second card is even: {3,2}.
We are dealing with a shuffled deck of three cards: 2, 3, and 4. There are three possible outcomes when dealing one card, and two possible outcomes when dealing the second card (since one card has already been dealt). Therefore, there are a total of 3x2=6 possible outcomes when dealing two cards, and 3x2x1=6 possible outcomes when dealing all three cards.
(a) What is P(E2 | E1), the probability the second card is even given that the first card is even?
There are two ways the first card can be even: 2 or 4. If the first card is 2, there are two possible outcomes for the second card: 3 or 4. If the first card is 4, there is only one possible outcome for the second card: 2. Therefore, there are three possible outcomes where the first card is even and the second card is even: {2,3}, {2,4}, and {4,2}. The probability of the second card being even given that the first card is even is therefore:
P(E2 | E1) = number of outcomes where E1 and E2 occur / number of outcomes where E1 occurs
P(E2 | E1) = 2 / 3
(b) What is the conditional probability that the first two cards are even given that the third card is even?
There is only one way the third card can be even: 2. If the third card is 2, there are two possible outcomes for the first card: 2 or 4. If the third card is 2 and the first card is 2, there is only one possible outcome for the second card: 4. If the third card is 2 and the first card is 4, there are two possible outcomes for the second card: 2 or 3. Therefore, there are three possible outcomes where the third card is even and the first two cards are even: {2,4,2}, {2,2,4}, and {4,2,4}. The probability that the first two cards are even given that the third card is even is therefore:
P(E1E2 | E3) = number of outcomes where E1 and E2 and E3 occur / number of outcomes where E3 occurs
P(E1E2 | E3) = 3 / 6 = 0.5
(c) Let Oi represent the event that the ith card dealt is odd numbered. What is P(E2 | O1), the conditional probability that the second card is even given that the first card is odd?
If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. The probability that the second card is even given that the first card is odd is therefore:
P(E2 | O1) = number of outcomes where O1 and E2 occur / number of outcomes where O1 occurs
P(E2 | O1) = 1 / 3
(d) What is the conditional probability that the second card is odd given that the first card is odd?
If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. Therefore, the conditional probability that the second.
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Related Questions
In which of the following expressions does the number 24 fill in the blank so that the equation is true? Select all that apply.
A) 8(3 + 5) = ___ + 40
B) 12(2 + 7) = ___ + 84
C) 8(4 + 2) = ___ + 16
D) 6(3 + 4) = 18 + ___
Answers
Answer:
a, b, and d
Step-by-step explanation: if you do the math you can find it
Kevin is a server at an all-you-wish-to eat sushi restaurant. At one table, the customers ordered 3 child meals and 2 adult meals, which cost $80 in total. At another table, the customers ordered 5 child meals and 3 adult meals, which cost $125 in total. How much does each child meal and adult meal cost?
Answers
Answer:
Read below for full answer :)
Step-by-step explanation:
We can conclude that the total cost of all meals was $205.
There were a total of 8 kids meals and 5 adult meals.
You'd have to divide 205 by 8, and you'd get 25.625.
Then, divide 205 by 5, and you'd get 41.
For example, we could say that each childrens meal was $15 ($120 total in kid's meals), and each adult was $17 ($85 total in adult meals).
When you total $85 and $120, it then given you a sum of $205.
There are many ways to complete this equation, but i feel that this is the easiest way.
Hope this helps! :)
what is the quotient of 2x^3 +3x^2+5x-4 divided by x^2 + x+ 1
Answers
Answer:
\(2*x+1+\frac{2*x-5}{x^2+x+1}\)
Step-by-step explanation:
Where, the quotient is 2·x + 1, and the reminder is 2·x - 5
Hence, the above is correct is as follows:
The given dividend is 2·x³ + 3·x² + 5·x - 4
The divisor is x² + x + 1
By long division of a polynomial we have;
2·x + 1 [Quotient]
(2·x³ + 3·x² + 5·x - 4) ÷ (x² + x + 1 )
2·x³ + 2·x² + 2·x
0 + x² + 3·x - 4
x² + x + 1
0 + 2·x - 5
Thurs, we have:
\(\frac{(2*x^3 + 3*x^2 + 5*x - 4)}{x^2+x+1} =2*x+1+\frac{2*x-5}{x^2+x+1}\)
Hence, the correct answer is \(2*x+1+\frac{2*x-5}{x^2+x+1}\)
[RevyBreeze]
Homework Part 1 of Points: 0 of 1 Save A survey of 1076 adults in a country, asking "As you may know, as part of its effort to investigate terrorism, a federal government agency obtained records from farger telephone and internet companies in order to compile telephone call logs and Internet communications. Based on what you have heard or read about the program, would you say that you approve or disapprove of this government program of those surveyed, 560 said they disapprove a. Determine and interpret the sample proportion. b. At the 1% significance level, do the data provide sufficient evidence to conclude that a majority (more than 50%) of adults in the country disapprove of thin povemment surveillance program? a. The sample proportion is (Round to two decimal places as needed.)
Answers
The sample proportion is approximately 0.52, indicating that around 52% of the surveyed adults disapprove of the government surveillance program.
What is the sample proportion of adults who disapprove of the government surveillance program based on the survey of 1076 adults in the country?To determine the sample proportion, we divide the number of individuals who disapprove of the government surveillance program by the total sample size. In this case, 560 individuals out of 1076 said they disapprove.
Sample proportion = Number of individuals who disapprove / Total sample size
Sample proportion = 560 / 1076 ≈ 0.52 (rounded to two decimal places)
The sample proportion is approximately 0.52. This means that among the surveyed adults, around 52% expressed disapproval of the government surveillance program.
If you have any further questions or need additional explanations, feel free to ask!
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how many shuffles to randomize a new deck of cards
Answers
Answer:
It takes 7 shuffles
Step-by-step explanation:
Summary. Based on this analysis, Diaconis has written that "seven shuffles are necessary and suffice to approximately randomize 52 cards." Of course, our technique has just given an upper bound for the distance between Rk and U . In fact, J.
Source: www.ams.org
which of the following is parallel to the line 2x + 4y =16
Answers
A linear function with a slope of -0.5 is parallel to the line 2x + 4y =16.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In slope-intercept format, the linear equation given is:
4y = 16 - 2x
y = -0.5x + 4.
When two lines are parallel, they have the same slope, hence a linear function with a slope of -0.5 is parallel to the line 2x + 4y =16.
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Jason, Marita, Alice, and Marcus were on a road trip. Jason drove 400 miles, Alice drove 1/6 of the way, Marita and Marcus each drove 0.25 of the way. If they drove a total of 1200 miles, who drove the longest?
(Show your work please)
F Jason H Marita
G Alice J Marcus
Answers
Which form of volunteering would increase public awareness of cancer?
reducing barriers
identifying needs
speaking publicly
supporting a decision
there are six black socks, 6 blue socks, 12 white socks, and 4 pattern socks in the drawer. what is the probability of pulling a blue sock replacing it and then drawing a pattern sock out of the drawer. answers 5/14 5/28 3/98 6/7
Answers
Answer:
3/98
Step-by-step explanation:
six black socks, 6 blue socks, 12 white socks, and 4 pattern socks= 28 socks
P( blue ) = blue /total = 6/28 = 3/14
Replace it
six black socks, 6 blue socks, 12 white socks, and 4 pattern socks= 28 socks
P ( pattern) = pattern/total = 4/28 = 1/7
P( blue,replace, pattern) = 3/14*1/7 = 3/98
a function f has maclaurin series given by 1 x22! x44! x66! ... x2n(2n)! ... . which of the following is an expression for f(x) ?
Answers
The correct expression for f(x) is f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .
The given Maclaurin series suggests that the function f(x) is an even function since all the odd powers of x have coefficients of zero. To find an expression for f(x), we can examine the pattern in the series.
Let's break down the terms in the series:
Term 1: 1
Term 2: x² / (2!)
Term 3: x⁴ / (4!)
Term 4: x⁶ / (6!)
From this pattern, we observe that the coefficient of each term is given by \(\dfrac{x^{(2n)}} { (2n)!}\), where n represents the index of the term.
Therefore, an expression for f(x) can be written as:
f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .....
This expression represents the summation of terms where each term is the power of x (2n) divided by the factorial of 2n, as indicated in the Maclaurin series.
So, the correct expression for f(x) is:
f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .....
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Which equation has the same solution as 7x−14=21?
Answers
Answer:
2x=10
Step-by-step explanation:
7x-14=21
x=5
2x=10 (divide both sides by two)
2x/2 10/2
x=5
Yky. we'd to provide the other options but to do this you need to +14 to both side. 21+14 then -14+14 cancel. so it's now
7x=35 then you divide 7 in both sides 7 cancels 35/7 =5
x=5
what is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area?
Answers
The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.
Define right circular cylinder?A cylinder with two circular bases and a line connecting their centers that is perpendicular to both bases.Volume of the right circular cylinder be;
v(c) = 12 in³ = π*r²*h
In which, h is the height of the cylinder,
Then , h = 12 / π*r²
Surface area of a right circular cylinder is:
S = area of base and top + lateral area
S(A) = 2*π*r² + 2*π*r*h ....eq 1
Put value of 'h' in equation (1)
S(r) = 2*π*r² + 2*π*r* ( 12 / π*r²)
S(r) = 2*π*r² + 24 /r
Differentiate both sides,
S´(r) = 4*π*r - 24 /r²
Put , S´(r) = 0 to get the critical points.
4*π*r - 24 /r² = 0
π*r - 6/r² = 0
π*r³ - 6 = 0
r³ = 1,91
r = 1,248 in
Check for the minimum surface area for r = 1,248 in.
Find the second derivative,
S´´(r) = 4*π + 48/r³
S´´(r) will always be positive.
Thus, the minimum surface area S is for r = 1,248 in.
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Line AB and line BC form a right angle at point B. If A = (2, 5) and B = (4, 4), what is the equation of line BC?
Answers
Answer:
y = 2x - 4
Step-by-step explanation:
To solve this problem, we must first calculate the slope of the line AB using the formula:
\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)
where:
m ⇒ slope of the line
(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line
Therefore, for line AB with points A = (2, 5) and B = (4, 4) :
\(m_{AB} = \frac{5 - 4}{2 - 4}\)
⇒ \(m_{AB} = \frac{1}{-2}\)
⇒ \(m_{AB} = -\frac{1}{2}\)
Next, we have to calculate the slope of the line BC.
We know that the product of the slopes of two perpendicular lines is -1.
Therefore:
\(m_{BC} \times m_{AB} = -1\) [Since BC and AB are at right angles to each other]
⇒ \(m_{BC} \times -\frac{1}{2} = -1\)
⇒ \(m_{BC} = -1 \div -\frac{1}{2}\) [Dividing both sides of the equation by -1/2]
⇒ \(m_{BC} = \bf 2\)
Next, we have to use the following formula to find the equation of line BC:
\(\boxed{y - y_1 = m(x - x_1)}\)
where (x₁, y₁) are the coordinates of a point on the line.
Point B = (4, 4) is on line BC, and its slope is 2. Therefore:
\(y - 4 =2 (x - 4)\)
⇒ \(y - 4 = 2x - 8\) [Distributing 2 into the brackets]
⇒ \(y = 2x-4\)
Therefore, the equation of line BC is y = 2x - 4.
6) Solne the DE: \( y^{\prime \prime}-5 y^{\prime}=x-2 \) by Undetermined Coefficients method.
Answers
The particular solution for the given differential equation is \(y_p = (-3)A + B\), and the general solution is \(y = C_1 e^{5x} + C_2 + (-3)A + B\), where \(C_1\) and \(C_2\) are arbitrary constants.
To solve the given differential equation using the undetermined coefficients method, we assume a particular solution in the form of \(y_p = Ax + B\) because the right-hand side of the equation is linear.
Differentiating \(y_p\) twice, we get \(y_p'' = 0\) since the derivative of a linear function is zero.
Substituting \(y_p\) and its derivatives back into the original equation, we have \(0 - 5(0) = x - 2\).
Simplifying, we obtain \(-5 = x - 2\).
Solving for \(x\), we get \(x = -3\).
the particular solution is \(y_p = (-3)A + B\).
The general solution of the given differential equation is \(y = y_h + y_p = C_1 e^{5x} + C_2 + (-3)A + B\), where \(C_1\) and \(C_2\) are arbitrary constants.
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Simplify the expression -4x(6x − 7).
Answers
Answer: -24x^2+28x
Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x
PLEASE HELP ASAP I’LL MARK BRAINLIEST Find the area of the figure.
Answers
Area of a square is s^2
Square’s area: 4mm^2
The radius is 3mm
Plug into the equation
1/2* π(3^2)
1/2* π(9)
We can use 3.14 as an estimate of pi
1/2*28.26
14.13mm^2
Now just add them both
Total area 18.13mm^2
A. {-3, 7, 8, 12}
B. {-8, -3, 5, 7}
C. {6, 8, 10, 12}
D. {-8, -3, 5, 6, 7, 8, 10, 12}
Answers
NEED YOUR HELP ASAP!!!!!
Carey correctly graphs a linear function. The slope of the functions is -1. The y-intercept is 3. Which is carey's graph?
Answers
Answer: You didn't show us the graphs so we can't tell you.
Step-by-step explanation:
If each shelf can hold at most 20 books, what is the least number of shelves needed to store the 175 books?
Answers
Answer- 9 shelves
In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.
HOPE THIS HELPS & GOOD LUCK!
Convert 3.9m^2 into cm^2
I will leave good review!
Answers
Answer:
Step-by-step explanation:
To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.
So,
3.9 m² = 3.9 × (100 cm / 1 m)²
3.9 m² = 3.9 × 10,000 cm²
3.9 m² = 39,000 cm²
Therefore, 3.9 square meters is equal to 39,000 square centimeters.
In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation.
After an 8-week exercise program Grace lost 45 pounds. She now weighs 122 pounds. How much did Grace weigh before she started her exercise program?
will give brainliest to best answer!
:3
Answers
Lost: 45 pounds
Weight after exercise: 122 pounds
X represents the weight before she started.
Loss = subtraction
Subtract the lost weight from original weight she started with.
Original - lost = weight after exercise weeks
x - 45 = 122
Add 45 on BOTH sides
x - 45 + 45 = 122 + 45
x = 167 pounds
Hope this helps!
82880 move the decimal point 4 places to the right plz
Answers
If the decimal point was right in front of the number, the decimal would be 8288.0 or the same as 8288.
Write two equivalent expressions to represent the area of the rectangle below.
Answers
Answer:
n-3*2
Step-by-step explanation:
What is the volume of the cylinder to the nearest whole number? a) 942 cm3 b) 3,534 cm3 c)471 cm3 d) 9,420 cm3
Answers
Answer:
V = 3534 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
the radius is 7.5 and the height is 20
V = pi ( 7.5)^2 * 20
V =1125 pi cm^3
Using the pi button for pi
V =3534.291735 cm^3
Rounding to the nearest whole number
V = 3534 cm^3
Answer:
b)3534 cm^3
Step-by-step explanation:
To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.
20% of 24 kg please help with this
Answers
Answer:
4.8kg
Step-by-step explanation:
Answer:
Step-by-step explanation:
24 / 5 = 4.8.
20% of 24 kg is 4.8kg
PLEASE HELP! Find the midpoint given (0,11) and (-6,3).
Answers
Answer:
(- 3, 7 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )
Here (x₁, y₁ ) = (0, 11) and (x₂, y₂ ) = (- 6, 3) , then
midpoint = ( \(\frac{0-6}{2}\), \(\frac{11+3}{2}\) ) = ( \(\frac{-6}{2}\), \(\frac{14}{2}\) ) = (- 3, 7 )
Answer:
(-3,7)
hope it helps........
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answers
The equations which has the same value of x as the given equation; Three-fifths (30 x minus 15) = 72 are;
3 (6x - 3) = 7218x - 9 = 72x = 4.5Which equations have the same value of x as Three-fifths (30 x minus 15) = 72?Since the given equation in the task content is;
Three-fifths (30 x minus 15) = 72
The word phrase can be written algebraically as follows;
3/5 ( 30x - 15 ) = 72
The equation can therefore be solved as follows;
(3/5 × 30x) - (3/5 × 15) = 72
= ( 3 × 6x ) - (3 × 3) = 72
= 3 (6x - 3) = 72............. Equivalent expression.
By the distributive property; we have;
18x - 9 = 72..................... Equivalent expression
And by solving for the value of x; we have;
18x = 81
x = 81 / 18
x = 4.5
On this note, the equations which have the same value for x as; Three-fifths (30 x minus 15) = 72 are;
3 (6x - 3) = 7218x - 9 = 72x = 4.5Read more on equivalent equations;
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According to Remland, which of the following is the primary code we use to signal identity?
Answers
The primary code we use to signal identity, according to Remland, is nonverbal communication.
Nonverbal communication refers to the transmission of messages without the use of words. It involves various forms of communication such as facial expressions, body language, gestures, posture, eye contact, and tone of voice. Remland, a researcher in the field of communication, emphasizes the significance of nonverbal cues in signaling identity.
Nonverbal cues play a crucial role in expressing our cultural, social, and personal identities. They can convey information about our emotions, attitudes, status, and affiliations. For example, the way we dress, our choice of accessories, and our body language can communicate aspects of our identity such as our gender, social group, or profession.
Nonverbal communication is particularly powerful because it often operates at an unconscious level and can convey messages that are difficult to express through words alone. These nonverbal signals can shape impressions, establish connections, and influence how others perceive and respond to us.
According to Remland, nonverbal communication is the primary code we use to signal identity. Understanding and interpreting nonverbal cues are essential for effective communication and for navigating social interactions, as they provide valuable insights into the identities and intentions of individuals.
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Can anyone give me the answer this is due today?
Answers
Answer: -12x + 41
Step-by-step explanation: Rearrange terms
(8 - 3x)(4) + 9
(-3 + 8)(4) + 9
2
Re-order terms so constants are on the left
(-3x + 8)(4) + 9
4( -3x + 8) plus 9
3
Distribute
4( negative 3 x plus 8) plus 9
negative 12 x plus 32 plus 9
4
Add the numbers
negative 12 x plus 32 plus 9
negative 12 x plus 41
Solution
-12x plus 41
ACB=ADE
ACD=ADC
ACB=ABC
ABC=ADE
Answers
ABC =ADE
WILL BE ITS ANSWER
For which equation would x = 4 be a solution?28 – 5.25 x = 2.754.25 x + 7 = 244.25 x ÷ 8 = 97 + 3.25 x = 29
Answers
Given
The equations,
a) 28 – 5.25 x = 2.75
b) 4.25 x + 7 = 24
c) 4.25 x ÷ 8 = 9
d) 7 + 3.25 x = 29.
To find:
For which equation would x = 4 be a solution?
Explanation:
It is given that,
a)
\(28-5.25x=2.75\)Put x=4,
\(\begin{gathered} \Rightarrow28-5.25(4)=2.75 \\ \Rightarrow28-21=2.75 \\ \Rightarrow7=2.75,\text{ which is a contradiction.} \end{gathered}\)Hence 4 is not a solution of a) 28 – 5.25 x = 2.75.
b)
\(4.25x+7=24\)Put x=4,
\(\begin{gathered} \Rightarrow4.25(4)+7=24 \\ \Rightarrow17+7=24 \\ \Rightarrow24=24 \end{gathered}\)Hence, 4 is the solution of b) 4.25 x + 7 = 24.
Thus, the answer is option b).