The conditional probability Pr(Y=y| X=x) is useful in many applications, such as in Bayesian inference and in modeling the relationship between two random variables.
In probability theory, the conditional probability of an event A given another event B is the probability of A happening given that B has already occurred. This is denoted as Pr(A|B) and can be calculated using the formula:
Pr(A|B) = Pr(A and B) / Pr(B)
where Pr(A and B) represents the probability of both A and B occurring and Pr(B) represents the probability of B occurring.
Similarly, the conditional probability of a random variable Y given another random variable X taking on a specific value x, denoted as Pr(Y=y| X=x), is the probability of Y taking on the value y given that X takes on the specific value x.
The formula for calculating Pr(Y=y| X=x) is:
Pr(Y=y| X=x) = Pr(X=x, Y=y)/(Pr(X=x))
This formula is derived from the definition of conditional probability. The numerator Pr(X=x, Y=y) represents the joint probability of X taking on the specific value x and Y taking on the value y. The denominator Pr(X=x) represents the probability of X taking on the specific value x, regardless of the value of Y.
By dividing the joint probability by the marginal probability, we are effectively restricting our attention to the subset of the sample space where X takes on the specific value x. We then calculate the probability of Y taking on the value y within this subset of the sample space.
The conditional probability Pr(Y=y| X=x) is useful in many applications, such as in Bayesian inference and in modeling the relationship between two random variables. It allows us to quantify the probability of one event or variable given information about another event or variable.
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Kendall went to the candy store and bought 2 pounds of candy. If 1/5 of Kendall's candy was chocolate, how many pounds of chocolate candy did Kendall buy?
The answer is 1/10
This is simple division
The equation is (1/5÷2)
I did my work on a sheet of paper so i know i did this correctly
My explanation of my work:
Keep change flip is the operation used here
So you keep 1/5 ,change the division sign to multiplication and flip the 2/1 into 1/2 so the new equation is (1/5x1/2) the answer to that is 1/10
Have an amazing day :)
-yO mAmA
Find the equation (in terms of x ) of the line through the points (-5,-4) and (3,-1)
Answer:
\(y=\frac{3}{8}x-\frac{17}{8}\)
Step-by-step explanation:
The slope: m= 3/8
hope this helps.
is 3.8 rational or irrational
Answer:
its rational
Step-by-step explanation:
The number 3.8 is a rational number.
We have,
A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero.
Rational numbers can be written in the form a/b, where a and b are integers.
In the case of 3.8, it can be expressed as 38/10.
The numerator (38) and the denominator (10) are both integers.
Therefore,
3.8 is a rational number.
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HELP plz! and please explain! ty<3
Answer:
6f
Step-by-step explanation:
Combining like terms is easy. Just think it like this: 4+3-1, and add the f on later. That is 6, and add the f on and you get 6f. It's like adding variables.
Hope this helps plz mark brainliest if correct :D
Solve the inequality
4x - 19 ≥ -27
The answer is X>-2. I uploaded a picture of the steps below. Hope this helps. :)
If f(x)=3x-7, find f(x)=2
Answer:
f(3) = 2 or (3, 2)
The y-value we solved for is 2.
Step-by-step explanation:
The equation they give you, all you need to do is plug in the x-value they give you.
f(x) the y-value in (x, y)
it will be on that bold, vertical line on the graph
2=3x-7
add 7 to both sides
9=3x
divide both sides by 3
x=3
y=2
Please help I need an answer ASAP!!!!!!!
Answer:
A its the mos resonable one
list all of the positive common divisors of 48 and 60: 1,2,3,4,6,8,12,16,24,48 note: enter your answers as a comma-separated list. [hint: your list should begin with 1,2,3]
The list of all the positive common divisors of 48 and 60 is:1, 2, 3, 4, 6, 12.
To find all the common divisors of 48 and 60, we need to first list the divisors of both numbers. So let's list out the divisors of both 48 and 60.
Divisors of 48:1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Divisors of 60:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Now, we can identify the common divisors by comparing the two lists. The common divisors of 48 and 60 are:1, 2, 3, 4, 6, 12
In division, we divide a number by any other number to get another number as a result. So, the number which is getting divided here is called the dividend. The number which divides a given number is the divisor.
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The box plots show the average wind speeds, in miles per hour, for two different islands.
Average Wind Speeds on Island A
2 box plots. The number line goes from 1 to 11. For the average wind speeds of cities on Island A, the whiskers range from 1 to 9.5, and the box ranges from 3 to 7. A line divides the box at 4. For the average wind speeds of cities on Island B, the whiskers range from 1.5 to 11, and the box ranges from 4 to 9. A line divides the box at 6.
Average Wind Speeds on Island B
Which explains, on a given day, which island is more likely to have a wind speed close to its median?
Island A because the median is closer to one end of the box in the box plot.
Island B because the median is closer to the center of the box in the box plot.
Island A because it has a smaller interquartile range.
Island B because it has a larger interquartile range.
Answer:
B
Step-by-step explanation:
I'm sorry if I'm wrong
Answer:
5
Step-by-step explanation:
meant b haha
Help me please!!
I’ll brainliest u if u get it rights
The ages of three girls; Mandy, Dora and Ann are, 113 base 4 , 133 base 4 , and 131 base 4 respectively;
find the difference between the sum of the ages of Dora and Ann and that of Mandy
Answer:
211 base 4
Step-by-step explanation:
Sum of dora and Ann = (133+131) base 4
= 330 base 4
Difference = (330-113) base 4
= 211 base 4
what's the answer for 1/2 of 3/5?
Answer:
3/10
Step-by-step explanation:
Evaluate yz + x² x=3.2, y=6.1, z=0.2
Answer:
Step-by-step explanation:
To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:
yz + x²
Substituting the given values, we get:
(6.1 * 0.2) + (3.2^2)
This simplifies to:
1.22 + 10.24
Therefore, the value of the expression is approximately 11.46.
11.46
gimme brainlyest gang
choose the option with the correct name of the segment/line/ray shown.
a. perpendicular bisector
b. angle bisector
c. median
d. altitude
Answer:
angel bisector
Step-by-step explanation:
this pic explains why
For the function y=-1+6cos(2pi/7(x-5)) what is the maximum value
The maximum value of the function y = -1 + 6cos((2π/7)(x-5)) is 5.
To find the maximum value of the function y = -1 + 6cos((2π/7)(x-5)), we can observe that the cosine function has a maximum value of 1 when the argument is 0.
In this case, the argument of the cosine function is (2π/7)(x-5). To find the maximum value of the function, we need to determine the value of x that makes the argument 0.
Setting (2π/7)(x-5) equal to 0, we have:
(2π/7)(x-5) = 0
To solve for x, we can multiply both sides by 7/(2π):
x - 5 = 0
Adding 5 to both sides:
x = 5
So, the argument of the cosine function is 0 when x = 5.
Substituting x = 5 into the original function:
y = -1 + 6cos((2π/7)(5-5))
y = -1 + 6cos(0)
y = -1 + 6(1)
y = -1 + 6
y = 5
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what is the y-intercept of the graph of y = 4^x-2?
Answer: Hope this helps you.
-2
Step-by-step explanation:
y = mx+b (B is y-int)
y = 4^x-2
-2 is clearly replacing the b (y-int) meaning b, the y-int, is -2
\(y = {4}^{x} - 2 \\ for \: y \: intercept \: x \: s \\ is \: 0 \\ y = {4}^{0} - 2 \\ y = 1 - 2 \\ y = - 1 \\ \)
Y intercept : (0,-1)
Hope it helps
please give brainliest
___ + 3 = 15 ; x = 4
how to make it equivalent help
Answer:
3x
Step-by-step explanation:
What do u mean do you have to put the x with something?
I need a answer fast thanks!
Answer:
Chart:
x y
-6 11
3 5
15 -3
-12 15
Step-by-step explanation:
The only things you can plug in are the domain {-12, -6, 3, 15}
Plug in the domain into equation to find y.
-6 :
y = -2/3 (-6) +7
y = +47
y=11
(-6,11)
3:
y = -2/3 (3) +7
y = -2 +7
y = 5
(3, 5)
15:
y = -2/3 (15) +7
y = -10 +7
y = -3
(15 , -3)
-12:
y = -2/3 (-12) +7
y = 8 + 7
y= 15
(-12,15)
Answer:
1) 11
2) 3
3) -3
4) -12
Step-by-step explanation:
eq(1):
\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)
1) x = -6
sub in eq(1)
\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)
2) y = 5
sub in eq(2)
\(x = (7-5)\frac{3}{2} \\\\x = 3\)
3) x = 15
sub in eq(1)
\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)
4)
sub in eq(2)
\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)
Andrea bough a bucket of colored chalk. The list below shows the fraction of each color of chalk in the bucket. 2/6 are yellow, 5/12 are blue, and 3/12 are green. Andrea told Michelle that less than 1/2 the chalk in the bucket is blue. Michelle said she is mistaken. Who is correct? Explain why you chose your answer.
Given the fraction of each colored chalk, Andrea is right that less than 1/2 the chalk in the bucket is blue.
How to solve fractions?Yellow = 2/6Blue = 5/12Green = 3/12Total = 2/6 + 5/12 + 3/12
= (4+5+3) / 12
= 12/12
= 1
Fraction of blue : Total chalk
= 5/12 : 1
Blue = 5/12 ÷ 1
= 5/12 × 1/1
= 5/12
= 0.42
So,
1/2 = 0.5
Therefore, Andrea is right that less than 1/2 the chalk in the bucket is blue.
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USE WORSKIN METHOD TO FIND THE GENERAL SOLUTION OF THE FOLLOWING SECOND ORDER LINEAR ORDINARY DIFFERNTIAL EQUATION? y²-10 y² + 25 Y ====2=²2
The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.
The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.
Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.
Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.
Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.
Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.
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the force, F newtons (N) between two particles is inversely proportional to the square of the distance, d m, between them. When the particles are 2m apart,
the force between them is 10 N. Find
1- the force between the particles when they are 5m apart,
2- the distance between the particles when the force between them is 25 N.
The force is 1.6N and the distance between them is 1.3 meters
The force between themAn inverse variation from force to the square of distance is represented s:
k = Fd^2
Where k represents the variation constant
When F = 10, d = 2.
So, we have:
k = 10 * 2^2
k = 40
Substitute k = 40 in k = Fd^2
Fd^2 = 40
When d = 5, we have:
F * 5^2 = 40
This gives
25F = 40
Divide by 25
F = 1.6
Hence, the force is 1.6N
The distance between themIn (a), we have:
Fd^2 = 40
When F = 25, we have:
25 * d^2 = 40
This gives
25d^2 = 40
Divide by 25
d^2 = 1.6
Take the square root of both sides
d = 1.3
Hence, the distance between them is 1.3 meters
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. A cylinder has a radius of 7 cm and a height of 12 cm. Calculate the total surface area. (Take π = 22/7)
Answer:
154cm^2
Step-by-step explanation:
Area of circle= pi×r^2
= 22/7 × (7cm)^2
= 22/7 × 49cm^2
= 154cm^2
Parallel lines cut by transversals s and t to form the diagram below . What is the value of x?
Answer:
Step-by-step explanation:
80 degrees
1. If a researcher accepts a true null hypothesis, she has made a _______ decision.a. businessb. hypotheticalc. incorrectd. correct
Answer:
d. correct
Step-by-step explanation:
if it helped u please mark me a brainliest :))
Question 5
10 pts
A grocery store sells 2 boxes of cereal for $4.95. Which method can be used to
find the total cost c of purchasing n boxes of cereal?
O Multiply n by the cost of one box.
O Multiply n by c.
O Divide n by the cost of one box.
Divide n by c.
Answer:
Multiply n by the cost of the box.
Step-by-step explanation:
hey there,
< For these kinds of problems I always like making ratio tables.
2 boxes → $4.95
n boxes → $?
To find the thing we don't know in any ratio table (marked by "?"), you have to multiply the two opposites and then divide by the last one standing. I know that sounds confusing so let me explain...
"Two opposites" means the two values that are right across from each other, but do not include the unknown ("?"). In this example, the two diagonally across from each other are "n" amd "4.95". "2" and "?" can't be right across from each other because one of those is a "?".
Multiply the two opposites. n × 4.95. Let's not actually simplify since this isn't what we are doing here in this question and leave it like this:
n × 4.95 = (n × 4.95)
Now that we found that, we have to divide it by the last number available. The last number available that we haven't used yet is "2" (it obbviously can't be the unkown number "?").
(n × 4.95)/2
Whatever the result of the above equation is, is the answer.
(n × 4.95)/2 = ?
In our situation, "?" means "c". This is how you would solve any ratio table, it might seem tricky at first but it's actually super easy.
In this question, we are not asked to divide by two because they want to know a method of solving using the cost of one box.
\(\frac{(n*4.95)}{2} / 2\)
n × (4.95/2)
4.95/2 is the cost of one box. Multiply that by "n" and there is your final answer. >
I seriously hoped this help cause this question was kind of hard to explain. Feel free to ask anything else.
Please helppppp me What’s the answer?
Answer:
She shaded above the line when she should have shaded below the line.
Step-by-step explanation:
hope this helps and is right. p.s. i really need brainliest :)
if this is wrong then I am incredibly sorry!
What is the acceleration of Romeo's 900 kg horse if it moves with a force of 9000N?
In right triangle ABC, if AC = 5/13 and AB = 1, what is the length of BC?
Answer:
BC = \(\frac{12}{13}\)
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
BC² + AC² = AB²
BC² + (\(\frac{5}{13}\) )² = 1²
BC² + \(\frac{25}{169}\) = 1 ( subtract \(\frac{25}{169}\) from both sides )
BC² = \(\frac{169}{169}\) - \(\frac{25}{169}\) = \(\frac{144}{169}\) ( take square root of both sides )
BC = \(\sqrt{\frac{144}{169} }\) = \(\frac{12}{13}\)
write the sun of twice a number and 17 is 81. what is the number
Answer:
2x + 17 = 81 is the equation
x=32
Step-by-step explanation:
2x + 17 = 81
subtract 17 from 81, which is 64
64 divided by 2 is 32
to check the answer, 2 times 32 = 64 + 17 = 81
hope this helped :)
Jake made a wooden cone with a diameter of 6 inches and a height of 4.5 inches. What is the volume of this cone?
Answer:
The volume of cone
V = (1/3) x base area x height
= (1/3) x (diameter/2)^2 x pi x height
= (1/3) x (6/2)^2 x pi x 4.5
= 42.41 (in3)
Hope this helps!
:)