Walter created this table to show a proportional relationship. Which values can be added to the table without changing the relationship?

A. 2 cups of flour for 2 batches
B. 4 cups of flour for 6 batches
C. 8 cups of flour for 4 batches
D. 12 cups of flour for 8 batches

X and Y are not independent

In order to answer this question, we need to refer back to Exercise 5.1.1, which defines the joint distribution of two random variables X and Y as:

P(X = 1, Y = 1) = 0.1
P(X = 1, Y = 2) = 0.2
P(X = 1.5, Y = 1) = 0.3
P(X = 1.5, Y = 2) = 0.4

a. To determine the conditional probability distribution of Y given that X = 1.5, we need to use the formula:

P(Y = y | X = 1.5) = P(X = 1.5, Y = y) / P(X = 1.5)

Using the joint distribution from Exercise 5.1.1, we can calculate the probabilities as follows:

P(Y = 1 | X = 1.5) = 0.3 / (0.3 + 0.4) = 0.4286
P(Y = 2 | X = 1.5) = 0.4 / (0.3 + 0.4) = 0.5714

Therefore, the conditional probability distribution of Y given that X = 1.5 is:

P(Y = 1 | X = 1.5) = 0.4286
P(Y = 2 | X = 1.5) = 0.5714

b. To determine the conditional probability distribution of X given that Y = 2, we use the same formula as above:

P(X = x | Y = 2) = P(X = x, Y = 2) / P(Y = 2)

Using the joint distribution from Exercise 5.1.1, we can calculate the probabilities as follows:

P(X = 1 | Y = 2) = 0.2 / (0.2 + 0.4) = 0.3333
P(X = 1.5 | Y = 2) = 0.4 / (0.2 + 0.4) = 0.6667

Therefore, the conditional probability distribution of X given that Y = 2 is:

P(X = 1 | Y = 2) = 0.3333
P(X = 1.5 | Y = 2) = 0.6667

c. To calculate E(Y | X = 1.5), we use the formula:

E(Y | X = 1.5) = ∑ y * P(Y = y | X = 1.5)

Using the conditional probability distribution of Y given that X = 1.5 from part a, we can calculate the expected value as follows:

E(Y | X = 1.5) = 1 * 0.4286 + 2 * 0.5714 = 1.714

Therefore, E(Y | X = 1.5) = 1.714.

d. To determine whether X and Y are independent, we need to check whether the joint distribution factors into the product of the marginal distributions:

P(X = x, Y = y) = P(X = x) * P(Y = y)

Using the joint distribution from Exercise 5.1.1, we can see that this condition does not hold, since for example:

P(X = 1.5, Y = 1) = 0.3
P(X = 1.5) * P(Y = 1) = 0.5 * 0.4 = 0.2

Therefore, X and Y are not independent.

To know more about conditional probability refer here:

https://brainly.com/question/30144287

#SPJ11

The point (180, -19) is on the terminal side of the angle θ, the exact values of the trigonometric functions are sin(θ) = -19/181, cos(θ) = 180/181, and tan(θ) = -19/180.

Since the point (180, -19) is on the terminal side of the angle θ, we can calculate the trigonometric functions using the coordinates.
First, find the distance from the origin to the point (180, -19). This distance will represent the hypotenuse (r) of the right triangle formed by the terminal side. Use the Pythagorean theorem:
r = √(x^2 + y^2) = √(180^2 + (-19)^2) = √(32400 + 361) = √(32761) = 181
Now that we have the hypotenuse (r), we can find the exact values of the trigonometric functions for the angle θ using the coordinates:
sin(θ) = y/r = -19/181
cos(θ) = x/r = 180/181
tan(θ) = y/x = -19/180
So, given that the point (180, -19) is on the terminal side of the angle θ, the exact values of the trigonometric functions are sin(θ) = -19/181, cos(θ) = 180/181, and tan(θ) = -19/180.

Learn more about exact value here, https://brainly.com/question/30695546

#SPJ11

The lower bound for P(X ∈ (uX - 3, uX + 3)) is given by P(|X - u| > 2σ) ≤ 1/4, These bounds obtained using Chebyshev's inequality provide an estimate of the probability ,

that X falls within the specified intervals (uX – 1, uX + 1) and (uX - 3, uX + 3), respectively. (a) Chebyshev's inequality states that for any random variable X with mean μ and standard deviation σ,

the probability that X deviates from its mean by more than k standard deviations is at most 1/k^2. In this case, the random variable X has a mean μ = u and a standard deviation σ = sqrt(22).

To obtain an upper bound for P(X ∈ (uX – 1, uX + 1)), we need to determine the value of k such that the probability of X deviating from its mean by more than k standard deviations is at most 1/2.

Using Chebyshev's inequality, we have: P(|X - u| > kσ) ≤ 1/k^2

Setting the right-hand side to 1/2, we can solve for k:

1/k^2 = 1/2

k^2 = 2

k = sqrt(2)

Therefore, the upper bound for P(X ∈ (uX – 1, uX + 1)) is given by:

P(|X - u| > sqrt(2)σ) ≤ 1/2

(b) To obtain a lower bound for P(X ∈ (uX - 3, uX + 3)), we need to determine the value of k such that the probability of X deviating from its mean by more than k standard deviations is at most 1/4.

Using Chebyshev's inequality, we have: P(|X - u| > kσ) ≤ 1/k^2

Setting the right-hand side to 1/4, we can solve for k:

1/k^2 = 1/4

k^2 = 4

k = 2

Therefore, the lower bound for P(X ∈ (uX - 3, uX + 3)) is given by:

P(|X - u| > 2σ) ≤ 1/4

These bounds obtained using Chebyshev's inequality provide an estimate of the probability that X falls within the specified intervals (uX – 1, uX + 1) and (uX - 3, uX + 3), respectively.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Yes, it is appropriate to compute the likelihood that a random ladybug in Raleigh will be larger than 1.5 cm.

With a mean of 0 and a standard deviation of 1, the standard normal distribution is a normal distribution. The standard deviation, which indicates how much a given measurement deviates from the mean, is given by the standard normal distribution, which has zero as its center.

As the sample size is sufficient (440000) and the standard deviation is known, it is appropriate to use a normal distribution to estimate the distribution of ladybug lengths. A 1.5 cm long ladybug's z-score can be calculated as follows:

z = (1.5 - 1) / 0.2 = 2.5

We can calculate the likelihood of a z-score being greater than 2.5 using a conventional normal distribution table to be roughly 0.0062. Hence, the likelihood that a random ladybug in Raleigh will be larger than 1.5 cm is around 0.0062 or 0.62%.

Therefore, the correct answer is option d. Yes. Clear my choice.

The complete question is;

American ladybugs have an average adult length of 1 cm with a known standard deviation of 0.2 cm. The population of American ladybugs in Raleigh was around 440000 last spring. Assume a normal distribution for the lengths of adult American ladybugs. Your niece asks you what's the probability of a random ladybug in Raleigh being bigger than 1.5 cm. Is it appropriate to calculate this probability? Select one:

a. No, because the population distribution is skewed.

b. No, because the sample size is less than 30.

c. No, because the empirical rule is violated.

d. Yes. Clear my choice

To learn more about standard normal distribution refer to:

https://brainly.com/question/13781953

#SPJ1

Answer:

An engaging digital escape room for students learning to find slope given graphs, tables and coordinate pairs. Students must unlock 5 locks by answering 20 slope questions. Questions are grouped 4 per puzzle, resulting in five 4-letter codes that will unlock all 5 locks.

It's also known as the room of escape, for the Learners who lean digitally can find slopes given graphs, tables, and coordinate pairs. Learners will open 5 locks/questions by solving the 20 slope questions.

Learn more:

brainly.com/question/21314641

Answer:

Q1: 42

Q8: 10

Step-by-step explanation:

PEMDAS

The answer is 25

Sooooo to find the hypotenuse you gotta use this formula: a^2+b^2=c^2.

Answer:

I think personification

Step-by-step explanation:

Answer:

the two equations you can use are

y = 2x - 3

y + x = 9

\(\\ \sf\longmapsto \dfrac{12.19}{5.7}\)

\(\\ \sf\longmapsto 2.14/lb\)

2.15/lb+2=2.17/lb

Brand 2 is a better deal and 2.17lb is the unit price

The number of possible combinations will depend on the size of the restaurant chain. However, we can always use the formula nCr to calculate the number of different possible ways to select r items from a set of n items.

To determine the number of different possible ways the general manager can select restaurants for the promotional program, we need to use the formula for combinations. Let's say there are n restaurants in the chain, and the manager needs to select r restaurants for the program. The formula for combinations is:
nCr = n! / r!(n-r)!
In this case, the manager needs to select a certain number of restaurants, so r is a fixed value. Let's assume the manager needs to select 5 restaurants for the program. Then the formula becomes:
nC5 = n! / 5!(n-5)!
We don't know the value of n, but we can calculate the number of possible combinations for different values of n. For example:
- If there are only 5 restaurants in the chain, then the manager has no choice but to select all of them. In this case, there is only one possible combination.
- If there are 10 restaurants in the chain, then the manager can select any 5 of them. Using the formula, we get:
nC5 = 10! / 5!(10-5)! = 252
So there are 252 different possible ways for the manager to select 5 restaurants from a chain of 10.
- If there are 20 restaurants in the chain, then the manager has even more choices. Using the formula, we get:
nC5 = 20! / 5!(20-5)! = 15,504
So there are 15,504 different possible ways for the manager to select 5 restaurants from a chain of 20.
In general, the number of possible combinations will depend on the size of the restaurant chain. However, we can always use the formula nCr to calculate the number of different possible ways to select r items from a set of n items.

To know more about combinations visit:

https://brainly.com/question/28065038

#SPJ11

The "switch" statement is useful when you need to test a single variable against a series of exact integer, character, or string values.

The switch statement is a control structure found in many programming languages, including C++, Java, and JavaScript. It allows you to evaluate a variable or expression and compare it against multiple cases.

Each case represents a specific value that the variable or expression is tested against. When a match is found, the corresponding block of code associated with that case is executed.

The switch statement is particularly useful when you have a variable that can take on different values and you want to perform different actions based on those values. Instead of writing multiple if-else statements, the switch statement provides a more concise and efficient way to handle such scenarios.

Learn more about Switch Statement here:

brainly.com/question/30763180

#SPJ11

Answer:

A. 37.

Step-by-step explanation:

In B, that is making a withdrawal.

In C, because of the *||*s around it, this means that the number inside of those lines will always be positive. But the negative is outside of the lines so it is still negative.

In D, you might think that the |-37| cancels out the - on the outside. But like I said, those lines mean that anything inside of the lines will always be positive. Meaning that the |-37| inside just becomes |37| and still turns negative because of the - on the outside.

Hope this helped, the detailed explanation took a minute! :D

Answer:

D.

x and y are the terms think about the letters in the expression and those are the terms.

The option that is NOT an augmented functional dependency is: Q --> P, because it removes the attribute from the left-hand side of the existing functional dependency, which is not allowed in an augmented dependency.

Functional dependency: It is a concept in database management systems that describes the relationship between two attributes or sets of attributes in a table. In a functional dependency A → B, A is the determinant or the attribute(s) that uniquely determines the value of B.

Augmented functional dependency : It is formed by adding one or more attributes to the determinant side of an existing functional dependency.

From the given options, the only one that is not an augmented functional dependency is "Q → P". This is because it does not involve adding any attributes to the determinant side of an existing functional dependency.

To learn more about the functional dependency:

https://brainly.com/question/28812260

#SPJ11

Answer: 580

Step-by-step explanation: i learned that just like 1 hour ago in school

The sum of two integers is also an integer.

What is an integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

When we conduct an operation on set members and always obtain a set member, the set is said to be closed under that operation. As a result, a set either possesses closure regarding a particular operation or it does not. A set is said to satisfy a closure property if it is closed by an operation or set of operations. A closure property is typically introduced as a hypothesis, known as the axiom of closure.

If a and b two integer.

Then the sum of the integer a + b is also an integer. Thus addition operation closer property.

To learn more about closer property, click on below link:

https://brainly.com/question/29798480

#SPJ4

In linear programming (LP), the value of one additional unit of a scarce resource is represented by the shadow price or dual price. It indicates the increase in the objective function value per unit increase in the availability of that resource, assuming all other constraints remain binding.

In linear programming, a scarce resource refers to a limited quantity of a particular input, such as labor, raw materials, or machine capacity. The objective of LP is to optimize a linear objective function while satisfying a set of linear constraints.

The shadow price or dual price associated with a resource represents the rate of change in the objective function value when the availability of that resource is increased by one unit. It provides information on the marginal value of the resource and helps in decision-making regarding the allocation of resources.

The shadow price is obtained by solving the dual LP problem, which involves maximizing or minimizing the dual variables corresponding to the resource constraints while keeping the objective function coefficients fixed.

For more questions like Programming click the link below:

https://brainly.com/question/30763902

#SPJ11

The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

Learn more about linear equations at.

https://brainly.com/question/1884491

#SPJ1

According to the information, the 7 gold medals that Australia won in the Olympics correspond to 20% of the medals that this country won.

To find the percentage of gold medals that Australia won in the Olympic games, we must take into account the available information and perform the following mathematical operation:

Rule of three

According to the above, the 7 gold medals won by Australia in the Olympic Games are equivalent to 20% of the medals won by this country.

Learn more about medals in: https://brainly.com/question/29023646

#SPJ1

Answer:

502.40 inches

Step-by-step explanation:

First we need to find the circumference of the wheel, which is given by pi times the diameter:

C = (3.14)(20) = 62.8 inches

That's how far the unicycle will travel in 1 revolution, so from there just multiply by 8

D = (62.8)(8) = 502.40 inches

The unicycle travel 502 inches in 8 revolutions

The circumference is the perimeter of a circle. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment.

Given that, a unicycle wheel has a diameter of 20 inches.

To find that how many inches will the unicycle travel in 8 revolutions, we will multiply the circumference to the asked number of revolutions.

Circumference = π × diameter

= 3.14 × 20 = 62.8 inches

The unicycle travel in 8 revolutions = 62.8 × 8 = 502.4 inches

In nearest hundred = 502 inches

Hence, the unicycle travel 502 inches in 8 revolutions

For more references on circumference, click;

https://brainly.com/question/28757341

#SPJ5

Answer:

where is the thing to answer

Answer:

Ok im going on your page to see the question

Answer:

1847.26 cubic inches

Step-by-step explanation:

The volume of a cylinder is given by the formula:

V = Ah

Where V is the volume of the cylinder, A is the area of the base, and h is the height of the cylinder. The area of the base can be shown as the formula for the area of a circle:

A = πr²

Where r is the radius of the circle.

Now, find the area of the base of the cylinder:

A = π(7)²

A = 153.93804

Next, plug this value into the equation for volume, substituting h for the height of the cylinder; 12 inches.

V = 153.93804(12)

V = 1847.26

Volume is given in cubic units, and the units for this cylinder are inches, so this cylinder has the following volume:

1847.26 cubic inches

Answer:

\(7.76\times 10^6\ \text{inches}\)

Step-by-step explanation:

We know that,

\(1\ \text{inch}=1.578 \times 10^{-5}\ \text{miles}\)

We need to convert 1225 miles to inches. It can be done as follows :

\(1\ \text{mile}=\dfrac{1}{1.578 \times 10^{-5}}\ \text{inches}\\\\1225\ \text{miles}=\dfrac{1225}{1.578 \times 10^{-5}}\ \text{inches}\\\\=7.76\times 10^6\ \text{inches}\)

So, there are \(7.76\times 10^6\ \text{inches}\) in 1225 miles.

Answer:

-3/2

Step-by-step explanation:

it starts with

D = -3/2

then -D = - -3/2 = 3/2

and then - -D = -3/2

Answer:

C= 2π14.5

C= 91.1061869

91.1061869 X 7.5 = 683.296402

A of a circle = πr squared

as the are two circles to a cylinder 2πr squared

2 X π X 14.5 = 1321.03971

add together

1321.03971 + 683.296402 = 2004.33611 ft squared

Answer:

3/4 is the answer

Step-by-step explanation: