If X and Y are independent standard normal random variables, determine the joint density function of
U = XV
=X/Y
Then use your result to show that has a Cauchy distribution.
The joint density function of u and v

The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

What is independent event ?

In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.

Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:

P(A and B) = P(A) x P(B)

If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.

According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.

We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.

If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.

This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.

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It is to score 35 points in 20 minutes greater than 49 goals in 35.

More than and less than signs are used to indicate whether one number is greater than or less than another. If the initial number surpasses the second number, the larger than symbol (>) is used. The sign () is used to indicate that the first number is smaller than the second number.

This sign is used to denote that one value is greater than the other. For

instance, it is accurate to say that 4 is more than 2. Hence, it may be

expressed simply 4 > 2. Let's now examine the greater than sign from both

its left and right sides.

35 / 20 = 1.75

49 / 35 = 1.4

Therefore, 35 points in 20 minutes is greater than 49 points in 35 minutes.

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Complete question -

35 points in 20 minutes or 49 points in 35 minutes? Find which is greater.

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:yesStep-by-step explanation:

yes

Answer:

3

Step-by-step explanation:

513 = 500 + 10 + 3

The 5 is worth 500.

The 1 is worth 10.

And the 3 is worth 3 !

Answer:

The value of 3 in 513 is the ones place.

Step-by-step explanation:

Answer:

2/3 divided by 4 = .16

Step-by-step explanation:

This problem is pretty simple. Since we cannot divide this we can change the division sign into a multiplication, but to do this we need to also take the reciprocal of 2/3, which means we flip th number so it becomes 3/2. Now we can simply multiply. (1/4)*(3/2) which should give you 3/8

Answer:

  (a)  42 = x + 29

Step-by-step explanation:

You want the equation showing how many cookies (x) Bella will bake when she returns home, adding to the 29 she already baked, to make a total of 42 cookies.

The numbers of cookies baked (29) and cookies to be baked (x) will add up to give a total of 42 cookies:

  42 = x + 29

__

Additional comment

We know the value of x will be found by subtracting 29 from 42.

  x = 42 -29 . . . . . . subtract 29 from both sides of the above equation

  x = 13

This knowledge might tempt one to choose one of the answers involving subtraction. Here, the question is not about the value of x. It is about the relationship between the numbers 42, 29, and x. The purpose of the equation is to describe that relationship.

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The difference in speed between Explorer B and Explorer A is 600 miles per hour.

In order to determine how fast the satellites are travelling, the average speed of the satellites have to be calculated. Average speed is the total distance covered per time.

Average speed = total distance / total time

Average speed of Space Explorer B = 74,400 / 12 = 6,200 miles per hour

Average speed of Space Explorer A = 72,800 / 13 = 5,600 miles per hour

Difference in speed = 6,200 miles per hour - 5,600 miles per hour = 600 miles per hour.

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Answer:

2 gallons converted to liters is 7.57 or 8 liters rounded

Answer:

p > - 8

Step-by-step explanation:

4p + 2 < 6(p + 3)

4p + 2 < 6p + 18

-2p < 16

p > - 8

Given:

Cost of students tickets is, c (s) = $8.

Cost of adult tickets is, c (a) = $10.

Total cost collected for by selling the tickets is, c (t) = $1,760.

Number of tickets sold is, n = 200.

The objective is to find the system of equations that can model the number of students and adults tickets sold at the booth.

Consider the number of students as x and number of adults as y.

Then, the equation of total numner of students will be,

Now, the cost equation can be calculated as,

Hence, the system of equations that can model the number of students and adults tickets are x + y = 200 and 8x + 10y = 1760,

Answer:

27.9

Step-by-step explanation:

3*3.1 = height = 9.3

9.3 * 3

Answer:11

Step-by-step explanation:

The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.

The correct answer is 4.

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.

Given information:

- Circle C (cats): 15

- Circle D (dogs): 21

- Circle F (fish): 12

- Overlap of C and F: 2

- Overlap of F and D: 0

- Overlap of D and C: 3

- Overlap of all 3 circles: 1

- Number outside of circles: 14

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.

From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.

To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.

Therefore, from the options given correct one is 4.

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Answer: 4

Step-by-step explanation:

trust me bro

Answer:  n = -1

Step-by-step explanation: distribute 7 to n +4 to get 7n +28 = 21

subtract 28 on both sides, to get 7n= -7 divide by positive 7, and get n=-1

plug it in to check 7(-1+4)=21

-1+4= 3

7(3)= 21

it checks out ^_^

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

She uses 12 gallons of petrol to drive 420 miles, averaging 35 miles per gallon.

A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of items being distributed among a set of individuals. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The outcome of dividing one integer by another is a quotient. When dividing a number into units of a measurable quantity, this is known as quotative division. For instance, we could wish to know how many groups there will be if we divide 8 into groups of 2.

Here,

Weight of gas=12 gallon

Distance travelled=420 miles

miles did her car travel per gallon of gas,

=420/12

=35 miles/gallon

She travels 35 miles/gallon when she used 12 gallons of gas to travel 420 miles.

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Answer:

this is your answer.

when x=2

y=2-16=-14

and similarly other.

Answer:

1.  x = -1  y= -2
2. infinitely many solutions

3. x = 6 y= -7

4.no solution

5. x = -3 y = -17

6. x= 3 y = 7

Step-by-step explanation:

1) y=x-1

7x+6y= -19

6y= -19 -7x

y= (-7x-19)/6

since x-1 and (-7x-19)/6 are both equal to y they are equal to each other

this is how to get x

x-1 = (-7x-19)/6

6x-6 = -7x-19

13x = -13

x = -1

now put back -1 in the equation to get y

y=x-1

y = -1 -1

y= -2

2)-10x+2y=-12

y=5x-6

2y= -12 + 10x

y= -6 + 5x

y = 5x - 6

5x-6 = 5x - 6

0 = 0

when something is

equal to itself its

infinitely many solutions

(when something is not equal to something its no solution)

((when something is equal to just one answer its one solution)

3) y= -4x+17

y=x-13

-4x+17 = x-13

30 = 5x

x = 6

y=x-13

y=6-13

y= -7

4) -3x-15y=8

x+5y=5

-3x-15y=8 -> y = -1/15(3x-8)

5y=5-x -> y= 1/5 (5-x)

-1/15(3x-8) = 1/5 (5-x)

-x-8/3 = 5-x

0 = 23/3

(when something is not equal to something its no solution)

5) -3x+6y=-3

3x-y=8

-3x+6y= -3 -> y = 1/6(3x-3)

3x-y=8 -> y = 3x-8

1/6(3x-3) = 3x-8

3x-3 = 18x-48

x-1 = 6x - 16

5x = -15

x = -3

3x-y=8

3(-3)-y=8

-9-8 = y

y = -17

6) -6x+6y=24

-3x-8y=1

-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4

-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)

1/8 (-3x-1) = x+4

-3x-1 = 8x+32

11x = 33

x= 3

-6x+6y=24

-6(3)+6y=24

-18 + 6y = 24

6y = 24 + 18

6y = 42

y = 7

∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer:both a and b are correct

Step-by-step explanation:

Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Using Chebyshev's theorem, at least 88.89% of the observations fall between 1,215 and 1,585, and approximately 99.47% of the observations fall between 1,020 and 1,780.

a. Chebyshev's theorem states that for any data set, regardless of the shape of the distribution, at least (1 - 1/k²) of the data values will fall within k standard deviations of the mean, where k is any number greater than 1.

Using Chebyshev's theorem, we can say that at least 1 - (1/2)² = 1 - 1/4 = 0.75, or 75% of the observations fall within 2 standard deviations of the mean.

So, for this data set, we know that the interval between 1,400 - 2(95) = 1,210 and 1,400 + 2(95) = 1,590 will contain at least 75% of the observations. To find the percentage of observations between 1,115 and 1,685, we can standardize these values:

z1 = (1,115 - 1,400)/95 = -2.99

z2 = (1,685 - 1,400)/95 = 2.99

Now we want to find the proportion of observations between -2.99 and 2.99, which is the same as the proportion between -3 and 3 since Chebyshev's theorem gives only a lower bound on this proportion. From standard normal distribution tables, we know that this proportion is approximately 0.9973, or 99.73%.

Therefore, we can say that at least 75% of the observations fall between 1,210 and 1,590, and approximately 99.73% of the observations fall between 1,115 and 1,685.

b. Using the same reasoning, we know that at least 1 - (1/3)² = 1 - 1/9 = 0.8889, or 88.89% of the observations fall within 3 standard deviations of the mean.

So, for this data set, the interval between 1,400 - 3(95) = 1,215 and 1,400 + 3(95) = 1,585 will contain at least 88.89% of the observations. To find the percentage of observations between 1,020 and 1,780, we can standardize these values:

z1 = (1,020 - 1,400)/95 = -4.00

z2 = (1,780 - 1,400)/95 = 3.99

We want to find the proportion of observations between -4 and 3.99. From standard normal distribution tables, we know that this proportion is approximately 0.9947, or 99.47%.

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53/6, 203/10 and 73/5 rounded to the nearest whole number are 9, 20 and 15 respectively

Approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up.

The numbers can be rounded to the nearest whole number as follows:

53/6 = 8.83 = 9          (round up)

203/10 = 20.3 = 20    (round down)

73/5 = 14.6 = 15           (round up)

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Answer:

the total dosage is 4.5 mg of tablets

Step-by-step explanation:

Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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Answer:

ok keep going more questions cause ido t get it what u trying to ask

Using the parentheses to rewrite the equation 8×9-2-3​ gives 67.

In mathematics, the order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved.

A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation. There is also another version called BODMAS but the principles are the same

Parenthesis            (  )

Exponent                a⁷

Multiplication          ×

Division                   ÷

Addition                  +

Subtraction             -

Given: 8×9-2-3​

We can rewrite the equation using parenthesis using PEMDAS:

Multiplication first, then followed by addition/subtraction:

8×9-2-3​ = (8 × 9) - 2 - 3

             = 72 - 2 - 3​

             = 67

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable