If you were to spin the spinner at left, what would be the probability of landing on green or orange? P(green or orange) Write your answer as a simplified fraction.

(a)  The Jacobian is 1/(x+y)^2, and the joint PDF is given by fU,V(u,v) = 2e^(-u)(1-v) for 0<u<∞ and 0<v<1.

(b) The distribution of U can be identified as the gamma distribution with shape parameter k = 2 and scale parameter θ = 1, denoted as U ~ Gamma(2, 1).

(c) The distribution of V can be identified as the beta distribution with shape parameters α = 1 and β = 1, denoted as V ~ Beta(1, 1).

(a) The joint probability density function (pdf) of U and V can be found using the concept of transformation of random variables.

We have U = X + Y and V = X/(X + Y).

To find the joint pdf, we need to calculate the Jacobian of the transformation.

The Jacobian of the transformation is given by:

J = ∂(u, v) / ∂(x, y) = 1 / ((1 - v)^(2))

Since X and Y are independent exponential random variables with parameter λ = 1, their pdf is given by:

f(x) = e^(-x) and f(y) = e^(-y)

Now, we can express U and V in terms of X and Y:

U = X + Y

V = X / (X + Y)

Using the Jacobian, the joint pdf of U and V is:

f(u, v) = f(x, y) * |J|

        = e^(-(x + y)) * (1 - v)^2

(b) The distribution of U can be identified as the Gamma distribution with shape parameter α = 2 and scale parameter β = 1. The Gamma distribution is a continuous probability distribution that is often used to model the waiting times or survival times.

The pdf of U is given by:

f(u) = (1/1!) * u^(2-1) * e^(-u/1)

     = u * e^(-u)

(c) The distribution of V can be identified as the Beta distribution with shape parameters α = 1 and β = 1. The Beta distribution is a continuous probability distribution defined on the interval [0, 1], often used to model probabilities or proportions.

The pdf of V is given by:

f(v) = (1/1!) * v^(1-1) * (1-v)^(1-1)

     = 1

Therefore, the distribution of V is a uniform distribution with support on the interval [0, 1].

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Step-by-step explanation:

Answer. in the attachment

Answer:

Yes they are.

They are congruent because they have two equal angles and one equal side

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

The function F(x) is a cubic function.

Here, we have,

given function is:

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

To determine the algebraic degree of the given (7,7)-function F(x), we need to find the highest exponent of x in the function.

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

The algebraic degree of a polynomial function corresponds to the highest exponent of the variable in the function.

Linear functions have an algebraic degree of 1, affine functions have an algebraic degree of 1 or 0, quadratic functions have an algebraic degree of 2, and cubic functions have an algebraic degree of 3.

so, we get,

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

Therefore, the function F(x) is a cubic function.

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The mean of the game is 9

To find the mean of a game with two possible outcomes, we need to multiply the value of each outcome by its probability and then add the results.

Let X be the random variable representing the outcome of the game. The first outcome has a value of 5 and a probability of 0.2, while the second outcome has a value of 10 and a probability of 0.8.

Thus, the expected value or mean of the game can be calculated as:

E(X) = (0.2 x 5) + (0.8 x 10)

= 1 + 8

= 9

Therefore, the mean of the game is 9

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Answer: $1841.38 .

Step-by-step explanation:

Given, the equation \(y=4.65(1.37)^x\) fits the graph of stock XYZ over the past month with an r=value of 0.9894.

At x= 19,

\(y=4.65(1.37)^{19}\\\\\Rightarrow\ y=4.65(395.9960)\\\\\Rightarrow\ y=1841.38\)

Hence, At x= 19 days , the worth of XYZ will be $1841.38 .

The area of the circle is 314 cm².

Given that a circle has a radius of 10 m, we need to find the area of the circle,

Area of the circle = π × radius²

= π × 10²

= 100 π cm² [in terms of π]

= 100 × 3.14

= 314 cm²

Hence the area of the circle is 314 cm².

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The translated question =

How to find the area of a circle from a radius of 10 m.

Answer:

x = -1

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

5x - (x + 4) + 1 = 3 - 2(x + 6)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

Answer:

3.5 pounds

Step-by-step explanation:

7/8 / 1/4 =7/8*4=7/2=3.5

A rectangle with an area of 12x² - 3x - 15 can have dimensions of (3x - 5) and (4x + 3), or vice versa.

To find the dimensions of a rectangle with a given area, we need to factor the expression 12x² - 3x - 15. By factoring the expression, we can determine the two dimensions of the rectangle.

The given expression can be factored as follows:

12x² - 3x - 15 = (3x - 5)(4x + 3)

The dimensions of the rectangle are (3x - 5) and (4x + 3), or vice versa. This means that the length of the rectangle is 3x - 5, and the width is 4x + 3. Alternatively, the length could be 4x + 3, and the width could be 3x - 5.

For example, if we take the length as 3x - 5 and the width as 4x + 3, the area of the rectangle is obtained by multiplying these two dimensions:

Area = (3x - 5)(4x + 3)

= 12x² + 9x - 20x - 15

= 12x² - 11x - 15

Thus, we have determined that a rectangle with an area of 12x² - 3x - 15 can have dimensions of (3x - 5) and (4x + 3), or vice versa.

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Answer:

Step-by-step explanation:

The root which is 2 is the fractional portion of your exponent

\(\sqrt{x^{7} y^{12} }\)

=\((x^{7} y^{12} )^{\frac{1}{2} }\)              >You can distribute 1/2 to each term by multiplying

\(=x^{\frac{7}{2} } y^{6\)

Answer:

980

Step-by-step explanation:

I did it

Answer: $23 per person

2,600,000/110,945 = 23.43035 (round to 5 decimal places)

The two significant digits of 23.43035 = 23

thus making it $23 per person.

Here is another example:

4,500,000/260,732= 17.25910

Two significant digits of 17.25910 = 17.25910 (without rounding). However, if it was 17.54210 it would be $18 per person. Hope those two examples help. If not let me know.

a. To determine the probabilities associated with different service lives, we can use the properties of the normal distribution. Given that the mean service life is six years with a standard deviation of one-half year, we can calculate the probabilities as follows:

(1) Probability of service lives of at least five years:

We need to calculate the area under the normal curve to the right of five years. Using the Z-score formula, we find the Z-score corresponding to five years: Z = (5 - 6) / 0.5 = -2. We can then look up the corresponding probability in a standard normal distribution table or use statistical software to find the probability associated with a Z-score of -2. This gives us the probability of service lives of at least five years.

(2) Probability of service lives of exactly six years: Since the service life follows a normal distribution, the probability of exactly six years is zero since it is a continuous distribution. We can assign a very small positive probability to approximate "exactly" six years. (3) Probability of service lives of seven and one-half years: Similarly, we calculate the Z-score corresponding to seven and one-half years: Z = (7.5 - 6) / 0.5 = 3. We find the probability associated with a Z-score of 3 to determine the probability of service lives of seven and one-half years or longer. b. If the manufacturer offers service contracts of four years, we want to find the percentage of televisions that fail from wear-out during this period. We can calculate this by finding the area under the normal curve to the left of four years. Using the Z-score formula, we find the Z-score corresponding to four years: Z = (4 - 6) / 0.5 = -4. The corresponding probability gives us the percentage of televisions expected to fail during the four-year service period.

c. To achieve an expected wear-out rate of 2 percent or 5 percent, we need to determine the service period corresponding to these rates. We can use the Z-score formula in reverse to find the Z-score that corresponds to the desired wear-out rate. From there, we can calculate the corresponding service period by rearranging the Z-score formula and substituting the desired wear-out rate and the given mean and standard deviation values.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The expression for the probability density function of the Weibull distribution will be: f(x) = k * x^(k-1) * e^(-x^k)

The expression for the probability density function (pdf) of a Weibull distribution is given by:

f(x) = k * x^(k-1) * e^(-x^k)

where:

x is the random variable

k is the shape parameter, which determines the shape of the distribution

e is the base of the natural logarithm

The shape parameter can take on any positive value, and the distribution is typically characterized by a shape that is either increasing or decreasing, depending on the value of k.

If the value of the k is less than 1, the distribution has a decreasing hazard rate, indicating that the failure rate decreases over time.

If the value of the k is greater than 1, the distribution has an increasing hazard rate, indicating that the failure rate increases over time.

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All veterinarians that responded to the questionnaire were included in the sample.

Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?

a. The sample consisted of all veterinarians on the list and therefore equaled the target population.

b. The sample consisted of all veterinarians who returned the questionnaire.

c. The sample consisted of all veterinarians who treat horses with NSAIDs.

d. None of the choices are correct.

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The interval on which the temperature was over 100°F is (0.79, 1.26).

To find the interval on which the temperature was over 100°F, we need to solve the inequality T(t) > 100.
First, let's rearrange the equation to isolate t:
T(t) = [4t / (t²+1)] + 98.6 > 100
[4t / (t²+1)] > 1.4
4t > 1.4(t²+1)
0 > 1.4t² - 4t + 1.4
Now we can use the quadratic formula to find the values of t that make this inequality true:
t = [-(-4) ± √((-4)² - 4(1.4)(1.4))] / [2(1.4)]
t = (4 ± √(16 - 7.84)) / 2.8
t ≈ 1.26 or t ≈ 0.79
Therefore, the temperature was over 100°F between the interval (0.79, 1.26).

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The radius of the circle can be determined using the Pythagorean theorem. Since the chord is 5 units away from the center of the circle, a right triangle can be formed where one leg is half the length of the chord (5 units) and the hypotenuse is the radius of the circle. Using the Pythagorean theorem, we can solve for the radius as follows:

r^2 = (10/2)^2 + 5^2

r^2 = 25 + 25

r^2 = 50

r = sqrt(50) = 5sqrt(2) units

Therefore, the radius of the circle is 5sqrt(2) units.

To further explain, the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the chord is a line segment connecting two points on the circle and is perpendicular to the radius passing through the midpoint of the chord. Since the chord is 10 units long and 5 units away from the center of the circle, the length of one leg of the right triangle is 5 units (half the length of the chord), and the length of the other leg is the radius of the circle. Using the Pythagorean theorem, we can solve for the unknown length of the radius.

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2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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Answer

Trapezoids

Step-by-step explanation:

Squares are not trapazoids.

rho.buses 12342476512457

Answer:

Step-by-step explanation:

Answer:

y + 2 = -0.069(x-+5)

Step-by-step explanation:

SInce the two lines intersects, we will equate it

Multiply x + 3y = 0 by 4;

4x + 12y = 0

4x-4y-13 = 0,

Subtracts both

12y +4y + 13 = 0

16y = 13

y = 13/16

get x;

x + 3(13/16) = 0

x = -39/16

The point of intersection is (0.8, -2.4) and (-5,-2)

Get the equation;

m = y2-y1/x2-x1

m = -2+2.4/-5-0.8

m = 0.4/-5.8

m = -0.069

Get the equation;

y - y0 = m(x-x0)

y - (-2)= -0.069(x-(-5))

y + 2 = -0.069(x-+5)

Answer:

4

Step-by-step explanation:

2+2=4

Answer:

fah)',55%9+*_)64•%π\¥)--_f

Answer:

2w+2(w+5)=1200

Step-by-step explanation:

Answer:

The number of

Fiction books = x = 2400 fiction books

Non fiction books = y = non fiction books

Step-by-step explanation:

Let the number of

Fiction books = x

Non fiction books = y

The libary has 4,000 books in total.

Hence: x + y = 4000........ Equation 1

The number of fiction books in a libary is %150 of the number of non-fiction books.

x = 150% of y

x = 150/100 × y

x = 1.5y

We substitute 1.5y for x in Equation 1

x + y = 4000

1.5y + y = 4000

2.5y = 4000

y = 4000/2.5

y = 1600 non fiction books

Solving for x

x = 1.5y

x = 1.5 × 1600

x = 2400 fiction books.

Therefore,

The number of

Fiction books = x = 2400 fiction books

Non fiction books = y = non fiction books

Answer:

20th visit

Step-by-step explanation:

4 and 10 both share 20 as the LCM.

and it'll be her 5th, consecutive 4th visit for the coupon and on that trip, because it's her 20th visit, it matches with every 10 visit's, therefore getting her both coupon's.

(great question, hope you're satisfied with my answer!)

Answer:

200%.

100% of 12 is 12 since for example if a coat is 10$ and 100% off then its now 0$. Therefore 200% is twice of 12 making it 24.

24=200% of 12

Step-by-step explanation: