1. Given n random numbers u₁, 2,...,, derive an expression for a random devi- ₂,.. ate of an n-stage hypoexponential distribution with parameters A₁ A₂ A

Answer:

x-intercept = (1/4, 0)

Step-by-step explanation:

Just change the y to 0 if you want to find the x-intercept of a linear equation.

0=-12x+3

-12x=-3

x=1/4

y=0

x-intercept = (1/4, 0)

The volume of material used in each cracker is 2,714.60 mm³

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the cylinder, h is the height, and π is a constant value of approximately 3.14.

Since the diameter of the entire cracker is 16 mm, the radius is half of that, which is 8 mm. The height of the cracker is given as 18 mm. Therefore, the volume of the cracker is:

V_cracker = π(8 mm)²(18 mm) = 3,619.38 mm³

The diameter of the hole is given as 8 mm, which means the radius is 4 mm. The height of the hole is the same as the height of the cracker, which is 18 mm.

Therefore, the volume of the hole is:

V_hole = π(4 mm)²(18 mm) = 904.78 mm³

Finally, we can calculate the volume of the material used in each cracker by subtracting the volume of the hole from the volume of the cracker:

V_material = V_cracker - V_hole = 3,619.38 mm³ - 904.78 mm³ = 2,714.60 mm³.

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Answer:

Yes it is a polynomial.

Step-by-step explanation:

3x² - 4ab + 2 is quadratic polynomial, since it has the highest power / degree of 2.

Note : -

Types of polynomials :

Answer:

\(4394\)

Step-by-step explanation:

the bird is

The rational function ƒ(x) that represents the average price per minute x years after 1998 is given by ƒ(x) = g(x) / h(x), where g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4 and h(x) = -8.25x³ + 53.1x² - 7.82x + 138.

To calculate the average price per minute x years after 1998, we need to find the ratio between the average monthly bill (g(x)) and the average number of minutes used (h(x)). Therefore, the rational function ƒ(x) is defined as ƒ(x) = g(x) / h(x).

Given that g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4 and h(x) = -8.25x³ + 53.1x² - 7.82x + 138, we can substitute these expressions into the rational function to obtain the final formula: ƒ(x) = (-0.27x³ + 1.40x² + 1.05x + 39.4) / (-8.25x³ + 53.1x² - 7.82x + 138).

This rational function represents the average price per minute x years after 1998 based on the given average monthly bill and average number of minutes used by U.S. mobile phone users. By plugging in different values for x, you can evaluate the function and obtain the corresponding average price per minute for each year.

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The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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Answer:

VW=21.6

Step-by-step explanation:

VW/(44-27.5)=36/27.5

VW/16.5=36/27.5

27.5SW=36(16.5)

27.5VW=594

VW=21.6

Answer:

f(x) = -19/9(x + 3)² + 5

Step-by-step explanation:

Given the vertex, (-3, 5) and the point, (0, 14):

Use the following quadratic equation formula in vertex form:

f(x) = a(x - h)² + k

where:

(h, k) = vertex

a = determines whether the graph opens up or down, and makes the graph wide or narrow.

h = determines how far left or right the parent function is translated.

k =  determines how far up or down the parent function is translated.

Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for a:

f(x) = a(x - h)² + k

14 = a(0 + 3)² + 5

14 = a(3)² + 5

14 = a(9) + 5

Subtract 5 from both sides:

-14 - 5 = 9a

-19 = 9a

Divide both sides by 9 to solve for a:

-19/9 = 9a/9

-19/9 = a

Therefore, the quadratic function in vertex form is:

f(x) = -19/9(x + 3)² + 5

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Answer:

100 sweets

Step-by-step explanation:

2x+30=5x

3x =30

x=10

total sweets = 100

Answer:

\(60st \\ = (60 \times 5 \times - 3.7) \\ = - 1110\)

Answer:

-1110

Step-by-step explanation:

given:

s = 5

t = -3.7

to find

60st

=60*s*t

=60*5*(-3.7)

=300*-3.7

=-1110

Answer:

m= 13/7

Step-by-step explanation:

(-5, 2) , (-12, -11)

Slope(m)

m= (y2-y1)/(x2-x1)

m= (-11 - 2)/(-12 + 5)

m= (-13)/(-7)

m= 13/7

The probability of it being sunny tomorrow (Xn+1=1) is 0.7, while the probability of it being rainy tomorrow (Xn+1=2) is 0.3

Based on the information provided, the weather at a holiday resort is modeled as a time-homogeneous stochastic process (Xn: n > 0), where Xn represents the state of the weather on day n, and can take on the value 1 for sunny weather and 2 for rainy weather.

Furthermore, for each day n greater than 1, the state of the weather on day n+1 (Xn+1) is conditionally independent of the history of the process prior to day n-2 (Hn-2 = {X0, X1, ..., Xn-2}), given the two most recent states of the process (Xn and Xn-1). The conditional distribution of Xn+1 given the two most recent states is as follows:

- If it was sunny both yesterday and today, then it will be sunny tomorrow with a probability 0.9.
- If it was rainy yesterday but sunny today, then it will be sunny tomorrow with a probability 0.8.
- If it was sunny yesterday but rainy today, then it will be sunny tomorrow with a probability 0.7.
- If it was rainy both yesterday and today, then it will be sunny tomorrow with a probability 0.6.

This information can be used to simulate the weather at the holiday resort over time, based on the current and past states of the process. For example, if the weather was sunny yesterday (Xn-1=1) and rainy today (Xn=2), then the probability of it being sunny tomorrow (Xn+1=1) is 0.7, while the probability of it being rainy tomorrow (Xn+1=2) is 0.3.r

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Answer:

The answer is 1/4

Step-by-step explanation:

1.) Take 75% and convert it to a decimal, which is 0.75

2.) Then multiply 1/3 by 0.75

3.) Your answer is 0.25, and when 0.25 is converted to a fraction it is 1/4.

The fraction of 1/3 that is equal to 75% is = 1/4

The percentage given is = 75%

The fraction given is = 1/3

To convert 75% into fraction is = 75/100

Therefore, 75/100 of 1/3

\( \frac{75 \times 1}{100 \times 3} \)

\( \frac{75}{300} \)

= 1/4

Therefore, the fraction of 1/3 that is equal to 75% is = 1/4.

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5.54. Without the joint and marginal distributions of X and Y, it is not possible to calculate the correlation and covariance or determine if the random variables are independent, orthogonal, or uncorrelated.

In problems 5.54, the lack of information regarding the joint and marginal distributions of X and Y prevents us from calculating the correlation and covariance between the variables. Therefore, it is not possible to determine if the random variables are independent, correlated, uncorrelated, or orthogonal based on the given information.

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Answer:

Los números son 81 y 243.

Step-by-step explanation:

Un sistema de ecuaciones lineales, también conocido como sistema lineal de ecuaciones o simplemente sistema lineal, es un conjunto de ecuaciones lineales que relacionan incógnitas entre sí.

Una solución de un sistema es una asignación de valores para las incógnitas que hace  verdadera cada una de las ecuaciones. Esto es, en los sistemas de ecuaciones, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.

En este caso las variables o incógnitas son los números "x" e "y".

Un tercio es la tercera parte de una cantidad y se calcula dividiendo por 3, mientras que un cuarto es la cuarta parte de una cantidad y se calcula dividiendo por 4.

Si un cuarto de la suma de dos números es 81 y un tercio de su diferencia es 54, el sistema de ecuaciones queda definido como:

\(\left \{ {{\frac{x+y}{4} =81} \atop {\frac{x-y}{3} =54}} \right.\)

Resolviendo por el sistema de sustitución, en primer lugar se debe despejar o aislar una de las incógnitas de una de las ecuaciones. En este caso, aislando la incógnita "x" de la primer ecuación se obtiene:

x +y= 4*81

x= 324 - y

Sustituyendo la expresión obtenida en la segunda expresión:

\(\frac{324-y-y}{3} =54\)

Resolviendo se obtiene:

324-y-y= 3*54

324 - 2*y= 162

-2*y= 162 - 324

-2*y= -162

y= (-162)÷ (-2)

y= 81

Reemplazando este valor obtenido en la expresión x= 324 - y se obtiene:

x= 324 - 81

x= 243

Los números son 81 y 243.

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

I would need the picture of the trapezoid to solve for you

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer:

x=-8

Step-by-step explanation:

y=8 is a horizontal line crossing the y-axis at 8

A line perpendicular to this would be a vertical line crossing the x-axis at -8

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

F

Step-by-step explanation:

b = 3 5/8 × x < -- Times

x is a variable that uses for the representation of the number of pies

Example : 3 pies there

b = 3 5/8 × 3

therefore b = 5.625 pounds

To solve for d:

1. Remove parenthesis:

2. Leave the terms with d in one side of the equation:

-Add 1.2 in both sides of the equation:

-Substract 0.3d and 0.1d in both sides of the equation:

3. Opperate similar terms:

4. Divide into (-0.2) both sides of the equation:

Alana's conclusion from the study is not appropriate.

Why is Alana's conclusion from the study is not appropriate?

What is an appropriate study?

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If a nonhomogeneous system of linear equations is underdetermined, it can have either infinitely many solutions or no solutions.

A nonhomogeneous system of linear equations is represented by the equation Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. When the system is underdetermined, it means that there are more unknown variables than equations, resulting in an infinite number of possible solutions. In this case, there are infinitely many ways to assign values to the free variables, which leads to different solutions.

To determine if the system has a solution or infinitely many solutions, we can use techniques such as row reduction or matrix methods like the inverse or pseudoinverse. If the coefficient matrix A is full rank (i.e., all its rows are linearly independent), and the augmented matrix [A | b] also has full rank, then the system has a unique solution. However, if the rank of A is less than the rank of [A | b], the system is underdetermined and can have infinitely many solutions. This occurs when there are redundant equations or when the equations are dependent on each other, allowing for multiple valid solutions.

On the other hand, it is also possible for an underdetermined system to have no solutions. This happens when the equations are inconsistent or contradictory, leading to an impossibility of finding a solution that satisfies all the equations simultaneously. Inconsistent equations can arise when there is a contradiction between the constraints imposed by different equations, resulting in an empty solution set.

In summary, when a nonhomogeneous system of linear equations is underdetermined, it can have infinitely many solutions or no solutions at all, depending on the relationship between the equations and the number of unknowns.

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Two triangle are congruent when the shape and size of both the triangle are same.

The given information is the SAS case.  Thus the option B is the correct option.

Two triangle are congruent when the shape and size of both the triangle are same.

Triangle congruence theorem are-

Given information-

The distance of the Evelyn from the airplane is 200 meters.

The initial angle at takeoff of the plane is 12 degrees.

Evelyn is approximately 104 meters from the plane.

The angle of elevation of the plane is 12°.

The triangle made for this situation is attached below.

As in the shown triangle below this question. The distance of Evelyn from the initial takeoff of the plane is shown.

This distance is equal to the base of the triangle. Therefore we get the one side of the tingle.

Now the plane is flied 100 meters, which gives the value of another side of the triangle as shown in the image below attached.

Angle of elevation of the plane is 12 degrees, which gives the one angle of the triangle.

Thus we have one side equal to the 100 meters, one angle equal to the 12 degrees and another side with equal to the 200 meters.

Thus it is the case of side angle side.

Hence, the given information is the SAS case.  Thus the option B is the correct option.

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Answer:

The correct answer would be Options B. D. and E.

Step-by-step explanation:

Just got this question correct on Edge. - hope this helps!

Brainliest would be greatly appreciated :)

Answer:

Step-by-step explanation:

∵ the properties of rhombus, all sides are equal.

∴MA=MQ

 MA=12

The answer is a 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is (11.8, 14.4).

Here, the researcher compares the effectiveness of two different instructional methods for teaching anatomy.

A sample of 153 students using method 1 produces a testing average of 61.1.

A sample of 179 students using method 2 produces a testing average of 74.2.

We are given that the standard deviation is known to be 11.45 for method 1 and 8.4 for method 2.

Let μ1 be the population mean of method 1, and μ2 be the population mean of method 2.

Then we want to find a 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2.

The formula for the confidence interval is: (X1 – X2) ± Z*σd / √n1 + n2

where: X1 is the mean of sample 1X2 is the mean of sample 2Z* is the z-value that corresponds to the desired confidence levelσd is the standard error of the difference between meansn1 is the sample size of sample 1n2 is the sample size of sample 2σd is calculated as follows :

σd = √(σ12 / n1) + (σ22 / n2)σd

    = √(11.45² / 153) + (8.4² / 179)σd

    = 1.882

The point estimate (X1 – X2) is: X1 – X2

= 74.2 – 61.1

= 13.1

The 99% confidence interval is: (13.1) ± (Z* * 1.882 / √(153 + 179))

We need to find the z-value that corresponds to a 99% confidence level.

Using a standard normal distribution table or calculator, we get Z* = 2.576.

Now, substituting Z* and the values we obtained, we get: (13.1) ± (2.576 * 1.882 / √332))13.1 ± 1.30

Thus, the 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is (11.8, 14.4).

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Answer:

G = (x+10) = 42 degrees

Step-by-step explanation:

G is equal to the angle across from it because of the lines being equal.

Then you plug in an equation to solve for all 180 degrees of a triangle            3x + x+10 + x+10 = 180

5x+20 = 180

5x=160

x=32

(32)+10 = 42

G = 42 degrees

Answer:

needed to add 36 non blue marbles in the bag. Sense Tome doesn't want to give the blue marbles up...

To find f'(3), where f(t) = u(t) * v(t) and given u(3), u'(3), and v(t), we can use the product rule of differentiation. By evaluating the derivatives of u(t) and v(t) at t = 3 and substituting them into the product rule, we can determine f'(3).

The product rule states that if f(t) = u(t) * v(t), then f'(t) = u'(t) * v(t) + u(t) * v'(t). In this case, u(t) is given as 2, 1, -2 and v(t) is given as t, t^2, t^3. We are also given u(3) = 2, 1, -2 and u'(3) = 7, 0, 4.

To find f'(3), we first evaluate the derivatives of u(t) and v(t) at t = 3. The derivative of u(t) is u'(t), so u'(3) = 7, 0, 4. The derivative of v(t) depends on the specific form of v(t), so we calculate v'(t) as 1, 2t, 3t^2 and evaluate it at t = 3, resulting in v'(3) = 1, 6, 27.

Now we can apply the product rule by multiplying u'(3) * v(3) and u(3) * v'(3) term-wise and summing them. This gives us f'(3) = (u'(3) * v(3)) + (u(3) * v'(3)) = (7 * 3) + (2 * 1) + (0 * 6) + (1 * 2) + (-2 * 27) = 21 + 2 + 0 + 2 - 54 = -29.

Therefore, f'(3) = -29.

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To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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