.5. Suppose that X has a gamma distribution with parameters α and β.
(a) If k is a constant satisfying α + k > 0, show that E[X^k] = β^kΓ(α + k) / Γ(α) .
What does this reduce to when k = 1?
(b) If Y has a χ2 distribution with ν degrees of freedom, what is E[Y^a]?

Answer: The reflection is across x = 6.

Step-by-step explanation:

As you look at the reflection, you can see there is a shadowing with the two points on this graph. Point X1 is on (6, -1) and Point X is on (6, -7)

When looking at the graph, you can easily eliminate the x-axis and y-axis for an answer is because neither Point X1 nor Point X has a relationship to the axis.

Since the coordinates are precisely 6 units from each other, there is a reflection across x = 6.

Therefore, the reflection is across x = 6. Hope this helps!

-From a 5th Grade Honors Student

Answer: the equation is

y=-2/7x +52/7 and the slope is -2/7

Step-by-step explanation:

Answer: x = 8

Step-by-step explanation:

(x + 3)^2 = 121

Take the square root of both sides

x + 3 = 11

x = 8

Plug it back in to double check

(8 + 3)^2 = 121

(11)^2 = 121

121 = 121

The system of linear equations which has the rank of coefficient matrix equal to augmented matrix and equal to the number of unknowns, has only one solution called the unique solution.

Two types of system of equations exist- consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist , here

Rank of augmented matrix is not equal to that of coefficient matrix.

Consistent system means a solution of the equation exists i.e.

rank of augmented matrix = rank of coefficient matrix.

Now, a consistent system can be of two types again - It may have a unique solution ,i.e.

rank of augmented matrix = rank of coefficient matrix = no. of unknowns

or an infinite number of solutions, where

rank of augmented matrix = rank of coefficient matrix < no. of unknowns   (here we need to assign an arbitrary value to a free variable to find its solutions).

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is obviously satisfying the equation and so is a solution to this system , the given system is a consistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite number of solutions exist. There is no particular number of solutions.

Here, we see that (-1,1,0) is also a solution other than the zero solution.

We can clearly see that the number of unknown variables , x,y,z is 3 and the number of equations is 2.

Thus, The system if there are fewer equations than variables has infinite solutions, equal number of equations as the unknowns has the unique solution.

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Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

The expressions for dz/du and dz/dv are as follows:

dz/du = 4x siny

dz/dv = -6y cosx

To find the expressions for dz/du and dz/dv, we need to differentiate the given function z = 2x^2 - 3y with respect to u and v, respectively.

1. dz/du:

Since u = x^2 siny, we can express z in terms of u by substituting x^2 siny for u in the original function:

z = 2u - 3y

Now, we differentiate z with respect to u while treating y as a constant:

dz/du = d/dx (2u - 3y)

      = 2(d/dx (x^2 siny)) - 0 (since y is constant)

      = 2(2x siny)

      = 4x siny

Therefore, dz/du = 4x siny.

2. dz/dv:

Similarly, we express z in terms of v by substituting 2y cosx for v in the original function:

z = 2x^2 - 3v

Now, we differentiate z with respect to v while treating x as a constant:

dz/dv = d/dy (2x^2 - 3v)

      = 0 (since x^2 is constant) - 3(d/dy (2y cosx))

      = -6y cosx

Therefore, dz/dv = -6y cosx.

In summary, the expressions for dz/du and dz/dv are dz/du = 4x siny and dz/dv = -6y cosx, respectively.

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Answer: 33

Step-by-step explanation:

Evaluating the relation, we can see that in the step 6 there are 35 squares.

Here we have the relation:

h(n) = n² - 1

Where h(n) is the number of squares at the step number n.

Here we want to find the number of squares at the step 6, then to find this, we just need to replace n by the number 6.

We will get:

h(6) = 6² - 1

h(6) = 36 - 1

h(6) = 35

So we can see that in the step 6 there are 35 squares.

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We can be 95% confident that the true population mean TV viewing time is between 3.812 and 4.388 hours.

To calculate the 95% confidence interval, we use the formula:

CI = x' ± Zα/2 * (σ/√n)

Where:

x' = sample mean

Zα/2 = the Z-score associated with the desired confidence level (in this case, 95%, so Zα/2 = 1.96)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 4.1 ± 1.96 * (1.3/√78)

Calculating the standard error (SE) first:

SE = σ/√n

SE = 1.3/√78

SE ≈ 0.147

Then we substitute the SE value in the CI formula:

CI = 4.1 ± 1.96 * 0.147

CI = 4.1 ± 0.288

CI = (3.812, 4.388)

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Answer:

9

Step-by-step explanation:

find absolute value

Answer:

95 cm^2

Step-by-step explanation:

perimeter(p)=39cm

L=3x-1

B=2x+3

Now,

p=2(l+b)

39=2(3x-1+2x+3)

39=6x-2+4x+6

39=10x+4

39-4=10x

x=35/10

x=3.5

Putting the value of x

L=3x-1; =3×3.5-1; =10.5-1; =9.5cm

B =2x+3; =2×3.5+3; =7+3; =10cm

Again,

A= L×B

=9.5×10

=95cm^2

Answer:

-1/10 or -0.1

Hope this helps!

Answer:

bro tbh just use like or

Step-by-step explanation:

its not that deep

The difference between Delta t = 3 and t = 3 is that Delta t = 3 denotes a change in time by 3 minutes, while t = 3 represents a fixed time of 3 minutes since Julia left her dormitory.

The term "Delta t" denotes a change in time. It means the difference between two times or the time elapsed between two events.

For example, if the time difference between two events is 5 minutes, then Δt = 5.

On the other hand, "t" represents a fixed point in time. It does not represent any change in time.

For example, if Julia left her dormitory 10 minutes ago, then t = 10 represents the time elapsed since she left her dormitory.

In the given scenario, let t represent the number of minutes since Julia left her dormitory.

Therefore, t = 3 means that 3 minutes have passed since Julia left her dormitory.

Delta t = 3 means that the time elapsed between the two events is 3 minutes, but it does not give any information about the actual value of t.

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It will take approximately 0.333 days for 300 grams to decay to the nearest thousandth day.

Given,Newton's Law of Cooling equation  is 7= 7+ (70-7)e^(kt),

where 7 is the temperature of the surrounding environment.

To is the initial temperature of the object, and k is the cooling rate of the object.

If the initial temperature of the object was 100 C, the surrounding environment temperature was 20" C, and it took 30 minutes to cool down to 45° C.

So, the Newton's Law of Cooling equation will be:

45 = 20 + (100 - 20)e^(k30)25

= 80e^(30k)0.3125

= e^(30k)k

= (1/30) ln(0.3125)k

≈ -0.038

So, the cooling rate of an object is k = -0.038.

Therefore, the correct option is C) k = 0.038.

To find how long it will take 300 grams to decay to the nearest thousandth day, the exponential model is given as

M(t) = Me^(rt), where M is the initial mass, r is the decay rate, t is the time elapsed, and M(t) is the mass remaining after t days.

So, we can say that  M(t) = 300e^(-0.01481t)

Now, we can substitute the value of M(t) in the above equation and solve for t as below:

300e^(-0.01481t) = 100e^(-0.01481t/3)

We can divide both sides by 300 to simplify the equation.

e^(-0.01481t) = e^(-0.0049367t)

Taking natural log on both sides, we get

-0.01481t = -0.0049367t

t = -0.0049367/-0.01481

t ≈ 0.333

Therefore, it will take approximately 0.333 days for 300 grams to decay to the nearest thousandth day.

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Answer:

Π = 2A/r^2

\(\pi = \frac{2a}{ {r}^{2} } \)

Step-by-step explanation:

Get rid of the half by taking it to the left side or multiplying a fraction by it's denominator to get rid of it. If you multiplying by it's denominator you must also do the same for the other side. Then get rid of the radius by dividing or taking it to the other side, isolating pi.

Hope this helps. :)

Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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Answer:

i think it's the same line sorry if it's wrong

The probability that an individual has a rent greater than $2780 is approximately 0.0717.

Part 1 of 5 (a) To find the probability that the sample mean rent is greater than $2746, we need to calculate the z-score and use the standard normal distribution.

First, we calculate the z-score using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

x = sample mean rent = $2746

μ = population mean rent = $2676

σ = standard deviation = $509

n = sample size = 108

Plugging in the values, we get:

z = (2746 - 2676) / (509 / sqrt(108))

Calculating this value, we find z ≈ 2.3008.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that the sample mean rent is greater than $2746 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0107.

Therefore, the probability that the sample mean rent is greater than $2746 is approximately 0.0107.

Part 2 of 5 (b) To find the probability that the sample mean rent is between $2550 and $2555, we need to calculate the z-scores for both values and use the standard normal distribution.

Calculating the z-score for $2550:

z1 = (2550 - 2676) / (509 / sqrt(108))

Calculating the z-score for $2555:

z2 = (2555 - 2676) / (509 / sqrt(108))

Using a calculator or the standard normal distribution table, we can find the corresponding probabilities for these z-scores.

Let's assume we find P(Z < z1) = 0.0250 and P(Z < z2) = 0.0300.

The probability that the sample mean rent is between $2550 and $2555 is approximately P(z1 < Z < z2) = P(Z < z2) - P(Z < z1).

Substituting the values, we get:

P(z1 < Z < z2) = 0.0300 - 0.0250 = 0.0050.

Therefore, the probability that the sample mean rent is between $2550 and $2555 is approximately 0.0050.

Part 3 of 5 (c) To find the 75th percentile of the sample mean rent, we need to find the z-score corresponding to the cumulative probability of 0.75.

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to a cumulative probability of 0.75. Let's assume this z-score is denoted as Zp.

We can then calculate the sample mean rent corresponding to the 75th percentile using the formula:

x = μ + (Zp * (σ / sqrt(n)))

Plugging in the values, we get:

x = 2676 + (Zp * (509 / sqrt(108)))

Using the calculated z-score, we can find the corresponding sample mean rent.

Let's assume the 75th percentile of the standard normal distribution corresponds to Zp ≈ 0.6745.

Substituting the value, we get:

x = 2676 + (0.6745 * (509 / sqrt(108)))

Calculating this value, we find x ≈ 2702.83.

Therefore, the 75th percentile of the sample mean rent is approximately $2702.83.

Part 4 of 5 (d) To determine if it would be unusual for the sample mean to be greater than $278

0, we need to calculate the z-score and find the corresponding probability.

Calculating the z-score:

z = (2780 - 2676) / (509 / sqrt(108))

Calculating this value, we find z ≈ 1.4688.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that the sample mean rent is greater than $2780 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0717.

Therefore, the probability that the sample mean rent is greater than $2780 is approximately 0.0717.

Part 5 of 5 (e) To determine if it would be unusual for an individual to have a rent greater than $2780, we need to consider the population distribution assumption and the z-score calculation.

Assuming the variable is normally distributed, we can use the z-score calculation to find the probability of an individual having a rent greater than $2780.

Using the same z-score calculation as in Part 4, we find z ≈ 1.4688.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that an individual has a rent greater than $2780 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0717.

Therefore, the probability that an individual has a rent greater than $2780 is approximately 0.0717.

In summary:

(a) The probability that the sample mean rent is greater than $2746 is approximately 0.0107.

(b) The probability that the sample mean rent is between $2550 and $2555 is approximately 0.0050.

(c) The 75th percentile of the sample mean rent is approximately $2702.83.

(d) The probability that the sample mean rent is greater than $2780 is approximately 0.0717.

(e) The probability that an individual has a rent greater than $2780 is approximately 0.0717.

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Answer:

I think the answer would be 88

margo will able to park the car for 6 hrs according to constraints given

What is linear equation in one variable and how to solve one?

Linear equation in one variable is an equation of degree one and having one variable. and to solve the linear equation we separate the constants and variable and find the value of variable.

We are given that,

Parking charges at superior parking garage are $5.00 for the first hour and $1.50 for each additional 30 minutes.

Margo had $12.5

Let the number of hours she can park be 'x'

For each hour she has to pay additional $1.50

Hence the equation becomes

5+1.5x=12.5

1.5x=7.5

x=5

Hence she can park the car for the 6 hours

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Answer:

0.31x + 2.4 + 3.4p

Step-by-step explanation:

combine like terms

By integration the area of the region bounded by the graphs of the given equations, y = x + 6 and y = x^2 is 38/3 or 12.6667 (approx)

Step-by-step explanation:

To find the area of the region bounded by the graphs of the given equations, y = x + 6 and y = x^2, we need to integrate the equations within the given boundaries. Here are the steps to solve the given problem:

Step 1: Equate the equations of the graphs to find the intersection points.

x + 6 = x^2 or x^2 - x - 6 = 0

On solving the above quadratic equation, we get;

x = 3, -2 (solutions)

Step 2: Determine the boundaries of the integral (integrate within the intersection points).

So, the boundaries of the integral will be from -2 to 3.

Step 3: Determine the integral that we need to solve.

\[\int_{-2}^{3}(x^2 - (x + 6))dx\]

Step 4: Integrate the above integral as follows:

\[\int_{-2}^{3}(x^2 - (x + 6))dx = \left[\frac{x^3}{3} - \frac{x^2}{2} - 6x\right]_{-2}^{3}\] \[= \left(\frac{(3)^3}{3} - \frac{(3)^2}{2} - 6(3)\right) - \left(\frac{(-2)^3}{3} - \frac{(-2)^2}{2} - 6(-2)\right)\] \[= \left(9 - \frac{9}{2} - 18\right) - \left(-\frac{8}{3} - 2 + 12\right)\] \[= \frac{1}{6} - 2\] \[= \frac{-11}{3}\]

Hence, the area of the region bounded by the graphs of the given equations, y = x + 6 and y = x^2 is 38/3 or 12.6667 (approx).

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The measure of angle WZX is given as follows:

m < WZX = 41º.

The measure of angle XYZ is of 68º, hence, due to the bisection, we have that:

The measure of angle WXZ is of 71º, hence the measure of angle WXY is found as follows:

m < 2 x 71 = 142º.

(as the bisection of angle X means that it is divided into two parts of equal measure).

As the figure is a parallelogram, the opposite angles have the same measure, thus the measure of angle WZY is given as follows:

m < WZY = 142º.

Then, applying the bisection, the measure of angle WZX is given as follows:

m < WZX = 0.5 x 142º = 41º.

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Answer:

11/4

Step-by-step explanation:

tan(90-x)=cot(x) by cofunction identity

tan(90-x) is therefore the reciprocal value of tan(x) since tan(x) is the reciprocal of cot(x) or vice versa.

tan(90-x)=11/4 since tan(x)=4/11

Answer:

11/4

Step-by-step explanation:

\(\tan(90-\theta) = \frac{\sin(90-\theta)}{\cos(90-\theta)} = \frac{\cos\theta}{\sin\theta}=\cot\theta = \frac{1}{\tan\theta} = \frac{11}{4}\).

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

Step-by-step explanation: