Let X be a random variable having the gamma
distribution with shape parameter α and scale parameter γ, where α is
know and γ is unknown. let Y = σ log X. Show that
(i) if σ > 0 is unknown, then the distribution of Y is in a location-scale
family;
(ii) if σ > 0 is known, then the distribution of Y is in an exponential family.
Compulsory both subparts required .

The final answer length of the other dimension of the garden is 9x units.

To find the length of the other dimension of the garden, we need to use the formula for the area of a rectangle:

Area = Length x Width

We are given the area and one dimension, so we can plug those values into the formula and solve for the other dimension:

[tex]81x^2-126x[/tex] = (9x-14)(Length)

To solve for the length, we need to divide both sides of the equation by (9x-14):

Length =[tex](81x^2-126x)/(9x-14)[/tex]

Now we can simplify the right side of the equation by factoring out a common factor of 9x:

Length = (9x)(9x-14)/(9x-14)

The (9x-14) terms cancel out, leaving us with:

Length = 9x

So the length of the other dimension of the garden is 9x units.

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Answer: A quarter or 1/4 rotation is 90°.

Step-by-step explanation:

A full rotation is 360 degrees, usually written as 360°. Half a rotation is then 180° and a quarter rotation is 90°.

18. The exact value of the product 3 sin(37.5°) cos( 7.5°) can be determined using the double angle formula for sine:
sin(2x) = 2 sin(x) cos(x)

Substituting x = 22.5° into the formula gives:
sin(45°) = 2 sin(22.5°) cos(22.5°)
Dividing both sides by 2 gives:
sin(45°)/2 = sin(22.5°) cos(22.5°)
Substituting the given values into the equation gives:
3 sin(37.5°) cos( 7.5°) = 3 (sin(45°)/2) (cos(45°)/2)
Simplifying gives:
3 sin(37.5°) cos( 7.5°) = 3/4
Therefore, the exact value of the product is 3/4.

19. The exact value of the sum cos (phi/12) - cos (5phi/12) can be determined using the sum-to-product formula for cosine:
cos(x) - cos(y) = -2 sin((x+y)/2) sin((y-x)/2)
Substituting x = phi/12 and y = 5phi/12 into the formula gives:
cos (phi/12) - cos (5phi/12) = -2 sin((phi/12 + 5phi/12)/2) sin((5phi/12 - phi/12)/2)
Simplifying gives:
cos (phi/12) - cos (5phi/12) = -2 sin(3phi/12) sin(2phi/12)
Therefore, the exact value of the sum is -2 sin(3phi/12) sin(2phi/12).

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In the given figure by using the alternative angles rule we know that x = 82°.

Alternate angles are a unique type of angle in geometry.

The collection of non-adjacent angles on either side of the transversal is known as alternate angles.

Alternative Interior Angles: Angles are created on the inside, or interior, of two other lines when a third line known as the transversal crosses them. These other lines are typically parallel.

The alternate internal angles are those that are perpendicular to one another.

So, in the given figure:

∠ABD = ∠BDC = 35° (Alternate angles)

Then, ∠DBC will be:

82 + 35 + x = 180

117 + x = 180

x = 180 - 117

x = 63°

Then, ∠DBC = ∠BDA = 63° (Alternate angles)

Now, ∠DAB = 63 + 35 + x = 180

= 63 + 35 + x = 180

= 98 + x = 180

= x = 180 - 98

= x = 82°

Therefore, in the given figure by using the alternative angles rule we know that x = 82°.

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Volume of square prism = 128 cm³

Volume of rectangular prism is, V = 60 cm³

Volume of cylinder is, V = 565.2 cm³

Volume of cone is, V = 188.4 cm³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The dimensions of the shapes are,

Square prism: 4 cm x 4 cm x 8 cm

Rectangular prism: 3 cm x 4 cm x 5 cm

Cylinder: radius 6 cm, height 5 cm

Cone: radius 6 cm, height 5 cm

Now, We know that;

Volume of square = Side² × Height

Hence, We get;

Volume of square = 4² × 8

                            = 128

And, Volume of rectangular prism is,

V = 3 cm x 4 cm x 5 cm

V = 60 cm³

Volume of cylinder is,

V = πr²h

V = 3.14 × 6² × 5

V = 565.2 cm³

Volume of cone is,

V = πr²h/3

V = 3.14 × 6² × 5/3

V = 565.2 /3

V = 188.4 cm³

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The original list price for the product was $487.09.

To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:

Therefore, the original list price for the product was $487.09.

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Brendan is currently 37 years old.

To solve this problem, we can use algebra. Let's let V represent Valerie's age and B represent Brendan's age. We can set up the following equations based on the information given in the question:
B = V + 5 (Brendan is 5 years older than Valerie)
B + 6 + V + 6 = 81 (In 6 years, the sum of their ages will be 81)
Simplifying the second equation, we get:
B + V + 12 = 81
B + V = 69
Substituting the first equation into the second equation, we get:
V + 5 + V = 69
2V = 64
V = 32
Now that we know Valerie's age, we can use the first equation to find Brendan's age:
B = 32 + 5
B = 37
So Brendan's current age is calculated to be 37 years

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The number of yards of ribbon Lynn used to make a bow is 1/16 yards.

To find out how many yards of ribbon Lynn used to make a bow, we need to subtract the amount of ribbon she had left from the amount she started with and then divide by the number of bows she made. We can do this using the following steps:

1. Convert the mixed numbers to improper fractions: 1(5)/(8) = 13/8 and 1(1)/(4) = 5/4
2. Subtract the two fractions: 13/8 - 5/4 = 13/8 - 10/8 = 3/8
3. Divide the result by the number of bows: (3/8) / 6 = 3/8 x 1/6 = 3/48 = 1/16

Therefore, Lynn used 1/16 yards of ribbon to make a bow.

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Since the elements in the reactants and products are identical, the principle of conservation of mass is applicable to chemical processes. Choice (b) is accurate.

chemical reaction, the transformation of one or even more substances (the reactants) into one or more distinct substances (the products). Chemical components or chemical combinations make up substances.

When atoms create or break molecular bonds, chemical processes take place. Reactants are the substances that begin a chemical reaction, and products are the substances that are created as a result of the reaction.

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Answer:

Step-by-step explanation:

alternate interior angles

More formally:

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel (Since ∠1 = ∠4)

Answer: Alternate Interior Angles Converse

Step-by-step explanation:

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

2(cot2 y + tan2 y) = 2(1) Verified

Verify the identity:

2 sec2 y - 2 cot2 y = cot(2y) - 2 cot(2y) = 2 - 2 sec(2y)

To prove the identity, start by applying the identity:

cot2 y = 1 - tan2 y

Substitute this in the left side of the equation:

2 sec2 y - 2(1 - tan2 y) = 2 sec2 y - 2 + 2 tan2 y

Simplify the equation by factoring out a 2 from the right side:

2 sec2 y - 2 + 2 tan2 y = 2(sec2 y - 1 + tan2 y)

Next, apply the identity:

sec2 y - 1 = cot2 y

Substitute this in the equation and simplify:

2(sec2 y - 1 + tan2 y) = 2(cot2 y + tan2 y)

Finally, apply the identity:

cot2 y + tan2 y = 1

Substitute this in the equation and simplify:

2(cot2 y + tan2 y) = 2(1)

The identity is thus verified.

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The true statement about the polynomials is (b) No, it's only with polynomials with a degrees of 1

Given that the polynomials f and g have a degree of 3

The composition of two functions, f ∘ g (read as "f composed with g"), is not commutative in general, meaning that f ∘ g is not necessarily equal to g ∘ f.

This holds true for polynomials of degree 3 as well.

In fact, if f and g are two different polynomials of degree 3, then f ∘ g and g ∘ f will be different polynomials in general.

The equation f ∘ g = g ∘ f holds true is when f and g are constant polynomials, that is, polynomials of degree 0 or 1.

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y = 3sin(πt). This function models the oscillation by representing the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds.

y = 3sin(πt). This function can be used to model the oscillation because it represents the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds. This means that for any given value of t, the value of y will be the sine of π multiplied by t, which will correspond to a certain distance from the equilibrium position. As the oscillation has a frequency of 1 cycle per second, the value of t will increase linearly, and the value of y will oscillate between a maximum and a minimum value. As the distance between the maximum and minimum points of the oscillation is 3 centimeters, the maximum and minimum values of y will be 3 when t is an integer multiple of π. Therefore, the function y = 3sin(πt) can be used to accurately model the oscillation.

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The narrator's thoughts on Sky's view of women is that the view is confusing and hypocritical.

The narrator thinks that Sky's perspective on women is unexpected, perplexing, absurd, and at odds with the person Sky appears to be. She is taken aback by Sky's refusal to perform any chores he views as falling under the purview of women.

The narrator is even more shocked that when Sky observes her "struggling with a bucket of water," he advises her not to fill the bucket all the way up rather than offering to assist her.

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The answer is \(a+b+c+d = 10\).

To find \(a+b+c+d\), we can use matrix multiplication to solve for each variable. Matrix multiplication is performed by multiplying the elements of each row of the first matrix by the corresponding elements of each column of the second matrix, and then summing the products.

So, we can set up the following equations:

\(10 = 1a + 2c\)

\(1 = 1b + 2d\)

\(-6 = 3a - 3c\)

\(-6 = 3b - 3d\)

Solving for each variable, we get:

\(a = 6 - 2c\)

\(b = (1 - 2d)/1\)

\(c = (6 + 3a)/(-3)\)

\(d = (3b + 6)/(-3)\)

Substituting the values of \(a\) and \(b\) into the equations for \(c\) and \(d\), we get:

\(c = (6 + 3(6 - 2c))/(-3)\)

\(d = (3((1 - 2d)/1) + 6)/(-3)\)

Solving for \(c\) and \(d\), we get:

\(c = -2\)

\(d = -1\)

Substituting these values back into the equations for \(a\) and \(b\), we get:

\(a = 6 - 2(-2) = 10\)

\(b = (1 - 2(-1))/1 = 3\)

So, \(a+b+c+d = 10 + 3 + (-2) + (-1) = 10\).

Therefore, the answer is \(a+b+c+d = 10\).

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a) The purchase price of the new equipment is $20,531.76.

b) The amount of interest that will have to be paid is $6,948.24.

The purchase price of the new equipment for New Bread Bakery can be found using the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + i)^(-n)) / i]

Where PV is the present value (or purchase price), PMT is the monthly payment, i is the monthly interest rate, and n is the number of payments.

Plugging in the given values:

PV = 458 * [(1 - (1 + 0.092/12)^(-5*12)) / (0.092/12)]

PV = 458 * [(1 - (1 + 0.00767)^(-60)) / 0.00767]

PV = 458 * [(1 - 0.6887) / 0.00767]

PV = 458 * 40.4624

PV = 18,531.76

The purchase price of the new equipment is $18,531.76. However, this does not include the down payment of $2000. So, the total purchase price is:

PV + Down Payment = 18,531.76 + 2000 = $20,531.76

To find the amount of interest that will have to be paid, we can subtract the purchase price from the total amount paid over the five years:

Interest = (458 * 5 * 12) - 20,531.76 = 27,480 - 20,531.76 = $6,948.24

Therefore, the amount of interest that will have to be paid is $6,948.24.

(a) The purchase price of the new equipment is $20,531.76. (b) The amount of interest that will have to be paid is $6,948.24.

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After being rotated 180 degrees anticlockwise around the origin, the picture of the point (4,8) is (-4,-8).

The fixed point is referred to as the rotational centre. The quantity of the rotation is described by the term "angle of rotation," which is measured in degrees. The equivalent of turning a figure 90 degrees anticlockwise is turning it 180 degrees clockwise. Hence, the resulting image of the point is (-1, 2).

Below are the guidelines for rotation: rotation 90 degrees clockwise: (x,y) results in (y,-x) rotation of (x,y) at 90 degrees anticlockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and anticlockwise results in (-x,-y).

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Answer:

Step-by-step explanation:

a=70

b=45

c=65

d=45

e=70

f=110

make sure to add degree symbol

Enjoy :)

Answer:[tex]1\frac{1}{2}[/tex]

The given sequence is A(n) = 6.3 + (n-1)(5).

To find the 6th term of the sequence, we substitute n = 6 into the formula:

A(6) = 6.3 + (6-1)(5)

A(6) = 6.3 + 25

A(6) = 31.3

Now, to find the 5th term of this sequence, we need to substitute n = 5 into the formula:

A(5) = 6.3 + (5-1)(5)

A(5) = 6.3 + 20

A(5) = 26.3

Therefore, the 5th term of the 6th term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.

Answer: To find the coordinates of D1.5(ABCD), we need to perform a dilation with center D and scale factor 1.5 on the coordinates of each point.

The coordinates of point D are (-5, -10). To dilate point A, we can subtract the coordinates of D from the coordinates of A, multiply by 1.5, and then add the coordinates of D back:

D1.5(A) = 1.5[(2, 0) - (-5, -10)] + (-5, -10) = 1.5(7, 10) + (-5, -10) = (6.5, 5)

Similarly, we can dilate points B and C:

D1.5(B) = 1.5[(8, -4) - (-5, -10)] + (-5, -10) = 1.5(13, 6) + (-5, -10) = (14.5, -4)

D1.5(C) = 1.5[(4, -6) - (-5, -10)] + (-5, -10) = 1.5(9, 4) + (-5, -10) = (7.5, 4)

Therefore, the coordinates of D1.5(ABCD) are A'(6.5, 5), B'(14.5, -4), C'(7.5, 4), and D(-5, -10).

Step-by-step explanation:

No, it is not true that every pyramid is a prism, because they have different properties.

A pyramid is a solid shape that has a base and triangular faces that meet at a point called the apex. The base of a pyramid can be any polygon, such as a square, triangle, or rectangle. A pyramid is named according to the shape of its base. For example, a pyramid with a square base is called a square pyramid.

A prism, on the other hand, is a solid shape that has two identical bases that are parallel to each other and rectangular faces that connect the bases. The bases of a prism can also be any polygon, and a prism is named according to the shape of its bases. For example, a prism with a rectangular base is called a rectangular prism.

So, while both pyramids and prisms are three-dimensional shapes with bases and faces, they have different properties and are not the same. Therefore, it is not true that every pyramid is a prism.

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10⁻³ is equal to 1/1000 or 0.001.

What are Exponents?

Exponents are a shorthand way of representing repeated multiplication of a number by itself. They are indicated by a superscript number placed to the right and above the base number.

The superscript number represents the number of times the base number is multiplied by itself. For example, 2³ means 2 multiplied by itself three times, which equals 8.

Exponents are used to simplify large and small numbers, and are fundamental to algebraic and mathematical calculations. Exponents have several rules, such as the power of a power rule, product rule, quotient rule, and negative exponents rule.

10⁻³ can be evaluated as:

1 / 10^3 = 1 / 1000

Therefore, 10⁻³is equal to 1/1000 or 0.001.

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Answer:

Step-by-step explanation:

graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95

It's B.

Explanation: I took the test

To find the equation for a line parallel to y = 2x + 1 and passing through the point (1,5), we need to remember that parallel lines have the same slope.

Since the slope of y = 2x + 1 is 2, the slope of the parallel line will also be 2.

Using the point-slope form of a linear equation, we can plug in the given slope and point to find the equation of the parallel line:

y - y1 = m(x - x1)

y - 5 = 2(x - 1)

Simplifying this equation gives us the equation for the parallel line:

y = 2x + 3

So, the equation for the line parallel to y = 2x + 1 and passing through the point (1,5) is y = 2x + 3.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The following values of x, makes the set of ratios equivalent:

2: 3 = 6: 9

4: 7 = 24: 42

(6*2)12: 48 = 3: 12

12: 15 = 16: 20

The ratio can be used to determine how much of one item is contained in the other by comparing two sums of the same units. Ratios fall into two different groups.

Whereas the second is a part to whole ratio, the first is a part-to-part ratio. The part-to-part ratio demonstrates the link between two independent entities or organisations.

Now here in the 1st set:

2:3 = 6:x

Now, x = 6×3/2

⇒ x = 9

Similarly,

4:7=x:42

⇒ x = 24

The next ratio we have:

2x:48= 3:12

⇒ x = 6

Now, the last ratio,

12:15 = x:20

⇒ x = 16

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Answer:

[tex](3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]

Step-by-step explanation:

Greetings!!!

Given expression

[tex]27m {}^{3} + 125n {}^{3} [/tex]

Apply exponents rule

Rewrite 27 as 3³

[tex] = 3 {}^{3} m {}^{3} + 125n {}^{3} [/tex]

Rewrite 125 as 5³

[tex] = 3 {}^{3} m {}^{3} + 5 {}^{3} n {}^{3} [/tex]

Apply exponent rule:

[tex]a {}^{m} b {}^{m} = (ab) {}^{m} \\ = 3 {}^{3} m {}^{3} = (3m) {}^{3} \\ = 5 {}^{3} n {}^{3} = (5n) {}^{3} [/tex]

Apply sum of cubes formula

[tex]x {}^{3} + y {}^{3} = (x + y) (x {}^{2} - xy + y {}^{2} )[/tex]

[tex](3m {}^{3}) + (5n {}^{3} ) = (3m + 5n)((3m) {}^{2} - 3m.5n + (5n {}^){2} ) \\ = (3m + 5n)((3m {}^{2} ) - 3m.5n + (5n {}^{2} ))[/tex]

simplify

[tex] = (3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]

If you have any questions tag me on comments

Hope it helps!!!