Suppose that Y1, . . . , Yn is a sample of size n from a Exp(θ), with θ > 0, E[Y1] = θ and V(Y1) = θ^2
.
a) Find the distribution of Y¯Bar and Y(1) = min(Y1, . . . , Yn).
b) Find the constants c1 and c2 such that T1 = c1Y(1) and T2 = c2Y¯Bar are unbiased the estimators of θ. Compare the MSE of T1 and T2
c) Show that Q(Y1, . . . , Yn; θ) = 2nY(1)/θ ∼ Chi-sqaure(2).
d) Construct a two-sided 1 − α confidence interval for θ using the pivot in c).

Answer:

The formula for the population P, of the town as a function of year t, if the population increases by 60 people per year, is:

P(t) = 1900 + 60t

where t is the number of years elapsed since t=0.

The formula for the population P, of the town as a function of year t is

P = 1900 + 60t

We have,

If the population increases by 60 people per year, then we can use the following formula to find the population P as a function of time t (in years):

P = 1900 + 60t

Here, the initial population at t=0 is 1900 people, and the population increases by 60 people per year,

So we add 60t to the initial population to get the population at time t.

For example,

If we want to find the population after 5 years, we can substitute t=5 into the formula:

P = 1900 + 60(5) = 2200

So the population after 5 years would be 2200 people.

Thus,

The formula for the population P, of the town as a function of year t is

P = 1900 + 60t

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The unknown side lengths of the given right triangle ∆LJK where LJ 30° and JK 5 are LJ = 6, and JK = 4.

Triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry. A triangle has three sides and three angles, usually measured in degrees. The angles always add up to 180°. Triangles can be classified according to the lengths of their sides or the sizes of their angles. Types of triangles include right, acute, obtuse, scalene, isosceles, and equilateral. Triangles are also used to form more complex shapes in geometry, such as polygons and circles.

To find the unknown side lengths of a right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of a triangle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is JK and the other two sides are LJ and JK.

We can use the Pythagorean Theorem to find the unknown side length of JK. We know that the angle LJ is 30°, so we can use the sine rule to calculate the length of side LJ. The sine rule states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all three sides. Therefore, we can calculate the length of LJ by dividing the sine of 30° (0.5) by the length of the opposite side (JK).

We can now use the Pythagorean Theorem to calculate the length of side JK. We know that the length of LJ is 6, and the length of JK is 5. We can plug these values into the equation a2 + b2 = c2, where a is the length of LJ (6), b is the length of JK (5), and c is the hypotenuse (JK). This yields the equation 36 + b2 = c2, which simplifies to b2 = c2 - 36. Since we know that c2 = 52, we can solve for b2 by subtracting 36 from 52, which gives us 16. The square root of 16 is 4, so the length of JK is 4.

Therefore, the unknown side lengths of the given right triangle ∆LJK where LJ 30° and JK 5 are LJ = 6, and JK = 4.

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Answer:

1st one.-sin(X)+5e^5x

In response to the stated question, we may state that Since [tex]\theta[/tex]is in the trigonometry fourth quadrant, [tex]\theta/2[/tex] is also in the fourth quadrant.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

a) We can use the double angle formula for sine to find sin 2theta:

[tex]sin 2\theta = 2sin \theta cos \theta\\sin^2 \theta + cos^2 \theta = 1\\sin^2 \theta + (3/10)^2 = 1\\sin^2 \theta = 1 - (9/100)\\sin \theta = \sqrt(91)/10 \\sin 2\theta = 2sin \theta cos \theta\\sin 2\theta = 2(\sqrt(91)/10)(3/10)\\sin 2\theta = 3\sqrt(91)/50[/tex]

b) To find the quadrant in which [tex]\theta/2[/tex] is located, we need to find [tex]\theta/2[/tex] first:

[tex]\theta/2 = (3\pi/2 + \theta)/2\\\theta/2 = 3\pi/4 + t\heta/2\\\theta/2 - \theta/2 = 3\pi/4\\\theta/2 = 3\pi/4\\\theta = 3\pi/2[/tex]

Since theta is in the fourth quadrant, [tex]\theta/2[/tex] is also in the fourth quadrant.

c) To find cos theta/2, we can use the half angle formula for cosine:

[tex]cos(theta/2) = \sqrt((1 + cos theta)/2)\\cos(theta/2) = \sqrt((1 + 3/10)/2)\cos(theta/2) = \sqrt(13/20)\\cos(theta/2) = \sqrt(13)/2sqrt(20)\\cos(theta/2) = \sqrt(13)/10[/tex]

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The calculated sum of the infinite series represented as 72 - 36 + 18 - 9 +... is 48

Given that we have the following infinite series

72 - 36 + 18 - 9 +...

In the above series, we have the following parameters

Initial value, a = 72

Common ratio, r = -36/72

When the above are evaluated, we have

Initial value, a = 72

Common ratio, r = -0.5

The sum of the infinite series is then calculated as

Sum = a/(1 - r)

When values are substituted, we have

Sum = 72/(1 + 0.5)

Evaluate

Sum = 48

Hence, the sum is 48

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Answer:

21 feet by 15 feet

hope this helps

Step-by-step explanation:

given quadratic equation is

simplification,

by using,

[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0

\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\

[/tex]

[tex]square[/tex]

[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]

[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]

Answer: 64°

Step-by-step explanation:

Had this problem and got it right

The volume of the triangular pyramid is 26 2/3 yd³

The formula for calculating the volume of a triangular pyramid is expressed with the equation

A = 1/3bh

Such that the parameters in the equation are;

The base area of the pyramid is;

Area = 1/2 × 4 × 5

Multiply the values

Base area =20/2

Base area = 10 yd

Substitute the value

Volume = 1/3 × 10 × 8

Multiply the values

Volume = 80/3

Divide the values

Volume = 26 2/3 yd³

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Answer: 11/9 or 1 2/9 or 11 over 9

Step-by-step explanation:

Firstly, you need to know what a fraction is.

A fraction is a segment (part of) a whole. To express a fraction, you write the numerator over the denominator. A numerator is the top part of the fraction, and it shows how much it is out of. The denominator shows how much it is out of.

Example: [tex]\frac{1}{3}[/tex]

That means it is 1 part out of 3 parts

Now you know what a fraction is, now let's add them.

Next, convert the word form into the number form:

2 over 3 is 2/3

plus is +

5 over 9 =is 5/9

Combine them:

2/3 + 5/9

Steps of the problem:

Firstly, you have to find the L.C.M (Lowest Common Multiple) of 3 and 9 because to add fractions, you need a common (same) denominator.

9 is the L.C.M of 3 and 9, as 9x1 = 9 and 3x3 = 9.

Mulitiply the numerator and denominator by 3:

2x3/3x3 = 6/9

Now, the equation is 6/9+5/9.

Add the numerators:

11/9

The answer is 11/9

If the question tells you to convert into a mixed number, then here's the following steps:

You have to find the highest number 11 goes into 9

It's 1.

Take the remainder (2) into the fraction:

2/9

Now, add 1 in front of it:

1 2/9

As a decimal, it is 1.2222222 (recurring).

If that helped you, please make me Brainliest!

Answer:

11 over 9 [tex](\frac{11}{9})[/tex]

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for [tex]\frac{2}{3} +\frac{5}{9}[/tex], we need to first convert these fractions so that they share a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

If a common denominator just refers to 2 fractions having the same denominator, we can simply multiply the numerator and denominator of the fraction [tex]\frac{2}{3}[/tex] by a number. To solve for that number, we can divide 9 by 3.

Now that we know that the number is 3, multiply both by 3.

Now the fraction looks like this: [tex]\frac{6}{9}[/tex].

We can now change the expression to this:

When adding fractions with the same denominator, we can just add the 2 numerators and keep the common denominator the same.

Now just insert 11 in as the numerator:

Therefore 2 over 5 plus 5 over 9 is 11 over 9.

Answer: LN = 15

Make a proportional relationship:

[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]

Insert the values:

[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]

cross multiply:

[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]

Simplify:

Answer:

The function g(x) = (x + 2)³ − 6 is obtained by applying three transformations to the parent function f(x) = x³.

First, g(x) is shifted 2 units to the left by subtracting 2 from x inside the parentheses:

g(x) = (x + 2 - 2)³ − 6 = (x)³ − 6

This shows that option C, "g(x) is shifted 2 units to the left and 6 units down," is not correct.

Next, g(x) is shifted 6 units down by subtracting 6 from the entire function:

g(x) = (x + 2)³ − 6 - 6 = (x + 2)³ - 12

This shows that option A, "g(x) is shifted 2 units to the right and 6 units down," is correct.

Finally, g(x) is not shifted left or right by any additional units, but it is shifted 2 units up by adding 2 to the constant term:

g(x) = (x + 2)³ − 6 + 2 = (x + 2)³ - 4

This shows that option B, "g(x) is shifted 6 units to the right and 2 units up," is not correct.

Therefore, the correct answer is option A: g(x) is shifted 2 units to the right and 6 units down.

Answer:

Step-by-step explanation:

Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".

Answer:

Step-by-step explanation:

Part A:

Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:

y = velocity of the runner in km/h

x = time in hours

The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:

y - 5 = -2/3(x - 1)

Simplifying this equation, we get:

3y - 15 = -2x + 2

Rearranging to standard form, we get:

2x + 3y = 17

So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.

Part B:

To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.

Here are the values of y for different values of x:

x = 0, y = 17/3

x = 1, y = 5

x = 2, y = 13/3

x = 3, y = 3

x = 4, y = 7/3

x = 5, y = 1

Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:

|

6.0 -| .

| .

5.5 -| .

| .

5.0 -| .

|.

4.5 -|

|

4.0 -| .

| .

3.5 -| .

| .

3.0 -| .

|.

2.5 -|

|

2.0 -| .

| .

1.5 -| .

| .

1.0 -|.

|

0.5 -|

|

--------------

0 1 2 3 4 5

The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.

Answer: CLICK THANKS IF YOU LIKE MY ANSWER. HAVE A GOOD DAY SIR/MAAM #KEEPSAFE

Part A:

Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:

v = 5 when t = 1

v = 3 when t = 3

To find the equation in standard form, we can first use point-slope form:

v - 5 = m(t - 1) (using the point (1, 5))

v - 3 = m(t - 3) (using the point (3, 3))

Simplifying both equations:

v - 5 = m(t - 1)

v - 3 = m(t - 3)

v = mt + (5 - m)

v = mt + (3m - 3)

Setting the right-hand sides equal to each other:

mt + (5 - m) = mt + (3m - 3)

Simplifying and rearranging:

-m = -2

m = 2

Substituting m = 2 into one of the equations above:

v = 2t + 3

This is the equation in two variables in standard form that describes the velocity of the runner at different times.

Part B:

To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:

When t = 0, v = 3, so the point (0, 3) is on the line.

When t = 1, v = 5, so the point (1, 5) is on the line.

When t = 2, v = 7, so the point (2, 7) is on the line.

When t = 3, v = 9, so the point (3, 9) is on the line.

When t = 4, v = 11, so the point (4, 11) is on the line.

When t = 5, v = 13, so the point (5, 13) is on the line.

Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:

    |

 15 +-------*

    |       |

 13 +           *

    |           |

 11 +               *

    |               |

  9 +                   *

    |                   |

  7 +                       *

    |                       |

  5 +                           *

    |                           |

  3 +---------------*-----------*

    0   1   2   3   4   5   6   7

The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.

Step-by-step explanation:

The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians, and they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.

Let's first draw a diagram to visualize the problem:

                    /  |

                  /     |

                 /       |P (plane)

                /        |

               /         |

              /          | h = 6900 ft

            /            

           / θ2.        |  

         /                |

       /                  |

   B ___/θ1__  _|___ A

           d

We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.

From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.

Let's use the tangent function to solve for d:

x = h / tan(74°) = 19906.5 ft

d - x = h / tan(63°) = 23205.2 ft

So,

d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.

Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

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Answer:

siuuuuuuuuuuuuuuuuuuuuuuuuuu

Answer:

Veronica is correct

Step-by-step explanation:

On Monday, Veronica earns 3 walks * $5.25 per walk = $15.75.

On Tuesday, Veronica earns 2 walks * $5.25 per walk = $10.50.

So far, Veronica has earned a total of $15.75 + $10.50 = $26.25.

To reach her goal of $86, Veronica needs to earn an additional $86 - $26.25 = $59.75.

Since Veronica earns $5.25 per walk, she needs to complete $59.75 ÷ $5.25 per walk = 11.38 walks.

Since Veronica cannot complete a fraction of a walk, she will need to complete 12 more walks (rounded up from 11.38) by the end of the week.

Answer: decrease in the GDP by 2.5%.

Step-by-step explanation:

The fraction of learners who do not cycle to school is equal to 9/10.

Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;

40 - [12 +2(12)] = 4

The number of learners who do not cycle to school is;

12 + 2(12) = 36

fraction of learners who do not cycle to school = 36/40

by simplification;

fraction of learners who do not cycle to school = 9/10.

Therefore, the fraction of learners who do not cycle to school is equal to 9/10.

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Answer:

1/4

Step-by-step explanation:

First, Pick a point

A (-4, 8) → A' (-1, 2)

We see that to get from A to A' we time 1/4

So, the scale of dilation is 1/4

[tex]f(-x)[/tex] is not equal to f(x), the function [tex]f(x) = 5x^3 + x[/tex] is neither even nor odd.

If a function meets the requirements for both odd and even, then the answer is yes. The function is both even and odd if  [tex]f(-x) = f(x)[/tex] and [tex]f(-x) = -f(x)[/tex] for every x in the domain of f.

These functions are known as the zero function or identically zero function because they imply that f(x) = 0 for all x in the domain of f.

The given function is [tex]f(x) = 5x³ + x.[/tex]

To know that a function f(x) is even if f(-x) = f(x) for all x in the domain of f.

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f.

Thus,

[tex]f(-x) = 5(-x)³ + (-x) = -5x³ - x[/tex]

[tex]f(x) = 5x³ + x[/tex]

Comparing f(-x) with f(x), we get:

[tex]f(-x) = -5x³ - x[/tex]

[tex]f(x) = 5x³ + x[/tex]

Since f(-x) is not equal to f(x), the function f(x) = 5x^3 + x is neither even nor odd.

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The equation y = -1/2(x-3)² + 5  reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.

In mathematics, a graph is a visual representation of a set of objects (called vertices or nodes) and the connections (called edges) between them.

The equation y = -1/2(x-3)² + 5 is a quadratic function in vertex form. The vertex of this parabola is at the point (3, 5), and the coefficient of the x²  term is negative (-1/2), which tells us that the parabola opens downwards. This means that the graph of this equation reduces.

To see why this is the case, consider the behavior of the y-values as x moves away from the vertex. Since the leading coefficient is negative, the y-values will decrease as x moves to the left or right from the vertex. Additionally, the squared term inside the parentheses means that the graph will be symmetric around the x-coordinate of the vertex, which is 3 in this case.

Thus, as x moves away from the vertex to the left or right, the y-values decrease in a symmetric manner, resulting in a graph that reduces. This can be seen in the shape of the parabola as it curves downwards from the vertex.

Therefore, the equation y = -1/2(x-3)² + 5  reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.

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Answer:

1. 57/16 or 3.5625 ounces of water

8 : 4.75

1 : 19/32  -----> divide both by 8

19/32x6=57/16 = 3.56 ounces

2. 2.4375 ounces of other ingredients

6-3.5625=2.4375

The baby born in week 40 weighs relatively less since its z-score -0.26, is smaller than the z-score of -0.16 for the baby born in week 32.

To find the z-score, we use the formula:

z = (x - μ) / σ

where x is the individual value, μ is the mean, and σ is the standard deviation.

For the 32-week gestation period baby (weight = 2575 grams):

For the 40-week gestation period baby (weight = 3075 grams):

Now, we round the z-scores to two decimal places:

Since the z-score for the 40-week baby (-0.26) is smaller than the z-score for the 32-week baby (-0.16), the correct answer is:

C. The baby born in week 40 weighs relatively less since its z-score -0.26, is smaller than the z-score of -0.16 for the baby born in week 32.

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Answer:

Step-by-step explanation:

12 to the second power (or 12 squared) is equal to 144.

Mathematically, it can be represented as:

12^2 = 12 x 12 = 144

Answer:i don't know the answer

Step-by-step explanation: i don't konw

The value οf the variable y is 9 when k is -3 in the given question.

In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.

A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.

A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.

Given: y=k x

where, x= -3 and k= -3

we can find the value of y by multiplying k with x,

so, y=k x

now, putting values as follows:

we get, y = -3 × -3

               = 9

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Answer:

48 cookies were in the bag.

Step-by-step explanation:

It said 12 was 25%, so you want to multiply it by 4 to get 100% and 100% of the bag was 48 cookies.

Answer:

subtract 20; 80, 60, 40

The pattern is to subtract 20 from the previous term.

Next three terms: 20, 0, -20.

Therefore, the sequence continues as follows:

80, 60, 40, 20, 0, -20.

Answer:0.25

Step-by-step explanation: