Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimetres (cm) to 1 d. P

The segment drawn from the apex to the circumference of the circle's base is 25 units long.

Let's denote the radius of the circular base of the cone by r, and the height of the cone by h. Then, the diameter of the base is given as 14 units, which means that the radius is r = 14/2 = 7 units.

We are given that the volume of the cone is 392π cubic units, which means that:

(1/3)πr²h = 392π

Simplifying this equation, we get:

r²h = 1176

Substituting r = 7, we get:

49h = 1176

Solving for h, we get:

h = 24

So the height of the cone is 24 units.

To find the length of a segment drawn from the apex to the edge of the circular base, we can use the Pythagorean theorem. Let's denote this length by L. Then, we have:

L² = r² + h²

Substituting r = 7 and h = 24, we get:

L² = 7² + 24²

L² = 625

Taking the square root of both sides, we get:

L = 25

Therefore, the length of the segment drawn from the apex to the edge of the circular base is 25 units.

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At the end of the year, the expression that shows the total number of students is [tex]22+s[/tex]

An expression is a mathematical phrase that can contain numbers, variables, and operators. It doesn't contain an equal sign (=) or a value.

Mrs. Jeffers started the school year with 22 students. During the school year, another s student joined her class.

The expression that shows the number of students at the end of the year is.[tex]22+s[/tex]

The symbol "+" is an operator that stands for addition, and "s" is a variable that represents the number of students who joined the class.

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The width of the rectangular field is 51 meters

To find the width of the rectangular field, we need to use the formula for the perimeter of a rectangle, which is:

Perimeter = 2 × (length + width)

We are given that the perimeter of the rectangular field is 292 m and the length is 95 m. So, we can plug in these values into the formula and solve for the width:

292 = 2 × (95 + width)

First, we can simplify the right side of the equation:

292 = 190 + 2 × width

Next, we can isolate the variable (width) on one side of the equation by subtracting 190 from both sides:

292 - 190 = 2 × width

102 = 2 × width

Finally, we can solve for the width by dividing both sides by 2:

width = 51 m

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The value of ML in the given quadrilateral which is a trapezoid is 58 units.

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, whereas another contends that a trapezoid can have several pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid under that definition.

We know that, A median on a trapezoid will be parallel to the bases, with a length equal to the sum of the bases divide by 2.

Thus,

45 = 3x + 11 + 10x - 12 / 2

45 = 13x - 1/ 2

90 = 13x - 1

91 = 13x

x = 7

Substitute the value of x in ML:

ML = 10x - 12

ML = 10(7) - 12

ML = 70 - 12

ML = 58

Hence, the value of ML in the given quadrilateral which is a trapezoid is 58 units.

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There were 0.00325 moles of oxygen gas (O2) involved in the reaction.

The magnesium oxide created will react with any oxygen in the air when the experiment is performed without a lid on the crucible.

Using the atomic mass of magnesium, we can calculate the number of moles of oxygen gas (O2) that reacted by first calculating the number of moles of magnesium that reacted:

Magnesium mass (Mg) = 0.12 g

Mg's atomic mass is 24.31 g/mol (from periodic table)

Mg's mass divided by its atomic mass yields the number of moles.

= 0.12 g / 24.31 g/mol

= 0.00494 mol

The chemical equation for the reaction of magnesium and oxygen to form magnesium oxide is 2Mg + O2 2MgO.

According to the equation, 2 moles of magnesium and 1 mole of oxygen combine to form 2 moles of magnesium oxide.

Thus, the following formula can be used to determine how many moles of O2 reacted:

Production of MgO moles as a function of mass

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these are the whole statements: Cosine function has a 24-period period. The cosine function's midline has the equation y = 19.25. The cosine function has a 15.25 amplitude.

A mathematical equation, such as 6 x 4 = 12 x 2, states that two amounts and values are equal. two. Countable noun. A scenario known as an equation means that two or more components must be taken into account in order to comprehend or understand the overall situation.

Midline = (34.5 Plus 4) / 2 (34.5 + 4) = 19.25 Maximum value plus Minimum value

As a result, the following equation represents the data's model for the midline of a cosine function:

y = 19.25

The biggest deviation from the function's midline is its amplitude in the cosine function. The maximum amount of v(x) was 34.5 cm/s, and the minimum is 4 cm/s, according to the data provided. The cosine function used to model the data has the following amplitude:

Amplitude is calculated as (highest value – minimum values) / 2 (or 34.5 - 4) / 2 (or 15.25).

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The total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.

A Latin word with the meaning "out of one hundred" is percentage.

Working with parts of 100 is much easier than working with thirds, twelfths, and other fractions, especially since many fractions lack a consistent (non-recurring) decimal equivalent.

Significantly, this also makes comparing percentages more simpler than comparing fractions with various denominators. This contributes to the widespread usage of the metric measuring system and decimal currencies.

Total students enrolled for art class = 58

Percentage of cancelled students = 10.3%

Then, Percentage of non-cancelled students = 100 - 10.3 = 89.7%

So,

Attended students = 89.7% of 58.

= 89.7*58 / 100

= 52.06

= 52 (approx)

Thus, the total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.

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The missing cοοrdinate r is 11

Slοpe is calculated by finding the ratiο οf the "vertical change" tο the "hοrizοntal change" between (any) twο distinct pοints οn a line. Sοmetimes the ratiο is expressed as a quοtient ("rise οver run"), giving the same number fοr every twο distinct pοints οn the same line.

First use pοint slοpe fοrm tο find yοur equatiοn

y - y1 = m ( x - x1) using (-6,3) and m= 1/2

y - 3 = 1/2 ( x - -6)

y - 3 = 1/2x + 3

Add 3 tο each side tο isοlate y

y -3 +3 = 1/2x +3 +3

y = 1/2x + 6

Nοw we knοw οur y-intercept is 6

Sο we can graph (-6, 3) and (0, 6) and draw a line

Nοw draw a vertical line at x = 10 because we want tο find the y value at x=10

y = 11

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See attached graph

The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.

Since we know that,

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value a.

2) Side opposite to 60 will be value a√3

3) Hypotenuse will be 2a.

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

The sides of an isosceles right triangle are in the ratio,

1:1:√2

where √2 is the hypotenuse.

For the example, BC = 2√2, then AC = 2√2  x √2 = 4.

Therefore, the three pairs are;

1. (AB = 6, BC = 6)

5. (AB = 4, AC = 4√2)

6.(BC = 2√2, AC = 4).

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The complete question is attached below:

Form refers to three-dimensional objects with depth, while shape pertains to the two-dimensional outline or boundary of an object.

We have,

In the context of geometry and visual representation, the terms "form" and "shape" have distinct meanings and characteristics.

Form generally refers to a three-dimensional object that has depth, such as a solid object or a structure with volume.

It encompasses objects that have length, width, and height, and it extends beyond a two-dimensional representation.

Form can have irregular or complex shapes and is not limited to a specific number of sides.

Shape, on the other hand, refers to the two-dimensional outline or boundary of an object.

It is limited to the external appearance or silhouette of an object without considering its depth or volume.

Shapes are typically described by their attributes, such as the number of sides (e.g., triangle, square) or specific geometric properties (e.g., circle, rectangle).

Thus,

Form refers to three-dimensional objects with depth, while shape pertains to the two-dimensional outline or boundary of an object.

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If the expression 1/2x was placed in the form ax^b where a and b are real numbers, then a + b equal to option (4) -1/2

The given expression is 1/(2x), which can be rewritten as:

1/(2x) = 1/2 × (1/x)

Here, we can see that the expression can be written in the form of ax^b, where a = 1/2 and b = -1.

To see why a = 1/2, notice that 1/2 is the coefficient of (1/x). And to see why b = -1, note that x^(-1) is the exponent on the variable x

So, we have:

1/(2x) = (1/2) × x^(-1)

And, a + b = (1/2) + (-1)

Add the numbers

= -1/2.

Therefore, the correct option is (4) -1/2.

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The probability that the first ball is yellow if the second ball is black is 1/14. The correct option is D.

The given question is a classic example of dependent events in probability. As the balls are drawn without replacement, the second event's outcome will depend on the outcome of the first event.

Probability = Number of favorable events/ Total number of events

The probability of the first ball being yellow is [tex](5/15)[/tex], while the probability of the second ball being black is [tex](3/14)[/tex].

Mathematically represented as P(Yellow ball on the first draw) = P(Yellow ball) = [tex]5/15[/tex]

P(Blackball on second draw given Yellow ball on the first draw) = P(Blackball | Yellow ball) = [tex]3/14[/tex]

As both the events are dependent, we need to find the joint probability of both the events, which can be calculated as P(Yellow ball on the first draw and Blackball on the second draw) = P(Yellow ball) × P(Blackball | Yellow ball)

P (Yellow ball on the first draw and blackball on second draw) = [tex](5/15) × (3/14) = 3/42 = 1/14.[/tex]

Therefore, the correct option is D.

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Answer:

So 3 blue buckets and 4 white buckets were purchased

Step-by-step explanation:

We can solve this by algebra

Let B = number of blue buckets bought

Let W = number of white buckets bought

Total buckets bought:
B + W = 7    (1)

Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water

Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water

Totally they can hold
2B + 5W gallons

We are given that they both can hold  26 gallons of water

So our second equation is
2B + 5W = 26   (2)

By eliminating one of the variable terms we can solve for the other variable term

Let's eliminate the term for variable B

Multiply equation (1) by 2

(1) x 2 ==> 2(B + W) = 2(7)

2B + 2W = 14    (3)

Subtract (3) from (2); B terms are same so they cancel out

(2) - (3):
2B + 5W = 26    [tex]\bold{-}[/tex]
2B + 2W = 14
---------------------
0    +  3W = 12
------------------------

3W = 12
W = 12/3

W = 4

Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7

B = 3

So 3 blue buckets and 4 white buckets were purchased

The exponential equation that fits the data points (0,35), (1,50), (2,100), (3,200), and (4,400) is y = 35 * (10/7)^x.

To find an exponential equation that fits the given data points, we can use the general form of an exponential equation:

y = a * b^x

where y is the dependent variable (in this case, the second coordinate of each data point), x is the independent variable (the first coordinate of each data point), a is the initial value of y when x is 0, and b is the growth factor.

Using the given data points, we can create a system of equations:

35 = a * b^0

50 = a * b^1

100 = a * b^2

200 = a * b^3

400 = a * b^4

The first equation tells us that a = 35, since any number raised to the power of 0 is 1. We can then divide the second equation by the first equation to get:

50/35 = b^1

Simplifying, we get:

10/7 = b

We can now substitute a = 35 and b = 10/7 into the remaining equations and solve for y:

y = 35 * (10/7)^x

This is the exponential equation that fits the given data points. We can use it to find the value of y for any value of x. This equation gives us a way to predict the value of y for any value of x.

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In this case, we are given a car dealership that offers a convertible that can be purchased in one of four colors: red, black, white, or silver. It is asked in the problem to give the probability for the next car purchased will be silver. since there are 300 silver colors, then the probability is 300/1500 or 1/5 in lowest terms. this is equal to 0.20.

The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and

a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:

4,500 dives x 2 scientists per dive = 9,000 scientists

Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.

2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:

4,500 dives x (1 pilot + 2 scientists)

= 4,500 x 3

= 13,500 people

Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

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The number of ways of doing both things is N = m × n

Since there are m ways of doing one thing and n ways of doing another, to find how many ways are there to do both, we proceed as follows.

Since there are m ways of doing one thing and n ways of doing another, to find the number of many ways to do both things,we multiply both numbers together.

So, then number of ways of doing both things is N = m × n

So, there are m × n ways of doing both things

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Answer:

8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

When n = 1:

n² + 7 = 1² + 7 = 8

When n = 2:

n² + 7 = 2² + 7 = 11

When n = 3:

n² + 7 = 3² + 7 = 16

When n = 4:

n² + 7 = 4² + 7 = 23

When n = 5:

n² + 7 = 5² + 7 = 32

When n = 6:

n² + 7 = 6² + 7 = 43

Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Answer:

When n = 1, n² + 7 = 1² + 7 = 8

When n = 2, n² + 7 = 2² + 7 = 11

When n = 3, n² + 7 = 3² + 7 = 16

When n = 4, n² + 7 = 4² + 7 = 23

When n = 5, n² + 7 = 5² + 7 = 32

When n = 6, n² + 7 = 6² + 7 = 43

The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

ᓚᘏᗢ

hope u have a good day man

The time in hours which it will take them for working together for terri is about 1.71 hours.

Inverse Proportion: When two quantities are related in such a way that the product of one quantity with the reciprocal of the other quantity remains constant, it is said to be in inverse proportion.

Let's calculate their working rate:

Terri takes 3 hours to complete the painting of her living room, so she can paint her living room in [tex]\frac{1}{3} hours[/tex]

Angela takes 4 hours to complete the painting of the living room, so she can paint her living room in [tex]\frac{1}{4} hours[/tex]

If both work together, then the time taken to complete the work will be less than the time taken by each of them individually.

To find the time taken by both working together, we will add their rates.

Terri's work rate = [tex]\frac{1}{3} hours[/tex]

Angela's work rate = [tex]\frac{1}{4} hours[/tex]

Work rate when working together = Terri's rate + Angela's rate= [tex]\frac{1}{3} + \frac{1}{4} = \frac{7}{12}[/tex]

Thus, both will take [tex]\frac{12}{7} = 1.71 hours[/tex] approximately to complete the painting of the living room when they work together.

Therefore, the time in hours is about 1.71 hours.

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Answer:

[tex]\frac{m}{11}[/tex]

Step-by-step explanation:

To write the given expression as a fraction, put m in the numerator and 11 in the denominator as shown: [tex]\frac{m}{11}[/tex]

This would be the quotient of m and 11 expressed as a fraction!

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Answer:

x = 10

y = -9

Step-by-step explanation:

x = -3y - 17

2x + 3y = -7

Plug in x

2 (-3y - 17) + 3y = -7

-6y - 34 + 3y = -7

-3y = 27

y = -9

Plug in the value you got for y back into the equation to find the x value

x = -3(-9) - 17

x = 10

New points of graph A'B'C'D' are A'(-2, -2), B'(-2, 0), C'(-4, 0), D'(-4, -1)

In graph theory, the term "translation" refers to a type of operation that moves all the vertices and edges of a graph by a fixed distance in a given direction. Specifically, a translation of a graph involves shifting every vertex a certain distance horizontally and/or vertically, without changing the shape or connectivity of the graph.

Translation: 4 left and 2 down

Start with a point at its original location and then move it 4 units to the left and 2 units down. This can be done by subtracting 4 from the x-coordinate and subtracting 2 from the y-coordinate of the point or shape.

Given points in a graph ABCD are, A(2, 0), B(2, 2), C(0, 2), D(0, 1)

Subtract 4 from the x-coordinate and subtract 2 from the y-coordinate, resulting in a new points of graph A'B'C'D' are A'(-2, -2), B'(-2, 0), C'(-4, 0), D'(-4, -1)

The figure shown in below diagram.

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Answer: $318/mo

Step-by-step explanation:

First, we get the remainder, which is the difference between $9, 632 and $2,000. That gives us $7, 632.

Then, since we know she will pay in 24 months, we assume she pays the same amount each month and divide $7, 632 by 24 = $318/mo

To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Given that two random variables follow a normal distribution with mean 0 and variance 1.

Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)

Now, The expected value of the product of two random variables is given by;

E[XY] = E[X]E[Y] + Cov(X,Y)

Where E[X] and E[Y] are the means of the two random variables X and Y respectively.

Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;

Cov(X,Y) = E[XY] - E[X]E[Y]

Now, E[X] = E[Y] = 0 as both have a mean of 0.

Cov(X, Y) = E[XY] - E[X]E[Y]

⇒ E[XY] = the expected value of the product of X and Y.

As X and Y are independent, their covariance will be zero, which implies;

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.

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Answer: x=1

Step-by-step explanation:

Vertical angles mean they are equal to each other. So first you would set the two equations equal to each other.

7x+26=4x+29

Then subtract 4x from both sides.

7x+26−4x=29

combine 7x and −4x to get 3x.

3x+26=29

Then subtract 26 from both sides.

3x=29−26

subtract 26 from 29 to get 3.

3x=3

Lastly divide both sides by 3.

3/3x=3/3

Divide 3 by 3 to get 1.

x=1

Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.

Here,

(i) Let the length of the rectangle be y cm.

Then, the perimeter of the rectangle is given by:

2(x + y) = 112

x + y = 56

y = 56 - x

(ii) The area of the rectangle is given by:

Area = length x breadth

597 = yx

Substituting y = 56 - x, we get:

597 = x(56 - x)

597 = 56x - x²

x² - 56x + 597 = 0

(iii) Using the quadratic formula,

x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))

x = (56 ± √(3136 - 2388)) / 2

x = (56 ± √(748)) / 2

x = (56 ± 2√(187)) / 2

x = 28 ± √(187)

Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).

(iv) The length of the rectangle is y = 56 - x.

Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:

d² = y² + x²

d² = (56 - x)² + x²

d² = 3136 - 112x + 2x²

d = √(3136 - 112x + 2x²)

Substituting the value of x from part (iii) into the above equation, we get:

d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)

d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))

d = √(37400 ± 168√(187))

d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)

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The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.

We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.

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The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.

A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).

The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.

A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:

The formula for the area of a trapezoid is as follows:

Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height

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U is a binomial random variable with n trials and probability of success given by 1 - p.

As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]

The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]

The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]

Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]

Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]

Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.

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