A bag contains 5 red, 4 green, and 3 blue marbles. what is the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble?

Answer:

24

Step-by-step explanation:

small side=12 because 30-60-90 tri.

12*2=24

Kayden has to work 3 hours the next week to earn $43.80.

We have given,

Kay Den worked 10 hours a week for his employer and took home $146. How many hours would he need to work the next week, at the same hourly rate, to make $43.80?

Kayden earned $146 for 10 hours.

If we calculate hourly wages,

Hourly wage of Kayden = [tex]\frac{146}{10}[/tex]

Hourly wage of Kayden = $14.6

If he is paid the same hourly wage,

We have to find, out how many hours will he have to work to earn $43.80

Let, him worked x hours.

14.6x = 43.80

[tex]x=\frac{43.80}{14.6}[/tex]

x = 3

Hence, it takes 3 hours.

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The number equivalent to the expression is 6(2f+1)

What is an expression ?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one math operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Mathematical operators like addition, subtraction, multiplication, and division are used to write an expression using numbers or variables. For instance, the expression for the mathematical formula "4 added to 2" will be 2+4.

To find the equivalent of the expression 12f + 6 is we take the common value out factorize it

12f+6

6(2f + 1)

This is the expression that is equivalent

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The transformation of y = x² can be described as, Right and left one and down one-half, right and left two and down two, and right and left three and down four and one-half are the points plotted from the vertex.

A transformation is a technique for moving or repositioning a shape. Every point in the shape is moved in the same direction and by the same amount. When a shape is rotated, a point is turned into the center. When a shape appears in a mirror line, it is said to be reflecting. When a shape is shifted a predetermined amount from its initial position, this is known as translation.

Given,

The transformation of y = x² can be described as,

A vertical stretch is the name for this change. Transformation of y = x² can be described as. Right and left one and down one-half, right and left two and down two, and right and left three and down four and one-half are the points plotted from the vertex.

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The dimensions of the poster with the smallest area is 24 x 36.

Let's let "W" be the overall width of poster and "H" be the overall height of the poster.

A = H•W

The area of the printed material is 384.

The width of the printed material is W - 4(2) or W - 8.

The height of the printed material is H - 6(2) = H - 12.

So the area of the printed material is (W - 8)(H - 12) and that equals 384

(W - 8)(H - 12) = 384

WH - 12W - 8H + 96 = 384

W(H - 12) - 8H = 288

W = (288 + 8H)/(H - 12)

the area equation (A = H•W), we get:

A(H) = H(288 + 8H)/(H - 12)

A(H) = (288H + 8H2)/(H - 12)

To find the minimum, take the derivative and set it equal to zero.

To take the derivative, we must use the quotient rule

If f(x) = u/v then f '(x) = (u'v - uv')/v2

In this case u = 288H + 8H2 so u' = 288 + 16H

and v = H - 12 so v' = 1 and v2 = (H - 12)² so

A'(H) = [(288 + 16H)(H - 12) - (288H + 8H2)(1)]/(H - 12)²

A'(H) = (288H - 3456 + 16H2 - 192H - 288H - 8H2)/(H - 12)²

A'(H) = (8H² - 192H - 3456)/(H - 12)²

A'(H) = 8(H² - 24H - 432)/(H - 12)²

Setting it equal to zero:

8(H² - 24H - 432)/(H - 12)² = 0

(H² - 24H - 432)/(H - 12)² = 0 This can only be zero if the numerator is zero so:

H² - 24H - 432 = 0

(H - 36)(H + 12) = 0

H = 36 or H = -12

We can neglect the negative answer since the poster can't be a negative height so H = 36. Since H = 36, and we know that W = (288 + 8H)/(H - 12), we can solve for W:

W = (288 + 8(36))/(36 - 12)

W = 24

H = 36

Therefore, the dimensions of the poster with the smallest area is 24 x 36.

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According to the y-intercept formula, x = 0 can be used to determine the y-intercept of the function y = f(x). Using this, the point on a graph whose x-coordinate is 0 is said to be the y-intercept of the graph. To get the y-intercept, just locate the point at where the graph crosses the y-axis.

What is Graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

The point where a graph intersects the y-axis is known as the y intercept. Any point on the y-axis has an x-coordinate of 0, as is known. Therefore, a y-intercept's x-coordinate is 0.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is Therefore, the y-intercept of the line y = x+ 3 is (0,3).

A function's y-intercept is the location on its graph where the y-axis would meet. We may utilize the fact that the x-coordinate of every point on the y-axis is 0 to construct the formula to locate the y-intercept. Specifically, a function's y-intercept has the following form (0, y). The following is the formula to determine the y-intercept:

Here are the methods to determine a function's y intercept: y = f (x),

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By using percentage, it can be calculated that

Toby sold the television for $2000

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage. For example 7% means [tex]\frac{7}{100}[/tex]

Here 7 can be expressed as a fraction of 100

This is a problem on percentage

Let Toby sold the Television for $x

Percentage commission for Toby = $1.75%

Commission for Toby = $[tex]\frac{1.75}{100} \times x[/tex]

By the problem,

[tex]\frac{1.75}{100} \times x = 35\\x = \frac{35 \times 100}{1.75}[/tex]

x = $2000

Toby sold the television for $2000

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The area of the rectangle wall is 30 square feet.

This room has a floor area that is square in shape. Square is defined as an object with equal sides of length and width. Given that the the floor area is 25 square feet, we can figure out the length and width by the following formula and calculation:

Given that (A) is area of a square, and (a) is the equal sides of a square

A = a²

25=a²

[tex]\sqrt{25} = a[/tex]

5 = a

Therefore each of the side of the floor is 5 feet.

Now that we know that the side of the of the square floor is 5 feet in length, given that the height of the room is 6 feet, we can then calculate the area of the rectangle wall with the following formula and calculation:

Area = width × height

Area = 5×6

Area = 30 square feet

Therefore the area of the wall is 30 square feet.

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Your question seems to be missing but I assume your complete question was:

"A square room has a floor area of 25 square feet. The height of the room is 6 feet. What is the area of the wall?"

The three sides of a triangle that is 3cm, 4cm, and 9cm not of the triangle.

Triangle:

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same

Here we have to find the given three sides of a triangle possible.

The three sides are 3cm, 4cm, and 9cm.

The property of a triangle is that the sum of two sides of a triangle is greater than the third side of a triangle.

The three sides are:

a = 3cm

b = 4cm

c = 9cm

a + b > c

3 + 4> 9

7> 9 which is incorrect

Therefore the three sides in not sides of a triangle.

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The set of side measurements that could be used to form a triangle is 9, 13, 21.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

9, 13, 21 : 9 + 13 > 21 ; 13 + 21 > 9 ; 9 + 21 > 13

8, 9, 18 : 8 + 9 < 18

3, 18, 21 : 3 + 18 = 21

2, 5, 9 : 2 + 5 < 9

Hence, the side measurements 9, 13, 21 is the only set that can be used to form a triangle.

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From power rules, the equation [tex](x^2)^{-2}+x^4*x^5[/tex] is represented by [tex]\frac{1}{x^4} +x^9[/tex] and the  [tex]\frac{x^2}{x^4} -(x^2)^2[/tex] is represented by [tex]\frac{1}{x^2} -x^4[/tex].

Knowing some of the main power rules.

For solving this question, you should identify which power rules you will apply and after that solve the expression.

The question gives two algebraic expressions.

(1)  [tex](x^2)^{-2}+x^4*x^5[/tex]

(2)  [tex]\frac{x^2}{x^4} - (x^2)^2[/tex]

The rules that you will be applied are: multiplication, power and exponent negative.

[tex](x^{-4})+x^9[/tex]=  [tex]\frac{1}{x^4} +x^9[/tex]

The rules that you will be applied are: division, power and  exponent negative.

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

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The quadratic equation is never smaller than zero, so the inequality has no solutions.

The correct option is never.

Here we have the following inequality:

3x^2 + 4x < - 5

To see when it is true, we need to isolate x.

We can rewrite the inequality as:

3x^2 + 4x + 5 < 0

So the inequality is true when the quadratic equation is smaller than zero.

But notice that it is a quadratic equation with a positive leading coefficient, so it opens upwards.

And the vertex is at:

x = -4/2*3 = -2/3

Evaluating the quadratic there we get:

3*(-2/3)^2 + 4*(-2/3) + 5 = 3.66

So the vertex has a positive y-value, this means that the quadratic equation is never negative, and thus, the inequality has no solutions.

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The approach to identify linear functions is whether the change in y will always have the same value for any given change in x.

Possibly the most significant mathematical function is the linear function. One of the simplest functions to comprehend, it frequently appears when you least expect it. We frequently turn more complex functions into linear functions for understanding purposes since it is so convenient to do so. The linear function is incredibly straightforward for one variable. A linear function is one with the formula f(x)=ax, where an is a real number of any value. The parameter an is the slope of the line through the origin that makes up the graph of the function f.

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Expected payment for Rosaria is $202,020.

The Unitary Method is the process by which we first determine the value of a single unit and then the value of the necessary number of units.

In the question asked Rosaria has three expenses to pay,

Rosaria will be required to pay,

$36,259 in tuition for one year.

Room and board cost $12,258.

$1,988 is the cost of the books and lab.

Rosaria must therefore pay $50,505 each year, which is equal to $36,259 plus $12,258 plus $1,988.

Rosaria must pay $202,020 over the course of four years since 4 x $ 50,505 = $202,020.

Rosaria therefore expects to pay $202,020.

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Rosaria will pay $202,020.

The unitary method is used to find the value of a single unit from a given multiple. For example, if the price of 40 pens is Rs. 400, then how to find the value of one pen here? It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.

In this,

Rosaria has to pay

Tuition for one-year costs = $36,259.

Room and board cost = $12,258.

Books and lab costs = $1,988.

Rosaria must therefore pay $50,505 each year, as $36,259 + $12,258 + $1,988.

so for four years

4 x $ 50,505 = $202,020.

Rosaria will pay $202,020 for the course of four years.

Therefore expects to pay $202,020.

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The diagram 1 and 3  produces the largest acceleration on the block in the horizontal direction

The diagram below show the application of a force f on a block of mass m

The force is defined as the product of mass and acceleration

The first picture represents the force pulling to right in the horizontal direction here the angle is zero therefore it will produce the largest acceleration on the block in horizontal direction. Because it depends on the angle which F cosθ

Similarly in the third figure the force is pushing on the block to the right. The angle is zero, therefore it will produce largest acceleration in horizontal direction

In other figures the angle is greater than zero therefore the acceleration in the horizontal direction will be small

Hence, the diagram 1 and 3  produces the largest acceleration on the block in the horizontal direction

The complete question is:

The diagrams below show the application of a force f on a block of mass m. which diagram(s) produces the largest acceleration on the block in the horizontal direction?

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Each probability lies between 0 to 1, If a customer purchases 2 stoves, the probability is 0.1379 they will also purchase two refrigerators, the average number of refrigerators purchased is 0.93, and the variance in the number of refrigerators purchased is 0.6051.

A)     0            1            2          stoves

0      0.08       0.14      0.12      0.34

1       0.09       0.17      0.13      0.39

2      0.05       0.18      0.04     0.27

RF    0.22       0.49     0.29     1

B) Each probability lies between 0 to 1

All the probabilities sum up to 1

C) P(2 Ref/ 2 stoves) = P(2 Ref and 2 stoves) / 2 stoves)

= 0.04/0.29 = 4/29 = 0.1379

D) Average number of Ref purchased E(x) = ∑xi pi

X        0          1         2

Prob.  0.34    0.39   0.27

= 0.39 + 0.54

= 0.93

E) Var(x) = ∈(x)² - (∈{x})²

= (0.39 + 1.08) - (0.93 * 0.93)

= 1.47 - 0.8649

= 0.6051

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a) Decision rule: t less than -1.314

b) Test statistics = -2.785

c) Reject H0

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The American Water Works Association reports that the per capita water use in a single-family home is 77 gallons per day.

Legacy Ranch is a relatively new housing development.

The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences.

(a) So, the decision rule is,

t is less that -1.314.

(b) Test statistics = (73 - 77) / (7.6 / √28)

    Test statistics = -2.785

(c)  The decision regarding H0 is, Reject H0.

Hence,

a) Decision rule: t less than -1.314

b) Test statistics = -2.785

c) Reject H0

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Jimmy, a high school student, has a 33 percent body fat percentage. This suggests that -

Men aged 20 to 39 should have 8% to 19% body fat, while women in the same age range should have 21% to 32% body fat, based on the American Journal of Clinical Nutrition as well as WebMD.

Thus, Jimmy, a senior in high school, has a body fat percentage of 33%. This implies that -

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Answer: x-2

and 2x+4

Step-by-step explanation:

As it determines how quickly the silicon is removed from the wafer. The etch rate is typically measured in angstroms per minute (A/min), which is the rate at which the silicon is removed from the wafer surface.

The pace at which a substance is eliminated or dissolved by a chemical or physical process is referred to as etch rate. Using this method, exact patterns may be made on the surface of a substrate, such a silicon wafer, is widespread in the semiconductor sector. Etch rate is commonly measured in angstroms per minute (/min) and is governed by the concentration and composition of the etching solution, the processing temperature and pressure, and the material being etched. A greater etch rate denotes a quicker removal of material, whereas a lower etch rate denotes a slower removal.

Etch rate plays a significant role in semiconductor production when determining the accuracy and precision of the finished product.

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The number of threads Marvin have left is 13 yards of thread

If  each spool thread is 10.5 yards 2 spools of thread will contain how many yards

= 10.5 * 2

= 21 yards

Marvin used 4 yards from each, hence Marvin used a total of 2 * 4 = 8 yards from the 2 spools of thread

The number of yards remaining is found by subtraction

= 21 - 8

= 13 yards

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The distribution of the probability of each outcome is

P(X = 0) = 0.25

P(X = 1) = 0.5

P(X = 2) = 0.25

Given that,

A family consists of two kids. There are four alternative results if the genders of these kids are stated in the order they are born: bb, bg, gb, and gg. Assume that these results are equally probable. Let x be the proportion of girls among all children.

We have to find the complete part 1 of 2 by finding the probability distribution of x. part: 0 / 20 of 2 parts

We know that,

A probability is obtained by dividing the number of desired outcomes by the total number of outcomes.

The chance of each result is represented by the distribution, so

P(X = 0) = 1/4 = 0.25

P(X = 1) = 2/4 = 0.5

P(X = 2) = 1/4 = 0.25

Therefore, The distribution of the probability of each outcome is

P(X = 0) = 0.25

P(X = 1) = 0.5

P(X = 2) = 0.25

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We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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The cost of 4 potted plants and 5 bags of compost is 35 dollars.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

Let x be the potted plants and y be the bags of compost.

We are given that the cost of 7 potted plants and 2 bags of compost is £41.

7x + 2y = 41

Now The cost of 3 potted plants and 4 bags of compost is £27.

3x + 4y = 27

Now solving both equation.

First, multiply the first equation by 2 then subtract from the second.

14x + 4y - 3x - 4y = 82 - 27

11x  = 55

x = 5

Therefore, 3x + 4y = 27

3(5) + 4y = 27

4y = 27 - 15

4y = 12

y = 3

Now, Emily wants to buy 4 potted plants and 5 bags of compost.

4x + 5y = 4(5) + 5(3)

= 20 + 15

= 35

The cost of 4 potted plants and 5 bags of compost is 35 dollars.

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Third quartile Q₃ of the given data is 11

correct option is: b

What is the 75th percentile value?

0.675

For instance, the median represents the 50th percentile, the first quartile represents the 25th percentile, and the third quartile represents the 75th percentile.

What exactly is Q3?

Q3, the third quartile, is known as the 'upper quartile,' and represents the 75th percentile, which means that only 25% of the values in the set are greater than this value.

given data:

7,14,8,10,7,8,9,7,14,6.

In ascending, order data is 6,7,7,7,8,8,9,10,14,14.

number of terms N = 10

therefore, third quartile Q₃ = [tex]\frac{3}{4} (n + 1)[/tex]

Q₃ = [tex]\frac{3}{4} (10 + 1)[/tex]

Q₃ = 8.25th term

Q₃ = 8th term + 0.25 = 11

therefore, therefore, third quartile Q₃ of the given data is 10

correct option is: b

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After 3 days the balance will be $1050.130

What does "compound daily rate" mean?

Daily compounded interest is higher than interest compounded on a monthly or quarterly basis due to the high frequency of compounding, which means interest is accrued daily and calculated by charging interest on principal plus interest earned daily.

How is compounded daily determined?

How Compounding Works

For the purpose of calculating compound interest:

Investment total: Start amount multiplied by interest rate plus one, then daily interest rate

The interest rate will be divided by 365 and the number of years (n) will be multiplied by 365 to determine daily compound interest.

Added Up Monthly: CI = P(1 + (r/12) ) 12t – P

P represents the principal sum.

r is the time and t is the decimal form of the interest rate.

Given that:

t: the amount of time. Assume that the $1,000 in the savings account from the preceding illustration earned daily compound interest at a rate of 6%. This results in an interest rate of 0.0164384% each day: 6% multiplied by 365.

[tex]At = $1,000 * (1 + 0.0164384)^3[/tex]

At = $1,000 × 1.050130

At = $1,050.130

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The main reason for checking a new mother every 15 minutes for the first hour after giving birth is to help in the early detection of a potential life-threatening complication for the new mother after delivery (postpartum).

At the first 24 hours after birth, all postpartum women should have regular assessment of vaginal bleeding, uterine contraction, fundal height, temperature and heart rate (pulse) regularly during the first 24 hours starting from the first hour after giving birth. In the postpartum period, blood pressure also should be monitored shortly after birth.

The postpartum nursing assessment is a significant aspect of care to identify early signs of complications in the woman who has just given birth. Following pregnancy, women are at risk for infection, hemorrhage, and the development of a Deep Vein Thrombosis (DVT).

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Answer:

No, a triangle cannot be created with these measurement.

Step-by-step explanation:

It must follow these rules:

a + b > c

b + c > a

a + c > b

The transformation can be categorized by the dimensions of the operand sets, distinguishing between planar transformations and spaces. They can also be classified on their properties.

The  types of transformations are:

Dilation The image is a larger or smaller version of the preimage; "shrinking" or "enlarging."

Reflection The image is a mirrored preimage; "a flip."

Rotation The image is the preimage rotated around a fixed point; "a turn."

Shear All the points along one side of a preimage remain fixed while all other points of the preimage move parallel to that side in proportion to the distance from the given side; "a skew.,"

Translation The image is offset by a constant value from the preimage; "a slide."

Rigid transformation

When creating the image, a rigid transformation does not alter the preimage's size or shape. There are three stiff transformations.

Reflection, rotation, and translation are examples of stiff transformations. These changes have no effect on the size or shape of the resulting image.

Non rigid transformations

The preimage's size, shape, or both can be altered using a non-rigid transformation.

Shear and dilation are two non-rigid transformations. The transformation will alter either the size, the shape, or both of the original images.

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One of people expected to receive a card with a number that matches its age.

What is expected value?

The anticipated value is an extension of the weighted average in probability theory. Informally, the anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

Let, a set of 1000 cards numbered 1 through 1000 is randomly distributed among 1000 people with each receiving one card.

[tex]x_i=\left \{ {1, if the i^t^h person card numbermatches his/her age } \atop {0 , Otherwise}} \right.[/tex]

[tex]X_i[/tex] is a new variable.

Expected one of 1,000 people to receive the card which matches its age is,

[tex]E(X_i) = \frac{1}{1000}[/tex]

Expected number of card is,

X= (i=1 to 1000)∑ Xi

E(X) = (i = 1 to 1000) ∑  E(Xi)

       = (i = 1 to 1000) ∑ (1 / 1000)

       = 1000 x (1 / 1000)

       = 1

E(X) = 1

Hence, One of people expected to receive a card with a number that matches its age.

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