Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.

On solving the provided question, we can say that Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\ = 0.9645 and Probability(5<x<9) = P(x<9) - P(x<5) = 0.0101 and P(x<9) = 0.0106

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\

= 0.9645

Probability(5<x<9) = P(x<9) - P(x<5)

= 0.0101

P(x<9) = 0.0106

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Answer:

let the boys and girls be 5x and 3x

the ratio of boys to girls= 5:3

the total girls = 35

the ratio of boys to girls = the total girls

5 =35

3 x

5x = 105

x= 105÷5

x= 25

5x= 5×25= 125

3x= 3× 25 = 75

A word problem for the given expression is the division of 3/4 cups of juice among two friends equally.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is an expression [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex].

Suppose that there are 3/4 cups of juice available.

There are two friends who are in need of this.

The total amount of juice has to be divided equally among these two friends.

Amount of cups of juice each friend gets = [tex]\frac{3}{4}[/tex] ÷ 2.

[tex]\frac{3}{4}[/tex] ÷ 2 = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]

So each friend gets 3/8 cups of juice.

Hence the division of a total of 3/4 cups of juice among two friends equally is a word problem for the given expression.

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Answer:

2^4*2^5=2^(4+5)=2^9

Step-by-step explanation:

When dealing with operations with exponents and multiplication, the exponent operations always come first.  So while the exponent 9 is correct for the answer, 4 is incorrect.

For example, if you were to solve each operation and eliminate every exponent, you would have

2^4*2^5=16*32=512 which is the same as 2^9=512.

As you can see, the exponent operation must come before the multiplication.

Step-by-step explanation:

trfg gh fg gyfggr d vd f fvy e ht4gjgdgdhdggygggg

The probability distribution table is shown below

From the question, we have the following parameters that can be used in our computation:

Dice = 2

This means that

Sample size = 6 * 6

Sample size = 36

So, the number of outcomes is 36

To determine the distribution table, we need to identify that the dice are distinct.

This means that (1, 2) and (2, 1) are not the same outcomes

We can create a probability distribution table for the score by listing all possible outcomes and their probabilities, and then determining the score for each outcome based on the rules given.

So, we have

Outcomes              Probability

(1, 1)                                   1/36

(1, 2)                                   1/36

(1, 3)                                   1/36

(1, 4)                                   1/36

(1, 5)                                   1/36

(1, 6)                                   1/36

........

(6, 1)                                   1/36

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The relationship between pendulum length and period is nonlinear. As the period is dependent on the square root of the length.

To  anatomize this relationship, the scholars would need to gather data on pendulum length and period, also fit a regression model.However, the residuals from the model would be  erratically distributed around zero, If the relationship is direct.

If the relationship is nonlinear, the residuals would parade a pattern, indicating that a direct model is not the  swish fit. In this case, a nonlinear model  analogous as the square root of pendulum length would give a better fit for the data. The scholars  probably set up that the residuals from the direct model were not  erratically distributed, hence they didn't favor the direct model.

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The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Then the equation of the line is given as,

(y - 5) = [(10 - 5) / (14 - 7)](x - 7)

y - 5 = (5/7)x - 1

y = (5/7)x + 4

At x = 63, the value of 'y' is given as,

y = (5/7)63 + 4

y = 45 + 4

y = 49

The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.

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Answer:

The actual distance between two cities that are 3 7/8 inches apart on the map is 279 miles.

Step-by-step explanation:

To find the actual distance between two cities, we need to convert the distance on the map to miles. The scale of the map is 3/4 inch equals 72 miles, which means 1 inch on the map is equal to 72/3=24 miles.

So, the actual distance between two cities on the map that are 3 7/8 inches apart is 24 * 3 7/8 = 279 miles.

Answer:

[tex]S_{18}=-792[/tex]

Step-by-step explanation:

The given arithmetic series is:

From inspection of the given series, the first term is 24.

The common difference is the difference between consecutive terms.

Therefore, the common difference of the given series is -8 as each term is 8 less than the previous term.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

To find the sum of the first 18 terms of the given series, substitute a = 24, d = -8 and n = 18 into the sum formula.

[tex]\implies S_{18}=\dfrac{1}{2}(18)\left[2(24)+(18-1)(-8)\right][/tex]

[tex]\implies S_{18}=9\left[48+(17)(-8)\right][/tex]

[tex]\implies S_{18}=9\left[48-136\right][/tex]

[tex]\implies S_{18}=9\left[-88\right][/tex]

[tex]\implies S_{18}=-792[/tex]

Therefore, the sum of the first 18 terms of the given arithmetic series is -792.

The child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.

A differential equation is an equation that contains one or more functions with its derivatives.

The distance between the kite and the child's hand level "d".

By using the Pythagorean theorem, we can write:

d² + h² = s²

Simplifying and solving for d, we get:

d² = s²-h²

d = √(s²-h² )

Let's call the length of the cord "L". Then, we can write:

d² + L² = s²

Differentiating both sides with respect to time (t), we get:

2d (dd/dt) + 2L (dL/dt) = 2s (ds/dt)

We want to find (dL/dt) when L = s and d = √(s²-h² )

(dd/dt) = 0 as the height of the kite above the child's hand level is constant.

(dL/dt) = (s(ds/dt) - d (dd/dt)) / L

Substituting in the values we found for d and L, we get:

(dL/dt) = s(ds/dt)) / √(s²-h² )

Therefore, the child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.

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The solution of the logarithmic expressions will be:-

19) 2logb4 - 2logb5

20) (1/2)logb (3)

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two expressions are logb 16/25 and logb √3.

The expressions will be solved as:-

E = logb 16/25

E = logb 16 - logb 25

E = logb 4² - logb 5²

E = 2logb 4 - 2logb 5

The second expression will be solved as:-

E =  logb √3.

E = ( 1 / 2 ) logb 3

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The offered statement states that there's 12 inches throughout 1 foot and 24 inches in 2 feet.

In the United States, Quebec, and the United Kingdom, the inch is a widely used conventional measure of length. In Japan, particularly for display screens, it is utilized for electrical components as well. The inch is also a commonly-used informal unit of measurement for display screens throughout most of continental Europe. Half, quarter, eighth, and sixteenths are the minor fractions that make up an inch. The size of both the line indicating each lowers as the sum or length does. Millimeters are used to divide centimeters (10 per centimeter).

In 1 feet there are 12 Inches.

12 inches/foot * 2 feet = 24 inches

So, 2 feet is equal to 24 inches.

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Answer:

Here is a table that can be used to solve the equation:

Operation Result

38.2 38.2

+ (-1) 37.2

= 11 False

The equation 38.2 + (-1) = 11 is not true for any value of x. There is no solution for this equation.

Oh, hello there! Let's work on this equation together.

38.2 + -1 = 11

Let's create a table to keep track of our work.

-1 38.2 11

+1 37.2 12

As you can see, we added 1 to both sides to cancel out the negative 1.

So now, our equation is 37.2 = 12.

Let's subtract 12 from both sides.

-12 37.2 11

-12 25.2 -1

And there you have it! The solution is 25.2.

quick caveat, there's no slope-intercept form per se for a vertical line, Check the picture below.

Answer:

C = 10m

Step-by-step explanation:

when c=20, m=2

when c=40, m=4

we can see that c is equals to 10 times the value of m

Therefore c = 10m

Answer:

Step-by-step explanation:

uhhhhh 8 lol

The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The area of the circle is 4π x² + 12πx + 9π. Then the radius is given as,

A = 4π x² + 12πx + 9π

πr² = π [(2x)² + 2 · 2x · 3 + 3²]

r² = (2x + 3)²

r = 2x + 3

The value of the radius should be more than zero. Then we have

r > 0

2x + 3 > 0

x > - 3/2

The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.

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The complete question is given below.

The area of a circle is 4π x 2 + 12πx + 9π.

a. What is an expression for the radius of the circle?

b. What is the least possible integer value of x for the circle to exist? Explain.

Six Sigma is a data-driven methodology for process improvement that aims to minimize defects and reduce variation in processes.

Six Sigma is a data-driven methodology for process improvement that aims to minimize defects and reduce variation in processes. It is a systematic approach to quality management that uses data and statistical analysis to identify and eliminate the root causes of defects and minimize errors in processes.

Six Sigma is based on the DMAIC (Define, Measure, Analyze, Improve, Control) methodology, which involves the following steps:

Define: Identify the problem and determine the goals of the project.

Measure: Gather data and establish a baseline for the process.

Analyze: Use statistical tools and techniques to understand the sources of variation in the process.

Improve: Develop and implement solutions to eliminate the sources of variation and reduce defects.

Control: Monitor and control the process to ensure sustained improvement.

Six Sigma uses a range of tools and techniques, including process maps, statistical analysis, and design of experiments, to achieve its goals. It is designed to be a highly disciplined approach to process improvement, and Six Sigma practitioners must be trained and certified to use the methodology effectively.

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Hi there, here's your answer:

The general formula of a circle:

[tex](x-h)^{2} +(y-k)^{2}=r^2\\[/tex]

Where the ordered pair (h, k) is the center of the circle.

Given (h, k) = (-6, -2)

We also have that the circle passes through a point (7, 12)

Which means that (7, 12) lies on the circumference of the circle.

Let this be labelled as [tex](x_{1}, y_{1})[/tex]

Since this point lies on the circumference of the circle, it must satisfy the equation when substituted in for (x, y).

Thus, we substitute [tex]x_{1}[/tex] for x and [tex]y_{1}[/tex] for y.

We get the final equation to be:

[tex](7+6)^2 + (12+2)^2 = r^2[/tex]

Or

[tex]169 + 196 = r^2[/tex]

[tex]r^2 = 365[/tex]

Thus, we get the final equation of the circle to be [tex](x+6)^2 + (y+2)^2 = 365[/tex]

Hope it helps!

Therefore , the solution of the given problem of function comes out to be the value of c for which f'(c) = 0 in the interval [-2, 2] is c = 0.

The study of numbers and their variable, as well as in out environment, architecture, and both real and imagined places, are all covered in the mathematics curriculum. A function range illustrates visually how the amounts of the inputs and the corresponding outputs for each are related. Simply stated, a function is a set of inputs that, when combined, produce specific outputs for each input. Each position is given a locale, region, or range.

Here,

Rolle's Theorem can be applied to $f(x) = x^2 - 3$ on the interval [-2, 2]. This is because f(x) satisfies the following conditions of Rolle's Theorem:

1 ) f(x) is continuous on the interval [-2, 2]

2 ) f(x) is differentiable on the interval (-2, 2)

3)  f(-2) = 1 and f(2) = 1

Since f(-2) = f(2), there must exist at least one point c in the interval (-2, 2) such that f'(c) = 0.

Taking the derivative of f(x) with respect to x, we get f'(x) = 2x. Setting f'(c) = 0, we have:

2c = 0

Solving for c, we get c = 0.

Therefore, the value of c for which f'(c) = 0 in the interval [-2, 2] is c = 0.

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The number of trains that can accommodate 2 passengers is x = 32, the number of trains that can accommodate 3 passengers is y = 1, and the number of trains that can accommodate 5 passengers is z = -11.

It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.

Let x, y and z be the number of trains that can accommodate 2 passengers, 3 passengers and 5 passengers, respectively.

From the information given, we have:

x + y + z = 20 (the total number of trains)

2x + 3y + 5z = 64 (the total number of passengers)

We also know that 10 trains were used during market day:

3 of the x trains, 2 of the y trains and 4 of the z trains.

So, we have:

2x + y + 5z = 10

Solving these three equations simultaneously, we can find the values of x, y and z:

Subtracting the first equation from the third equation:

0 + y + 4z = -10

y + 4z = -10

Subtracting 2 times the first equation from the second equation:

-x + 3y + 4z = 32

y + 4z = 42

Subtracting the last two equations:

x = 32

Substituting the value of x back into the first equation:

32 + y + z = 20

y + z = -12

Substituting the value of y and z back into the third equation:

2x + y + 5z = 10

64 + y + 5z = 10

y + 5z = -54

Solving these two equations simultaneously, we can find the values of y and z:

Subtracting the second equation from the last equation:

4z = -44

z = -11

Substituting the value of z back into the second equation:

y + 5z = -54

y - 55 = -54

y = 1

Therefore, the number of trains that can accommodate 2 passengers is x = 32, the number of trains that can accommodate 3 passengers is y = 1, and the number of trains that can accommodate 5 passengers is z = -11.

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Answer: The function that models the cost of the house over time can be written as y = 200,000 * (1 + 0.03)^x, where x is the number of years and y is the value of the house.

To find the value of the house at the end of ten years, we need to plug in x = 10 into the function:

y = 200,000 * (1 + 0.03)^10 = 200,000 * 1.33489 = 266,978.8

So the value of the house at the end of ten years is $266,978.8.

Step-by-step explanation:

The missing amounts are a) $79,000, b) $22,000, c) $51,000, d) $15,000  and  e) $6,000.

We have,

The theory used in this question is the basic accounting equation which states that Assets = Liabilities + Equity.

This equation can be used to determine the missing amounts in the summaries of Greene's Goods and Solar Enterprises.

Step 1: Start with the beginning of year data for Greene's Goods. We know that the Total Assets = $110,000, Total Liabilities = $85,000 and that the Total Owner's Equity is missing. We can use the basic accounting equation to solve for Total Owner's Equity.

Assets = Liabilities + Equity

110,000 = 85,000 + Equity

Equity = 25,000

Step 2: Now look at the ending of year data for Solar Enterprises. We know that the Total Assets = $180,000, Total Liabilities = $50,000 and that the Total Owner's Equity is missing. We can use the basic accounting equation to solve for Total Owner's Equity.

Assets = Liabilities + Equity

180,000 = 50,000 + Equity

Equity = 130,000

Step 3: Lastly, look at the changes in owner's equity for each proprietorship. For Greene's Goods, we know that Additional Investment = $7,000 and Drawings = $37,000. We can use the basic accounting equation to solve for the missing amount.

Change in Equity = Additional Investment + Drawings

Change in Equity = 7000 + 37000

Change in Equity = $44,000

For Solar Enterprises, we know that Additional Investment

= $25,000 and Drawings = $15,000.

We can use the basic accounting equation to solve for the missing amount.

Change in Equity = Additional Investment + Drawings

Change in Equity = 25000 + 15000

Change in Equity = $40,000

Therefore, the missing amounts are:

a) $79,000

b) $22,000

c) $51,000

d) $15,000

e) $6,000

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The elements in C U (B' ∩ A') is {5, 6, 7, 8,  9}.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, and the complement of sets.

We have,

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1, 2, 5, 6}

B = {2, 3, 4, 6, 7}

C = {5, 6, 7, 8}

Now,

A' = U - A = {3, 4, 7, 8, 9}

B' = U - B = {1, 5, 8, 9}

C' = U - C = {1, 2, 3, 4, 9}

Now,

(B' ∩ A')

= {1, 5, 8, 9} ∩  {3, 4, 7, 8, 9}

= {8, 9}

And,

C U (B' ∩ A')

= {5, 6, 7, 8} U {8, 9}

= {5, 6, 7, 8, 9}

Thus,

C U (B' ∩ A') = {5, 6, 7, 8,  9}

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The complete question:

Sets A, B, and C are subsets of the universal set U.

These sets are defined as follows.

U = 1, 2, 3, 4, 5, 6, 7, 8, 9

A = 1, 2, 5, 6

B = 2, 3, 4, 6, 7

C = 5, 6, 7, 8

Find C U (B' ∩ A').

Answer:

Here is the function table for the given equation:

x H(x)

1 2

2 1

3 0

4 -1

5 -2

Note: The table shows the result of the equation H(x) = -x + 3 for different values of x.

Step-by-step explanation:

a) The value of the bulldozer at any time t should be given by the equation,

                                      V = 140500- 5600t

b) The value of the bulldozer after 7 years is  $1,01,300

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

a)To answer the problem above, we make the assumption first that the depreciation is a straight-line method in order to solve for the depreciation rate.

                                d = (140500 - 17300)/ 22 = 5600

The value of the bulldozer at any time t should be given by the equation,

                                      V = 140500- 5600t

b)  Substitute t=7 into the equation

                      V = 140500- 5600(7)

                         = 140500- 39200

                         = 1,01,300

The value of the bulldozer after 7 years is  $1,01,300

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The range of the function, given the graph of a relation, can be found to be −2 ≤ y ≤ 7 .

Graphs can be used to determine a function's domain and range. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.

The range here would therefore be the y - values that the relations fall within. The lowest y - value is - 2 as no relation goes below this. The highest y - value is 7.

The range is therefore -2 ≤ y ≤ 7.

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A = [[-3, 10], [-3, 9], [-3, -10]], b = [-14, -7, 19] Ax = b's matrix equation has a solution in the form of T. x.

Only if the matrix equation Ax = b has a solution x is the vector [-14,-7,19] a linear combination of the vectors [-3,-3,-3] and [10,9,-10]. The vector [-14,-7,19] must be transposed for this to hold true, and A must be the matrix of coefficients of the linear combination of the two vectors. As a result, A is a 3x2 matrix and its formula is as follows: A = [[-3, 10], [-3, 9], [-3, -10]], and b = [-14, -7, 19]T. The vector [-14,-7,19] is a linear combination of the two vectors [-3,-3,-3] and [10,9,-10] if there is a solution x to the matrix equation Ax = b.

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