construct a 95% confidence interval for the mean difference µd using a sample of paired data for which summary statistics are given. assume the parent populations are normally distributed. assume the sample mean difference d

To find the general solution for the given ordinary differential equation (ODE):

xdy - [y + xy^(2)(1 + ln(x))]dx = 0

We can rearrange the terms and separate the variables:

xdy = [y + xy^(2)(1 + ln(x))]dx

Dividing both sides by x and rearranging the terms:

dy/y + y(ln(x) + 1)dx = dx

Now, let's integrate both sides:

∫(dy/y) + ∫[y(ln(x) + 1)]dx = ∫dx

Integrating the left-hand side with respect to y and the right-hand side with respect to x:

ln|y| + y(ln(x) + 1) = x + C

where C is the constant of integration.

We can simplify the equation further:

ln|y| + yln(x) + y = x + C

Combining the logarithmic terms:

ln|y| + yln(x) = x + C - y

To eliminate the logarithm, we can take the exponential of both sides:

e^(ln|y| + yln(x)) = e^(x + C - y)

Using the properties of exponents:

|y| * x^y = e^(x + C - y)

We can rewrite the absolute value expression as a piecewise function:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

So, the general solution to the given ODE is the combination of these two equations:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

These equations represent the family of solutions to the given ordinary differential equation (ODE).

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The composite function g(f(x)) = 3x² + 9x - 25. Given that f(x) = x²  + 3x - 8 and g(x) = 3x - 1, we need to find the composite function g(f(x)). This means we'll substitute the entire f(x) function into the g(x) function.

Step 1: Identify f(x) and g(x)
f(x) = x²  + 3x - 8
g(x) = 3x - 1
Step 2: Substitute f(x) into g(x) for the variable x
g(f(x)) = 3(f(x)) - 1
Step 3: Replace f(x) with its expression, which is x^2 + 3x - 8
g(f(x)) = 3(x²  + 3x - 8) - 1
Step 4: Distribute the 3 to each term inside the parentheses
g(f(x)) = 3x²  + 9x - 24 - 1
Step 5: Combine like terms (in this case, just the constants)
g(f(x)) = 3x²  + 9x - 25
So, the composite function g(f(x)) = 3x²  + 9x - 25. If anyone has difficulty with these problems, we recommend reviewing Sections 1.1-1.3 for a better understanding of function compositions and related topics.

To find the function g o f, we need to substitute the function f(x) into the function g(x) wherever we see x. So, g o f(x) = g(f(x)).
First, we find f(x):
f(x) = x²  + 3x - 8
Now we substitute f(x) into g(x):
g(f(x)) = g(x²  + 3x - 8)
= 3(x²  + 3x - 8) - 1
= 3x²  + 9x - 25
Therefore, g o f(x) = 3x²  + 9x - 25.
Given that f(x) = x²  + 3x - 8 and g(x) = 3x - 1, we need to find the composite function g(f(x)). This means we'll substitute the entire f(x) function into the g(x) function.

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In theory, Option D. All of these stages occurs at prisoner classification.

Prisoner classification occurs during transfer, in preparation for release, and after problems occur. All of these stages are important for assessing an inmate's risk and providing appropriate security.

Prisoner classification involves assessing an inmate's risk level and providing an appropriate security level based on the results. This assessment is conducted during various stages, such as during transfer to another institution, in preparation for release, and after the inmate encounters problems. The classification process may involve evaluating an:

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 300\\ P=\textit{original amount deposited}\\ r=rate\to 6.4\%\to \frac{6.4}{100}\dotfill &0.064\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &17 \end{cases}\)

\(300 = P\left(1+\frac{0.064}{12}\right)^{12\cdot 17} \implies 300=P\left( \frac{377}{375} \right)^{204} \implies \cfrac{300}{ ~~ \left( \frac{377}{375} \right)^{204} ~~ }=P \\\\\\ \cfrac{300}{ ~~ \frac{377^{204}}{375^{204}} ~~ }=P\implies 300\cdot \cfrac{375^{204}}{377^{204}}=P\implies 100\approx P\)

The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.

Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of  important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.

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The probability that a voter is either female or Democrat is 0.64 or 64%.

To calculate the probability, we need to determine the number of individuals who are either female or Democrat and divide it by the total number of voters.

From the table, we can see that there are 405 females and 253 Democrats. However, we need to be careful not to double-count the individuals who fall into both categories.

To find the number of individuals who are either female or Democrat, we add the number of females (405) and the number of Democrats (253), and then subtract the number of individuals who are both female and Democrat (150).

So, the number of individuals who are either female or Democrat is 405 + 253 - 150 = 508.

Now, we divide this number by the total number of voters, which is 802, to get the probability: 508 / 802 ≈ 0.64 or 64%.

Therefore, the probability that a voter is either female or Democrat is approximately 0.64 or 64%.

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Step-by-step explanation:

∠ACB=90∘

[∠ from diameter]

In ΔACB

∠A+∠ACB+∠CBA=180∘

∠CBA=180∘

−(90+30)

∠CBA=60∘ (1)

In △OCB

OC=OB

So, ∠OCB=∠OBC        

[The sides are equal]

∠OCB=60∘

∠OCD=90∘

∠OCB+∠BCD=90°

∠BCD=30∘ (2)

∠CBO=∠BCO+∠CDB    

[external ∠ bisectors]

60=30+∠CDB

∠CDB=30° (3)

from (2) & (3)

BC=BD    

[The ∠.S are equal]

Solve for dy/dx:   dy/dx = (-2x) / (2y) = -x / y which gives the slope of tangent line using implicit differentiation

To find the slope of a tangent line using implicit differentiation, follow these steps:

1. Start with the given equation that represents the relationship between x and y in the form of an equation involving both variables, for example: F(x, y) = 0.

2. Differentiate both sides of the equation with respect to x using the chain rule whenever necessary. Treat y as a function of x and apply the derivative rules accordingly.

3. After differentiating, have a resulting equation involving both x, y, and their derivatives (dy/dx). Rearrange the equation if necessary to isolate dy/dx on one side.

4. Solve for dy/dx to find the derivative of y with respect to x. This will give the slope of the tangent line at any given point on the curve defined by the implicit equation.

Note: The resulting expression for dy/dx may involve both x and y variables. To find the slope of the tangent line at a specific point, substitute the coordinates of that point into the expression for dy/dx.

Here's an example to illustrate the process:

Given the implicit equation: \(x^2 + y^2 = 25\)

1. Start with the equation: \(x^2 + y^2 = 25.\)

2. Differentiate both sides with respect to x:

  2x + 2y * (dy/dx) = 0

3. Rearrange the equation to isolate dy/dx:

  2y * (dy/dx) = -2x

4. Solve for dy/dx:

  dy/dx = (-2x) / (2y)

         = -x / y

Now, have the expression for the slope of the tangent line in terms of x and y. To find the slope at a specific point, substitute the coordinates of that point into the expression.

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Answer:

786

Step-by-step explanation:

Answer:

Helena',s savings... h=78+6

Answer:

6 3/100

Step-by-step explanation:

brainliest pls

\( \Large{\boxed{\sf n = 8}} \)

\( \\ \)

The perimeter of a rectangle is given by the following formula:

\( \Large{\sf P = 2L + 2W } \)

Where:

\( \\ \)

\( \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf L &=\sf 3n - 9 \\ \sf W &=\sf n + 5 \\ \end{cases} } \)

\( \\ \)

Substitute these values into our formula:

\( \sf P = 2(3n - 9) + 2(n + 5) \)

\( \\ \)

Expand the expression of the perimeter using the following distributive property.

\(\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \sf\boxed{ \sf Distributive \: property \text{ : } }} \\ \\ \sf\star \: \red{ \large{ a (b + c) = ab + ac }} \end{array}}\\\end{gathered} \end{gathered}}\)

\( \\ \)

We get:

\( \sf P = 2(3n) + 2(-9) + 2n + 2(5) \\ \\ \sf P = 6n - 18 + 2n + 10 \\ \\ \boxed{\sf P = 8n - 8 } \)

\( \\ \)

Since the perimeter is equal to 56, the value of n satisfies the following equality:

\( \sf 8n - 8 = 56 \)

\( \\ \)

To solve this equation, let's add 8 to both sides:

\( \sf 8n - 8 + 8 = 56 + 8 \\ \\ \sf 8n = 64 \)

\( \\ \)

Now, divide both sides of the equation by 8:

\( \sf \dfrac{8n}{8} = \dfrac{64}{8} \\ \\ \\ \boxed{\boxed{\sf n = 8}} \)

\( \\ \\ \)

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The exchange rate to convert cuban pesos into swiss franc is

Exchange rate, the price of a country's money in relation to another country's money. An exchange rate is “fixed” when countries use gold or another agreed-upon standard, and each currency is worth a specific measure of the metal or other standard.

If 11 swiss franc = 289.07 cuban pesos

then, 1 swiss = 289.07/11

= 26.28 cuban pesos

Therefore ;

1 cuban pesos = 1/26.28 swiss francs

1 cuban pesos = 0.038 swiss francs

therefore the exchange to covert cuban pesos into swiss francs is 1 cuban pesos is 0.038 swiss francs.

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The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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The solution is the two percent changes are not the same, and the second percent change is greater

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage

Given data ,

Let the initial value of the pens = $ 4.09

Let the final value of the pens = $ 3.59

So , the percentage change is calculated by

Percentage decrease = ( ( final value - initial value ) / initial value ) x 100

Substituting the values in the equation , we get

Percentage decrease = ( ( 3.59 - 4.09 ) / 4.09 ) x 100

Percentage decrease = ( -0.5 / 4.09 ) x 100

Percentage decrease = -0.122249 %

Therefore , the approximate percentage decrease = -0.1 %

Now ,

The value of the pens is increased to = $ 4.09

So , the percentage change is calculated by

Percentage increase = ( ( final value - initial value ) / initial value ) x 100

Substituting the values in the equation , we get

Percentage increase = ( ( 4.09 - 3.59 ) / 3.59 ) x 100

Percentage increase = ( 0.5 / 3.59 ) x 100

Percentage increase = 0.13927 %

Therefore , the approximate percentage increase = 0.1 %

Hence , the two percent changes are not the same, and the second percent change is greater

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The correct statement regarding the probability of choosing a person at random who is a junior and plays video games, and whether these events are independent, is given as follows:

P(junior and video games) = 32%; The two events are not independent.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in this problem are given as follows:

Hence the probability is of:

P(junior and video games) = 48/150 = 0.32 = 32%.

The separate probabilities are given as follows:

The multiplication of these probabilities is of:

0.66 x 0.4 = 0.264.

Which is different of 0.32, hence these events are not independent.

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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To compute the integral ∫\(\int\limits^0_{10} }x *cos(x)} \, dx\)ousing the composite rectangle rule, we divide the interval into subintervals and approximate the integral as the sum of the areas of the rectangles.

To apply the composite rectangle rule, we start by dividing the interval [0, 10] into smaller subintervals of equal width. Let's assume we choose n subintervals. The width of each subinterval will be Δx = (10 - 0) / n = 10/n.

Next, we evaluate the function x*cos(x) at the right endpoint of each subinterval and multiply it by the width Δx to get the area of each rectangle. We then sum up the areas of all the rectangles to approximate the integral.

To guarantee that the absolute error is less than 0.2, we need to choose an appropriate number of subintervals. The error of the composite rectangle rule decreases as the number of subintervals increases. By increasing the value of n, we can make the error smaller and ensure it is less than 0.2.

In practice, we would perform the computation by choosing a specific value for n and calculating the sum of the areas of the rectangles. However, without performing the computation, we can guarantee that the absolute error will be less than 0.2 by selecting a sufficiently large value of n.

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Answer:

\(d = 14\)

\((-2,-1)\)

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define

(5, -1)

(-9, -1)

Step 2: Find distance d

Step 3: Find Midpoint

The height of the cliff is approximately 551.04 feet.

We may use trigonometry, and more specifically the tangent function, to resolve this issue. The ratio of the adjacent side's length to the opposite side's length is known as the tangent of an angle.

In this instance, the cliff's base is 1183 feet in height and the angle of elevation is 25.24 degrees. Let's use "h" (in feet) to represent the cliff's height.

The tangent function gives us:

tan(25.24°) = h / 1183

To find the value of h, we can rearrange the equation:

h = tan(25.24°) * 1183

Now we can calculate the height of the cliff:

h ≈ tan(25.24°) * 1183

Using a calculator, the approximate value is:

h ≈ 0.4664 * 1183

h ≈ 551.04 feet

Therefore, the height of the cliff is approximately 551.04 feet.

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Based on the scatterplot, the correct relationship between the GPA and IQ score of the students is positive and roughly linear.

For student A, the IQ score is approximately 110 and the GPA is approximately 2.

The correct reason for considering points A, B, and C as unusual is that students A and B have two lowest GPAs but moderate IQs, while student C has the lowest GPA but moderate IQ.

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In a one-mean z-test, the observed value of the test statistic z is denoted as z₀.

The P-value represents the probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true.

To express the P-value in terms of Φ (the cumulative distribution function of the standard normal distribution), we consider the following cases:

a. Left-tailed test:
For a left-tailed test, the alternative hypothesis is that the population mean is less than the null hypothesis value.

The P-value is the probability of observing a z-value smaller than or equal to the observed value, z₀. Therefore, the P-value can be expressed as:
P-value = Φ(z₀)

b. Right-tailed test:
For a right-tailed test, the alternative hypothesis is that the population mean is greater than the null hypothesis value.

The P-value is the probability of observing a z-value greater than or equal to the observed value, z₀.

This is equivalent to the area under the curve to the right of z₀. Therefore, the P-value can be expressed as:
P-value = 1 - Φ(z₀)

c. Two-tailed test:
For a two-tailed test, the alternative hypothesis is that the population mean is not equal to the null hypothesis value.

The P-value is the probability of observing a z-value as extreme as or more extreme than the observed value, z₀, in either tail of the distribution.

This involves considering the area to the left of -z₀ and the area to the right of z₀. Since the standard normal distribution is symmetric, these areas are equal.

Therefore, the P-value can be expressed as:
P-value = 2 * (1 - Φ(|z₀|))

Note: In all cases, |z₀| represents the absolute value of z₀, ensuring that the P-value is positive.

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A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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To find the 85th percentile of combined test scoresZ-score is given by; Z = (X - μ) / σ0.85 = (X - 1499) / 345By solving for X, we getX = μ + σZ = 1499 + 345(1.0364) = 1850.4Therefore, the combined scores corresponding to the 85th percentile is 1850.4.

The given data isMean

= μ

= 1499 Standard deviation

= σ

= 345a) To find the 30th percentile of combined test scoresz-score is given by;  Z

= (X - μ) / σLet's plug in the values  Z

= (X - μ) / σ0.30

= (X - 1499) / 345By solving for X, we getX

= μ + σZ

= 1499 + 345(-0.5244) = 1301.21Therefore, the combined scores corresponding to the 30th percentile is 1301.21.b) To find the 75th percentile of combined test scoresZ-score is given by; Z

= (X - μ) / σ0.75

= (X - 1499) / 345By solving for X, we getX

= μ + σZ

= 1499 + 345(0.6745)

= 1725.4Therefore, the combined scores corresponding to the 75th percentile is 1725.4.c) .To find the 85th percentile of combined test scores Z-score is given by; Z

= (X - μ) / σ0.85

= (X - 1499) / 345By solving for X, we getX

= μ + σZ

= 1499 + 345(1.0364)

= 1850.4Therefore, the combined scores corresponding to the 85th percentile is 1850.4.

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Answer: the answer is 40

Answer:

Hello,

measure of b=40°

Step-by-step explanation:

A proof in picture

The angle measure of the indicated side is as follows:

∠Q = 60 degrees.

The measure of the angle indicated can be found as follows:

The measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs.

Using this theorem,

arc PR = 360 - 240 = 120 degrees

∠Q = 1 / 2 (240 - 120)

Therefore,

∠Q = 1 / 2 (120)

∠Q = 120 / 2

∠Q = 60 degrees.

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Answer:

x = 81, y = 68, z = 99

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Consider the triangle on the left, then

x = 180 - (36 + 63) = 180 - 99 = 81

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle on the right, thus

13 + y = x , that is

13 + y = 81 ( subtract 13 from both sides )

y = 68

Consider the triangle on the right

z = 180 - (13 + y) = 180 - (13 + 68) = 180 - 81 = 99

On average, you can expect to lose about $21.76 over the course of 740 bets.

The probability of drawing two clubs without replacement from a standard deck is:

P(Clubs and then Clubs) = (13/52) x (12/51) = 0.0588

The probability of not drawing two clubs is:

P(Not Clubs or Not Clubs) = 1 - P(Clubs and then Clubs) = 1 - 0.0588 = 0.9412

If you win, you receive $14, and if you lose, you pay $3. Therefore, the expected value of this bet is:

Expected value = (Probability of Winning x Amount Won) - (Probability of Losing x Amount Lost)

Expected value = (0.0588 x $14) - (0.9412 x $3) = -$0.0294

This means that on average, you can expect to lose about 2.94 cents per bet. If this same bet is made 740 times, the expected total value is:

Expected total value = Expected value x Number of Bets

Expected total value = -$0.0294 x 740 = -$21.76

So, on average, you can expect to lose about $21.76 over the course of 740 bets.

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Step-by-step explanation:

\(\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ \)

\(\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ \)

\(\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ \)

\(\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ \)

\(\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ \)

\(\longrightarrow \tt { 250 \times 100 = P \times 50} \\ \)

\(\longrightarrow \tt { 25000 = P \times 50} \\ \)

\(\longrightarrow \tt { \dfrac{25000}{50} = P } \\ \)

\(\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ \)

Therefore principal is $500.

Let the total number of balls be x.

→ Red balls + Blue balls + Yellow balls = Total number of balls

\(\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ \)

\(\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ \)

\(\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ \)

\(\longrightarrow \tt{ 31x + 1260= 35x} \\ \)

\(\longrightarrow \tt{ 1260= 35x-31x} \\ \)

\(\longrightarrow \tt{ 1260= 4x} \\ \)

\(\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ \)

\(\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ \)

Total number of balls is 315.

A/Q,

3/5 of the balls are blue.

\(\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ \)

\(\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ \)

\(\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ \)

\(\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ \)