Let X be a discrete random variable, all of whose moments are equal to š. Show that M(t) = žet + ſ is one possible moment generating function for X. Then determine the probability mass function for X in this case.

Answer:

the third one

Step-by-step explanation:

-5 is the least out of all of them and 6 is the greatest so then you can put the numbers in between

Answer:

r≈3.39cm

Step-by-step explanation:

Using the formula

V=πr2h/3

r=3V

πh=3·72

π·6≈3.38514cm

The expressions for dz/du and dz/dv are as follows:

dz/du = 4x siny

dz/dv = -6y cosx

To find the expressions for dz/du and dz/dv, we need to differentiate the given function z = 2x^2 - 3y with respect to u and v, respectively.

1. dz/du:

Since u = x^2 siny, we can express z in terms of u by substituting x^2 siny for u in the original function:

z = 2u - 3y

Now, we differentiate z with respect to u while treating y as a constant:

dz/du = d/dx (2u - 3y)

      = 2(d/dx (x^2 siny)) - 0 (since y is constant)

      = 2(2x siny)

      = 4x siny

Therefore, dz/du = 4x siny.

2. dz/dv:

Similarly, we express z in terms of v by substituting 2y cosx for v in the original function:

z = 2x^2 - 3v

Now, we differentiate z with respect to v while treating x as a constant:

dz/dv = d/dy (2x^2 - 3v)

      = 0 (since x^2 is constant) - 3(d/dy (2y cosx))

      = -6y cosx

Therefore, dz/dv = -6y cosx.

In summary, the expressions for dz/du and dz/dv are dz/du = 4x siny and dz/dv = -6y cosx, respectively.

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Answer:

2.32x10^-11

here ya go luv <3

When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.

We need to apply Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction for two different media.

Step 1: Calculate the angle of refraction in the first material using Snell's Law.
n1 * sin(i1) = n2 * sin(r1)
1 * sin(60°) = 1.20 * sin(r1)
sin(r1) = 0.5/1.20
r1 ≈ 25.4°

Step 2: Repeat the process for the remaining materials, using the previous angle of refraction as the new angle of incidence. Calculate the final angle of refraction in the last material.

For the second material:
1.20 * sin(25.4°) = 1.40 * sin(r2)
r2 ≈ 21.4°

For the third material:
1.40 * sin(21.4°) = 1.32 * sin(r3)
r3 ≈ 22.9°

For the fourth material:
1.32 * sin(22.9°) = 1.28 * sin(r4)
r4 ≈ 23.3°

Step 3: Calculate the angle of emergence in air.
1.28 * sin(23.3°) = 1 * sin(e)
e ≈ 29.4°

When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.

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Step-by-step explanation:

The Extreme Value Theorem states that a continuous function on a closed, bounded interval must have both an absolute minimum and an absolute maximum. The function f(x)=xsin(x) is continuous on the domain [0,∞], but this domain is not closed and bounded, so the Extreme Value Theorem does not apply and there is no contradiction.

The Extreme Value Theorem is an important theorem in calculus that states that a continuous function on a closed, bounded interval will always have both an absolute minimum and an absolute maximum. This is an important principle that can be used to identify extrema of a function without having to graph it. In the case of the function f(x)=xsinx with domain\([0,[infinity]),\)the domain is not closed and bounded, so the Extreme Value Theorem does not apply. In this case, there is no absolute minimum and no absolute maximum on the domain. This does not contradict the Extreme Value Theorem because the theorem only applies to continuous functions on closed, bounded intervals. As such, the Extreme Value Theorem is a useful tool for finding extrema of continuous functions on closed, bounded intervals. However, it does not apply to all functions and its limitations should be kept in mind when attempting to identify extrema of a particular function.

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You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

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Step-by-step explanation:

Part A):  h * d.

Part B): She Earns 10.75 x 22 1/2 which is 241 7/8, or 241.675

Answer:

150 CDs

Step-by-step explanation:

From the question, we are told that:

28% of Sumiko's CDs are Chinese music CDs.

42% of these are English music CDs The rest are Japanese music CDs.

Let the total number of CDs = 100%

Therefore the percentage of Japanese CDs is calculated as:

100% - (28% + 42%)

100% - 70%

= 30%

There are 45 Japanese music CDs.

Let us represent total number of CDs = x

Hence,

30% of x = 45 Japanese music CDs

Hence,

30/100 × x = 45

30x/100 = 45

Cross Multiplication

30x = 100 × 45

Divide both sides by 30

x = 4500/30

x = 150 CDs

Therefore, the total number of CDs = 150 CDs

Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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Answer:

The value of p(-a) must be 0

There is an x intercept of the function at (-a,0)

Step-by-step explanation:

(x + a) is a factor of a function p(x)

that means, that p(x) must have an x-intercept at the point x = -a

This can be written in two different ways,

If (x + a) is a factor of a polynomial function, p(x), then the two statements that are true are:

A factor of a polynomial function is a binomial that, when multiplied by another polynomial, gives the original polynomial function. If (x + a) is a factor of p(x), then p(x) can be written as (x + a)q(x), where q(x) is another polynomial function.

According to the Factor Theorem, if (x + a) is a factor of p(x), then p(a) = 0. This means that the value of the polynomial function at x = a is 0.

Additionally, if p(a) = 0, then there is an z-intercept of the function at (a,0). This is because the z-intercept is the point where the function crosses the z-axis, and this occurs when the value of the function is 0.

Therefore, the two statements that are true are "The value of p(a) must be 0" and "There is an z-intercept of the function at (a,0)".

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\frac{3}{4} = \frac{12}{x}

We can first get rid of the fractions by cross-multiplying (multiplying the numerator from one side by the denominator of the other side, and setting the two results equal to each other):

3 * x = 4 * 12

3x = 48

Finally, we can divide both sides by 3 to get the x by itself.

3x = 48

\frac{3x}{3} = \frac{48}{3}

x = 16

Answer:

76,650

Step-by-step explanation:

Answer: 187, 565

Step-by-step explanation:can i have brainliest?

To conduct a regression analysis for the given data, we'll follow the steps as outlined:

Q2.1 To test the hypothesis that X is a good predictor of Y, we need to perform a regression analysis and examine the significance of the regression model. The regression model will help us determine if there is a statistically significant relationship between the independent variable (X) and the dependent variable (Y). We will perform a hypothesis test to evaluate the significance of the regression coefficients.

Q2.2 The parameters of the linear equation are as follows:

- Slope (β₁): The slope parameter represents the change in the dependent variable (Y) for a unit change in the independent variable (X). It indicates the rate of change in Y with respect to X.

- Intercept (β₀): The intercept parameter represents the value of the dependent variable (Y) when the independent variable (X) is zero. It determines the starting point of the linear relationship between X and Y.

Q2.3 To assess the strength of the model, we can use both the regression model and correlation analysis:

- Regression Model: The strength of the model can be evaluated by examining the coefficient of determination (R²). R² represents the proportion of the total variation in the dependent variable (Y) that is explained by the independent variable (X). A higher R² value indicates a stronger relationship between X and Y.

- Correlation Analysis: We can calculate the correlation coefficient (r) between X and Y. The correlation coefficient measures the strength and direction of the linear relationship between X and Y. A value close to +1 or -1 indicates a strong linear relationship, while a value close to 0 suggests a weak relationship.

Q2.4 To show the linear line on the scatter plot graph and the linear equation, we'll plot the data points on a scatter plot and draw the best-fit line, which represents the linear equation. The linear equation can be expressed as Y = β₀ + β₁X, where β₀ is the intercept and β₁ is the slope.

Q2.5 To determine the predicted value of Y given X is 93.1, we substitute the value of X into the linear equation and calculate the corresponding Y value using the estimated slope and intercept from the regression analysis.

Q2.6 To plot the normal probability plot and the residual plot vs X, we'll analyze the normality of the residuals. The normal probability plot helps us assess whether the residuals follow a normal distribution. A straight line in the normal probability plot indicates that the residuals are normally distributed. The residual plot vs X helps us identify any patterns or deviations in the residuals, which may suggest issues with the regression model, such as heteroscedasticity or nonlinearity.

Note: To conduct a full regression analysis, including hypothesis testing, calculation of regression coefficients, and other statistical measures, we require statistical software or programming languages such as R or Python.

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Good measures are robust, valid, objective, simple, and precisely definable.

In the context of measurement, good measures possess certain qualities that make them reliable and useful. Based on the options provided, the following qualities apply:

Robust: Good measures are robust, meaning they are resistant to outliers or extreme values that may affect the accuracy of the measurement.

Valid: Good measures are valid, meaning they accurately measure what they are intended to measure and provide meaningful information.

Objective: Good measures are objective, meaning they are free from bias or subjective interpretation, ensuring consistency and fairness.

Simple: Good measures are simple, making them easy to understand and apply. They avoid unnecessary complexity and confusion.

Precisely definable: Good measures have clear and precise definitions, ensuring consistent interpretation and allowing for replication in different contexts.

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The midsegment theorem indicates that the lengths of the segments are;

What is the midsegment theorem?

The midsegment theorem states that a segment drawn by joining the midpoints of two sides of a triangle is parallel to and half of the length of the third side of the triangle.

Whereby the segment BD is the midsegment of the triangle ACE, we get;

BD = (1/2) × AE

CD = (1/2) × CE (Definition of D the midpoint of CE)

BC = (1/2) × AC (Definition of B the midpoint of AC)

Therefore;

1. CD = (1/2) × CE ; If CD = 19 cm, then (1/2) × CE = CD = 19 cm

A. 19 cm

2. BD = (1/2) × AE; If BD = 21 cm

AE = 2 × BD = 2 × 21 cm = 42 cm

BD+ AE = 21 cm + 42 cm = 63 cm

B. 63 cm

3. BD = (1/2) × AE; If BD = 2·x - 1, AE = x + 4, we get;

2·x - 1 = (1/2) × (x + 4) = x/2 + 2

2·x - 1 = x/2 + 2

2·x - x/2 = 2 + 1 = 3

(3·x/2) = 3

x = 3 × 2/3 = 2

BD = 2 × 2 - 1 = 3

C. 3

4.  BD = (1/2) × AE; If AE = 32 cm, then (1/2) × BD is; (1/2) × (1/2) × 32 = 8

(1/2) BD = 8 cm

D. 8 cm

5. BC = (1/2) × CA; If CA = 56 cm, then BC = (1/2) × 56 cm = 28 cm

(1/2) × BC therefore is; (1/2) × 28 cm = 14 cm

A. 14 cm

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The area of the polygon is 37.81 units and the perimeter is 33.02 units.

The given points are in order, we have:

a(-3, 2)

f(2, -3)

b(0, 5)

c(3, 2)

d(5, 4)

e(7, 2)

g(0, -1)

Using the distance formula, we can find the lengths of the sides of the polygon. Then, we can add up the lengths of all the sides to find the perimeter of the polygon.

As per the shown figure,

Length of side fa = 7.07 units

Length of side ef = 7.07 units

Length of side de = 7.6 units

Length of side cd = 2.8 units

Length of side bc = 4.24 units

Length of side ab = 4.24 units

The perimeter of the polygon is:

= fa + ef + de + cd + bc + ab

= 7.07 + 7.07 + 7.6 + 2.8 + 4.24 + 4.24

= 33.02 units

The area of the polygon is:

= area of rectangle (1) + area of sqare (2)

= 7.07 × 4.24 + 2.8 × 2.8

= 37.81 units

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The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.

The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.

Given, the double integral ∫∫yA and the region y = x-6 and x = y²

y = x-6

x = y²

y² = y +6

y² - y - 6 = 0

y² - 3y +2y - 6 = 0

(y-3) (y+2) = 0

y = 3 and y = -2

\(\int\int\limits_\triangle {y} \, dA\\ \\\)

= \(\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}\)

The value for the double integral is 125/12.

Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.

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Answer: x = 6

Step-by-step explanation: 1/6x + 2/3 x = 5 first just add the like terms 5/6 x = 5 then 5*6 /5 = x hope it helps ;)

Answer:

c = 40 + 0.79m

Step-by-step explanation:

The base cost is $40.

So we have:

c = 40

Then, since an additional $0.79 is charged for every mile driven, we add:

+ 0.79m

So then our equation is:

c = 40 + 0.79m

where c = total cost

and m = number of miles driven

Answer:

A: \(csc(\theta)\)

Step-by-step explanation:

Let's rewrite the expression in terms of sine and cosine, then simplify what can be simplified.:

\(sin(\theta) \cdot \frac{cos^2(\theta)}{sin^2(\theta)}\cdot \frac 1{cos^2(\theta)} =\\\frac1{sin(\theta)} = csc(\theta)\)

Answer:

7)

to work it out:

180-110= 70

because there are two unknown angle we're gonna assume they're both the same amount. So if they are both the same and equal then we need to half 70 which will be equal to the two sided. So. 70/2= 35

So the 2 x's = 35 each

8)

you need to put this all into an equation so:

7x-11 + 5x-2 + 2x-3 = 180 degrees

12x - 9 + 2x-3

10x + 6

Actual answer:

14x-16

Step-by-step explanation:

The standard deviation the manufacturer must achieve to reduce the 36-month failure rate to only 10% is approximately 4 months, the correct option is (d) .

If manufacturer wants to reduce 36-month failure rate to only 10 percent , then

We need to find value of standard deviation that corresponds to a 36-month lifespan such that only 10% of machines fail before that time.

We can find this by finding the corresponding z-score that corresponds to a cumulative probability of 0.10.

We know , "z = (x - μ)/σ" ;

where:

⇒ x = 36 (desired lifespan)

⇒ μ = 42 (mean lifespan)

⇒ σ = standard deviation we want to find

⇒ z = z-score that corresponds to a cumulative probability of 0.10

Substituting the given values and solving for "σ", we get:

⇒ -1.28 = (36 - 42)/σ

⇒ σ = (42 - 36)/1.28

⇒ 4.69

So , the standard deviation is approximately 4 months.

Therefore, The correct option is (d) 4 months.

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The given question is incomplete , the complete question is

A manufacturer claims that lifespans for their copy maxhines (in months) can be described by a Normal model N(42,7).

The manufacturer wants to reduce the 36-month failure rate to only 10%. Assuming the mean lifespan will stay the same, what standard deviation must they achieve?

(a) 1 months

(b) 2 months

(c) 3 months

(d) 4 months.

Answers to both subparts are shown:

So, (A) fraction of the game Tim wins:

Then, the fraction will be:

(B) Games Tim wins in 30 games.

So, a number of games won:

Therefore, answers to both subparts are shown:

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The correct question is shown below:

(A) tim played 20 games of draughts he won 16 of those games.what fraction of the game did he win

b) he played 30 more games he had then 68% of all his games how amny of 30 games did he wi

Derek must deposit approximately $682.32 each year for the next 10.0 years.

To determine the annual deposit amount Derek must make for the next 10 years, we need to calculate the present value of the future withdrawals and then calculate the equal annual deposits needed to achieve that amount.

Withdrawal in 6 years = $12,544.00

Withdrawal in 10 years = $12,340.00

Current balance = $3,909.00

Interest rate = 5.18%

Number of years = 10

First, let's calculate the present value (PV) of the future withdrawals using the formula:

PV = Future value / (1 + Interest rate)^Number of years

Present value of the withdrawal in 6 years:

PV1 = $12,544.00 / (1 + 0.0518)^6

Present value of the withdrawal in 10 years:

PV2 = $12,340.00 / (1 + 0.0518)^10

Next, we need to determine the equal annual deposits needed for the next 10 years to achieve the desired amount. Let's denote the annual deposit amount as X.

Using the present value of the future withdrawals and the current balance, we can calculate X using the formula:

X = (PV1 + PV2 - Current balance) / ((1 - (1 + Interest rate)^(-Number of years)) / Interest rate)

Substituting the calculated values:

X = (PV1 + PV2 - $3,909.00) / ((1 - (1 + 0.0518)^(-10)) / 0.0518)

By plugging in the calculated present values and solving the equation, we can find the required annual deposit amount.

To determine the annual deposit amount Derek must make for the next 10 years, we need to calculate the present value of the future withdrawals and then calculate the equal annual deposits needed to achieve that amount.

We start by calculating the present value (PV) of the future withdrawals, which takes into account the time value of money. By dividing the future value of each withdrawal by the compound interest factor, we obtain the present value.

Next, we calculate the annual deposit amount using the present value of the future withdrawals and the current balance. The formula considers the present value, the number of years, and the interest rate. It helps us determine the equal annual deposits needed to reach the desired amount.

By substituting the calculated present values and solving the equation, we find the required annual deposit amount for the next 10 years.

Please note that in this calculation, Derek's account may temporarily become negative prior to year 10 as long as it reaches zero by year 10.

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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