In a dice game, you win if the two dice come up 10 or higher. Otherwise, you lose $1. What should be the profit for winning to make this game fair?.

The comparison between the distance he biked and swam is 3 : 1.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information the comparison of the distance he swam to the distance he biked can be represented in the form of ratios.

Given, He rode his bike 3/4 miles and swam for 1/4 mile.

Therefore, The ratio of biking : swimming = 3/4 : 1/4.

Now, Multiplying by 4 to get rid of the denominator we have,

Biking : Swimming = 3 : 1.

As the days in both comparisons increase in the same manner the ratio will remain the same.

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(a) The method of moments estimator for p is obtained by equating the sample mean to the population mean and solving for p. That is,
$\frac{1-p}{p} = \frac{1}{n} \sum_{i=1}^{n} X_i$
$\Rightarrow p = \frac{1}{\frac{1}{n} \sum_{i=1}^{n} X_i + 1}$
So the method of moments estimator for p is $\hat{p} = \frac{1}{\bar{X} + 1}$

(b) The likelihood function for p is
$L(p) = \prod_{i=1}^{n} P(X_i = x_i) = \prod_{i=1}^{n} (1-p)^{x_i}p = (1-p)^{\sum_{i=1}^{n} x_i}p^n$
Taking the natural logarithm and differentiating with respect to p, we get
$\frac{d}{dp} \ln L(p) = \frac{d}{dp} [\sum_{i=1}^{n} x_i \ln(1-p) + n \ln p] = -\frac{\sum_{i=1}^{n} x_i}{1-p} + \frac{n}{p}$
Setting this equal to zero and solving for p gives
$\hat{p} = \frac{n}{\sum_{i=1}^{n} x_i + n}$
So the MLE of p is $\hat{p} = \frac{n}{\sum_{i=1}^{n} X_i + n}$

(c) The posterior distribution of p is obtained by multiplying the prior distribution by the likelihood function and normalizing. That is,
$f(p|X_1,...,X_n) \propto f(p) L(p) = \frac{p^{\alpha-1}(1-p)^{\beta-1}}{B(\alpha,\beta)} (1-p)^{\sum_{i=1}^{n} x_i}p^n$
$= p^{\alpha+n-1}(1-p)^{\beta+\sum_{i=1}^{n} x_i-1}$
So the posterior distribution of p is a Beta distribution with parameters $\alpha+n$ and $\beta+\sum_{i=1}^{n} x_i$.

(d) The Bayes estimator of p under squared error loss is the posterior mean, which is
$\hat{p}_B = \frac{\alpha+n}{\alpha+\beta+\sum_{i=1}^{n} x_i + n}$

(e) If both $\alpha$ and $\beta$ goes to 0, then the Bayes estimator of p under squared error loss becomes
$\hat{p}_B = \frac{n}{\sum_{i=1}^{n} x_i + n} = \frac{n}{n + \sum_{i=1}^{n} X_i}$
which is the same as the MLE of p.

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Let's assume Megan invests x dollars at 5 percent interest and (5900 - x) dollars at 11 percent interest. The interest earned from the 5 percent investment is then 0.05x, and the interest earned from the 11 percent investment is 0.11(5900 - x).

According to the given information, the total annual interest earnings are $541. We can set up the equation:

0.05x + 0.11(5900 - x) = 541

Simplifying the equation, we have:

0.05x + 649 - 0.11x = 541

Combining like terms, we get:

-0.06x = -108

Dividing both sides by -0.06, we find:

x = 1800

Therefore, Megan invested $1800 at 5 percent interest and $4100 (5900 - 1800) at 11 percent interest.

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Answer:

2

Step-by-step explanation:

1+1

2

2 ones equals 2 in total.

You can also use a calculator to input:

1

+

1

press equal

and it should give you 2.

Hope this helps :)

Answer:

If the interest is yearly $2702.87 will be owed

Step-by-step explanation:

first you would need to find out how much 11.3% of $1205 is which is $136.17. And since the interest is yearly you would multiply the $136.17 by the 11 years which would be $1497.87. Then you would add the amount that they borrowed to the interest that they would owe after 11 years which would be $1497.87 + $1205 = $2702.87. So after 11 years the total amount that must be repaid is $2702.87

Using the line of best fit, it is found that a person would remember 5 words after being distracted by 7 text messages.

Researching the problem on the internet, it is found that it states that the number of words a person remembers after being distracted by x text messages is given by a linear function.

Looking at the line, it is found that when x = 7, N(x) = 5, hence a person would remember 5 words after being distracted by 7 text messages.

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Answer:

12-2t

Step-by-step explanation:

boi

Answer:

1st segment = 68 cm

2nd segment = 51 cm

3rd segment = 17 cm

Step-by-step explanation:

First, identify the expression for each segment. Let x = the length of the 3rd segment.

1st segment: 4x

2nd segment: 3x

3rd segment: x

Next, we need to solve for x so we can substitute it into each expression and solve for each segment length. To do so, we need to utilize the segment addition postulate.

⭐What is the segment addition postulate?

Make the equation as per the segment addition postulate.

4x + 3x + x = 136

8x = 136 . . . . . . add like terms (terms with the same variable)

x = 17 . . . . . . . . divide both sides by 8 to isolate the x variable

Finally, substitute x into each segment expression to solve for their lengths.

1st segment: 4x

1st segment: 68 cm

2nd segment: 3x

2nd segment: 51 cm

3rd segment: x

3rd segment: 17 cm

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Answer:

It is a polynomial equation with two terms usually joined by a plus or minus sign

Answer:

Binomial means when two expressions are there

Eg: 5xy, 7ny

This are 2 expression so we say this as binomials

I guess you understood

The amount of natural gas that homeowners can expect to use per month is influenced by various factors, including insulation levels and outdoor temperature.

However, without additional information or an established relationship between these factors, it is not possible to provide a precise estimate.

Insulation levels and outdoor temperature are just a few of the many factors that affect natural gas usage.

Other factors such as the size and efficiency of the heating system, the size and layout of the home, the insulation of walls and windows, and individual usage patterns can significantly impact gas consumption.

To obtain a more accurate estimate, it is recommended to consult energy professionals, utility companies, or use energy consumption calculators specifically designed for estimating natural gas usage based on multiple variables.

These tools take into account various factors to provide a more accurate estimation of monthly natural gas consumption.

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Answer:

68

Step-by-step explanation:

Answer:

The correct answer is 78.

Answer:

The answer is in the picture

Step-by-step explanation:

hope it helps!

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The prime factorizations of the given integers: a) 39 = 3 x 13

b) 81 =3 x 3 x 3 x 3

c) 101 = 101 (101 is a prime number)

d) 143 = 11 x 13

e) 289 = 17 x 17

f) 899 = 29 x 31

The prime factorization of an integer is the expression of that integer as the product of its prime factors.

We can find the prime factorization of an integer by dividing it by its smallest prime factor and repeating the process with the quotient until we are left with a prime number.

Here are the prime factorizations of the given integers: a) 39 = 3 x 13

b) 81 =3 x 3 x 3 x 3

c) 101 = 101 (101 is a prime number)

d) 143 = 11 x 13

e) 289 = 17 x 17

f) 899 = 29 x 31

To find the prime factorization of 39, we divide it by its smallest prime factor, which is 3.

The quotient is 13, which is also a prime number.

Therefore, the prime factorization of 39 is 3 * 13.

For 81, we divide it by its smallest prime factor, which is 3.

The quotient is 27, which is not a prime number.

We repeat the process with 27 and divide it by 3 to get a quotient of 9.

We repeat the process again with 9 and divide it by 3 to get a quotient of 3, which is a prime number. Therefore, the prime factorization of 81 is 3 x 3 x 3 x 3.

For 101, we see that it is a prime number, so its prime factorization is simply 101.

For 143, we divide it by its smallest prime factor, which is 11.

The quotient is 13, which is a prime number.

Therefore, the prime factorization of 143 is 11 * 13. For 289, we divide it by its smallest prime factor, which is 17.

The quotient is 17, which is a prime number.

Therefore, the prime factorization of 289 is 17 * 17.

For 899, we divide it by its smallest prime factor, which is 29. The quotient is 31, which is a prime number.

Therefore, the prime factorization of 899 is 29 * 31.

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The statement comparing Manuel’s and Gretchen's data is written in the blanks below.

Gretchen's data values are more spread out than,  lie closer together than or are in the same shape as Manuel's data values because the median and interquartile range, standard deviation and interquartile range, mean and median, or mean and standard deviation are (smaller for Gretchen's data than,  larger for Gretchen's data than or the same as) for Manuel's data. A standard deviation (or σ) is a degree of the way dispersed the records is in terms of the mean. Low trendy deviation manner records are clustered across the mean, and excessive trendy deviation shows records are greater unfold out.

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The angle between the vector (3 - √2)i + 3j and the positive x-axis can be determined using trigonometry.

To find the angle between the vector and the positive x-axis, we can use the arctan function. The angle can be calculated by taking the arctan of the y-component divided by the x-component of the vector.

In this case, the vector is given as (3 - √2)i + 3j. The x-component is 3 - √2, and the y-component is 3. Using the arctan function, we can calculate the angle as arctan(3 / (3 - √2)).

By substituting the values into a calculator or using trigonometric identities, we can find the angle. It is important to note that the arctan function returns an angle in radians. If we want the result in degrees, we can convert it by multiplying the result by 180/π.

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Answer:

$16

Step-by-step explanation:

15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

To find the number of candy bars needed to bring the average cost down to $0.80, we can use the formula for average:

(sum of costs)/(number of candy bars).

Let's denote the number of candy bars needed as x. We know that the sum of costs for the group of ten candy bars is 10 * $0.89 = $8.90.

To bring the average down to $0.80, the sum of costs for the x candy bars must be (10 * $0.89 + x * $0.72).

Now we can set up the equation:

(10 * $0.89 + x * $0.72)/(10 + x) = $0.80.

Simplifying this equation, we get:

8.9 + 0.72x = 0.8(10 + x).

Solving for x, we find that x = 15.

Therefore, 15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

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complete question:

A group of ten candy bars has an average cost of $0.89 per candy bar. How many bars must be bought at the cost of $0.72 a piece to bring the average down to $0.80?

Answer: last one: 5x+5y=25

Step-by-step explanation:divide everything by 5 to get x+y=5 and subtract both sides by x to get y=-x+5 with -1/1 as slope and 5 constant

a = 2 cm

b = 55 mm = 5,5 cm

c = 10 cm

d = 60 mm = 6 cm

Perimeter: 2 + 5,5 + 10 + 6 = 23,5 cm

The area of carpet the school need to order for the room, the school is designing the new classroom shown in the figure is 5 sq. cm

What is area?

Area is the region covered by the two dimensional shapes like square, rectangle, rhombus, triangle, circle etc. The area of square is given by side x side. The rectangle area is found by length times width.

Here the coordinates of the given quadrilateral are, A(2,2); B(1,4); C(3,5); D(4,3)

To identify the type of quadrilateral we need to find the distance between the points: Distance formula=\(\sqrt{(X-x)^{2}+(Y-y)^{2} }\)

AB=\(\sqrt{(1-2)^{2}+(4-2)^{2} }\)

   =\(\sqrt{5}\)

BC=\(\sqrt{(3-1)^{2} +(5-4)^{2} }\)

   =\(\sqrt{5}\)

CD=\(\sqrt{(4-3)^{2} +(3-5)^{2} }\)

   =\(\sqrt{5}\)

DA=\(\sqrt{4-3)^{2} +(3-2)^{2} }\)

    =\(\sqrt{5}\)

As length of all sides are equal, it can be rhombus or a square.

Now length of diagonals,

AC=\(\sqrt{(3-2)^{2} +(5-2)^{2} }\)

    =\(\sqrt{10}\)

BD=\(\sqrt{(4-1)^{2} +(3-4)^{2} }\)

    =\(\sqrt{10}\)

As the length of diagonals are equal, the given quadrilateral is a square.

Area of square= side x side

                        =\(\sqrt{5}\) x  \(\sqrt{5}\)

                        = 5 sq. units

∴The area of carpet to be ordered is 5 sq. units

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The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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The numbers 3, 4, and 7 likely refer to specific shapes that are programmed into the toy's code and represented by specific patterns of 1s and 0s.

To understand how codecs work, it is helpful to think of them as translators. When digital information is transmitted, it is often compressed to reduce the amount of data that needs to be transmitted.

In the case of Tracy the turtle's shape toy, the codecs are responsible for encoding the shapes into digital information that can be transmitted to the toy's display. The toy's display then decodes this information to display the shapes. The numbers 3, 4, and 7 likely refer to specific patterns of 1s and 0s that represent the shapes programmed into the toy.

In mathematical terms, codecs use various algorithms to compress and decompress digital information. These algorithms often involve complex mathematical formulas that are used to analyze and reduce the amount of data that needs to be transmitted.

Codecs are an essential component of digital communication and are used in everything from video streaming to text messaging.

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Complete Question:

Does anyone know 3. 4. 7 Kid's Shapes Toy for Tracy the turtle in codecs?

13+v+2v=v+3+4

Combine like terms

13+3v=v+7

Move letters to the left

13+3v-v =7

13+2v=7

Subtract constant

2v=7-13

2v=-6

divide both side by 2

2v/2 = -6/2

v = -3

Answer:

$2.90

Step-by-step explanation:

6 × 0.15 = 0.9

2 + 0.9 = 2.9

R(x) = -30(x - 6)² + 320

This equation for the revenue is a quadratic equation model written in the form of completing the square;

This form appears like so:

f(x) = a(x + b)² + c

It is quite useful, especially for this type of question;

Firstly, if a is positive, the quadratic equation will be a u shaped graph when illustrated, if negative, it will be an n shaped graph;

What this means is if a is positive, the vertex of the graph is the lowest point, i.e. the minimum value of f(x), and if a is negative, the vertex will be the highest point, i.e. the maximum value of f(x);

Secondly, the coordinates of the vertex will be:

(-b, c)

So, with regards to the question:

We have -30 in the position of a, the curve is therefore n shaped and the vertex is the highest point (known as the local maximum);

And in place of b and c, we have -6 and 320, so the coordinates of this local maximum are:

(6, 320)

We interpret this like so:

320 is the highest possible value of R(x), which represents revenue, so $320 is the maximum revenue according to this model, and it is achieved when x = 6, i.e. when the price is increased by $0.90 (= 6 × $0.15);

Finally, to get the new ticket price, we add this to the original price to get $2.90.

The unexplained variance in regression analysis is also known as residual variance. It represents the variation in the dependent variable that cannot be accounted for by the independent variable(s) included in the model.

Residual variance is an important measure in regression analysis because it represents the extent to which the model does not fit the data.

A high residual variance indicates that there is a lot of unexplained variation in the dependent variable, which may be due to factors not included in the model or due to measurement error. On the other hand, a low residual variance indicates that the model explains most of the variation in the dependent variable, which suggests that the model is a good fit for the data.

Residual variance is the unexplained variation in the dependent variable in regression analysis, and it is an important measure of how well the model fits the data.

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An eigenvector corresponding to λ₂ = 2 - i is v₂ = [-1, 1].

To find the eigenvalues of matrix A, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

Let's compute the determinant:

det(A - λI) = |[2 - λ -1]|

|[ 1 2 - λ]|

Expanding along the first row, we have:

(2 - λ)(2 - λ) - (-1)(1) = (2 - λ)² + 1 = λ² - 4λ + 5 = 0

To solve this quadratic equation, we can use the quadratic formula:

λ = (-(-4) ± √((-4)² - 4(1)(5))) / (2(1))

= (4 ± √(16 - 20)) / 2

= (4 ± √(-4)) / 2

Since we are working over the complex numbers, the square root of -4 is √(-4) = 2i.

λ₁ = (4 + 2i) / 2 = 2 + i

λ₂ = (4 - 2i) / 2 = 2 - i

Now, let's find the eigenvectors corresponding to each eigenvalue.

For λ₁ = 2 + i, we solve the equation (A - (2 + i)I)v = 0:

[2 - (2 + i) -1] [x] [0]

[ 1 2 - (2 + i)] [y] = [0]

Simplifying, we have:

[0 -1 -1] [x] [0]

[ 1 0 - i] [y] = [0]

From the first equation, we have -x - y = 0, which implies x = -y.

Choosing y = 1, we have x = -1.

Therefore, an eigenvector corresponding to λ₁ = 2 + i is v₁ = [-1, 1].

For λ₂ = 2 - i, we solve the equation (A - (2 - i)I)v = 0:

[2 - (2 - i) -1] [x] [0]

[ 1 2 - (2 - i)] [y] = [0]

Simplifying, we have:

[0 -1 -1] [x] [0]

[ 1 0 i] [y] = [0]

From the first equation, we have -x - y = 0, which implies x = -y.

Choosing y = 1, we have x = -1.

In summary:

λ₁ = 2 + i has eigenspace span {[-1, 1]}

λ₂ = 2 - i has eigenspace span {[-1, 1]}

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Answer:

x>-7/3, x<-1

Step-by-step explanation:

Hope this helped!!!

Answered by NONE other than the #QUEEN herself!!

The standard error in the distribution of sample means, assuming a sample size of 30, is approximately 0.71.

To calculate the standard error in the distribution of sample means, you need the standard deviation of the population and the sample size. The standard error represents the average deviation of sample means from the population mean.

Given that the mean of the differences in word counts is -6.96 and the standard deviation is 3.88, these values pertain to the population of differences in word counts.

To calculate the standard error, you also need to know the sample size. Let's assume the sample size is denoted by "n."

The formula to calculate the standard error is:

Standard Error = Standard Deviation / √(Sample Size)

In this case, the standard deviation is 3.88, and the sample size is denoted by "n." Since the sample size is not given, I'll assume a sample size of 30 for illustration purposes.

Standard Error = 3.88 / √(30)

Calculating this expression:

Standard Error ≈ 0.707

Rounding to two decimal places, the standard error in the distribution of sample means is approximately 0.71.

Please note that the calculation of the standard error requires the sample size, which is missing in your question. The value of the standard error may vary depending on the actual sample size used.

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