Gerolamo Cardano in his book, The Gambling Scholar, written in the early
1500s, considers the following carnival game. There are six dice. Each of the
dice has ve blank sides. The sixth side has a number between 1 and 6|a
dierent number on each die. The six dice are rolled and the player wins a
prize depending on the total of the numbers which turn up.
(a) Find, as Cardano did, the expected total without nding its distribution.
(b) Large prizes were given for large totals with a modest fee to play the
game. Explain why this could be done.

the logarithm of the likelihood function and differentiate it with respect to both alpha and beta.

(a) The MLE of β is given by [tex]$$\hat{\beta} = \frac{\sum_{i=1}^n X_i}{n \alpha}.$$[/tex]

(b) The likelihood function for the data in Exercise 7.10(c) is given by [tex]$$L(\alpha, \beta) = \alpha^n \beta^{-n\alpha} \prod_{i=1}^n X_i^{-\alpha}.$$[/tex]We can take the logarithm of both sides to obtain[tex]$$ \ell(\alpha, \beta) = n \log \alpha - n \alpha \log \beta - \alpha \sum_{i=1}^n \log X_i.$$[/tex]Taking the partial derivatives of the log-likelihood function and setting them to 0 yields [tex]$$\frac{\partial \ell}{\partial \alpha} = \frac{n}{\alpha} - n \log \beta - \sum_{i=1}^n \log X_i = 0 \quad \text{and} \quad \frac{\partial \ell}{\partial \beta} = -\frac{n \alpha}{\beta} = 0.$$[/tex]Sol

Using the data from Exercise 7.10(c), we take the logarithm of the likelihood function and differentiate it with respect to both alpha and beta. We then set the partial derivatives to 0 to obtain equations for alpha and beta which can be solved to find the MLEs.

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Let D be the region bounded by the lines y = 0, y = x, x = 1, and x = 2. In order to express the double integral as an iterated integral with reversed order of integration, we first need to sketch the region D.

The double integral could be expressed as an iterated integral with reversed order of integration as follows:

[tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex]

The region is bounded by the lines y = 0, y = x, x = 1, and x = 2. This forms a triangle-like shape with 1 and 2 being the x-coordinates of the vertices and y = 0 being the base of the triangle. Then, we can express the double integral as: [tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex], where the order of integration is reversed from the original double integral. This means that first we are integrating with respect to y from 0 to x, and then we are integrating with respect to x from 1 to 2.

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Answer:

81.74 cm²

Step-by-step explanation:

Use tan(x) to find x

tanθ = opposite/adjacent

tan(36) = x/15

15tan(36) = x

area of triangle = [tex]\frac{1}{2}[/tex]*b*h

[tex]\frac{1}{2}[/tex]*15tan(36)*15 = 81.74 cm² (2 d.p.)

Answer:

k>0: ]-∞, 1[ v ]9 , +∞[

Step-by-step explanation:

we know that D > 0 because the anwser has to have two outcomes so:

b²-4.a.c>0 => (k-3)²-4.k.1>0 <=> k²-6k+9-4k>0 <=> k²-10k+9>0

=> D=8² : x1 = 9 v x2 = 1

k>0: ]-∞, 1[ v ]9 , +∞[

Answer:

Hello! Rx-axis means that they want the coordinates after they are reflected over the x-axis.

The original coordinates are as follows:

Q (1, 5)

R (3, -1)

S (0, 0)

T (-2, 3)

Reflecting a coordinate (x, y) over the x-axis results in the new coordinates being (x, -y).

Performing this translation over the 4 given points, we obtain:

Q' (1, -5)

R' (3, 1)

S' (0, 0)

T' (-2, -3)

hope this helps :)

The conclusion statement of the hypothesis is to reject the null hypothesis and accept the alternative hypothesis and the z score of -121.70 is in the rejection area

How to calculate the hypothesis?

In order to calculate, the hypothesis test we have to make inferences about the population data. It is also used to check if the results of an experiment are valid.

Here we have given that an analyst wants to know if the proportion of smokers in the population is the same in USA and Canada. in order to test this hypothesis she collects data from individuals, both smokers and non-smokers, living in these countries. your task is to help the analyst perform her hypothesis test. in order to do this you need to compute various statistics using excel. use 5% level of significance.

Here we have the following sample of data,

0.17 0.06 0.16 0.12 0.40

Through the given samples, we have identified the following values,

Count, N: 5

Sum, Σx: 0.91

Mean, μ: 0.182

Variance, σ2:  0.013376

Then the hypothesis test is written as,

The critical value (cutoff point) is 2.132. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since -121.70 is less than 2.132, we reject the null hypothesis. We accept the alternative hypothesis.

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Answer:

1) $468

2) 7668

Step-by-step explanation:

1) 6.5% of 7200 is 468. Therefore, this is the amount it had increased.

2) 7200+468=7668 Total for the end of the year

Answer:

the second solution would be correct 12x < 200

Step-by-step explanation:

12x < 200

12(12) <200

144 < 200

P = ∫(i^2 dl / 6πε0 c^3) × a^2

where q is the charge, ε0 is the permittivity of free space, c is the speed of light, and a is the acceleration of the charge.

Now consider a small element of length dl around the ring through which the current i flows. The power radiated from this element can be written as

dP = (i^2 dl / 6πε0 c^3) × a^2

where a is the acceleration of the charge in the element due to the changing magnetic field.

The total power radiated from the entire ring is obtained by integrating this expression over the length of the ring.

P = ∫(i^2 dl / 6πε0 c^3) × a^2

This is the general expression for the radiated power of the current distribution around the ring.

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Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. 

The meanings of the word equation and its cognates in various languages can vary slightly.

For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.

Equations come in two varieties: identities and conditional equations.

According to our question-

Given line: 2x+5y−7=0

the mid - point of the line segment joining point (2,7) and (−4,1) is

( 2(2−4 )2(7+1))=(−1,4)

the equation of the line will be

y−y 1=m(x−x 1)y−4=( 5−2 )(x+1)

5y−20=−2x−2

2x+5y=18

Hence,  Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.

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The statement given in the question holds true . We get this result after analyzing the given data set .

Given , hypothesis is ,

Let d be any positive integer not equal to2 , 5 or 13 .

Show that one can find distinct a , b  in the set {2,5,13,d} such that ab-1 is not a perfect square.

Using the modular way to solve this question we get ,

d = 0 , 3 = | 4 |

Then , we get the result as ,

13d - 1 , which is not a perfect square.

d = 2|4|

we get , 2d -1

which again is not a perfect square.

Similarly after checking the value for all the possible cases , we will get the result that the hypothesis is correct.

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7.5

Step-by-step explanation:

3:8=×:20 so x=20×3÷8=7.5

The required equation for the variation of k is given as k = Fd² / xy.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,

F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)

Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²

Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy

Thus, the required equation for the variation of k is given as k = Fd² / xy.

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To calculate the volume of a cylindrical tank, you will need to use the formula for the volume of a cylinder, which is:

V = πr^2h

Where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

To use this formula, you will need to first calculate the radius of the base of the tank. To do this, you will need to divide the diameter of the tank (170 feet) by 2.

Once you have calculated the radius, you can plug the value into the formula along with the height of the tank (60 feet) to find the volume of the tank.

Answer:

Step-by-step explanation:

height of the tank= 60 feet

diameter = 170 feet.

as we know, radius = 2 *diameter

therefore radius = diameter /2

                            =  170/2

                             =85 feet

volume of cylinder =  πr²h

 π =3.14    

                               = 3.14 ×85×60

                                =10927.2 feet²  

Answer:

15 ñ

Step-by-step explanation:

On solving the provided question, we can say that net annual cost of the given account is  18

equation: a statement stating the equality of two expressions having variable- and/or number-filled expressions. Since equations are essentially questions, finding a way to answer them has spurred the development of mathematics.

Net annual cost is that monthly fee X 12 +  fee per check X number of checks per month X 12

[tex]= ($3.75 X 12) + ($0.25 X22 X 12)\\ = $111[/tex]

Net annual cost is service charges - Interest earnings

[tex]= ($15 X 3) - (0.06 X $600 X 9 / 12)= $18[/tex]

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Answer:

sorry new don't understand the app

Answer:

x = -10

y = 1

Step-by-step explanation:

To use the Gauss-Jordan Elimination Method to solve for x and y, we need to put the augmented matrix in row-echelon form. The first step is to eliminate the x-coefficient in the second row by adding 4 times the first row to the second row. This gives us the following matrix:

[ 6 6 | -18 ]

[ 0 -10 | -10 ]

Next, we need to eliminate the y-coefficient in the second row. We can do this by adding 5 times the second row to the first row, which gives us the following matrix:

[ 1 -10 | -10 ]

[ 0 -10 | -10 ]

Now, the matrix is already in row-echelon form, so we can read the solution directly from the matrix. The solution is x = -10 and y = 1. Therefore, the solutions to the system of linear equations are:

x = -10

y = 1

Note that there may be other solutions to the system of equations, depending on the specific equations that the matrix represents. The Gauss-Jordan Elimination Method will always give us one possible solution, but there may be other solutions as well.

The probability generating function of a discrete nonnegative integer valued random variable X is defined by ø(s) = E[s] = Σp;si j=0, where pj is the probability mass function of X. P{XY} = P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij,Therefore, ø(s) = Σ pi pj sij = P{XY}

In this problem, we are also given a geometric random variable Y with parameter p 1 s, where 0 < s < 1. Y is independent of X. To show that ø(s) = P{XY}, we must show that the two expressions are equal.

First, we note that the probability of X and Y being equal to i and j, respectively, is given by P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij. This is because the probability of X being equal to i is pi, and the probability of Y being equal to j is pj (where p is the parameter of the geometric distribution). Since sij is the product of i and j, the probability of both X and Y being equal to i and j, respectively, is pi pj sij.

We can now substitute this expression into the probability generating function for X. We have that ø(s)

= E[s] = Σp;si j=0

= Σ pi pj sij

= P{XY}

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The Probability P [tex](20\leq x\leq 36)[/tex] = 0.7500

What is probability ?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

Given : the mean μ = 28

standard deviation σ = 4

small value = 20 and big value = 36

by chebychev's inequality,

μ - kσ = small value

28-k(4) = 20

k = 2

also,

μ + kσ = big value

28 + k(4) = 36

k = 2

The Probability P [tex](20\leq x\leq 36)[/tex] = [tex]1-1/k^{2}[/tex]

[tex]= 1-1/2^{2} \\=3/4\\=0.7500[/tex]

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Using correlation and it's value of coefficient , The answer is b. 0.50

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.

we have 25% variance confidence.

[tex]r ^ {2} = 0.25[/tex]

[tex]r=\sqrt {0.25}[/tex]

[tex]r=0.50[/tex]

The answer is b.0.50

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If a linear regression equation predicts more than 25% of the variance in the Y scores, then the correlation between X and Y must be greater than (c) r = 0.35.

Correlation (r) quantifies the strength and direction of the linear relationship between two variables. A correlation of 0.35 indicates a moderate positive linear association, suggesting that as X increases, Y tends to increase as well, and vice versa.

When the correlation surpasses this threshold, it implies that a substantial portion of the variability in Y can be explained by changes in X. However, it's important to interpret the correlation value within the context of the specific data and the field of study.

Other factors like sample size and potential outliers can also influence the significance of the correlation. In summary, a correlation greater than (c) 0.35 signifies a meaningful connection between X and Y, contributing to the prediction of Y scores using the linear regression equation.

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In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares is 0.17.

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The measure of the angles in the given figure of the triangle is given by: m∠1= 56  ,m∠2= 56 and m∠3= 74.

As given in the question,

In the given triangle MPQ we have,

Sum of all the interior angles in the triangle is 180 degrees.

m ∠P + m ∠M + m∠1 =180°

⇒58° + 66° + m∠1=180°

⇒m∠1= 180° - ( 58° + 66°)

⇒m∠1=56°

From the figure , ∠1 and ∠2 are vertically opposite angles:

⇒m∠1= m∠2

⇒m∠2=56°.

In triangle QNO we have,

m ∠O + m∠2 + m∠3 =180°

⇒50° + 56° +m∠ 3=180°

⇒106° + m∠3= 180°

⇒m∠3= 180° - 106°

⇒m∠3=74°

Therefore, the measure of the required angles in the given triangles are m∠1= 56  ,m∠2= 56 and m∠3= 74.

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Answer:

The equation that accurately represents Liam's balance, y, after x days is y = -12.75 - 10x.

This equation takes into account the fact that Liam's balance is already -$12.75 and that he is charged a $10 overdraft fee each day his balance is below $0. As the number of days, x, increases, the total amount of overdraft fees he is charged will also increase, resulting in a decrease in his balance.

For example, if Liam's balance is -$12.75 after 0 days, his balance will be -$22.75 after 1 day (y = -12.75 - 10(1) = -22.75), and his balance will be -$32.75 after 2 days (y = -12.75 - 10(2) = -32.75).

Answer:

he could play 4 games and have some change left over

Step-by-step explanation:

renting shoes cost 5 dollars and each game costs 8 dollars so 40-5=35 35/8=4.375

Answer:

R = 0≤ y ≤ 800

D = 0≤ x ≤ 16

.

.

.

.

Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),

there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.

Given that;

H₀ : σ = 0.02

H₁ : σ > 0.02

The test statistics is;

X² = ( n-1 )s² / σ²  = ( 15 - 1)(0.016)² / (0.02)²

= 0.003584 / 0.0004

= 8.96

degree of freedom

df = n - 1 = 15 - 1 = 14

For right tailed test, critical value at 0.01 level of significance is 29.141.

Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),

Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.

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The percentage of total that Maya spend on fruit is 55%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Maya spent a total of $80 at the grocery store. of this amount, she spent $44 on fruit. The percentage of total that she spend on fruit will be:

= Amount on fruit / Total amount × 100

= 44/80 × 100

= 55%

The percentage is 55%.

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Complete question

maya spent a total of $80 at the grocery store. of this amount, she spent $44 on fruit. what percentage of total did she spend on fruit

Answer:

e

Step-by-step explanation:

because it's number is common