Consider a roulette wheel. Roulette wheel has 2 green slots, 18 red slots, and 18 black slots. The wheel is spun and we are interested in the number of spins before the Rth success. : Let success be landing in a green slot. Find the following probabilities. A) identity the distribution with the parameters B) the 8th success occurs on the 17th spin. C) the 13th success occurs between the 31st and the 34th spin. PLEASE SOMEONE HELP <3

Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.

To determine the number of planks required, we need to calculate the total amount of wood needed for all 18 students' treasure boxes.

Each treasure box has two identical rectangular sides.

Each side is cut from a wooden plank that is 5/9 feet long and 1 foot wide.

Therefore, the area of each side is [tex](5/9) \times 1 = 5/9[/tex] square feet.

Since there are two identical sides for each treasure box, the total area of wood needed for one treasure box is [tex](5/9) \times 2 = 10/9[/tex] square feet.

To find the total wood needed for 18 students' treasure boxes, we multiply the area per treasure box by the number of treasure boxes:

Total wood needed [tex]= (10/9) \times 18 = 20[/tex] square feet.

So, Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.

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Question: What is the number of planks required for Mr. Penny's 18 students to each construct one treasure box if the rectangular sides of the treasure box will be cut from wooden planks that are 5/9 feet long and 1 foot wide?

The dot plot that most accurately displays Miss Little's class data is illustrated below.

To create a dot plot, we first need to determine the range of the data, which is the difference between the highest and lowest values. In this case, the range is from 8 to 16. We then draw a number line that spans the range, and mark each data point along the line with a dot.

Let's take a look at the first data set: 13, 14, 9, 12, 16, 11, and 10. The range is from 9 to 16, so we draw a number line from 9 to 16. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 13, one dot above 14, two dots above 9, one dot above 12, one dot above 16, one dot above 11, and one dot above 10.

We repeat this process for the second data set: 9, 8, 10, 10, 11, 15, and 10. The range is from 8 to 15, so we draw a number line from 8 to 15. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 9, one dot above 8, three dots above 10, one dot above 11, one dot above 15, and zero dots above 14.

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Complete Question:

Miss. Little wants to know how many pairs of shoes each of her students owns. She decides to ask each of her students to write the number of pairs of shoes that he or she owns. This data is displayed in the provided chart. Plot the dot plot that most accurately displays Miss Little's class data.

13 14 9 12 16 11 10

9 8 10 10 11 15 10

This procedure is not appropriate because (A) the two sample proportions were not computed from independent samples.

Independent samples are those chosen at random such that their observations do not depend on the values of other observations. Many statistical analyses are predicated on the assumption of independent samples. Others are intended to evaluate non-independent samples.

Assume that quality inspectors want to compare two laboratories to see if their blood tests produce identical results. Both labs receive blood samples drawn from the same ten children for analysis.

The test results are not independent because both labs analyzed blood samples from the same ten youngsters. The inspectors would need to perform a paired t-test, which is based on the assumption that samples are dependent, to compare the average blood test results from the two labs.

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Correct question:

A polling organization asks a random sample of 1,000 registered voters which of two candidates they plan to vote for in an upcoming election. Candidate A is preferred by 400 respondents, Candidate B is preferred by 500 respondents, and 100 respondents are undecided. George uses a large sample confidence interval for two proportions to estimate the difference in the population proportions favoring the two candidates. This procedure is not appropriate because

(A) the two sample proportions were not computed from independent samples

(B) the sample size was too small

(C) the third category, undecided, makes the procedure invalid

(D) the sample proportions are different: therefore the variances are probably different as well

(E) George should have taken the difference interval for a single proportion instead 500-400 1,000 and then used a large sample confidence

Dominick has earned $6,465.55 - $4,420.00 = $2,045.55 more interest than Ryan after 10 years.

To solve this problem, we can use the formulas for compound interest and simple interest.

Compound interest formula:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

Where:

A = the amount after time t

P = the principal

r = the annual interest rate

n = the number of times the interest is compounded per year

t = time in years

Simple interest formula:

I = Prt

Where:

I = the interest earned

P = the principal

r = the annual interest rate

t = time in years

Using the compound interest formula for Dominick's account:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

A = 6500(1 + 0.068/365)^(365*10)

A ≈ $12,965.55

Using the simple interest formula for Ryan's account:

I = Prt

I = 65000.06810

I = $4,420.00

Dominick's account has earned: $12,965.55 - $6,500 = $6,465.55 in interest.

Ryan's account has earned: $4,420.00 in interest.

Therefore, Dominick has earned $6,465.55 - $4,420.00 = $2,045.55 more interest than Ryan after 10 years.

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The two possible values for angle H in triangle GHI are approximately 93.1 degrees and 273.1 degrees, rounded to the nearest tenth of a degree

To find the possible values of angle H in triangle GHI, we can use the law of cosines.

Let's label angle H as x. Then, we can use the law of cosines to solve for x:

               cos(x) = (9.3² + 9.6² - 2(9.3)(9.6)cos(109))/ (2 * 9.3 * 9.6)

Simplifying this equation, we get:

                cos(x) = -0.0588

To solve for x, we can take the inverse cosine of both sides:

                       x = cos⁻ ¹ (-0.0588)

Using a calculator, we can find that x is approximately 93.1 degrees.

However, there is another possible value for angle H. Since cosine is negative in the second and third quadrants,

We can add 180 degrees to our previous result to find the second possible value for angle H:

                     x = 93.1 + 180 = 273.1 degrees

So the two possible values for angle H are approximately 93.1 degrees and 273.1 degrees, rounded to the nearest tenth of a degree.

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Answer:

If Mohal waits on 16 tables, he can expect to earn $25 wages + ($15 tips x 16 tables) = $265 in a day.

If Mohal waits on 1 table, he can expect to earn $25 wages + ($15 tips x 1 table) = $40 in a day.

Zombie Epsilon would require 52.5 days of doses, Zombie Zeta would need 163.3 days, and Zombie Eta would require 636e days to be cured.

To develop a theoretical antidote, you would need to consider the virus strand, concentration (mag/ml), and the equation to calculate the number of doses needed.

For Zombie Epsilon, Zeta, and Eta, the amounts of virus are 150, 230, and 636 mag/ml, respectively. To create an effective antidote, you would need to identify the specific virus strands for each zombie type (e.g., strand 3.5 for Epsilon, 7.1 for Zeta, and "e" for Eta).

Using the provided information, the equation should be used to determine the number of days (doses needed) for each zombie type. As an example, let's assume the equation is as follows: Days = (Amount of Virus * Strand) / 10.

For Zombie Epsilon: Days = (150 * 3.5) / 10 = 52.5 days
For Zombie Zeta: Days = (230 * 7.1) / 10 = 163.3 days
For Zombie Eta: Days = (636 * e) / 10 = 636e days (where e is a constant value)

In this theoretical scenario, Zombie Epsilon would require 52.5 days of doses, Zombie Zeta would need 163.3 days, and Zombie Eta would require 636e days to be cured.

Please note that this is a fictional scenario and not based on real-life medical information.

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The equation of the plane is -x(tan(r/4)) + z(sin(r/4)) = 1.

Let the equation of the plane be Ax + By + Cz = D. Since the plane contains the y-axis, we know that x = 0 when y = 0. Therefore, the equation becomes:

0A + 0B + Cz = D

=> Cz = D

This means that the plane is perpendicular to the y-axis and intersects the z-axis at z = D/C.

Now, we need to find the values of A, B, and C. Since the plane makes an angle of r/4 with the positive x-axis, we can use the direction cosines to find these values. The direction cosines of a vector are the cosines of the angles it makes with the x, y, and z axes.

Let the direction cosines of the vector perpendicular to the plane be (l, m, n). Then, we have:

cos(r/4) = l/√(l^2 + m^2 + n^2)

=> l = cos(r/4) / √2

cos(π/2) = m/√(l^2 + m^2 + n^2)

=> m = 0

cos(π/2) = n/√(l^2 + m^2 + n^2)

=> n = sin(r/4) / √2

Therefore, the vector perpendicular to the plane is:

(l, m, n) = (cos(r/4) / √2, 0, sin(r/4) / √2)

Since the plane contains the y-axis, we know that it is perpendicular to the vector (0, 1, 0). Therefore, the dot product of the two vectors is zero:

0A + B + 0C = 0

=> B = 0

Finally, we can use the fact that the vector (A, B, C) is perpendicular to the vector (cos(r/4) / √2, 0, sin(r/4) / √2) to find A and C:

A(cos(r/4) / √2) + 0 + C(sin(r/4) / √2) = 0

=> A = -C(tan(r/4) / √2)

Therefore, the equation of the plane is:

-C(tan(r/4) / √2)x + 0y + C(sin(r/4) / √2)z = D

Multiplying through by √2/C and setting D = √2, we get:

-x(tan(r/4)) + z(sin(r/4)) = 1

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The equation of the tangent line to the curve at (1,4) is: y = 8x - 4

To verify whether the point (1,4) is on the curve [tex]\sqrt{xy}= x^2y - 2,[/tex]

We can substitute x=1 and y=4 into the equation and see if it is satisfied:

√(14) = 1^24 - 2

2 = 2

Since the equation is true, (1,4) is on the curve.

To find the tangent line to the curve at the point (1,4),

We need to find the derivative of the equation with respect to x and evaluate it at x=1:

[tex]\sqrt{xy} = x^2y - 2[/tex]

Differentiating with respect to x:

[tex](1/2)(x^{(-1/2))}(y) + (1/2)(y^{(-1/2))}(x) = 2xy[/tex]

Simplifying and evaluating at x=1, y=4:

[tex]2 + (1/2)(4^{(-1/2))(1)} = 8[/tex]

The slope of the tangent line is 8.

Using point-slope form, the equation of the tangent line to the curve at (1,4) is:

y - 4 = 8(x - 1)

y = 8x - 4

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The overall limit is undefined as the the second limit is undefined

The given limit is of the indeterminate form 0/0 and hence we can apply l'Hôpital's Rule to evaluate it.

Applying l'Hôpital's Rule, we get:

lim sin(3x) / (3x) = lim [cos(3x) * 3] / 3 = cos(3x)

Now, we need to evaluate lim (3x)/(1 - cos(x)) as x approaches 0.

Again, this limit is of the indeterminate form 0/0, so we can apply l'Hôpital's Rule once again:

lim (3x)/(1 - cos(x)) = lim (3)/(sin(x)) = 3/0 (which is undefined)

Since the second limit is undefined, the overall limit is also undefined.

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1/70 is the probability of having slips numbered 1, 2, 3, and 4 drawn in order from the box.

To calculate the probability of drawing slips numbered 1, 2, 3, and 4 in order from a box containing slips numbered 1 through 8, we need to first find out the total number of possible outcomes when drawing four slips without replacement from the box.

The number of ways to draw 4 slips from a set of 8 slips without replacement is given by the combination formula:

= 8!/4!(8-4)! = 70

This means there are 70 possible outcomes when drawing four slips from the box.

To calculate the probability of drawing slips 1, 2, 3, and 4 in that order, we need to consider that there is only one way to draw the slips in that specific order, out of the 70 possible outcomes.

Therefore, the probability of drawing slips 1, 2, 3, and 4 in order is:

P(1,2,3,4 in order) =  number of favorable outcomes/total number of possible outcomes = 1/70

So the probability of drawing slips numbered 1, 2, 3, and 4 in order from the box is 1/70.

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The residual for the amount of monthly interest paid on a loan after 30 months is $0.13.

To find the residual, we need to compare the actual value of monthly interest paid after 30 months with the predicted value based on the regression equation.

The regression equation is:

monthly interest = 968 - 3.34x

To find the predicted value for 30 months, we substitute x = 30 into the equation:

monthly interest = 968 - 3.34(30) = 865.8

So the predicted value for monthly interest after 30 months is $865.8.

The residual is the discrepancy between the actual and expected values:

residual = actual value - predicted value

residual = $865.93 - $865.8 = $0.13

Therefore, the residual for the amount of monthly interest paid on a loan after 30 months is $0.13.

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Answer:

1243 ft³

Step-by-step explanation:

Given the volume formula for a cylinder:

[tex]V=\pi r^{2} h[/tex]

and we know that the radius is 6 and the height is 11, we can substitute:

[tex]V=\pi 6^{2} 11[/tex]

square 6

V=π36(11)

use 3.14 for pi and multiply everything together

V=3.14(36)(11)

simplify

V=1243.44

1243.44 rounded to the nearest whole number is 1,243 ft³.

Hope this helps! :)

The balance of Ana's checking account after the transaction on October 22 is $1,213.49.

To determine the balance of Ana's checking account after the transaction on October 22, we'll follow these steps:

1. Start with the initial balance on October 8: $1,093.12
2. Subtract the withdrawal for rent on October 15: $1,093.12 - $525.50 = $567.62
3. Add the deposit from the paycheck on October 22: $567.62 + $645.87 = $1,213.49

The balance of Ana's checking account after the transaction on October 22 is $1,213.49.

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It would take approximately 20 hours for the bacteria to triple in number.

Given that the bacteria population doubles every 10 hours, we can use exponential growth to determine the time it would take for the population to triple.

Let's represent the initial population as P0 and the time it takes for the population to triple as t.

Using the concept of exponential growth, we can express the population at time t as P(t) = P0 * 2^(t/10).

Since we want the population to triple, we set P(t) = 3 * P0:

3 * P0 = P0 * 2^(t/10).

We can cancel out P0 from both sides of the equation:

3 = 2^(t/10).

To solve for t, we can take the logarithm of both sides. Using the base-2 logarithm (log2) gives us:

log2(3) = t/10.

Using a calculator, we find that log2(3) is approximately 1.585.

Now, we can solve for t:

1.585 = t/10.

Multiplying both sides of the equation by 10 gives us:

15.85 = t.

Rounding to the nearest hour, the time it would take for the bacteria population to triple is approximately 16 hours.

Therefore, the bacteria population would take approximately 20 hours to triple in number.

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Answer:

B

Step-by-step explanation:

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given we can see that the line intersects with the Y-Intercept at (0,3), we can use process of elimination and erase answer choices A and D.

Now we are left with answr choices B and C, lets see where the line intersects with the X axis.

Helpful Tip:

If the line intersects with the X-Axis in between whole numbers, like for example this line intersects between 1 and 2, the slope will always be a fraction, which in this case the only fraction that we have left in answer choice B, which leads us to our answer.

There are 9 tables with 4 chairs in the restaurant.

Let's establish the variables:

Let x be the number of tables with 4 chairs

Let y be the number of tables with 5 chairs

Let z be the number of tables with 6 chairs

We know that there are a total of 19 tables, therefore:

x + y + z = 19 (equation 1)

We also know that the total number of people that can be accommodated in tables with 4 or 5 chairs is 64, therefore:

4x + 5y = 64 (equation 2)

We want to find the value of x, so we need to eliminate y from the equations above. We can do this by multiplying equation 2 by 4, and then subtracting it from equation 1:

x + y + z - 16x - 20y = 19 - 256

Simplifying:

-15x - 19y = -237

Dividing both sides by -19:

x = 9

Therefore, there are 9 tables with 4 chairs.

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Translated Question: Clear the selection Question 2: In a restaurant for 94 people there are 19 tables that can seat 4.5 or 6 people. If we know that the total number of tables with 4 or 5 chairs can accommodate 64 people, how many tables have 4 chairs?

The set R is not a subset of I. the only subset of I from the given options is A

The set I represents all isosceles triangles.

The set E represents all equilateral triangles, and an equilateral triangle is a special case of an isosceles triangle where all sides are equal. Therefore, the set E is a subset of I.

The set S represents all scalene triangles, and a scalene triangle is not isosceles since it does not have any equal sides. Therefore, the set S is not a subset of I.

The set A represents all acute triangles, and an acute isosceles triangle is a triangle where all angles are less than 90 degrees and two sides are equal in length. Therefore, the set A is a subset of I.

The set O represents all obtuse triangles, and an obtuse isosceles triangle is a triangle where one angle is greater than 90 degrees and two sides are equal in length. Therefore, the set O is not a subset of I.

The set R represents all right triangles, and a right isosceles triangle is a triangle where one angle is equal to 90 degrees and two sides are equal in length. the only subset of I from the given options is A.

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The required answer is x = 14

To solve this problem, we can use algebraic equations. Let's start by representing the number of points that Aisha has with the variable "x".

According to the problem, we know that Carter has 7.5 more points than Aisha, so we can write:
Carter = x + 7.5
An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations). These are further classified by degree: linear equation for degree one. quadratic equation for degree two.

We also know that Jamila has 4.5 more points than Carter, which means:

Jamila = (x + 7.5) + 4.5

a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. In mathematical logic, a variable is either a symbol representing an unspecified term of the theory (a meta-variable), or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation.
Finally, we know that Jamila has 26 points:

Jamila = 26

Now we can solve for x:

(x + 7.5) + 4.5 = 26

x + 12 = 26

x = 14

Therefore, Aisha has 14 points.

To show the work:

Aisha = x

Carter = x + 7.5

Jamila = (x + 7.5) + 4.5

Jamila = 26

(x + 7.5) + 4.5 = 26

x + 12 = 26

x = 14

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The watermelon is hitting the ground at around 10.33 seconds.

To find out when the watermelon hits the ground, we need to look for the time when the height of the watermelon is zero. This is because the watermelon will be on the ground at that point.

The x-intercepts of the function h(t) give us the times when the height is zero. So, we know that the watermelon will hit the ground at t = -0.33 seconds and t = 10.33 seconds.

However, the negative value doesn't make sense in this context, so we can ignore that solution. Therefore, the watermelon is hitting the ground at around 10.33 seconds.

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The second derivative yⁿ (y'') is 48x² - 6, and the third derivative yᵐ (y''') is 96x.

To calculate the second and third derivatives of the function y = 4x^4 - 3x² + 7x:

1. First, calculate the first derivative, y':
y' = dy/dx = (d/dx)(4x^4 - 3x² + 7x)
Using the power rule for derivatives, we get:
y' = 16x³ - 6x + 7

2. Now, calculate the second derivative, y'' (also denoted as yⁿ when n=2):
y'' = d²y/dx² = (d/dx)(16x³ - 6x + 7)
Applying the power rule again:
y'' = 48x² - 6

3. Finally, calculate the third derivative, y''' (also denoted as yᵐ when m=3):
y''' = d³y/dx³ = (d/dx)(48x² - 6)
Using the power rule one more time:
y''' = 96x

So, the second derivative yⁿ (y'') is 48x² - 6, and the third derivative yᵐ (y''') is 96x.

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Answer:

Her dad is 36 years old and brother is 12

Step-by-step explanation:

Since Alesha's brother is one year older you need to add 11+1 to get her brothers age, which is 12.
To get Alesha's dad's age you need to multiply 12x3, which is 36.

So, Alesha's dad is 36 and her brother is 12

(a)The equation x - 7 = 2x - 14 + 1 has 7 as a solution (when v = 2) and an extraneous solution of -8.

(b) To have a real number solution, the value of bx + c should be nonzero.

(a) To create an equation of the form x - a = vb(x) + c with 7 as a solution and an extraneous solution, we can start with the equation:

x - 7 = v * (x - 7) + 1

Simplifying this equation, we have:

x - 7 = vx - 7v + 1

Rearranging the terms, we get:

x - vx = 7v - 6

Now, let's assume v = 2. Substituting this value, the equation becomes:

x - 2x = 14 - 6

Simplifying further, we have:

-x = 8

Multiplying both sides by -1, we get:

x = -8

(b) To ensure that there is a real number solution to the equation x - a = vb(x) + c, it must be true that vb(x) + c does not result in division by zero or any other mathematical operation that would lead to an undefined or imaginary number. This implies that bx + c should not be equal to zero, as dividing by zero is undefined.

Therefore, to have a real number solution, the value of bx + c should be nonzero.

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Answer:

Area = w(l)  l = 5 + w

Step-by-step explanation:

The system of equations to describe the earnings by Avery and Janelle would be:

Avery's earnings: y = 120x + 300

Janelle's earnings: y = 24x + 60s

The problem provides two scenarios with different methods for earning money. Avery earns a fixed amount of $120 each week, in addition to a one-time bonus of $300. To represent this situation as an equation, we can use the formula:

y = 120x + 300

where y is Avery's total earnings, x is the number of weeks she works, and 300 is the one-time bonus she receives.

For Janelle, her earnings consist of a fixed weekly rate of $24 plus a variable amount based on the number of students she teaches.

We can represent Janelle's earnings as an equation using the formula:

y = 24x + 60s

where y is Janelle's total earnings, x is the number of weeks she works, and s is the number of students she teaches.

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The surface area of the triangular prism is

The surface area of the triangular prism is

= area of the two side rectangles + area of the base rectangles + area of the 2 triangles

= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24

= 2160 + 1296 + 1296

= 5752 square millimeters

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The probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

In a probability context, an event refers to an outcome or set of outcomes of an experiment or process. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of winning the lottery can be calculated using the formula:

Probability of winning = 1 / odds

Here, the odds of winning are given as 1-in-3,598. So, the probability of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla has bought 10 lottery tickets. So, the probability of winning the $200 prize with at least one ticket can be calculated as the complement of the probability of not winning with any of the tickets. That is:

Probability of winning with at least one ticket = 1 - Probability of not winning with any ticket

The probability of not winning with a single ticket is 1 - 0.000278 = 0.999722. So, the probability of not winning with all 10 tickets is:

Probability of not winning with all 10 tickets = (0.999722)¹⁰

= 0.997247

Therefore, the probability of winning with at least one ticket is:

Probability of winning with at least one ticket = 1 - Probability of not winning with all tickets

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

So, the probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

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Shayla's probability of winning the $200 prize with 10 lottery tickets are at 0.2753%.

An event in the context of probability is a result, or series of results, of an experiment or procedure. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.

The following formula can be used to determine the likelihood of winning the lottery:

Probability of winning = 1 / odds

The odds of winning in this case are 1 in 3,598. Therefore, the likelihood of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla purchased ten lottery tickets. As a result, the likelihood that at least one ticket will win the $200 reward can be computed as the complement of the likelihood that none of the tickets will win. Which is:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

The likelihood that a single ticket won't be the winner is 1 - 0.000278 = 0.999722. Consequently, the likelihood of not winning with all ten

tickets is:

with all ten tickets, what is the likelihood of not winning = (0.999722)¹⁰

= 0.997247

Consequently, the following is the likelihood of winning with at least one ticket:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

Shayla's chances of winning the $200 prize with 10 lottery tickets are at 0.2753%.

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1) If you get 2 and 5, the multiplication is 10, which is not a multiple of 6. so, you would win.

2) If you get 4 and 2, the multiplication is 8, which is not a multiple of 6. so, you would win.

3) If you get 1 and 6, the multiplication is 6, which is a multiple of 6. so, I would win.

The question asks about probability  which player would win if the numbers rolled are 2 and 5. To answer this, we calculate the product of 2 and 5, which is 10. Since 10 is not a multiple of 6, the person who did not roll the dice (i.e., "you") would win.

The question asks which player would win if the numbers rolled are 4 and 2. We calculate the product of 4 and 2, which is 8. Since 8 is not a multiple of 6, "you" would win again.

The question asks which player would win if the numbers rolled are 1 and 6. We calculate the product of 1 and 6, which is 6. Since 6 is a multiple of 6, the person who rolled the dice (i.e., "me") would win.The game described in the question involves rolling two dice and calculating the multiplication of the two numbers rolled. The outcome of the game depends on whether the product is a multiple of 6 or not.

The solution also provides a general explanation of how to calculate the probability of rolling a multiple of 6 with two dice. To do this, we count the number of ways to roll each multiple of 6 (there are two ways to roll a 6, one way to roll a 12, and no ways to roll an 18) and divide by the total number of possible outcomes (which is 36, since there are 6 possible outcomes for each die and 6*6=36 possible combinations of two dice). This gives us a probability of 1/12, or approximately 0.0833, for rolling a multiple of 6. We can then calculate the probability of not rolling a multiple of 6 by subtracting this probability from 1, which gives us 11/12, or approximately 0.9167.

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The maximum value of s is 9261, which is obtained when x = y = z = 7.

To find the maximum value of s=xyz, we can use the AM-GM inequality, which states that the arithmetic mean of a set of non-negative numbers is greater than or equal to the geometric mean of the same set of numbers.

Mathematically, this can be represented as:[tex](1/3)(x + y + z) \geq (xyz)^(1/3)[/tex]Multiplying both sides of the inequality by[tex]3(xyz)^(1/3)[/tex],

we get: [tex](x + y + z) \geq 3(xyz)^(1/3)[/tex] Now,

we can substitute the given value of x + y + z = 21, to obtain: 21 ≥ [tex]3(xyz)^(1/3)[/tex]

Cubing both sides of the inequality, we get: [tex]21^3 \geq 27(xyz)[/tex]

Simplifying the expression, we obtain: s=[tex]xyz \leq (21^3)/27[/tex]= 9261.

The maximum value of s=xyz is obtained when x = y = z = 7, and the value of s is equal to 9261. This result is obtained using the AM-GM inequality, which is a useful tool for solving optimization problems involving non-negative numbers.

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