The theater sells two types of tickets: adult tickets for $14 and child tickets for $6.
Last night, the theater sold a total of 438 tickets for a total of $5012. How many adult tickets did the theater sell last night?

The correct order of the steps in a hypothesis test are as follows:

Determine the null and alternative hypotheses.

Select a sample and compute the z-score for the sample mean.

Determine the probability at which you will conclude that the sample outcome is very unlikely.

Draw a conclusion about the unknown population using what is known about the sample.

First, you need to define the null and alternative hypotheses. The null hypothesis is the assumption that there is no significant difference between the sample and the population mean, while the alternative hypothesis is the opposite. Then, you need to select a random sample from the population and calculate the z-score for the sample mean. This involves finding the difference between the sample mean and the population mean, divided by the standard deviation of the sample mean.

Next, you need to determine the probability, known as the alpha level, at which you will conclude that the sample outcome is very unlikely, assuming that the null hypothesis is true. This is often set to 0.05 or 0.01. If the probability of obtaining the observed sample mean under the null hypothesis is lower than the alpha level, then the null hypothesis is rejected in favor of the alternative hypothesis.

Finally, you can draw a conclusion about the unknown population using what is known about the sample. If the null hypothesis is rejected, it suggests that there is a significant difference between the sample and the population mean, and the alternative hypothesis may be accepted.

Therefore, the correct order of the steps in a hypothesis test is to first determine the null and alternative hypotheses, then select a sample and calculate the z-score, determine the probability, and finally draw a conclusion based on the observed results.

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Mike works 39 hours per week at Job A and 20 hours per week at Job B.

We need to formulate some expressions here.

Let:

Hours Mike works at Job A = x

Hours Mike works at Job B = y

We know that:

x + y = 59 ---------- equation 1

We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:

6x + 7y = 374 --------- equation 2

Now we have two equations with two unknowns, which we can solve simultaneously.

Using substitution method:

solve for x in terms of y:

x = 59 - y

We can substitute this expression for x into equation 2:

6(59 - y) + 7y = 374

Simplifying and solving for y:

354 - 6y + 7y = 374

y = 20

So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:

x + 20 = 59

x = 39

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The fuel remaining after the tenth hr is 42,000 Pounds. It can be solved by multiplication and subtraction techniques.

What is multiplication?
When a quantity is added many times then the process is called multiplication. For example if 2 is added 10 times then the result will be 20. In terms of multiplication it can be written as 2 X 10 = 20.

After the first hour fuel in the plane is 150,000 pounds. Hence, calculate the amount of fuel consumed in 9 hr to find the remaining fuel after the tenth hr.

The four engines consume a total of 12,000 in one hr. Hence, total fuel consumed in 9 hr = (Fuel consumed in one hr)(Total hr)

                              = (12000 Pounds)(9 hr)

                              = 108,000 Pounds

Now, fuel remaining after the tenth hr = 150,000 - 108,000

                                                               = 42,000 Pounds

Hence, the fuel remaining after the tenth hr is 42,000 Pounds. It can be solved by multiplication and subtraction techniques.

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The mean of the binomial distribution with n = 40 and p = 3/5 is approximately 24.0.

A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, commonly referred to as "success" and "failure."

The key parameters of a binomial distribution are:

n: the number of trials

p: the probability of success in each trial

q: the probability of failure in each trial (q = 1 - p)

The mean, or expected value, of a binomial distribution with parameters n and p is given by the formula:

E(X) = n * p

where X is a random variable that follows a binomial distribution.

Substituting n = 40 and p = 3/5 into the formula, we get:

E(X) = 40 * (3/5) = 24

Rounding to the nearest tenth, we get:

y ≈ 24.0.

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Answer:

y=5

Step-by-step explanation:

16-11= 5.

So y must be 5

pls give brainiest

Answer:

answer y-5

Step-by-step explanation:

do 16-11

The three angles in the triangle ABC are approximately 0.45 radians (A and C) and 1.37 radians (B).

To determine the three angles in the triangle ABC, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of the angles opposite those sides. The law of cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite those sides:

```

a^2 = b^2 + c^2 - 2bc cos(A)

b^2 = a^2 + c^2 - 2ac cos(B)

c^2 = a^2 + b^2 - 2ab cos(C)

```

We can use these equations to solve for the three angles in the triangle ABC.

First, we need to find the lengths of the sides of the triangle. We can use the distance formula to find the lengths of the sides AB, BC, and AC:

```

AB = sqrt((7-2)^2 + (7-2)^2) = sqrt(50)

BC = sqrt((4-2)^2 + (8-2)^2) = sqrt(52)

AC = sqrt((7-4)^2 + (7-8)^2) = sqrt(10)

```

Now we can use the law of cosines to solve for the angles:

```

cos(A) = (b^2 + c^2 - a^2) / 2bc

cos(B) = (a^2 + c^2 - b^2) / 2ac

cos(C) = (a^2 + b^2 - c^2) / 2ab

```

```

cos(A) = (50 + 10 - 52) / (2 * sqrt(50) * sqrt(10)) = 0.9

cos(B) = (50 + 52 - 10) / (2 * sqrt(50) * sqrt(52)) = 0.2

cos(C) = (10 + 52 - 50) / (2 * sqrt(10) * sqrt(52)) = 0.9

```

Now we can use the inverse cosine function to find the values of A, B, and C:

```

A = acos(0.9) ≈ 0.45 radians

B = acos(0.2) ≈ 1.37 radians

C = acos(0.9) ≈ 0.45 radians

```

Therefore, the three angles in the triangle ABC are approximately 0.45 radians (A and C) and 1.37 radians (B).

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To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

Rule:(a,b)=(a,-b)

D(-3,0)=D'(-3,-0)

E(-5,4)=E'(-5,-4)

F(-2,7)F'(-2,-7)

G(3,8)=G'(3,-8)

I believe the angle between ne and se is 90° :)

The events are independent, the probability of selecting any combination of r days is the product of the probabilities of selecting each day, which is the same as the distribution of the unordered set of r days when N(n) = r.

(a) The distribution of N(n) is a binomial distribution, since the events are independent and occur with a fixed probability p. Therefore, N(n) follows a Binomial distribution with parameters n and p:

N(n) ~ Binomial(n, p)

(b) The distribution of T1 is a geometric distribution, as it represents the number of trials until the first success (event occurs) in a sequence of independent Bernoulli trials with probability p. Therefore, T1 follows a Geometric distribution with parameter p:

T1 ~ Geometric(p)

(c) The distribution of Tr is a negative binomial distribution, as it represents the number of trials until the rth success (event occurs) in a sequence of independent Bernoulli trials with probability p. Therefore, Tr follows a Negative Binomial distribution with parameters r and p:

Tr ~ Negative Binomial(r, p)

(d) Given that N(n) = r, the unordered set of r days on which events occurred has the same distribution as a random selection (without replacement) of r of the values 1, 2, ..., n. This is because each event occurs independently and with a fixed probability p. When you select r days randomly (without replacement), the probability of each day being selected is p, and the probability of each day not being selected is (1-p). Since the events are independent, the probability of selecting any combination of r days is the product of the probabilities of selecting each day, which is the same as the distribution of the unordered set of r days when N(n) = r.

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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The equation of the parabola is \($\dfrac{(x - 4)^2}{8(y - 1)} = 1$\)

The equation of a parabola with focus (h, k + p) and directrix y = k - p can be written as:

\($\dfrac{(x - h)^2}{4p(y - k)} = 1$\)

In this case, the focus is (4, 3) and the directrix is y = -1. Comparing this with the general equation of a parabola, we can determine the value of p.

k + p = 3 (since the y-coordinate of the focus is 3)

k - p = -1 (since the equation of the directrix is y = -1)

Adding these two equations, we get:

2k = 2

Dividing by 2, we find:

k = 1

Substituting this value back into one of the equations, we can solve for p:

1 + p = 3

p = 2

So, the value of p for this parabola is 2.

The equation of the parabola can be written as:

\($\dfrac{(x - 4)^2}{8(y - 1)} = 1$\)

This represents a parabola with focus at (4, 3) and directrix y = -1.

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Answer:

This week her gross wage is equal to $216.25

Step-by-step explanation:

From the question it self we can make the following equation.

Let  "W" be the gross wage for the week.

Let  "V" be the value of the goods she sells.

then.....

W = $140 + 0.05V

(Where $140 is the price she will be paid for just working and 0.05V is the commission she will get paid this week)

Now that we know what "v" equal to, we can easily find out her Gross Wage this week by inserting in the value of V. And so we get.......

W = $140 + 0.05V

W = $140 + 0.05 x 1525

W = $140 + 76.25

W = $216.25

Step-by-step explanation:

4 is -4

-4 → ( 4 - 4 = 0)

the additive identity of any given number is 0

The difference of the lengths of their sides is 1m.

The area of a square is simply calculated by multiplying the sides by itself.

In this case, it should be noted that an area has 36m². The side will be ✓36 = 6m

The second area is 49m². The side will be:

= ✓49 = 7m

Therefore, the difference will be to subtract the values and this will be:

= 7m - 6m

= 1m.

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Leah would use 208 square centimeters of construction paper to wrap the box.

to calculate the amount of paper leah uses to wrap the box, we need to determine the surface area of the box.

first, let's calculate the surface area of the triangular base. since it's a right angle with sides labeled as 12 cm, 10 cm, and 10 cm, we can use the formula for the area of a right triangle:

area of triangular base = (1/2) * base * height

area of triangular base = (1/2) * 12 cm * 8 cm

area of triangular base = 48 square cm

next, let's calculate the surface area of the rectangular side. the length of the rectangular side is 20 cm, and its height is 8 cm, which are adjacent to the triangular base.

surface area of rectangular side = length * height

surface area of rectangular side = 20 cm * 8 cm

surface area of rectangular side = 160 square cm

now, let's calculate the total surface area of the box by summing the areas of the triangular base and the rectangular side:

total surface area = area of triangular base + surface area of rectangular side

total surface area = 48 square cm + 160 square cm

total surface area = 208 square cm

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Answer:

5in

Step-by-step explanation:

If 1in=210 you just divide 1050 by 210 and you get 5, so your answer is 5in.

I hope this helps :)

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

Rounding to 2 decimal places, the shaded area is 234 cm².

What is the radius of circle?

The radius of a circle is the distance from the center of the circle to any point on the circumference of the circle. It is half of the diameter of the circle.

The diameter of the circle is 0.2 meters, which means the radius of the circle is 0.2 / 2 = 0.1 meters.

The height of the square is a fifth of the diameter of the circle, so the height of the square is 0.2 / 5 = 0.04 meters.

To find the shaded area in cm, we need to find the area of the circle and subtract the area of the square. The area of the circle is given by the formula πr², where r is the radius of the circle. The area of the square is simply the height multiplied by the width, which is equal to the diameter of the circle.

So, the area of the circle is π * 0.1² = 0.0314 square meters. The area of the square is 0.2 * 0.04 = 0.008 square meters. The shaded area is the difference between these two, or 0.0314 - 0.008 = 0.0234 square meters.

To convert the area to cm², we need to multiply by 10⁴. The shaded area in cm² is 0.0234 * 10⁴ = 234 cm².

Rounding to 2 decimal places, the shaded area is 234 cm^2.

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The area of the circle is approximately 866.36 cm (sqr). The circumference of a circle can be used to find its radius. The formula for the circumference of a circle is given:

C = 2πr

C is the circumference, π is the mathematical constant pi (22/7), and r is the radius. Given the circumference of the circle is 246 cm, we can find the radius by rearranging the formula:

r = C / (2π) = 246 / (2 * 22/7) = 246 / 44 * 7/2 = 246 / 44 * 7/2 = (246 * 7/2) / 44 = (246 * 7) / (2 * 44) = (246 * 7) / 88 = (1722) / 88 = 19.68 cm

Now that we have found the radius, we can use it to find the area of the circle. The formula for the area of a circle is given by:

A = πr^2

Where A is the area, π is the mathematical constant pi (22/7), and r is the radius. Plugging in the value of the radius we found earlier:

A = π * 19.68^2 = 22/7 * 19.68^2 = 22/7 * 386.1184 = 866.36 cm\(square\)

So the area of the circle is approximately 866.36 cm\(square\).

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(a) To construct the truth table for (¬P0​∧¬P1​) and ¬(P0​∧P1​), we need to consider all possible truth values for P0​ and P1​ and evaluate each formula for each combination of truth values.

P0 P1 ¬P0∧¬P1 ¬(P0∧P1)

T T     F             F

T F     F             T

F T     F             T

F F     T             T

The two formulas are not equivalent since they produce different truth values for some combinations of truth values of P0​ and P1​. For example, when P0​ is true and P1​ is false, the first formula evaluates to false while the second formula evaluates to true.

(b) To construct the truth table for (P2​⇒(P3​∨P4​)) and ((P2​∧¬P4​)⇒P3​), we need to consider all possible truth values for P2​, P3​, and P4​ and evaluate each formula for each combination of truth values.

P2 P3 P4 P2⇒(P3∨P4) (P2∧¬P4)⇒P3

T T T T T

T T F T T

T F T T F

T F F F T

F T T T T

F T F T T

F F T T T

F F F T T

The two formulas are equivalent since they produce the same truth values for all combinations of truth values of P2​, P3​, and P4​.

(c) To construct the truth table for P5​ and (¬¬P5​∨(P6​∧¬P6​)), we need to consider all possible truth values for P5​ and P6​ and evaluate each formula for each combination of truth values.

P5 P6 P5 ¬¬P5∨(P6∧¬P6)

T T T T

T F T T

F T F T

F F F T

The two formulas are equivalent since they produce the same truth values for all combinations of truth values of P5​ and P6​.

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1 milligram = 0.001 gram

x milligrams = 6 grams

By crossmultiplying, it becomes

0.001 * x = 6 * 1

0.001x = 6

x = 6/0.001

x = 6000

The mass in milligrams is 6000 milligrams

The number of times both services left the interchange together from 9am to 12 noon is 0.

Let's call the number of 15-minute intervals that have passed since 9 am "t".

So, the time that bus number 801 leaves the interchange after t intervals is 9am + 15t minutes.

Similarly, the time that bus number 802 leaves the interchange after t intervals is 9 am + 20t minutes.

For both services to leave the interchange at the same time, the number of 15-minute intervals that have passed since 9 am must be the same for both buses.

In other words, 15t must equal 20t.

Dividing both sides of this equation by 5, we get 3t = 4t.

This equation has no solution, which means that bus number 801 and bus number 802 never leave the interchange at the same time from 9am to 12 noon.

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The most general antiderivative of f(x) = x^(5) − x^(3) + 6x is F(x) = (1/6)x^(6) − (1/4)x^(4) + 3x^(2) + C and the most general antiderivative of f(x) = x^(4) is F(x) = (1/5)x^(5) + C.

a. The most general antiderivative of f(x) = x^(5) − x^(3) + 6x is F(x) = (1/6)x^(6) − (1/4)x^(4) + 3x^(2) + C, where C is the constant of integration.

To check this answer, we can differentiate F(x) using the power rule and the constant multiple rules:

F'(x) = (1/6)(6x^(5)) − (1/4)(4x^(3)) + 3(2x)
= x^(5) − x^(3) + 6x

This equals the original function f(x), so our antiderivative is correct.

Note that we do not need to use absolute values in this case because x^(5), x^(3), and 6x are all defined for all values of x.

b. The most general antiderivative of f(x) = x^(4) is F(x) = (1/5)x^(5) + C, where C is the constant of integration.

To check this answer, we can differentiate  F(x) using the power rule and the constant multiple rules:

F'(x) = (1/5)(5x^(4))
= x^(4)

This equals the original function f(x), so our antiderivative is correct.

Again, we do not need to use absolute values because x^(4) is defined for all values of x.

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Car seats come in many styles and sizes, including infant, convertible, full-sized boosters, and backless boosters, which provide a range of options to accommodate different ages and needs.

Backless boosters are another type of car seat commonly used for older children who have outgrown their convertible car seats. These boosters do not have a built-in backrest and are designed to elevate the child to the proper height to use the vehicle's seat belt safely. They provide a simple and portable solution for children who have reached the appropriate height and weight requirements.

Backless boosters offer some advantages. Firstly, they are lightweight and compact, making them easy to transfer between vehicles or store when not in use. Their simplicity makes them an affordable option for families on a budget. Additionally, many backless boosters come with adjustable armrests and cup holders for added comfort and convenience.

However, it is important to note that backless boosters may not provide the same level of side-impact protection as car seats with built-in backrests. Therefore, it is crucial to consider the child's age, weight, and height, as well as the specific safety regulations in your country or region when selecting the appropriate car seat.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The probability that John will roll more than 4 times until the dice roll sums to 8 three times is 4 times = 1 - (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

To find the probability that John will roll more than 4 times until the dice sum to 8 three times, we need to calculate the probability of him rolling 4 or fewer times and subtract it from 1.

Let's calculate the probability of John rolling 4 or fewer times. To do this, we need to find the probability of him rolling the sum of 8 three times or more within 4 rolls.

First, let's find the total number of possible outcomes for rolling two dice, which is 36 (6 possibilities for each dice).

Next, let's find the number of favourable outcomes for rolling the sum of 8 three times or more within 4 rolls.

We can use combinations to calculate this. For the first roll, the possible combinations that result in a sum of 8 are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). So, there are 5 favourable outcomes for the first roll.

For the second roll, we need to find favourable outcomes given that the first roll was not a favourable outcome. We need to subtract the outcomes that were already counted.

So, there are 4 favourable outcomes for the second roll. Similarly, for the third roll, we subtract the outcomes that were already counted and find 3 favourable outcomes.

Finally, for the fourth roll, we subtract the outcomes that were already counted and find 2 favourable outcomes.

To find the probability, we divide the number of favourable outcomes by the total number of possible outcomes. Probability of rolling the sum of 8 three times or more within

4 rolls = (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

Now, we can find the probability of rolling more than 4 times by subtracting this probability from 1.

Probability of rolling more than

4 times = 1 - (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

The probability that John will roll more than 4 times until the dice roll sums to 8 three times is the result obtained in the calculation above.

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