A circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees. What is the length of the arc?

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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The required value of the integral is 9x^(1/2) cos√x - (1/2) ∫9 sin√x x^(-1/2) dx

When different individuals or objects are brought together, such as when all of the district's elementary school children attend the new middle school or when snowboarding is introduced to all ski slopes, integration takes place.

The general formula for integration by parts is ∫u dv = uv - ∫v du. Choosing u = cos√x and dv = 9 dx, we have:

du = (1/2) sin√x dx and v = 9x^(1/2)

Therefore, the integral becomes:

∫9 cos⁡√x dx = 9x^(1/2) cos√x - (1/2) ∫9 sin√x x^(-1/2) dx

This can be further simplified if desired, but this is the result obtained by using integration by parts.

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Answer:  Brainliest Award pls

To find the base of a triangle with a given height and area, you can use the formula for the area of a triangle:

Area = (base * height) / 2

So, you can set up the equation:

24 = (base * 12) / 2

Solving for the base:

24 * 2 / 12 = base

base = 48 / 12 = 4

So, the base of the triangle is 4 inches.

Step-by-step explanation:

To find the base of a triangle with a given height and area, you can use the formula for the area of a triangle:

Area = (base * height) / 2

So, you can set up the equation:

24 = (base * 12) / 2

Solving for the base:

24 * 2 / 12 = base

base = 48 / 12 = 4

So, the base of the triangle is 4 inches.

The system of equation x = 4y - 1 and 2x - 8y = 7 has no solutions

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

x = 4y - 1  

multiply the equation by 2:

2x = 8y - 2

2x - 8y = -2     (1)

Also:

2x - 8y = 7     (2)

Subtracting equation 2 from 1 to solve by elimination method:

0 = -9

The equation has no solutions

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The problem involves calculating the probability of having 390 or more working devices in a box of 400 electronic devices, where each device works properly with a probability of 0.95. This type of problem can be solved using the binomial distribution.

The binomial distribution models the number of successful outcomes in a fixed number of independent Bernoulli trials. In this case, each device working properly can be considered as a Bernoulli trial with success probability 0.95. The total number of trials (i.e. devices) is 400.

Using the binomial distribution, we can calculate the probability of having exactly k successful outcomes (i.e. working devices) in n trials (i.e. devices). This probability is given by the formula:

P(k) = ([tex]{n}_C_{k}[/tex]) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, p is the success probability, and (1-p) is the failure probability.

To calculate the probability of having 390 or more working devices, we need to sum the probabilities of having 390, 391, 392, ..., 400 working devices:

P(390 or more) = P(390) + P(391) + ... + P(400)

This can be calculated using a binomial distribution calculator or by writing a program to calculate the binomial coefficient and probability for each value of k.

Finally, to express the result as a percentage, we need to multiply the probability by 100.

In conclusion, the percentage of boxes containing 390 or more working devices can be calculated using the binomial distribution, which models the number of successful outcomes in a fixed number of independent Bernoulli trials.

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Answer:

I got you

1. Use a calculator (its ur bestie fr fr)

2. Organization is key it might help with solving the problems

3. Ask someone or a teacher if you don’t understand

4. Remember COMBINE LIKE TERMS (ex: x+3x)

Step-by-step explanation:

The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(5 x 1/4), (3 x 7/9), and (2 x 5/6)

Then simplify each expression, then we have

⇒ 5 x 1/4

⇒ 1/4 + 1/4 + 1/4 + 1/4 + 1/4

⇒ 5 / 4

⇒ 1 ¹/₄

⇒ 3 x 7/9

⇒ 7/9 + 7/9 + 7/9

⇒ 7/3

⇒ 2 ¹/₃

⇒ 2 x 5/6

⇒ 5/6 + 5/6

⇒ 5/3

⇒ 1 ²/₃

The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

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The system of equations for this problem can be represented as:

y = 0.50x - 15 (for Team A's popcorn sales)

y = 0.75x - 25 (for Team B's cotton candy sales)

where x represents the number of items sold and y represents the profit earned. To graph the system of equations, we can plot the two lines on the same coordinate plane and find the point where they intersect, which represents the point at which both teams earn the same amount of profit.

At the point of intersection, both teams earn the same amount of profit. To find the profit earned, we can substitute the x-value of the point of intersection into one of the equations and solve for y. The profit earned would be the y-value at the point of intersection.

can't graph sorry

Answer:

Option 1 : x² + 4x + 4

Option 2 : x² + 20x + 100

Option 3 : x² + 6x + 9

Step-by-step explanation:

Looks like you got two of them right, one wrong and one missing. The first option is also a perfect square.

Here is how it evaluates:

If a trinomial expression can be a perfect square then it can be of the form (x + a)^2 = x² + 2ax + a² . Therefore the last term must be a perfect square of a number and the second term is twice the first term x and a = 2ax

So examining the choices we get

) The probability that a randomly selected

medical student who took the test had a total

score that was less than 484 = .

) The probability that a randomly selected study

participant's response was between 504 and 516

= .

) The probability that a randomly selected study

participant's response was more than 528 =

.

) Option D is

Only the event in (c) is unusual as its probability is

less than .

The and parts of the question are not

complete.

B) Find the probability that a randomly selected

study participant's response was between 504

and 516

C) Find the probability that a randomly selected

study participant's response was more than 528.

D) Identify any unusual event amongst the three

events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ =

Standard deviation = o = .

A) Probability that a randomly selected medical

student who took the test had a total score that

was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value

minus the mean then divided by the standard

deviation.

z = (x-μ)/o = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table

for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study

participant's response was between 504 and 516

= P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x -μ)/σ = (504 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516-500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ Z ≤ 1.54)

We'll use data from the normal distribution table

for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ Z ≤1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study

participant's response was more than 528 = P(x >

528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table

for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1-0.99643

= 0.00357

) Only the in () is as its probability

is less than ..

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The complete question is as follows -

In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.4.

A) Find the probability that a randomly selected medical student who took the test had a total score that was less than 484. The probability that a randomly selected medical student who took the test had a total score that was less than 484 is:_______.

B) Find the probability that a randomly selected study participant's response was between 4 and 6 The probability that a randomly selected study participant's response was between 4 and 6 is:_______.

C) Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant's response was more than 8 is:________.

The probability that a randomly selected medical student who took the test had a total score that was less than 480 is 0.49, which means that approximately 49% of medical students had a score lower than 480.

To calculate the probability that a randomly selected medical student who took the test had a total score that was less than 480, we need to start by looking at the data given. In this case, the data tells us that the mean score was 500 and the standard deviation was 50. This means that the scores are normally distributed, which means that the probability of finding a score lower than 480 can be calculated using the normal distribution formula. We can use this formula to calculate the area under the curve (or probability) below the score of 480. The result of this calculation is 0.49, which means that approximately 49% of medical students had a score lower than 480.

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Answer:

Step-by-step explanation:

To determine if they can use 26 of one type and 14 of the other, we need to calculate the cost for each scenario and compare it to their budget of $400.

If they use 26 round tables, it would cost 26 * $10 = $260.

And if they use 14 square tables, it would cost 14 * $10 = $140.

The total cost would be $260 + $140 = $400, which is equal to their budget.

Now, we need to make sure that they can seat all the guests with the tables they plan to rent.

If they use 26 round tables, they can seat 26 * 6 = 156 guests.

And if they use 14 square tables, they can seat 14 * 8 = 112 guests.

The total number of guests they can seat would be 156 + 112 = 268.

since they expect at least 260 guests to attend and they can seat 268 guests, the table rental plan of 26 round tables and 14 square tables is feasible both financially and in terms of seating capacity.

3 hours to take second tap alone empty the tank.

Given data :

Time taken by tap A to empty the tank = 4 hours

Work done by tap A in 1 hour = [tex]\frac{1}{4}[/tex]

Time taken to empty the tank by both taps = 1 hours

Time taken to empty the tank by tap B = Total time taken - time taken by A

=4 - 1 = 3

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The matrix v is the left singular vector, and the matrix σ is a diagonal matrix containing the singular values of the matrix a, but inverted. The matrix uT is the transpose

The singular value decomposition of a is:

a = uσvT

where

u = (1/√2, 0, -1/√2)

σ = (5, 0, 0)

vT = (3/5, 4/5, 0)

The pseudoinverse of a is:

a = vσuT

where

v = (3/5, 4/5, 0)

σ = (1/5, 0, 0)

uT = (√2/5, 0, -√2/5).

The singular value decomposition and pseudoinverse of the 1-by-3 matrix a = 3 4 0 are u = (1/√2, 0, -1/√2), σ = (5, 0, 0), vT = (3/5, 4/5, 0) and v = (3/5, 4/5, 0), σ = (1/5, 0, 0), uT = (√2/5, 0, -√2/5), respectively.

The singular value decomposition of the 1-by-3 matrix a = 3 4 0 is u = (1/√2, 0, -1/√2), σ = (5, 0, 0), vT = (3/5, 4/5, 0). This means that the matrix can be written as a product of three matrices, u, σ and vT. The matrix u is a unitary matrix, and the matrix σ is a diagonal matrix containing the singular values of the matrix a. The matrix vT is the transpose of the matrix v, which is the right singular vector. The pseudoinverse of a is v = (3/5, 4/5, 0), σ = (1/5, 0, 0), uT = (√2/5, 0, -√2/5). This means that the matrix a can be written as a product of three matrices, v, σ and uT, which is the inverse of the matrix u. The matrix v is the left singular vector, and the matrix σ is a diagonal matrix containing the singular values of the matrix a, but inverted. The matrix uT is the transpose

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The identity matrix of C is invertible, when its determinant is zero.

A matrix is a collection of numbers arranged in rows and columns. In linear algebra, we often work with square matrices, which are matrices with the same number of rows and columns.

Here we have given that for which numbers c is this matrix not invertible.

Here we have to consider that an important property of a square matrix is its invertibility, which determines whether or not the matrix can be "reversed" to get back to the identity matrix.

Therefore, the number "c" for which the matrix is not invertible is when the determinant of the matrix is zero. In other words, the matrix is singular and has no inverse. This can occur when the rows of the matrix are linearly dependent, meaning that one row can be written as a linear combination of the other rows. When this happens, the matrix collapses to a lower-dimensional space, and its determinant becomes zero.

In conclusion, a matrix is not invertible when its determinant is zero, and this is because the matrix has linearly dependent rows and collapses to a lower-dimensional space.

Complete Question:

For which three numbers c is this matrix not invertible, and why not?

[tex]A = \begin{bmatrix}2 &c &8 \\ c& c &7 \\ c&c & c\end{bmatrix}[/tex]

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Answer: hola

Step-by-step explanation:

Total amount of admission fee for the group of 26 students is 82.5$+135$ which is equal to 217.5 dollars.

There are a total of 26 students and the special offer is valid up to 11 students only.

Each of the 15 students will have to pay $135 as a special offer.

There are 11 more students, nevertheless, in addition to the great offer.

Each student paid an additional 7.5 dollars.

Therefore, the cost for 11 students is 11*(7.5$)=82.5$.

The total fee that is now owing is 82.5 + 135 dollars, which is equivalent to 217.5 dollars.

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At t = 10ms, the current can be found by substituting t=10 into the given equation for the current: [tex]I(t) = 5e^(-t/6). This gives I(10) = 5e^(-10/6) = 0.25 A.[/tex]

[tex]I(t) = 5e^(-t/6)[/tex]

[tex]At t = 1ms: I(1) = 5e^(-1/6) = 3.26 AAt t = 6ms: I(6) = 5e^(-6/6) = 0.77 AAt t = 10ms: I(10) = 5e^(-10/6) = 0.25 A[/tex]

At t = 1ms, the current can be found by substituting t=1 into the given equation for the current: [tex]I(t) = 5e^(-t/6).[/tex] This gives [tex]I(1) = 5e^(-1/6) = 3.26 A.[/tex]

At t = 6ms, the current can be found by substituting t=6 into the given equation for the current: [tex]I(t) = 5e^(-t/6)[/tex]. This gives [tex]I(6) = 5e^(-6/6) = 0.77 A.[/tex]

At t = 10ms, the current can be found by substituting t=10 into the given equation for the current: [tex]I(t) = 5e^(-t/6)[/tex]. This gives [tex]I(10) = 5e^(-10/6) = 0.25 A.[/tex]

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If g(2) = 12 and g'(x) ≥ 1/2 for 2 ≤ x ≤ 6, the smallest value g(6) can be g(6) ≥ 14.

g(2) = 12 and g'(x) ≥ 1/2 for 2 ≤ x ≤ 6.

From the mean value theorem we know that if at [2, 6] g(x) is continuous as well as differentiable then there exists (2, 6) as

{g(6) - g(2)}/(6 - 2) = g'(x)

As we know that g'(x) ≥ 1/2, so

{g(6) - g(2)}/(6 - 2) ≥ 1/2

Now simplify

{g(6) - g(2)}/4 ≥ 1/2

As g(2) = 12, now put the value

{g(6) - 12}/4 ≥ 1/2

Multiply by 4 on both side, we get

g(6) - 12 ≥ 2

Add 12 on both side, we get

g(6) ≥ 14

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the length of the midsegment of the trapezoid will be √58.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, Quadrilateral TEST is a trapezoid with coordinates at T(-3, 0), E(-2, 3), S(4, 3), and T(5, 0),

Its, diagonal or midsegment will be TS or ET'

From the formula of the distance between two coordinates:

D = √((x -x')² + (y - y')²)

Thus,

TS = √((-3 - 4)² + (0 - 3)²)

TS = √49 + 9

TS= √58

Since TEST' is a trapezoid thus its Diagonal will be the same  TS = ET'

Therefore,  the length of the midsegment of the trapezoid will be √58.

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Answer:

Y=5x+2

first find the rise over run (slope) (m value in the y=mx+b equation) you do this by using your table. notice how much the y side rises by (5) and how much the x side runs by (1) the slope is 5/1 (5) the y-intercept is 2, we know this from the table.

It is clear that even with full-time, year-round employment at the federal minimum wage, the annual income is still below the poverty line. California's minimum wage provides slightly better wages, but it still remains below the poverty line.

Annual income:

Federal minimum wage: $15,080

California's minimum wage: $16,640

Marketing managers: $110,000

Police officers: $55,680

Child-care workers: $14,500

Difference between annual wage and federal poverty line:

Federal minimum wage: -$10,470

California's minimum wage: -$8,910

Marketing managers: $55,000

Police officers: $8,550

Child-care workers: -$10,830

Difference between annual wage and median household income:

Federal minimum wage: -$57,040

California's minimum wage: -$49,560

Marketing managers: $45,000

Police officers: $420

Child-care workers: -$63,010

However, child-care workers' annual income is still well below the poverty line and the median household income. This highlights the importance of providing a living wage for all workers, especially those in low-wage industries.

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The cost of a taco and burrito respectively $1.70 and $0.40.

Let x be the cost of a taco and y be the cost of a burrito.

From the first given information, Thelma ordered 2 tacos and 1 burrito and paid $3.79. So we can write an equation:

2x + y = 3.79

From the second given information, Louise ordered 2 burritos and 1 taco and paid $4.58. So we can write another equation:

2y + x = 4.58

To find x and y, we need to solve the system of linear equations. One way to do this is by using the elimination method. We can subtract the first equation from the second to eliminate x:

2y = 0.79

y = 0.395

Now that we have y, we can substitute it back into the first equation to find x:

2x + 0.395 = 3.79

2x = 3.395

x = 1.698

So the cost of a taco is $1.70 and the cost of a burrito is $0.40.

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The probability that a student studied for 4 hours is 0.3.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1.

Given A group of students was surveyed in a middle school class,

the table for records,

Number of Hours          Total Number of Students

0                                                      1

1                                                       3

2                                                      2

3                                                      10

4                                                       9

5                                                       7

6                                                        3

To determine the probability;

The number of students that has 4 hours is 9

The total number of students = 30

P(4 hours) = 9/30

P(4 hours) = 0.3

Hence probability is 0.30.

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Answer:

6 feet

Step-by-step explanation:

Statistics is a branch of mathematics that deals with collecting data about the world. Hence, option C is the correct answer.

The study of data gathering, analysis, interpretation, presentation, and organization is known as statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics might be considered a subfield of applied mathematics. However, uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can determine the uncertainty and variation in many sectors. The probability, which is a key concept in statistics, essentially determines these uncertainties.

According to the definition of statistics; the study of data gathering, analysis, interpretation, presentation, and organization is known as statistics.

Hence, statistics is a branch of mathematics that deals with collecting data about the world. Hence, option C is the correct answer.

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The function C = 2x + 12y, has minimum value 60 at points (18,2) and (30,0).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given objective function -

C = 2x + 12y

Subjected to the constraints -

2x + 12y ≥ 60

x + y ≥ 20

x ≥ 0, y ≥ 0

First consider the inequality 2x + 12y ≥ 60.

The equation of the above inequality is as follows -

2x + 12y = 60

Find two points that satisfies the above equation.

Take x = 6, then -

2(6) + 12y = 60

12 + 12y = 60

12y = 60 - 12

12y = 48

y = 4

The first point is (6,4).

Take x = 0, then -

2(0) + 12y = 60

0 + 12y = 60

12y = 60

y = 5

The second point is (0,5).

Substitute (x,y) = (0,0) and see the direction of the region for 2x + 12y ≥ 60.

2(0) + 12(0) ≥ 60

0 ≥ 60

This is not true.

Therefore, the region is non-origin side.

Now consider the inequality x + y ≥ 20.

The equation of the above inequality is as follows -

x + y = 20

Find two points that satisfies the above equation.

Take x = 0, then -

0 + y = 20

y = 20

The first point is (0,20).

Take y = 0, then -

x + 0 = 20

x = 20

The second point is (20,0).

Substitute (x,y) = (0,0) and see the direction of the region for x + y ≥ 20.

0 + 0 ≥ 20

0 ≥ 20

This is not true.

Therefore, the region is non-origin side.

Plot the graph.

From the graph see that the corner points are (0,20), (18,2) and (30,0).

Now plug these points in the objective function and see for which point the objective function has the minimum value.

C = 2x + 12y

C = 2(0) + 12(20)

C = 0 + 240

C = 240

C = 2(18) + 12(2)

C = 36 + 24

C = 60

C = 2(30) + 12(0)

C = 60 + 0

C = 60

Therefore, the minimum value 60 is at points (18,2) and (30,0).

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The answer inequality of the given line will be -4<n<5.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0).

These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

The endpoints of the given line are -4 and +5.

So the value of inequality should lie between these two lines only.

The inequality can be written as n< 5 and n>-4

or -4<n<5

Hence the answer inequality of the given line will be -4<n<5.

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If the population variable x is normally distributed , then (b) Both intervals are equally likely to contain μ with probability ≈ 0.95.

The two intervals are :

(i) the z-interval [tex]\bar{x}[/tex] ± 1.960σ/√n   and    (ii) the t-interval [tex]\bar{x}[/tex]± t₀.₀₂₅,ₙ₋₁S/√n  ;

the critical value of z interval is = 1.96  ;

by using the normal table , we get , p = 0.95  ;

So , the z interval is with p = 95% ;

the t interval is t₀.₀₂₅,ₙ₋₁ = critical value ,

On comparing with [tex]t_{\frac{\alpha}{2} }[/tex],ₙ₋₁ = t₀.₀₂₅,ₙ₋₁ ,

we get , α/2 = 0.025 ⇒ So , α = 0.05   .

this interval is also 95% confidence interval .

Therefore , both the intervals are equally likely to contain μ with probability ≈ 0.95.

The given question is incomplete , the complete question is

Which is more likely to contain µ, the z-interval [tex]\bar{x}[/tex] ± 1.960σ/√n or the t-interval [tex]\bar{x}[/tex]± t₀.₀₂₅,ₙ₋₁S/√n? Assume that the population variable x is normally distributed.

Choose the correct answer below.

(a) The interval [tex]\bar{x}[/tex]±t₀.₀₂₅,ₙ₋₁S/√n has a higher probability of containing µ.

(b) Both intervals are equally likely to contain μ with probability ≈ 0.95.

(c) The interval  [tex]\bar{x}[/tex]± 1.96σ/√n has a higher probability of containing μ.

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The formula for calculating the sample mean is to take the sum of the values divided by the total number of values.

In this case, the two players would take the sum of the number of rounds they survived in their 101010 attempts, and then divide that sum by 101010. That would give them their individual sample means for the number of rounds survived.

To calculate the difference in the sample means of two players playing 101010 attempts, we can first calculate the sample mean of each player. This can be done by taking the sum of all attempts and then dividing that by the number of attempts. For example, if Player 1 had 5 attempts and survived 3 rounds, the sample mean would be 3/5 or 0.6. If Player 2 had 8 attempts and survived 4 rounds, the sample mean would be 4/8 or 0.5. We can then subtract the sample mean of Player 1 from the sample mean of Player 2 to get the difference in the sample means, which in this example would be 0.6 - 0.5 = 0.1.

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