Find the area of the indicated region under the standard normal curve.The area between z=−1.3z=−1.3 and z=1.4z=1.4 under the standard normal curve.

The only possible degree for the polynomial p+q is 11.

Given the degree of polynomial p is 11 and the degree of polynomial q is 7, we can find all possible degrees of the polynomial p+q by considering their highest-degree terms.

When adding polynomials, the resulting polynomial will have the degree that corresponds to the highest-degree term. In this case, we have two options:

1. The highest-degree terms of both polynomials are of different degrees. In this case, the degree of p+q will be the maximum of the two given degrees, which is max(11, 7) = 11.

2. The highest-degree terms of both polynomials are of the same degree and their coefficients have opposite signs, causing them to cancel out when added. In this scenario, the degree of p+q will be less than the maximum degree, i.e., less than 11.
However, given that the degrees of p and q are different (11 and 7), it is not possible for their highest-degree terms to cancel out.

Therefore, the only possible degree for the polynomial p+q is 11.

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43 4/5 cups of cheese is needed to make 10 pizzas.

We will use the Unitary method, that is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

Given that it takes 4 3/4 cups of cheese, 7/8 cups of olives, and 2 5/8 cups of sausage to make a signature pizza.

For making one pizza, amount of cheese needed =  4 3/8 cups = 35/8  cups.

Now the total amount of cheese needed to make 10 pizzas, we need to multiply  35/8  cups by 10.

So, 350/8  cups = 43 4/5 cups

Thus,  43 4/5 cups of cheese is needed.

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The smallest number that appears in both lists is 11. Therefore, the least possible value of n that satisfies both conditions is 11.

To find the least possible value of n, we need to find the smallest number that satisfies both conditions.

We can start by listing out some numbers that have a remainder of 2 when divided by 3: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 188, 191, 194, 197, 200, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 233, 236, 239, 242, 245, 248, 251, 254, 257, 260, 263, 266, 269, 272, 275, 278, 281, 284, 287, 290, 293, 296, 299, and so on.

Out of these numbers, we need to find the ones that also have a remainder of 1 when divided by 5. The numbers that have a remainder of 1 when divided by 5 are: 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, and so on.

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Therefore, the linearization of f(x) = cos(x) at a = π/2 is L(x) = π/2 - x.

The linearization of a function f(x) at a point a is given by:

L(x) = f(a) + f'(a)(x - a)

where f'(a) denotes the derivative of f(x) evaluated at x = a.

In this case, we have:

f(x) = cos(x)

a = π/2

First, let's find f'(x):

f'(x) = -sin(x)

Then, we can evaluate f'(a):

f'(π/2) = -sin(π/2) = -1

Next, we can plug in the given values into the formula for linearization:

L(x) = f(a) + f'(a)(x - a)

L(x) = cos(π/2) + (-1)(x - π/2)

L(x) = 0 - x + π/2

L(x) = π/2 - x

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Answer: To find the initial population size of the fish species, we can simply substitute t = 0 into the exponential function and evaluate:

P(0) = 1000 / (1 + 7e^(0.3*0)) = 1000 / (1 + 7e^0) = 1000 / 8 = 125

Therefore, the initial population size of the fish species was approximately 125 individuals.

To find the population size after 7 years, we can substitute t = 7 into the exponential function and evaluate:

P(7) = 1000 / (1 + 7e^(0.3*7)) ≈ 638

Therefore, the population size of the fish species after 7 years was approximately 638 individuals (rounded to the nearest whole number).

The initiall population size is: 125. Rounded to the nearest whole number, the population size after 7 years is 18.

Initial population size is:
To find the initial population size, we need to find P(0). Plug t=0 into the given equation:

P(0) = 1000/(1+7e^(0.3*0))
P(0) = 1000/(1+7*1) = 1000/8 ≈ 125

The initial population size of the species is approximately 125.

Population size after 7 years is:
To find the population size after 7 years, we need to find P(7). Plug t=7 into the given equation:

P(7) = 1000/(1+7e^(0.3*7))
P(7) ≈ 1000/(1+7e^2.1) ≈ 1000/(1+7*8.166) ≈ 1000/(1+57.162) ≈ 1000/58.162 ≈ 17.19

The population size after 7 years is approximately 17.

Your answer:
The initial population size is: 125

Population size after 7 years is: 17

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The equivalent expression is  log(6) + log(7)

There are two rules for logarithmic relations that we need to know here, these are:

log(a*b) = log(a)+ log(b)

log(a/b) = log(a) - log(b)

Here we have the product of 6 and 7 in the argument, then we can write the equivalent expression:

log(6*7) = log(6) + log(7)

That is the correct option.

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The  speed of the moving end of the sprinkler in feet per minute is 34.48 food per hour

Speed in mathematics is defined as the distance an object travels in a given amount of time. Also, It can be calculated using the formula Speed = Distance ÷ Time, where distance is equal to the time taken to travel and time is equal to the number of seconds needed to travel.

The given parameters are

The distance is = 50-foot long

Time is given as = 1.45 hours

Speed = Distance/Time

Speed = 50 foot long/1.45 hurs

Therefore the Speed = 34.48 food per hour

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The functions represented by the graphs are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

f(x) = |x|

The function g(x) is a translation down two units of the parent function f(x), hence it is given as follows:

g(x) = |x| - 2.

The function h(x) is a translation up three units of the parent function f(x), hence it is given as follows:

h(x) = |x| + 3.

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The product of the two matrices is  [2 - 3]    x  [1  -  4]

                                                            [ 3   2]       [4     1]

option B.

A product matrix is also known as matrix multiplication, which involves the multiplication of two matrices, to get or simply to a single matrix.

For example, if P and Q are the two matrices, then the product of the two matrices P and Q are denoted by:

Y = PQ.

For the given question; we have the first matrix as; (2 - 3i) and the second matrix as (1 - 4i).

Matrix (2 - 3i) is transformed to [2 - 3]

                                                   [ 3   2]

Matrix (1 - 4i) is transformed to [1  -  4]

                                                  [4     1]

The product of the two matrices =  [2 - 3]    x  [1  -  4]

                                                          [ 3   2]       [4     1]

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Using diagonals from a common vertex, the number of triangles that could be formed from a 19-gon  is 16 triangles.

If you choose a vertex of a 19-gon, then you can draw diagonals from this vertex to 16 other vertices of the 19-gon (not including adjacent vertices).

Each of these diagonals will form a triangle with the chosen vertex. Therefore, the number of triangles that can be formed using diagonals from a common vertex of a 19-gon is 16 triangles.

When you choose a vertex of a 19-gon, you can draw diagonals to 16 other vertices of the 19-gon. Each of these diagonals forms a distinct triangle with the chosen vertex. Therefore, the total number of triangles that can be formed is 16.

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In this case, the likelihood function is the product of the Poisson probability mass function evaluated at each data point in the training data. To compute the log-likelihood, we take the natural logarithm of this product. To maximize the log-likelihood function, we take the derivative of it with respect to the parameter and set it equal to zero. Solving for the parameter gives us the maximum likelihood estimate.

To help you with your question, let's go through the process of using maximum likelihood estimation (MLE) for a Poisson distribution step by step.

1. Given training data drawn from a Poisson distribution, we have the probability mass function (PMF) as:
P(X=k) = (λ^k * e^(-λ)) / k!, where k is a non-negative integer and λ is the parameter we want to estimate.

2. The likelihood function, which is the joint probability of obtaining the sample given the model, is the product of individual probabilities:
L(λ) = Π P(X_i=k_i), for i = 1 to n, where n is the number of data points.

3. For MLE, we compute the log-likelihood function, which is the natural logarithm of the likelihood function:
log(L(λ)) = Σ log(P(X_i=k_i)), for i = 1 to n.

4. Plugging in the PMF, the log-likelihood becomes:
log(L(λ)) = Σ [k_i * log(λ) - λ - log(k_i!)], for i = 1 to n.

5. To maximize the log-likelihood function, we take its derivative with respect to λ and set it to 0:
d(log(L(λ))) / dλ = Σ [k_i/λ - 1] = 0.

6. Solve for the MLE estimate of λ:
λ_MLE = Σ k_i / n, where n is the number of data points.

The resulting estimate for λ, λ_MLE, is in accordance with the definition of λ in a Poisson distribution, as it represents the average number of events in the sample. The resulting estimate for the Poisson distribution parameter is the sample mean of the training data. This is in accordance with the definition of the Poisson distribution, where the mean and variance are equal to the parameter lambda.

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To maximize the likelihood function, we take the derivative with respect to θ and set it equal to zero: d/dθ[L(θ|X1,X2,...,Xn)]=−n/θ+(X1+X2+⋯+Xn)/θ2=0.

The MLE for θ in the exponential distribution is simply the sample mean of the observed data.

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson point process. X1,X2,...,XnX1,X2,...,Xn is a random sample of size n from this distribution, which means that each XiXi is an independent and identically distributed random variable with the same exponential distribution.

The probability density function (pdf) of the exponential distribution is given by f(x:θ)=(1/θ)e−x/θ, where θ is the scale parameter. This means that the probability of observing a value x from the distribution is proportional to e−x/θ, with the constant of proportionality being 1/θ.

To estimate the value of θ based on the observed data, we can use the method of maximum likelihood estimation (MLE). The likelihood function for the sample X1,X2,...,XnX1,X2,...,Xn is given by L(θ|X1,X2,...,Xn)=∏i=1n(1/θ)e−Xi/θ=(1/θ)n e−(X1+X2+⋯+Xn)/θ.

Solving for θ, we get θ=(X1+X2+⋯+Xn)/n, which is the sample mean.

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If both eigenvalues of a 2x2 matrix A are complex with nonzero real part, then the critical point of the system x' = Ax is a center.

A center is a type of critical point where the solutions of the system oscillate around the critical point, without converging or diverging. The center has the property that the solutions move along closed trajectories, which are ellipses in the case of a 2x2 system. The orientation and size of the ellipses depend on the values of the eigenvalues and eigenvectors of the matrix A.

In general, centers are not stable or unstable in the sense of Lyapunov. Instead, they are neutral points where the solutions of the system do not change in magnitude, but only in direction.

The classification of a critical point as a center is important because it indicates the existence of periodic solutions in the system. These periodic solutions are of interest in many applications, such as in the study of oscillatory behavior in physical systems, or in the analysis of biological rhythms.

In summary, if both eigenvalues of a 2x2 matrix A are complex with nonzero real part, then the critical point of the system x' = Ax is a center, and the solutions of the system move along closed trajectories, without converging or diverging.

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Answer:

y(t) = 3/4exp(4t) - 1/4exp(-4t) - 1/2

z(t) = -3/4exp(4t) - 1/4exp(-4t) - 2

Step-by-step explanation:

Given system of differential equations:

dy/dt = 2y + 2z

dz/dt = 2y + 2z

We can write this system in matrix form as:

d/dt [y z] = [2 2] [y z]

Let A = [2 2]. Then the system can be written as:

d/dt [y z] = A[y z]

The solution to this system is given by:

[y z] = exp(At) [y(0) z(0)]

where exp(At) is the matrix exponential of At.

To find exp(At), we first need to find the eigenvalues and eigenvectors of A. The characteristic equation of A is:

det(A - lambdaI) = 0

=> det([2-lambda 2; 2 2-lambda]) = 0

=> (2-lambda)(2-lambda) - 4 = 0

=> lambda1 = 4, lambda2 = 0

The eigenvectors corresponding to lambda1 = 4 and lambda2 = 0 are:

v1 = [1 1] and v2 = [-1 1]

We can now write A as:

A = PDP^-1

where P = [v1 v2] and D = [4 0; 0 0]. Then,

exp(At) = Pexp(Dt)P^-1

We can compute exp(Dt) as:

exp(Dt) = [exp(4t) 0; 0 1]

Therefore,

exp(At) = [1/2 1/2; -1/2 1/2] [exp(4t) 0; 0 1] [1/2 -1/2; 1/2 1/2]

Now, we can find the solution to the system as:

[y z] = exp(At) [y(0) z(0)]

=> [y z] = [1/2 1/2; -1/2 1/2] [exp(4t) 0; 0 1] [1/2 -1/2; 1/2 1/2] [-1; -2]

=> [y z] = [1/2 1/2; -1/2 1/2] [exp(4t) 0; 0 1] [3/2; -1/2]

=> [y z] = [1/2 1/2; -1/2 1/2] [3/2exp(4t); -1/2]

=> [y z] = [3/2exp(4t)/2 - 1/2exp(-4t)/2; -3/2exp(4t)/2 - 1/2exp(-4t)/2]

Therefore, the solution to the system of differential equations with the given initial conditions is:

y(t) = 3/4exp(4t) - 1/4exp(-4t) - 1/2

z(t) = -3/4exp(4t) - 1/4exp(-4t) - 2

The probability of 12 successes in 30 trials with a 0.20 probability of success on a single trial is approximately 0.0139.

To find the probability of x successes in n trials with a probability p of success on a single trial, you can use the binomial probability formula:
P(x) = C(n, x) * (p^x) * ((1-p)^(n-x))
where C(n, x) is the number of combinations of n items taken x at a time.
In this case, n = 30, x = 12, and p = 0.20. Plug these values into the formula:
P(12) = C(30, 12) * (0.20^12) * ((1-0.20)^(30-12))
Calculate C(30, 12), which is the number of combinations of 30 items taken 12 at a time:
C(30, 12) = 30! / (12! * (30-12)!) = 86493225
Now, calculate the rest of the equation:
P(12) = 86493225 * (0.20^12) * (0.80^18) ≈ 0.0139

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According to a report by the U.S. Department of Agriculture, in 2019, 7.7% of head-of-household Americans were uncertain of having enough food to meet the needs of all the members of their household.

This is a slight increase from the previous year. It is important to note that food insecurity disproportionately affects certain groups, such as households with children, low-income households, and households headed by minorities. The COVID-19 pandemic has also had a significant impact on food insecurity rates in the United States.

In 2019, approximately 10.5% of head-of-household Americans were uncertain of having enough food to meet the needs of all members of their household. This statistic, also known as food insecurity, reflects the number of households that had difficulty at some point during the year providing enough food for all their members due to a lack of resources. It is essential to address this issue to ensure that all families have access to adequate nutrition and can lead healthy lives.

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a. The population of the city can be modeled using the exponential growth function:

y = 600(1 + 0.018)^x

with x being years from 0 to 10, where x = 0 corresponds to the year 2010. We can create a table to show the population for each year from 2010 to 2020:

(you can see above)

We can see from the table that the population of the city is increasing each year, and the rate of increase is accelerating. This is because the growth function is exponential, not linear. We know it is exponential because the function has a power of x in the exponent, which causes the rate of growth to increase over time. If the function were linear, the rate of growth would be constant.

b. To predict the population in 2025, we can use the same function with x = 15 (since 2025 is 15 years after 2010):

y = 600(1 + 0.018)^15

y ≈ 846.5 (in thousands)

Therefore, we can predict that the population of the city in 2025 will be approximately 846,500 citizens.

By using the model, the missing values that complete the expression include the following:

48 + 32 = 8(6 + 4).

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of big rectangle = L × B

48 = 8 × 6

Area of small rectangle = L × B

32 = 8 × 4

For the required expression, we have:

48 + 32 = 8(6 + 4).

80 = 8(10)

80 = 80

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

[tex]-\cos^2(x)+\sin(x)=1\implies -[1-\sin^2(x)]+\sin(x)=1 \\\\\\ \sin^2(x)+\sin(x)-2=0\implies [\sin(x)]^2+\sin(x)-2=0 \\\\\\ ( ~~ \sin(x)-1 ~~ )( ~~ \sin(x)+2 ~~ )=0 \\\\[-0.35em] ~\dotfill\\\\ \sin(x)-1=0\implies \sin(x)=1\implies x=\sin^{-1}(1)\implies x=\frac{\pi }{2}[/tex]

now, what's wrong with the 2nd factor? sin(x) + 2 = 0?

well, we can go ahead and make it sin(x) = -2, however, let's recall that sine is never less than -1 or even more than 1, so that's out of range for sine.

Answer:

316.78

Step-by-step explanation:

area of 360 circle = pi*radius*radius

area of 360 circle = pi*11*11

area of 360 circle = pi*11*11

area of 360 circle = 380.13

360/300 = 380.13/x

114039/360 = x

x=316.775

The sine function that matches the equation in the graph is given as follows:

y = 2sin(x) - 2.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The function varies between -4 and 0, for a difference of 4, hence the amplitude is given as follows:

A = 4/2

A = 2.

The function varies between -4 and 0, instead of between -2 and 2, for a vertical shift of -2, hence the coefficient C is given as follows:

C = -2.

The period of the function is of 2π, hence the coefficient B is given as follows:

B = 1.

Thus the function is:

y = 2sin(x) - 2.

The graph is given by the image presented at the end of the answer.

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Option D (9) is not a probability and is not a possible answer choice for a probability question.

To find the probability of the intersection of events A and B (denoted as P(A ∩ B)), we need to know how many elements are in both A and B. Since there are 2 repeated elements between the events, this means that there are a total of 7 - 2 = 5 distinct elements between them.

Therefore, P(A ∩ B) = 5/7.

Note that none of the answer choices provided match this result exactly. Option A is the closest with a probability of 4/7, but this is the probability of A alone, not the intersection of A and B. Option B (2/7) is the probability of B alone and option C (5/7) is the probability of either A or B occurring, not the intersection.

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Answer: 2.09

Step-by-step explanation: 0.85e^0.075(12)

The dimension of the board either 4 by 6 square inches or 6 by 4 square inches.

We know that,

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

here,

let the length of the board be x, and width be w,

The perimeter of the rectangle board  = 20

2 (l + w) = 20

l + w = 10

l = 10 - w

Now,

area of the board = 24

l × w = 24

(10 - w)w = 24

10w - w² = 24

w² -10w + 24 =0

(w - 4)(w -6) = 0

So,

w = 4 or 6

Now,

Lengths = 10 - 4 or 10 - 6

             =  6 or 4

Thus, the dimension of the board either 4 by 6 square inches or 6 by 4 square inches.

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The required, 4.5 × 10⁵ as an ordinary number is 450,000.

An ordinary number is a number that is expressed in the usual way, using digits 0-9 without any exponent notation or other mathematical symbols.

4.5 × 10⁵ means 4.5 multiplied by 10 raised to the power of 5. To write this as an ordinary number, we simply need to perform this multiplication:

4.5 × 10⁵ = 4.5 × 100,000 = 450,000

Therefore, 4.5 × 10⁵ as an ordinary number is 450,000.

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The correct answer is not listed in the options, so there might have been a mistake in the question or the choices provided. To find the fourth ordered pair using the two sequences, we need to apply each rule to the previous result, starting from the given starting points.

Using Rule 1, starting from 1:
- Multiply by 2: 1 x 2 = 2
- Add one third: 2 + (1/3) = 7/3
So the first term of the fourth ordered pair is 7/3.
Using Rule 2, starting from 0:
- Add one half: 0 + 1/2 = 1/2
- Multiply by 4: (1/2) x 4 = 2
So the second term of the fourth ordered pair is 2.
Therefore, the fourth ordered pair is (7/3, 2).

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1. The equation y + 3/4(y+30) = 478 can be used to find y, Elena's score in her first game. False

2. The difference between the score in Elena's first game and her second game is 34. True

3. The equation z/4y + 30 = 478 can be used to find y, Elena's score in her first game. False

4.  Elena's scores 222 in her first game

To find Elena's scores in the game, we used the equation:

x = 3/4y + 30 since x + y = 478

3/4y + 30 + y = 478

7/4y + 30 = 478

7/4y = 478 - 30 = 448

448 x 4 /7 = 256

It means that Elena's scored 256 in her first game and 222 in her second game.

The above answer is based on the questions below as seen in the picture

Elena bowls two games on Saturday. Her serve in the second game is 30 more than 3/4 of her score in the first game. Elena's total score for the two games is 478.

Determine with each statement about Elena's bowling games is true;

1 The equation y + 3/4(y+30) = 478 can be used to find y, Elena's score in her first game.

2. The difference between the score in Elena's first game and her second game is 34.

3. The equation z/4y + 30 = 478 can be used to find y, Elena's score in her first game.

4. Elena's scores 222 in her first game.

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x ≈ 0.625.

To solve the exponential equation 3 + 4^(4x-3) + 6 = 11, we first need to isolate the exponential term.

Subtracting 3 and 6 from both sides, we get:

4^(4x-3) = 2

To solve for x, we can take the natural logarithm of both sides:

ln(4^(4x-3)) = ln(2)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the left side:

(4x-3)ln(4) = ln(2)

Dividing both sides by ln(4), we get:

4x-3 = ln(2)/ln(4)

Simplifying the right side using a calculator, we get:

4x-3 ≈ -0.5

Adding 3 to both sides, we get:

4x ≈ 2.5

Dividing by 4, we get:

x ≈ 0.625

Therefore, the exact solution with natural logarithms is:

x = (ln(2)/ln(4) + 3)/4

And the approximate solution correct to three decimal places is:

x ≈ 0.625

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Based on the information provided, the researcher's hypothesis is that people who use their phones before bed get less sleep than the recommended 7 hours per night by the national sleep foundation.

The researcher samples 30 people who report using their phones immediately before bedtime and records their average hours of sleep per night. To test the hypothesis, a one-sample t-test is conducted to compare the number of hours of sleep the phone users get relative to the national sleep foundation recommendations.

The results of the t-test will indicate whether the average number of hours of sleep the phone users get is significantly different from the recommended 7 hours per night. If the results show that the phone users get significantly less sleep than the recommended amount, this could indicate a negative effect of phone use on sleep quality.
The researcher hypothesizes that people who use their phones before bed get less sleep than the National Sleep Foundation's recommendation of at least 7 hours per night for adults. A one-sample t-test is conducted to compare the average number of hours of sleep for a sample of 30 phone users against this recommended value. The test will help determine if there's a significant difference between the sleep duration of phone users and the recommended sleep duration.

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In this probability experiment, the sample space is S = {2,3,4,5,6,7,8,9,10,11,12,13). The event E is defined as E = {3,4,5,6). Assuming that each outcome is equally likely, we can list all the outcomes of the experiment as follows:

1. If we roll a 2, it is not included in event E, so the outcome is not included.
2. If we roll a 3, it is included in event E, so the outcome is included.
3. If we roll a 4, it is included in event E, so the outcome is included.
4. If we roll a 5, it is included in event E, so the outcome is included.
5. If we roll a 6, it is included in event E, so the outcome is included.
6. If we roll a 7, it is not included in event E, so the outcome is not included.
7. If we roll an 8, it is not included in event E, so the outcome is not included.
8. If we roll a 9, it is not included in event E, so the outcome is not included.
9. If we roll a 10, it is not included in event E, so the outcome is not included.
10. If we roll an 11, it is not included in event E, so the outcome is not included.
11. If we roll a 12, it is not included in event E, so the outcome is not included.
12. If we roll a 13, it is not included in event E, so the outcome is not included.

Therefore, the outcomes of the experiment that are included in event E are 3, 4, 5, and 6.

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