Can someone please help with these 4

Answer:

Step-by-step explanation:

Sure! Here's a number line showing the distance of 0.75 kilometers:

0 -------------|-------------|------------- 0.75 km

The "0" on the left represents the starting point (such as home), and the "|---|" in the middle represents the distance of 0.75 kilometers to the destination (such as school).

Answer:

--------------------------

Find the prime factors of 1352:

We need another factor of 2 as a minimum added in order to have even number of same factors:

Hence we need to multiply the given number by 2.

If we total up the dots plot for 3, 4, and 5 pets, we find that 3 people have 2 pets at home, 10 individuals have at least 3 pets at home.

The fact that dogs are the most common pet in the world shouldn't be shocking. There is a reason why there are tens of millions of dogs living in the United States alone, which is why some people say that dogs are a man's greatest friend. Around the world, at least one dog is kept in one-third of all households.

A fully domesticated animal kept constitutes a "household pet." a pet kept by you for personal company, like a dog, cat, reptile, bird, or mouse. Any kind of horse, cow, pig, sheep, goat, chicken, turkey, other captive fur-bearing animal is not considered a household pet, nor is any animal that is typically kept for food or profit.

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The total number of people with pets at home is 11, which is the sum of the heights of the columns.

What is equation?

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.

Based on the given dot plot, we can answer the following questions:

How many people have 2 pets at home?

Answer: Two people have 2 pets at home, as indicated by the two dots in the second column.

How many people have at least 3 pets at home?

Answer: Six people have at least 3 pets at home, as indicated by the dots in the third column and beyond.

How many more people have 2 pets than 5 pets?

Answer: There are no dots in the last column, which represents 5 pets. Therefore, the difference between the number of people with 2 pets and those with 5 pets is 2 - 0 = 2.

How many people have less than 3 pets at home?

Answer: Three people have less than 3 pets at home, as indicated by the dots in the first two columns.

Therefore, the total number of people with pets at home is 11, which is the sum of the heights of the columns.

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Answer:

0 and 180 degrees.

Step-by-step explanation:

We can start by using a trigonometric identity to rewrite sin2x in terms of cos2x:

sin2x = 1 - cos2x

Substituting this into the given equation, we get:

cos2x = 1 + (1 - cos2x)

Simplifying this equation, we get:

2cos2x = 2

Dividing both sides by 2, we get:

cos2x = 1

Solving for x, we get:

2x = 0°, 360°x = 0°, 180°

Therefore, the solutions to the equation cos2x = 1 + sin2x in the interval 0° ≤ x ≤ 360° are x = 0° and x = 180°.

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Let X and Y be independent random variables, uniformly distributed in the interval [0, 1 ]. The CDF of X - Y is FZ(z) = (1/2)(1+z)^2 for -1 ≤ z ≤ 0, 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1, 0 for z < -1 or z > 1. The PDF of X - Y is fZ(z) = z + 1 for -1 < z < 0, 1 - z for 0 < z < 1, 0 otherwise.

To find the CDF of X - Y, we first note that the range of X - Y is [0, 1]. Let Z = X - Y, then:

FZ(z) = P(Z ≤ z) = P(X - Y ≤ z)

We can write this as an integral over the joint distribution of X and Y:

FZ(z) = ∫∫[X - Y ≤ z] fXY(x, y) dx dy

Since X and Y are independent, the joint distribution is simply the product of their marginal distributions:

fXY(x, y) = fX(x) fY(y) = 1 * 1 = 1

for 0 ≤ x, y ≤ 1.

Thus, we have:

FZ(z) = ∫∫[X - Y ≤ z] dx dy

= ∫∫[Y ≤ X - z] dx dy

= ∫0^1 ∫0^(x-z) 1 dy dx + ∫0^1 ∫(x-z)^1 1 dy dx

= ∫0^(1+z) (1-z) dx

= (1/2)(1+z)^2 for -1 ≤ z ≤ 0

= 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

Therefore, the CDF of X - Y is:

FZ(z) =

(1/2)(1+z)^2 for -1 ≤ z ≤ 0

1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

0 for z < -1 or z > 1

To find the PDF of X - Y, we differentiate the CDF:

fZ(z) = dFZ(z)/dz =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

Therefore, the PDF of X - Y is:

fZ(z) =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

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Answer:

Step-by-step explanation:

First the max degree is 360

Then multiply by 5/8

360 x 5/8 = 1800/8

1800/8 = 225

Answer: 225

Answer:

N and E is 90 degrees

N and S is 180 degrees

N and W is 90 degrees

The Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :

[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]

What do you mean by Taylor's series ?

The Taylor's series is a way to represent a function as a power series, which is a sum of terms involving the variable raised to increasing powers. The series is centered around a specific point, called the center of the series. The Taylor's series approximates the function within a certain interval around the center point.

The general formula for the Taylor's series of a function f(x) centered at [tex]x = a[/tex] is:

[tex]f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...[/tex]

where [tex]f'(a), f''(a), f'''(a),[/tex] etc. are the derivatives of f(x) evaluated at [tex]x = a[/tex].

Finding the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] :

We need to find the derivatives of the function at [tex]x=0[/tex]. We have:

[tex]f(x) = 1 + 3e^x + x^2[/tex]

[tex]f(0) = 1 + 3e^0 + 0^2 = 4[/tex]

[tex]f'(x) = 3e^x+ 2x[/tex]

[tex]f'(0) = 3e^0 + 2(0) = 3[/tex]

[tex]f''(x) = 3e^x + 2[/tex]

[tex]f''(0) = 3e^0 + 2 = 5[/tex]

[tex]f'''(x) = 3e^x[/tex]

[tex]f'''(0) = 3e^0 = 3[/tex]

Substituting these values into the general formula for the Taylor's series, we get:

[tex]f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...[/tex]

[tex]f(x) = 4 + 3x + 5x^2/2 + 3x^3/6 + ...[/tex]

Simplifying, we get:

[tex]f(x) = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]

Therefore, the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :

[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]

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Answer:

1 - [tex]\frac{2\sqrt{2} }{3}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{3}-\sqrt{6} }{\sqrt{3}+\sqrt{6} }[/tex]

rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

the conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{6}[/tex]

= [tex]\frac{(\sqrt{3}-\sqrt{6})(\sqrt{3}-\sqrt{6}) }{(\sqrt{3}+\sqrt{6})(\sqrt{3}-\sqrt{6}) }[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{3-\sqrt{18}-\sqrt{18}+6 }{3-\sqrt{18}+\sqrt{18}+6 }[/tex]

= [tex]\frac{9-2\sqrt{18} }{3+6}[/tex]

= [tex]\frac{9-2(3\sqrt{2}) }{9}[/tex]

= [tex]\frac{9-6\sqrt{2} }{9}[/tex]

= [tex]\frac{9}{9}[/tex] - [tex]\frac{6\sqrt{2} }{9}[/tex]

= 1 - [tex]\frac{2\sqrt{2} }{3}[/tex]

The Dcpromo wizard will guide you through e. All of the above installation scenarios

A utility in Active Directory called DCPromo (Domain Controller Promoter) installs and uninstalls Active Directory Domain Services and promotes domain controllers. Since Windows 2000, every version of Windows Server contains DCPromo, which creates forests and domains in Active Directory. It works with Windows Server and houses all network resources as a centralised security management solution.

The functionality aids in building a completely new forest structure. It allows for both the addition of a new domain tree to an existing forest and the addition of a child domain to an existing domain. Additionally, it degrades the domain controllers and ultimately deletes a domain or forest.

Complete Question:

The dcpromo wizard will guide you through which of the following installation scenarios? [check all that apply]

Creating an entirely new forest structure.

Adding a child domain to an existing domain.

Adding a new domain tree to an existing forest.

Demoting domain controllers and eventually removing a domain or forest

All of the above

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Answer:

56

90

56

Step-by-step explanation:

easy easy lol.

aaaaa

The area of the enlarged logo will be 9 times larger than the original logo.

When an object is enlarged or scaled up how does it area change ?

When an object is enlarged or scaled up by a factor of [tex]k[/tex], both its length and width are multiplied by [tex]k[/tex]. Therefore, the new length is [tex]k[/tex] times the original length, and the new width is [tex]k[/tex] times the original width.

The area of the new object is the product of the new length and width, which is ([tex]k[/tex] times the original length) multiplied by ([tex]k[/tex] times the original width), or [tex]k^2[/tex] times the original area.

Therefore, the area of an object increases by a factor of [tex]k^2[/tex] when the object is enlarged or scaled up by a factor of [tex]k[/tex].

Calculating how many times larger the area of the enlarged logo will be :

The original logo has dimensions of 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches.

Mr. James wants to enlarge the logo so that the dimensions are 3 times larger than the original. This means the new dimensions will be 9 inches by 15 inches.

To determine how many times larger the area of the enlarged logo will be, we need to compare the areas of the original logo and the enlarged logo. The area of the enlarged logo is 9 x 15 = 135 square inches.

To find out how many times larger the area of the enlarged logo is compared to the original logo, we divide the area of the enlarged logo by the area of the original logo:

135 square inches ÷ 15 square inches = 9

Therefore, the area of the enlarged logo will be 9 times larger than the area of the original logo.

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The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.

This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.

Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.

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Complete question is:

Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)

50

An error

80

70

100

The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.

We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.

A parabola with a vertex at (1,3) and an opening downhill is depicted by the equation.

A parabola is an equation of a curve with a spot on it that is equally spaced from a fixed point and a fixed line.

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical plane circle. The same curves can be defined by a number of apparently unrelated mathematical descriptions, which all correspond to it. A point and a line can be used to depict a parabola.

Equation given: 3x² - 6x + 4y - 9 = 0. When the given equation's graph is plotted, it is discovered that the parabola that is created is opened downward and has a vertex at the spot. ( 1,3). The graph and the following response are attached.

The equation that depicts a parabola with a vertex at (1,3) opening downward is option C, making it the right choice.

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Answer:

Parabola with a vertex at (1, 3) opening downward.

Step-by-step explanation:

Answer:The specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius (or Kelvin).

To find the specific heat of the unknown substance, we can use the following equation:

Q = m x c x ΔT

where Q is the heat gained or lost, m is the mass of the substance, c is its specific heat, and ΔT is the change in temperature.

In this problem, we know the mass and initial and final temperatures of both the unknown substance and the water, as well as the specific heat of water. We can use this information to calculate the heat gained by the water, which must be equal to the heat lost by the unknown substance:

Heat gained by water = Heat lost by unknown substance

m(water) x c(water) x ΔT(water) = m(substance) x c(substance) x ΔT(substance)

We can plug in the values we know and solve for the specific heat of the unknown substance:

m(water) = 75.0 g

c(water) = 4.18 J/g°C

ΔT(water) = 27.1 °C - 20.00 °C = 7.1 °C

m(substance) = 100.0 g

ΔT(substance) = 200.0 °C - 27.1 °C = 172.9 °C

75.0 g x 4.18 J/g°C x 7.1 °C = 100.0 g x c(substance) x 172.9 °C

Simplifying this equation, we get:

c(substance) = (75.0 g x 4.18 J/g°C x 7.1 °C) / (100.0 g x 172.9 °C)

c(substance) = 0.197 J/g°C

Therefore, the specific heat of the unknown substance is 0.197 J/g°C.

Step-by-step explanation:

Answer:

The specific heat of the unknown substance is 0.39 J/g°C.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of energy, which states that the heat lost by the unknown substance is equal to the heat gained by the water and the calorimeter. We can express this principle mathematically as:

Q_lost = Q_gained

where Q_lost is the heat lost by the unknown substance, and Q_gained is the heat gained by the water and calorimeter.

We can calculate Q_lost using the formula:

Q_lost = m × c × ΔT

where m is the mass of the unknown substance, c is its specific heat, and ΔT is the change in temperature it undergoes.

We can calculate Q_gained using the formula:

Q_gained = (m_water + m_calorimeter) × c_water × ΔT

where m_water is the mass of the water, m_calorimeter is the mass of the calorimeter, c_water is the specific heat of water, and ΔT is the change in temperature of the water and calorimeter.

Since the system reaches an equilibrium temperature, we can set Q_lost equal to Q_gained and solve for the specific heat of the unknown substance (c).

Here's the calculation:

Q_lost = Q_gained

m × c × ΔT = (m_water + m_calorimeter) × c_water × ΔT

100.0 g × c × (200.0 °C - 27.1 °C) = (75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)

Simplifying:

c = [(75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)] / (100.0 g × (200.0 °C - 27.1 °C))

c = 0.39 J/g°C

Therefore, the specific heat of the unknown substance is 0.39 J/g°C.

Answer: x = 5 and x = 1.

Step-by-step explanation:

To solve fg(x) = gf(x), we need to find the expressions for fg(x) and gf(x) and then set them equal to each other.

fg(x) = f(g(x)) = f(x² + 2) = 2(x² + 2) - 3 = 2x² + 1

gf(x) = g(f(x)) = g(2x - 3) = (2x - 3)² + 2 = 4x² - 12x + 11

Now we set fg(x) equal to gf(x) and solve for x:

2x² + 1 = 4x² - 12x + 11

2x² - 12x + 10 = 0

Dividing both sides by 2 gives:

x² - 6x + 5 = 0

This quadratic equation factors as:

(x - 5)(x - 1) = 0

So the solutions are x = 5 and x = 1.

Therefore, the solutions to fg(x) = gf(x) are x = 5 and x = 1.

A vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the null space. The orthogonal vector is :

A = [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]

The orthogonal complement of the subspace V contains any vector perpendicular to V. This orthogonal subspace is denoted V⊥. (pronounced "V perp").

By this definition, null space is the orthogonal complement of row space. Every x perpendicular to the line satisfies Ax = 0 and lies in null space.

vice versa. If v is orthogonal to null space, it must be in row space. Otherwise, we can add this v as an extra row of the matrix without changing its null space. The rice space will become larger, breaking the rule of r+(n−r) = n.

The column space extent of A. These two vectors are the basis of col(A) , but they are not normalized.

In this case, the columns of A are already orthonormal, so you don't need to use the Gram-Schmidt procedure. To normalize a vector and then divide it by its norm:

                   [tex]\left[\begin{array}{ccc}1&2&1\\2&4&3\\3&6&4\end{array}\right][/tex]

and the vector after orthogonal process is:

                  [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]

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(a) The country will first experience shortages of food in approximately 26.6 years

(b) If the country doubled its initial food supply and maintained a constant rate of increase in the supply, shortages would still occur in approximately 38 years.

(c) If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, shortages would still occur in approximately 55.4 years.

a. Let P(t) be the population of the country at time t (in years), and F(t) be the food supply of the country at time t.

We know that P(0) = 4 million, and P'(t) = 0.05P(t), which means that the population is increasing by 5% per year.

We also know that F(0) = 8 million, and F'(t) = 0.25 million, which means that the food supply is increasing by 0.25 million people per year.

When the food supply is just enough to feed the population, we have P(t) = F(t), so we can solve for t as follows:

4 million x (1 + 0.05)^t = 8 million + 0.25 million x t

[tex]4(1 + 0.05)^t = 8 + 0.25t\\\\t \approx 26.6 \ years[/tex]

b. If the country doubled its initial food supply, then F(0) = 16 million. We can use the same equation as before and solve for t:

4 million x  (1 + 0.05)^t = 16 million + 0.25 million x t

[tex]4(1 + 0.05)^t = 16 + 0.25t\\\\t \approx 38 \ years[/tex]

c. If the country doubled the rate at which its food supply increases and doubled its initial food supply, then we have F(0) = 16 million and F'(t) = 0.5 million. Using the same equation as before, we get:

4 million x  (1 + 0.05)^t = 32 million + 0.5 million x t

[tex]4(1 + 0.05)^t = 32 + 0.5t\\\\t \approx 55.4 \ years[/tex]

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The discount rate that should be applied to a new project's cash flows is the Weighted Average Cost of Capital (WACC). To calculate WACC, you need to first calculate the cost of debt. This is done by taking the face value of the bonds ($1000) multiplied by the coupon rate (8%) multiplied by (1 - the tax rate (26%)), which equals 5.92%. The cost of debt is then calculated by taking the market value of the debt (6,380 x $1,000 x 99.1%) and dividing this by the total market value of the debt plus the market value of the equity (6,380 x $1,000 x 99.1% + 76,650 x $50 + 14,250 x $80), which equals 5.22%.

Next, you need to calculate the cost of equity using the Capital Asset Pricing Model (CAPM). This is done by taking the risk-free rate (3.21%) plus the market risk premium (9.79%) multiplied by the firm's beta (1.47), which equals 17.18%.

The WACC is then calculated by taking the cost of equity multiplied by the proportion of equity (76,650 x $50 + 14,250 x $80 divided by the total market value of the debt plus the market value of the equity) plus the cost of debt multiplied by the proportion of debt (6,380 x $1,000

Answer:

m = 1

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-1,0) (0,1)

We see the y increase by 1 and the x increase by 1, so the slope is

m = 1

Answer:

The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.

Answer:

The area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.

Step-by-step explanation:

A semicircle is a two-dimensional shape that is exactly half of a circle.

The area of a circle is given by the formula:

[tex]\sf A=\pi r^2[/tex]

where A is the area of the circle, and r is the radius of the circle.

The diameter of a circle is twice its radius.

Given the diameter of the semicircle is 28 cm, the radius is:

[tex]\sf r = \dfrac{28}{2} = 14 \; cm[/tex]

Substituting this into the formula for the area of a circle, we get:

[tex]\sf A = \pi(14)^2[/tex]

[tex]\sf A = 196 \pi[/tex]

Finally, divide this by two to get the area of the semicircle:

[tex]\sf Area\;of\;semicircle = \dfrac{1}{2} \cdot 196 \pi[/tex]

[tex]\sf Area\;of\;semicircle = 98 \pi\; cm^2[/tex]

So the area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.

Answer:

The total labor charges for the job are P3,500.

Step-by-step explanation:

To find the total labor charges for a job that takes 2 1/2 hours, we need to look at the labor charges for each hour and a half-hour fraction and add them up.

For the first hour, the charges are P1,200. For the second hour, the charges are P1,400. For the third hour (the half-hour fraction), the charges are P1,800 / 2 = P900.

So, the total labor charges for 2 1/2 hours of work are

P1,200 + P1,400 + P900 = P3,500

Therefore, the total labor charges for the job are P3,500.

Thus, the rectangular fence has a 15-meter width.

We must determine the fence's length. The equation A=lw, where l seems to be the length & w is the width, determines the surface area A of a rectangle.

Let the variable "w" stand in for the rectangular fence's width.

We are aware that the fence's perimeter measures 54 metres in total.

Since a rectangle's opposite sides are identical in length and the fence contains four sides, we may write the following equation to get the perimeter:

(Length + Width)2 = the perimeter

Inputting the values provided yields:

54 = 2(12 + w)

After simplifying and finding "w," we arrive at:

54 = 24 + 2w

2w = 30

w = 15

Hence, the rectangular fence's width is 15 meters.

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It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.

X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.

X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.

Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.

Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.

The expected value of X is E[X] = np = 35(20/50) = 14.

The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.

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The approximate probability that more than 10% of the sample would report that they experienced extreme levels of stress during the past month, obtained using the z-score for the proportion of the sample, and the standard error, is about 96.327%

The z-score of a sample proportion, z can be obtained using the formula;

z = (p - π)/√(π·(1 - π)/n)

Where;

p = The sample proportion

π = The proportion of the population

n = The sample size

The percentage of the students out of the 1750 students that experienced extreme levels of stress in the school, p = 15%

The number of students in the sample used by the newspaper, n = 160 students

The number of students in the sample that replied "yes" = 10%

The true proportion of the students that experience stress = 15%

The probability that ,more than 10% of the sample would report that they experienced extreme levels of stress during the past month can be found as follows;

The standard error is; SE = √(p × (1 - p)/n)

Therefore;

SE = √(0.15 × (1 - 0.15)/160) ≈ 0.028

The z-score is therefore;

z = (0.1 - 0.15)/0.028 ≈ -1.79

z = -1.79

The z-score indicates the number of standard deviations the proportion of the sample is from the true proportion

The proportion on the of the sample which is larger than 10% is obtained from the area under the normal curve, to the right of the z-score of -1.79, which is obtained as follows;

The z-value at z = -1.79 is 0.03673, which indicates that the area to the left of the z-value is 0.03673, and the area to the right is; (1 - 0.03673) = 0.96327

The probability observing a sample proportion more than 10% if the actual proportion is 15% is therefore; 0.96327 = 96.327%

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As a result, the probability that the average battery life exceeds 553.9 minutes is 0.0262 (or 2.62%). The answer, rounded to four decimal places, is 0.0262.

Probability serves as an indicator of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies happenings rather than their properties. It is applied in many fields, including statistics, fund, science, and engineering.

The central limit theorem can be used to approximate the sample mean distribution as a normal distribution with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size.

The standard error of the mean (SE) is calculated as follows:

SE = σ/√n

Where n is the sample size and is the population standard deviation.

SE = 83/√160 = 6.575

Z = (X - μ) / SE

Where X represents the sample mean, is the population mean, and SE represents the standard error of the mean.

Z = (553.9 - 541) / 6.575 = 1.94

As a result, the probability that the average battery life exceeds 553.9 minutes is 0.0262 (or 2.62%). The answer, rounded to four decimal places, is 0.0262.

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