What is the area of this trapezoid? Enter your answer in the box. Ft²
Trapezoid with parallel sides labeled 13 feet and 31 feet. The dashed perpendicular
segment between them is labeled 16 feet

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{5x + 2 = 3}[/tex]

[tex]\large\textsf{SUBTRACT 2 to BOTH SIDES}[/tex]

[tex]\mathtt{5x + 2 - 2 = 3 - 2}[/tex]

[tex]\large\textsf{SIMPLIFY it}[/tex]

[tex]\mathtt{5x = 3 - 2}[/tex]

[tex]\mathtt{5x = 1}[/tex]

[tex]\large\textsf{DIVIDE 5 to BOTH SIDES}[/tex]

[tex]\mathtt{\dfrac{5x}{5} = \dfrac{1}{5}}[/tex]

[tex]\large\textsf{SIMPLIFY it}[/tex]

[tex]\mathtt{x = \dfrac{1}{5}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{x = \dfrac{1}{5}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: (x-y)

Step-by-step explanation:

To find the range you must subtract the largest number from the smallest.  

BODMAS rule, helps us to determine the value of expression. The expanded value of expression,

63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}], is equals to the 61.14.

Mathematical operations such as addition, subtraction, multiplication, and division are included in arithmetic operations. For solving expression according to specific priority, we use the BODMAS rule, which follows as

Now, we have an expression, 63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}] say x

=> x = 63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}]

we have to calculate value of x,

Using BODMAS rule,

=> x = 63 - [(- 3){- 13 }] ÷ [3{5 + 2}] (expands inner bracket)

=> x = 63 - [ 39 ] ÷ [3×7]

=> x = 63 - [ 39 ÷ 21]

=> x = 63/1 - 13/7

Taking least common multiple, (1,7) = 7

=> x = ( 63×7 - 13)/7

=> x = (441 - 13)/7 = 428/7

=> x = 61.14

Hence, value of expression is 61.14.

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The equation of the line is y = (-1/3)x + 2.

This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The place on the x-axis where the line crosses. This is the x-intercept of the linear function.

If the line is horizontal (and not the x-axis), the linear function will have no x-intercept.

Here, the line crosses the x-axis at 6.

The place on the y-axis where the line crosses. This is the y-intercept of the linear function

Here, the line crosses the y-axis at 2.

If a line crosses the x-axis at the point (6,0), it means that the line intersects the x-axis when the y-coordinate is 0 and the x-coordinate is 6. Similarly, if the line crosses the y-axis at the point (0,2), it means that the line intersects the y-axis when the x-coordinate is 0 and the y-coordinate is 2.

We can use these two points to find the equation of the line using the slope-intercept form:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope, we can use the two points (6,0) and (0,2):

m = (y2 - y1) / (x2 - x1)

m = (2 - 0) / (0 - 6)

m = -1/3

To find the y-intercept, we can use the point (0,2):

y = mx + b

2 = (-1/3)(0) + b

b = 2

Therefore, the equation of the line is y = (-1/3)x + 2.

This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.

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Based on the deliveries of each day, the total number of deliveries made by the drivers is 521.

In order to determine the total deliveries, add the number of deliveries for each day together.

The addition is determining the total value or summing two or more numbers. The addition is one of the four basic operations in mathematics. The other basic operations are subtraction, multiplication and division. The sign that represents addition is +.

Here is the complete question: To schedule enough drivers for an upcoming week. a local pizza shop manager recorded the number of deliveries each day from the previous week 38,54,44,61,97,103,124. What is the total number of deliveries?

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Carrying an ax in one's teeth is a dangerous and potentially deadly action.

The weight and sharpness of the ax could easily cause injury or even death if it were to slip or the individual were to lose their balance.

Additionally, carrying an ax in this manner would likely result in the person being unable to communicate effectively, as their mouth would be occupied and their ability to speak clearly would be hindered.

If someone were to attempt to carry an ax in their teeth, they would be risking their safety and potentially the safety of those around them.

It is not a recommended or advisable course of action, and anyone who witnessed such behavior should exercise caution and avoid interacting with the individual until the ax has been safely secured.

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The height of the balcony from which the ball was kicked is 40 feet.

A ball was kicked into the air from the balcony of an apartment building.

The height of the ball, in feet, can be represented by the equation y= -16t^2+24t +40

where t is the time in seconds since the ball was kicked and y is the height of the ball.

The equation to represent the height of the ball is given as:

y = -16t² + 24t + 40Where y represents the height of the ball in feet and t represents the time in seconds since the ball was kicked.

To find the height of the balcony from which the ball was kicked, we need to find the initial height of the ball.

That is when the ball is at the balcony of the apartment building.

This happens when t = 0.

Substituting t = 0 in the equation, we get:

y = -16(0)² + 24(0) + 40y = 40

Therefore, the height of the balcony from which the ball was kicked is 40 feet.

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cot⁻¹(-2.1) ≈ -1.068 radians

g⁻¹(f(4π)) = π/2.

When answering questions on the Brainly platform, it is important to be factually accurate, professional, and friendly. Additionally, it is important to be concise and not provide extraneous amounts of detail. Irrelevant parts of the question should be ignored, and any typos should be corrected as necessary. When answering a question, it is helpful to repeat the question in your answer to ensure that the answer is clear and understandable. A step-by-step explanation should be provided in your answer to help the student understand the solution. Finally, when using specific terms in your answer, it is important to define them and use them accurately.

Now, let's answer the given questions:

1. Use a calculator to find the approximate value of the expression.
cot−1(−2.1) cot−1(−2.1)≈
To find the approximate value of cot⁻¹(-2.1), we can use a calculator.
Using a calculator, we get:
cot⁻¹(-2.1) ≈ -1.068
Therefore, cot⁻¹(-2.1) ≈ -1.068 radians (rounded to two decimal places).

2. Let f(x)=sinx, −2π ≤ x ≤ 2π and g(x)=cosx, 0 ≤ x ≤ π. Find the exact value of the composite function.
g⁻¹(f(4π​)) g⁻¹(f(4π​))= (Simplify your answer, including any radicals. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)
We know that f(x) = sin(x) and g(x) = cos(x).
Therefore,
f(4π) = sin(4π) = 0
Now, we need to find g⁻¹(0).
Since g(x) = cos(x), we know that g⁻¹(x) = cos⁻¹(x).
Therefore, g⁻¹(0) = cos⁻¹(0)
We know that cos(π/2) = 0, so cos⁻¹(0) = π/2 or 90°.
Therefore, g⁻¹(f(4π)) = g⁻¹(0) = cos⁻¹(0) = π/2.
Thus, g⁻¹(f(4π)) = π/2.

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The object will be 6.1 m from the ground after 2 seconds.

The falling object model is used to calculate the height of an object after it has been dropped for a certain period of time. The equation used is h=h0−1/2gt2, where h0 is the initial height, g is the acceleration due to gravity and t is the time elapsed.

For example, if an object is dropped from a height of 15 m and falls for 2 seconds, we can calculate the height it will be at after 2 seconds.

The equation is then h=15−1/2(9.8)22

h=15−4.9•4

h=6.1 m

Therefore, the object will be 6.1 m from the ground after 2 seconds.

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The statement required to complete the proof is

            Statement                                        Reason

6 ∠ CDB and ∠ BDE are supplementary    If two angles form a linear pair,

                                                                      then they are supplementary

In geometry, a linear pair is a pair of adjacent angles formed by two intersecting lines. The angles in a linear pair are always supplementary, which means they add up to 180 degrees.

According to the proof,  

line 2 of the proof have it that ∠ BDE = ∠ BED

hence we say that ∠ CDB is congruent to ∠ AEB since they are supplementary to same angle

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Using trigonometric functions, the width of the volleyball court is approximately 31.13 meters.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The basic trigonometric functions are:

Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.

Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.

Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

We can use basic trigonometry to solve this problem.

Let's assume that the width of the volleyball court is "x" meters.

From the corner of the court to the opposite player, we have a right triangle with the following sides:

the adjacent side: x meters (since it is parallel to the court's sideline)

the opposite side: 18 meters (since it is perpendicular to the sideline)

the hypotenuse: we don't know it yet, but we can find it using the given angle.

We can use the tangent function to find the hypotenuse:

tan(30) = opposite / adjacent

tan(30) = 18 / x

Multiplying both sides by x:

x * tan(30) = 18

x = 18 / tan(30)

x = 18 / 0.5774

x ≈ 31.13 meters

Therefore, the width of the volleyball court is approximately 31.13 meters.

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the domain is D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and the range is R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}.

Why is it?

The graph shows all the possible test scores when there are only 10 equally weighed problems, and no partial credit is given. The domain represents all possible values of the independent variable, which in this case is the number of correct answers. The range represents all possible values of the dependent variable, which in this case is the score.

Looking at the graph, we can see that the domain consists of all non-negative integers from 0 to 10, inclusive. So the domain can be written as:

D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

On the other hand, the range consists of all possible scores, which range from 0 to 100. So the range can be written as:

R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}

Therefore, the domain is D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and the range is R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}.

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The column headings of a check register and the information that go in that location are:

A check register, also known as a cash disbursements journal, is where you record all of your company's check and cash transactions during an accounting period. A check register is used by businesses to calculate the running balance of their checking account.

A check register will usually show the checking account's running balance. It functions similarly to a real-time record of the bank account. The bookkeeper can ensure that the total bank balance and the check register are in sync.

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a.F=kx is the formula that expresses F as a function of x

b. k=F/x=8/0.3=26.67.

c.72.01 lbs

Hooke's law is a principle of physics that describes the elasticity of springs when stretched or compressed. The amount of stretch or compression of the spring is directly proportional to the force applied, according to the law.What is Hooke's Law and how can you express F as a function of x?Hooke's law is a principle of physics that describes the elasticity of springs when stretched or compressed. The amount of stretch or compression of the spring is directly proportional to the force applied, according to the law. F=kx is the formula that expresses F as a function of x using the constant of proportionality k.What is the value of k in part (a)?It is given that F=kx, and that the weight of 8 pounds stretches a spring from its natural length of 10.4 inches to a length of 10.7 inches. We have to find the value of k.8 pounds, according to Hooke's law, stretches the spring 10.7-10.4=0.3 inches from its natural length.Using F=kx, we can say that the force applied is 8 pounds, or F=8. Therefore, we have k=F/x=8/0.3=26.67.What weight will stretch the spring in part (b) to a length of 13.1 inches?We are given that the spring stretches from its natural length of 10.4 inches to a length of 13.1 inches. To find the force required to produce this extension, we need to subtract the natural length from the final length, as we did before.13.1-10.4=2.7 inches is the distance by which the spring will be stretched.The formula for F is still F=kx, and we know the value of k, which is 26.67. Thus, F=26.67*2.7=72.01 lbs.

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The directional angles of [tex]\vec u[/tex] are approximately 101.14° with respect to the x-axis, 164.08° with respect to the y-axis, and 82.46° with respect to the z-axis.

To find the directional angles of  [tex]\vec u[/tex] , we can use the following formula:

[tex]cos\theta = u_i / |u|[/tex]

where θ is the angle between the vector and the positive x, y, or z-axis, [tex]u_i[/tex]  is the x, y, or z-component of the vector, and |u| is the magnitude of the vector.

First, we can calculate the magnitude of [tex]\vec u[/tex]  as:

[tex]|u| = \sqrt{((-8)^2 + (-40)^2 + 7^2)} = \sqrt{(1749)[/tex]

Next, we can calculate the directional angles as:

[tex]cos\theta x = -8 / \sqrt{(1749)[/tex] ≈ [tex]-0.1939[/tex]

θx ≈ 101.14°

[tex]cos\theta y = -40 / \sqrt{(1749)[/tex] ≈ -0.9679

θy ≈ 164.08°

[tex]cos\theta z = 7 / \sqrt{(1749)[/tex] ≈ 0.1441

θz ≈ 82.46°

Therefore, the directional angles of [tex]\vec u[/tex] are approximately 101.14° with respect to the x-axis, 164.08° with respect to the y-axis, and 82.46° with respect to the z-axis.

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The complete question is :

Let [tex]\vec{u}= -8i -40j + 7k[/tex] be a vector in space. Calculate and give the directional angles of u in degrees.

The semicircle's radius is roughly 1.38 cm, and its perimeter is roughly 5.37 cm.

the perimeter of the semicircle is:

P = l + C(semi)

P = r + πr

P = (1 + π)r

P ≈ 5.37 cm

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.

from the question:

Let's start with finding the radius of the semicircle.

The formula for the area of a semicircle is:

A = (πr²)/2,

where A is the area and r is the radius.

We are informed that the semicircle's area is 6 [tex]cm^2[/tex]. So, we can enter this value into the formula and find r:

6 = (πr²)/2

Multiplying both sides by 2:

12 = πr²

Dividing both sides by π:

r² = 12/π

Taking the square root of both sides:

r = √(12/π)

Now we can simplify this expression by rationalizing the denominator:

r = √(12/π) * (√π/√π)

r = √(12π)/π

r ≈ 1.38 cm

Thus, the semicircle's radius is roughly 1.38 cm.

We must multiply the circumference of the semicircle by the length of the straight edge to determine the semicircle's perimeter. The formula for calculating a circle's circumference is:

C = 2πr

But for a semicircle, we only need half of the circumference:

C(semi) = πr

So the perimeter of the semicircle is:

P = l + C(semi)

P = r + πr

P = (1 + π)r

P ≈ 5.37 cm

As a result, the semicircle's radius is roughly 1.38 cm, and its perimeter is roughly 5.37 cm.

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The length of the rectangle is 10 inches and the rectangle is 10 inches long and 2 inches wide.

The total distance around the outside of the rectangle is termed as Perimeter of a rectangle. It is equal to the sum of the lengths of all four sides of the rectangle.

Let's assume that the width as "w" inches.

As per the problem statement, the length of the rectangle is 5 times its width, which means that the length is 5w inches.

The perimeter of a rectangle is :

P = 2(l + w)

Substituting the values, we get:

24 = 2(5w + w)

Simplifying the above equation, we get:

24 = 12w

Dividing both sides by 12, we get:

w = 2

So, the width of the rectangle is 2 inches.

The length is 5 times of width, that is:-

l = 5w = 5(2) = 10

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As per the unitary method, the amount saved by Aaron after one year is  $780

We can use the following formula to find out how much Aaron saves per month:

Amount saved per month = Total amount saved / Number of months

We can use this formula to find out how much Aaron saves per month for each period:

For the first period (3 months):

Amount saved per month = 195 / 3

= 65

For the second period (4 months):

Amount saved per month = 260 / 4

= 65

For the third period (6 months):

Amount saved per month = 390 / 6

= 65

For the fourth period (7 months):

Amount saved per month = 455 / 7

= 65

We can see that Aaron saves $65 per month, regardless of the time period. Therefore, we can use this value to find out how much he will save in one year (12 months):

Amount saved in 1 year = Amount saved per month x Number of months

= 65 x 12

= 780

Therefore, we can predict that Aaron will save $780 after one year.

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Answer:

C. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is a linear function.

B. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.

B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.

Step-by-step explanation:

Answer: Your welcome!

Step-by-step explanation:

1. Answer: D. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an exponential function. As time increases, the amount of water in the bucket will increase exponentially (each successive unit of time will add a multiple of the original amount).

2. A. The amount earned is described by a linear function. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.

3. Answer: B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.

An exponential function is one in which the value of a variable increases or decreases by a constant factor for each equal time interval. In this case, the balance of the savings account increases by a fixed amount of interest each month, which is calculated from the current balance. This amount is multiplied by the current balance, resulting in an exponential function.

The sampling distribution could be represented numerically as follows: P [tex]N(0.03, 0.027^2)[/tex]

A sample distribution is a statistical probability that is obtained by taking random samples from a certain population. It depicts the distribution of frequency on how dispersed certain outcomes will be for a particular population and is also referred to as a finite-sample distribution.

Since they enable you to comprehend a particular sample statistic in the context of other potential values, sampling distributions are crucial for inferential statistics. Importantly, they enable you to compute probabilities related to your sample.

σ [tex]=\sqrt{[p(1-p)/n]}[/tex]

where [tex]p[/tex] is the population proportion [tex](0.03)[/tex] , n is the sample size [tex](133)[/tex], and sqrt denotes the square root function.

Substituting in the values, we have:

σ [tex]=\sqrt{ [(0.03)(1-0.03)/133] ≈ 0.027}[/tex]

Since the sample size is large [tex](n = 133)[/tex] and the population proportion is not close to [tex]0[/tex] or [tex]1[/tex], we can use the normal distribution to approximate the sampling distribution of the sample proportion. The mean of the sampling distribution is equal to the population proportion [tex](0.03)[/tex]. Therefore, the distribution of the sample proportion of students drinking more than [tex]3[/tex] cups of coffee each day is approximately normal with a mean of [tex]0.03[/tex] and a standard deviation of [tex]0.027[/tex].

The notation for the sampling distribution can be written as follows:

P [tex]N(0.03, 0.027^2)[/tex]

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Answer:x = 10

Step-by-step explanation:

13+7=20

2 x 10 = 20

x=10

Answer:

x = 10

Step-by-step explanation:

[tex]2x-7=13[/tex]

First, add 7 to both sides.

[tex]2x-7 + 7=13 + 7[/tex]

This cancels the -7 on the left side because [tex]-7 + 7 = 0[/tex].

[tex]2x=20[/tex]

Then, we can divide both sides by 2 to isolate one multiple of x.

[tex]2x=20\\\overline{\ 2\ } \ \ \ \ \overline{\, 2 \: }[/tex]

[tex]\boxed{x = 10}[/tex]

Answer:

Step-by-ste10p explanation:

Answer:

I would say twv

Step-by-step explanation:

The least biased sampling strategy is D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.

Four new sampling strategies have been proposed to help PTV determine whether enough cable subscribers are likely to purchase high-speed Internet Service. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.A) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they would be interested. This type of sampling strategy is known as convenience sampling.

This technique is biased since only those who watch the local TV news and are interested in high-speed internet services can participate in the survey. The majority of the consumers who are in need of high-speed internet may not watch the local TV news. Hence the survey is biased and does not represent the entire population.B) Hold a meeting in each of the fifteen towns and tally the opinions expressed by those who attend the meetings. This type of sampling strategy is called a Quota sampling. It is biased since there is no guarantee that everyone will attend the meeting or that they will represent the opinions of the entire population.

This sampling strategy also has a higher risk of selection bias since the people who are likely to attend the meeting are the ones who are interested in the product.C) Randomly select one street in each town and contact each of the households on that street. This type of sampling strategy is called Cluster Sampling. This method is less biased compared to the other two strategies mentioned earlier. Since each street is chosen at random, there is a higher chance of getting opinions from a wider range of customers. However, this strategy can still be biased as the opinions may differ from one street to another.D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen. This type of sampling strategy is called Systematic Sampling.

This strategy is the least biased among the four strategies. Since customers are selected randomly, there is a higher chance of obtaining a representative sample. The opinions of customers who have discontinued the services are not included, and the survey can only be conducted with current customers. 

Hence, the least biased sampling strategy is D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.

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A. Using similar triangles, Slope of AB = Slope of AC = 42

B. The y-intercepts = 63; Slope = 42

The slope of a graph refers to the measure of the steepness of a line or a curve on a graph, calculated as the ratio of the vertical change (rise) between two points on the line to the corresponding horizontal change (run). In other words, it represents how much the y-axis changes for a given change in the x-axis.

A. Using similar triangles, we have the following:

Slope of AB = 147 - 105 / 2 -1 = 42/1

= 42

Slope of AC = 147 - 63 / 2 - 0 = 84/2

= 42

B. The line intercepts the y-axis at 63, therefore, the y-intercept is 63.

Slope of the graph is 42.

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Solution is in da attachment!! :D

Answer:

Assuming an ideal pulley system, the force required to lift a 10 Newton box with one pulley would be 10 Newtons. This is because the force required to lift an object using a pulley system is equal to the weight of the object being lifted. In an ideal pulley system, there is no friction or energy loss, so the force required is equal to the weight of the object. Therefore, if the weight of the box is 10 Newtons, a force of 10 Newtons would be required to lift it with one pulley.

Population parameters are the real values of the variance, mean, and standard deviation of a population. These parameters are often unknown but can be estimated from a sample of the population.

When conducting a survey, it is important to select participants in a way that avoids bias and represents the population as accurately as possible. Simple random selection, in which individuals are selected randomly and every individual has an equal chance of being selected, is one way to achieve this.

Deviation score is the difference between an individual score and the mean of the population or sample. In this case, the deviation score for X = 45 in a population with a mean of 50 is -5.

In systematic sampling, every Kth member of the population is selected, making it a more efficient way of sampling compared to random sampling, but it requires that the population is well-ordered and homogeneous.

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