Find the sum of and .2푥+1

⇒First take out the highest common factor 2 form the quadratic equation and divide each and every term of that equation by that common factor.

⇒Factorise the equation and equate the factors of the equation to 0 and solve for the unknown variable x.

⇒Below are the steps on solving for the unknown variable.

[tex]2(x^{2} -14x+49)=0 \\\frac{2(x^{2} -14x+49)}{2} =\frac{0}{2} \\x^{2} -14x+49=0\\(x-7)(x-7)=0\\x-7=0\\x=7[/tex]

Answer:

Eighty biscuits.

Step-by-step explanation:

We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits

[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]

We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.

[tex]Biscuits=4*20=80[/tex]

Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.

[tex]Flour:\\1000-4(180) = 280g[/tex]

After making 4 servings we still have 280g of flour left.

If we repeated a hypothesis test 1000 times, the number of times we would expect to commit a Type I error, assuming the null hypothesis were true, would depend on the significance level (α) of the test.

A Type I error occurs when we reject the null hypothesis when it is actually true. The significance level of a test (α) is the probability of making a Type I error when the null hypothesis is true. In other words, if we set a significance level of α = 0.05, we are saying that we are willing to tolerate a 5% chance of making a Type I error.

Assuming a significance level of α = 0.05, if we repeated the test 1000 times, we would expect to make a Type I error in approximately 50 tests (0.05 x 1000 = 50). This means that in 50 out of the 1000 tests, we would reject the null hypothesis even though it is actually true.

However, it is important to note that the actual number of Type I errors we make in practice may differ from our expectation, as it depends on the specific characteristics of the population being tested and the sample sizes used in each test.

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The equations without absolute value for the given conditions are: 1. y = -3x + 6 if x > 5; 2. y = -x - 6 if x < -2; 3. y = x - 6 if 3 ≤ x ≤ 5, and y = -x - 6 if x < 3.

1. When x > 5, the expression (x - 3) is positive, (x + 2) is positive, and (x - 5) is positive. Thus, to get absolute value we can rewrite the equation as:

y = (x - 3) + (x + 2) - (x - 5)

Simplifying this, we get:

y = 2x - 4

2. When x < -2, the expression (x - 3) is negative, (x + 2) is negative, and (x - 5) is negative. Thus, we can rewrite the equation as:

y = -(x - 3) - (x + 2) + (x - 5)

Simplifying this, we get:

y = -2x + 6

3. When -2 ≤ x ≤ 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is negative. Thus, we can rewrite the equation as:

y = -(x - 3) + (x + 2) - (x - 5)

Simplifying this, we get:

y = 10 - x

When x > 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is positive. Thus, we can rewrite the equation as:

y = -(x - 3) + (x + 2) + (x - 5)

Simplifying this, we get:

y = -2x + 6

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250 is the total surface area of the solid.

How do you determine surface area?

The whole surface of a three-dimensional form is referred to as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face.

                         Instead, you may write out the cuboid's length, width, and height and apply the formula surface area (SA)=2lw+2lh+2hw.

Each side of a cube with side length = 5  has an area of 25; the overall area is 6 x 25 = 150

A cube with sides of length 5 has an area of 25 on each side, making its overall area 6 x 25 or 150.

Both have a combined area of 150 + 150 = 300

300 - 25 - 25 = 250 is the result from each of the two cubes.

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Answer:

z = 32°

vertical angles are equal to each other. 32° ≅ z°

Answer:

No, q=15 is not a solution to the inequality.

Step-by-step explanation:

As given, q=15. So, substituting is the best way to solve this problem.

Step 1: Substitute

[tex]\frac{15}{5}=3[/tex]

[tex]15-20=-5[/tex]

Step 2: Substitute values into inequality

[tex]3 < -5[/tex]

Equation is false since 3 is a bigger value than -5.

Hope this helps ya!

Answer:

Step-by-step explanation:

The composite function (f + g)(3) when evaluated from f(x) = −3x² + 3x and g(x) = 2x+5 is -7

Given that

f(x) = −3x² + 3x and

g(x) = 2x+5

To perform the operation (ƒ + g)(3), we need to add the functions ƒ(x) and g(x) first, and then evaluate the sum at x = 3.

ƒ(x) = −3x² + 3x

g(x) = 2x + 5

To add the functions, we simply add their corresponding terms:

(ƒ + g)(x) = ƒ(x) + g(x) = (−3x² + 3x) + (2x + 5)

When the like terms are evaluated, we have

(ƒ + g)(3) = −3x² + 5x + 5

Now, we can evaluate the sum at x = 3:

(ƒ + g)(3) = −3(3)² + 5(3) + 5

So, we have

(ƒ + g)(3) = −27 + 15 + 5

Lastly, we have

(ƒ + g)(3) = -7

Therefore, (ƒ + g)(3) = -7.

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As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.

given

The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.

To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.

As a result, we have:

sin 30° = (6/2x)

Adding two times to both sides:

2x * sin 30° = 6

Using sin 30°, which has a value of 0.5:

x = (6/(2 * 0.5)) = 6/1 = 6

Consequently, the side YZ is 6 units long.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

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The answer to subtracting the two polynomials is 2x2 - 10x - 7.  The process of subtracting polynomials is like that of subtracting any other type of numerical expression.

Polynomials are mathematical expressions consisting of variables, coefficients, and exponents. They are used to represent a variety of functions, such as polynomial equations, rational equations, and trigonometric functions.

In this case, our like terms are 2x2 and 4x2, and -6x and -4x, and -4 and +3. We begin by subtracting the coefficients of the like terms. We subtract the coefficient of the term with the highest power first. In this case, that is 2x2 and 4x2, we subtract 2 from 4 to get 2. Next, we subtract the coefficients of the terms with the second highest power. This is -6x and -4x, so we subtract -6 from -4 to get -2. Thus, our answer now reads 2x2 -2x.

Finally, we subtract the coefficients of the terms with the lowest power. This is -4 and +3, so we subtract -4 from 3 to get -7. Thus, our answer now reads 2x2 -2x -7.

This answer can then be placed in the proper position on the grid.

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The value of x given the following image is 13.

What is congruent angle?

When two angles have the same magnitude, they are considered congruent. In other words, they have the same angle degree. For example, if one angle measures 45 degrees, any other angle that also measures 45 degrees is congruent to it.

Congruent angles are denoted by the symbol ≅. So, if angle A and angle B have the same measure, we can write it as:

Angle A ≅ Angle B

Congruent angles have the same properties and characteristics, including being able to fit into the same spaces and be formed by the same geometric shapes. In practical terms, congruent angles are identical when placed side by side.

Finding the value of x :

Angle ABC and Angle EBD are congruent.

Value of Angle ABC is (-3x+14) degrees.

Value of Angle EBD is (-x-12) degrees.

Equating the two angles we get ,

[tex]-3x+14=-x-12[/tex]

[tex]-2x=-26[/tex]

[tex]2x=26[/tex]

[tex]x=13[/tex]

Therefore, the value of x given the following image is 13.

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Samantha would fill in the following information on the survey sheet based on the data provided:

Sex: Female

Age: 13-14

How much pressure do you feel to achieve at school? c. A lot

Samantha, a 14-year-old girl, would complete the survey slip by selecting "Female" under "Sex," "13-14" under "Age," and "A lot" under "How much pressure do you feel to achieve at school?"

This indicates that Samantha is feeling a significant amount of pressure to succeed academically. It's common for high school students to feel pressure to perform well in school, and this can be due to various factors such as parental expectations, college aspirations, or personal goals.

As a school counselor, it's essential to understand the level of pressure students are experiencing to provide appropriate support and guidance. Identifying and addressing the sources of pressure can help students like Samantha better manage stress and achieve academic success.

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The question is -

A school counselor conducted a survey among a group of high school students using the following survey slip:

Survey (please tick the correct boxes)

Sex:  Male  Female

Age:  13-14  15 -16  17–18

How much pressure do you feel to achieve at school?

a. None b. A little c. A lot  And d. the unbearable amount

Show, by completing the survey slip on the answer sheet, how Samantha – a 14-year-old girl who feels a lot of pressure to achieve at school – would complete the survey

The angle of elevation of the sun is 38.24 degrees (rounded to two decimal places).

The ratio of the height of the tree and the length of the shadow can be found by using the formula for tan which is given by:

tan(x) = (opposite/hypotenuse)

In the given problem statement, the height of the tree is opposite to the angle we are trying to find and the length of the shadow is the hypotenuse of the right-angled triangle. Therefore, we can say that:

tan(x) = opposite/hypotenuse = 86/110

We can use the inverse tangent function to find the value of x. This is because tan is the ratio of the opposite side (height of the tree) to the adjacent side (length of the shadow), and the inverse tangent function gives the angle that has that ratio.

So, tan x = 86/110 => x = tan⁻¹ (86/110) = 38.24 degrees (rounded to two decimal places). Therefore, the angle of elevation of the sun is 38.24 degrees.

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A minimum score of 88.95 is required to receive an "A" grade on the exam.

To determine the minimum score required to receive an "A" grade on an exam, we must first understand the meaning of standard deviation and mean. The mean is the average of a set of values, whereas the standard deviation is a measure of how far apart the values are from the mean. The minimum score required to receive an "A" grade is determined by calculating the z-score that corresponds to the top 12.3 percent of exam scores.

The formula for calculating the z-score is given as: z = (x - μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. Solving for z, we have: z = invNorm(1 - 0.123) = invNorm(0.877) ≈ 1.15. The inverse normal distribution function is used to determine the value of z that corresponds to the area to the right of the z-score. We can then use the formula for the z-score to solve for the raw score (x):
x = zσ + μ
Substituting the values we have, we get:
x = 1.15(17) + 68 ≈ 88.95
Therefore, a minimum score of 88.95 is required to receive an "A" grade in the exam.

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If the population growth rate is 3.5 percent every year then the population of the town after 7 years would be 14940.

Given that population grows 3.5 percent every year.

So, the increase in population after one year

= 3.5% of 12000

= (3.5/100) × 12000

= 420

Thus the increase in population after 7 year would be,

= population increase in one year × 7

= 420×7 = 2940

Hence population of the town after 7 years = (present population + increase in population)

= 12000 + 2940

= 14940

So the population of the town after 7 years with 3.5 % growth every year would be 14490.

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In a sampling distribution of means, the distribution will approximate the normal distribution, the mean of the sampling distribution will equal the mean of the population and the standard deviation of the sampling distribution is based on Central Limit Theorem, option A.

The central limit theorem (CLT) of probability theory states that, under the assumption that all samples are of equal size and regardless of the population's actual distribution shape, the distribution of a sample variable approaches a normal distribution (i.e., a "bell curve") as the sample size increases.

In other words, the central limit theorem (CLT) is a statistical assumption that, given a sufficiently enough sample size from a population with a limited degree of variance, the mean of all sampled variables from the same population will be roughly equal to the mean of the entire population. According to the law of large numbers, these samples also resemble a normal distribution, with their variances almost equaling the variation of the population as the sample size increases.

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Complete question:

In a sampling distribution of means... 1. the distribution will approximate the normal distribution (bell curve). 2. the mean of the sampling distribution will equal the mean of the population 3. the standard deviation of the sampling distribution is called the standard error. This is based on the...

Central Limit Theorem

Standardization of Transformation

Z-Score Distribution Table

Relative Frequency of Probability

Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade.

To calculate Serena's overall grade, we need to first determine the weight of the final exam. We know that the assignments are worth 45% and the quizzes are worth 40%, which leaves 100% - 45% - 40% = 15% for the final exam.

Next, we can calculate Serena's grade for each component of the course. Her grade for assignments is 78% and her grade for quizzes is 65%. We can calculate her grade for the final exam by multiplying her score of 96% by the weight of the final, which is 15%:

Final grade = (0.45 * 78%) + (0.4 * 65%) + (0.15 * 96%)

Final grade = 35.1% + 26% + 14.4%

Final grade = 75.5%

Therefore, Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade. In this case, Serena's strong performance on the final exam helped to boost her overall grade, even though her scores on the assignments and quizzes were not as high. It's also worth noting that this calculation assumes that all assignments, quizzes, and the final exam were weighted equally within their respective categories (i.e., each assignment was worth the same percentage of the assignment grade).

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Answer:

16x + 3

Step-by-step explanation:

Simplify by combining like terms.  Add the terms with x, then add the integers.

8x + 8x + 4 - 1 = 16x + 3

Answer:

Let's call the length of the hypotenuse SD as x.

Since the altitude from T to SD divides SD into two parts, let the length of the shorter part be y. Then the length of the longer part is x-y.

Using similar triangles, we have:

TU/TS = ST/TD

Substituting the values we have:

TU/(3√5) = √5/UD

TU = (3/5)UD

Using the Pythagorean theorem in triangle TUS, we have:

TU² + (3√5)² = TS²

(3/5 UD)² + 45 = ST²

9/25 UD² + 45 = ST²

Using the Pythagorean theorem in triangle TUD, we have:

TU² + UD² = TD²

(3/5 UD)² + UD² = x²

9/25 UD² + UD² = x²

34/25 UD² = x²

UD² = (25/34)x²

Substituting the value of UD² in the equation ST² = 9/25 UD² + 45, we get:

ST² = 9/25 (25/34)x² + 45

ST² = 45/34 x² + 45

Since y = x-y-1, we have y = (x-1)/2.

Using the Pythagorean theorem in triangle TUD, we have:

(1/4) (x-1)² + UD² = x²

(1/4) (x² - 2x + 1) + (25/34)x² = x²

(1/4)(x²) + (25/34)x² - (1/2)x + (1/4) = 0

(59/68)x² - (1/2)x + (1/4) = 0

Using the quadratic formula, we get:

x = [1/2 ± √(1/4 - 4(59/68)(1/4))]/(2(59/68))

x = [1/2 ± (3√34)/17]/(59/34)

x = 17/59 ± 6√34/59

Since x is the hypotenuse SD, we have:

UD² = (25/34) x²

UD² = (25/34) [(17/59 ± 6√34/59)²]

UD² = 136/59 ± 204√34/295

Therefore, the exact lengths of the two parts of the hypotenuse are:

SD = x = 17/59 ± 6√34/59

SU = x-y = (x-1)/2 = 8/59 ± 3√34/59

UD = y = (x-1)/2 = 8/59 ± 3√34/59

TU = (3/5) UD = (3/5) [8/59 ± 3√34/59] = 24/295 ± 9√34/295

ST² = 45/34 x² + 45 = 45/34 [(17/59 ± 6√34/59)²] + 45

ST = √[45/34 [(17/59 ± 6√34/59)²] + 45]

Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.

We know that the cost per mile is $0.20, so we can set up an equation:

Cost = $20 + $0.20 x Distance

We can substitute $50 for Cost and solve for Distance:

$50 = $20 + $0.20 x Distance

$30 = $0.20 x Distance

Distance = $30 / $0.20

Distance = 150 miles

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The answer based on debt to assets ratio for east and west company are,

East company debt to assets ratio is equal to 0.44.

West company debt to assets ratio is equal to 0.28.

After comparing both the company debt to assets ratio East company is at higher level of financial risk.

Assets = Liabilities + Equity

For East company,

206,000 =  91,000 + 115,000

Assets = 206,000

liabilities = 91,000

Equity = 115,000

For West company,

603,000 =  169,000 + 434,000

Assets = 603,000

liabilities = 169,000

Equity = 434,000

Debt-to-assets ratio = Total liabilities divided by the total assets.

Debt-to-assets ratio for East

= 91,000 / 206,000

= 0.44

Debt-to-assets ratio for West

= 169,000 / 603,000

= 0.28

Comparing the two ratios,

0.44 > 0.28

This implies,

Company East has a higher debt-to-assets ratio is greater than the compared to Company West.

This represents that Company East has a higher level of financial risk.

As larger proportion of their assets are financed through debt.

This shows it is difficult to repay if the company experiences financial difficulties.

Company West has a lower level of financial risk as smaller proportion of their assets are financed through debt.

Therefore, the answer of the following questions are,

Debt to asset ratio of east company = 0.44

Debt to asset ratio of west company = 0.28

Company east has a higher financial risk level .

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 7 !

__________________

hope it helps ⸙

a) The sum of the given series is 7 / (1 + 2z)

b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).

The given series can be expressed as

7 – 14z + 28z^2 - 56z^3 + ...

This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is

sum = a / (1 - r)

Substituting the values of a and r, we get

sum = 7 / (1 + 2z)

So, the sum of the given series is 7 / (1 + 2z).

For the series to converge, the absolute value of the common ratio must be less than 1. That is,

|r| = |−2z| < 1

Simplifying this inequality, we get

1/2 < |z|

So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).

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The given statement regarding the GDP of major economies of the world is False.

To determine the accuracy of this statement, we would need to gather data on the real GDP per capita growth rates of major economies between 1982 and 2009 and compare them. Without this data, we cannot definitively say whether the statement is true or false. However, based on historical trends and current economic data, it is unlikely that Italy had the highest growth rate of real GDP per capita during this time period.

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The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.

Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:

P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]

P(X>=10) = 0.719

Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.

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Answer:

Step-by-step explanation:

Let's use algebra to solve this problem.

Let's start by assigning variables to the unknown quantities. Let G be the initial number of green beads and Y be the initial number of yellow beads.

We know that the number of green beads is 1/3 the number of yellow beads:

G = (1/3)Y

After giving away some beads, he had 42 green beads and 270 yellow beads left. So we can set up two equations using this information:

G - 2f = 42

Y - 3f = 270

where f is the number of friends he gave the beads to.

Now we can substitute G = (1/3)Y into the first equation:

(1/3)Y - 2f = 42

Multiplying both sides by 3, we get:

Y - 6f = 126

Now we have two equations that we can solve simultaneously:

Y - 3f = 270

Y - 6f = 126

Subtracting the first equation from the second, we get:

3f = 144

So f = 48. He gave the beads to 48 friends.

To find the total number of beads he had at first, we can use the equation G = (1/3)Y:

G + Y = (4/3)Y = (4/3)(270) = 360

So he had a total of 360 beads at first.

The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.

As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.

If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.

Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.

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As a result, we should not be concerned that the sample does not accurately reflect the population.

We can learn more about average, population, and sample.

What is the population?

The entire group of people, items, or objects that we want to draw a conclusion about is known as the population. For example, if we want to learn about the average age of people in the United States, then the entire population is every individual in the United States.

What is a sample?

A smaller group of individuals, objects, or items that are selected from the population is known as a sample. A random sample is a sample in which every individual in the population has an equal chance of being selected for the sample.

What is an average?

A statistic that summarizes the central tendency of a group of numbers is known as an average.

The mean is the most commonly used average in statistics. The mean is calculated by adding up all the numbers in a group and then dividing by the number of numbers in the group. If we want to learn about the average salary of all teachers in the United States, we'd have to sample every teacher. That's not a feasible option. Instead, we take a smaller sample, which should be representative of the population, and then use the information gathered from that sample to make predictions about the population as a whole.

If we assume that the five teachers in the example are a random sample of all teachers in the United States, then we can conclude that the average salary of all teachers in the United States is around $49,000. As a result, we should not be concerned that the sample does not accurately reflect the population.

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