Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. Sienna wants to know the probability that at least 2 of the colors will be the same. Which of the following is the best simulation? Explain your reason for your answer.

A. Roll a standard number cube 5 times for each trial. Let each number represent a different color. Run 50 trials and find the fraction of times that at least two of the same number are rolled.

B. Create a spinner with 5 equal sections. Label each section with a different color. Spin the spinner 7 times to see if it lands on the same color two or more times.


C. Create a spinner with 7 equal sections. Label each section with a different color. Spin the spinner 5 times for each trial. Run 50 trials and find the fraction of times the spinner lands on the same color two or more times.


D. Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Answer:

y = sec(x-2) - 1

Step-by-step explanation:

We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.

The correct answer is:

x-intercept = -6, y-intercept = 3To

find the x-intercept, we set y = 0 and solve for x.

-3x + 6(0) = 18

-3x = 18

x = -6

Therefore, the x-intercept is -6.

To find the y-intercept, we set x = 0 and solve for y.

-3(0) + 6y = 18

6y = 18

y = 3

Therefore, the y-intercept is 3.

The correct answer is:

x-intercept = -6, y-intercept = 3

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

To determine which answer is bigger, let's calculate the values after the given changes and compare them.

Increasing 28 by 25%:

To calculate the increase, we need to find 25% of 28 and add it to 28.

25% of 28 = (25/100) * 28 = 7

Increased value = 28 + 7 = 35

Decreasing 40 by 15%:

To calculate the decrease, we need to find 15% of 40 and subtract it from 40.

15% of 40 = (15/100) * 40 = 6

Decreased value = 40 - 6 = 34

Comparing the results:

The increased value of 28 by 25% is 35, while the decreased value of 40 by 15% is 34.

Therefore, 35 is bigger than 34.

Hamilton’s Method:A large chair store needs to assign 12 buyers to its five stores, with the number of employees for each store given below:5 buyers to store 1;3 buyers to store 2;2 buyers to store 3;1 buyer to store 4;1 buyer to store 5

A chair store needs to assign 12 buyers to its 5 stores. The number of employees for each store is shown below:

Hamilton’s Method: A large chair store needs to assign 12 buyers to its five stores, with the number of employees for each store given below:5 buyers to store 1;3 buyers to store 2;2 buyers to store 3;1 buyer to store 4;1 buyer to store 5; The number of buyers assigned to each store is as follows:

Store 1 gets 5 buyers Store 2 gets 3 buyers store 3 gets 2 buyers store 4 gets 1 buyer Store 5 gets 1 buyer Jefferson’s Method: To find out how many buyers should be assigned to each store using Jefferson’s Method, the following steps should be taken:

Step 1: Find the total number of buyers to be assigned

Step 2: Divide each store’s employee by the total number of employees

Step 3: Multiply the result of Step 2 by the total number of buyers store 1 gets 5.400 buyers store 2 gets 3.240 buyers store 3 gets 1.920 buyers store 4 gets 0.720 buyers store 5 gets 0.720 buyers

Webster’s Method: To find out how many buyers should be assigned to each store using Webster’s Method, the following steps should be taken:

Step 1: Find the total number of buyers to be assigned

Step 2: Divide each store’s employee by the total number of employees

Step 3: Multiply the result of Step 2 by the total number of buyers step 4: Round up the result of Step 3 to the nearest integer Store 1 gets 5 buyers store 2 gets 3 buyers store 3 gets 2 buyers store 4 gets 1 buyerStore 5 gets 1 buyerHill-Huntington's Method: To find out how many buyers should be assigned to each store using Hill-Huntington's Method, the following steps should be taken:

Step 1: Find the total number of buyers to be assigned

Step 2: Divide each store’s employee by the square root of the total number of employees

Step 3: Multiply the result of Step 2 by the square root of the total number of buyers store 1 gets 5 buyers Store 2 gets 3 buyers Store 3 gets 2 buyers Store 4 gets 1 buyer Store 5 gets 1 buyer

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A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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The slope of line N is -3/4.

To find the y-intercept of line M and the slope of line N, we need to understand their equations, which are in slope-intercept form: y = mx + b,

where m represents the slope and b represents the y-intercept.Line M is given by the equation:

y = -3x + 7. Here, we can see that the slope, m, is -3, and the y-intercept, b, is 7.

Therefore, the y-intercept of line M is 7.Line N is given by the equation: 3x + 4y = 8.

To find the slope of this line, we can solve for y:4y = -3x + 8y = (-3/4)x + 2

Here, we can see that the slope, m, is -3/4.

Therefore, the slope of line N is -3/4.

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We can conclude that `An(B-C) = AnB - AnC` using double inclusion proofs.

Given a universal set `U` and subsets `A`, `B` and `C`.To prove: `An(B-C) = AnB - AnC`.

Now, we can prove this statement by double inclusion proofs. Let `x` be an arbitrary element of `U`.

Proof of `An(B-C) ⊆ AnB - AnC`:

Suppose that `x ∈ An(B-C)`, then `x ∈ A` and `x ∈ B-C`.

By definition of `B-C`, we have `x ∈ B and x ∉ C`.

Therefore, `x ∈ B` and `x ∉ C` implies that `x ∈ B` and `x ∉ AnC`.

Therefore, `x ∈ AnB` and `x ∉ AnC` implies that `x ∈ AnB - AnC`.

Hence, we have shown that `An(B-C) ⊆ AnB - AnC`.

Proof of `AnB - AnC ⊆ An(B-C)`:

Suppose that `x ∈ AnB - AnC`, then `x ∈ AnB` and `x ∉ AnC`.

By definition of intersection, we have `x ∈ A and x ∈ B`.Now, since `x ∈ AnC`, we have `x ∈ A and x ∈ C`.Since `x ∈ A` is a common element, we can combine both sets `B` and `C` to get `B ∪ C`.

Now, since `x ∈ B ∪ C`, we can write this as `x ∈ B ∪ (U-C)` or `x ∈ B - C or x ∈ A ∩ (U-C)`.

Thus, `x ∈ An(B-C)`.Hence, we have shown that `AnB - AnC ⊆ An(B-C)`.

Therefore, we can conclude that `An(B-C) = AnB - AnC` using double inclusion proofs.

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a. The premium for this coverage will depend on the  individual's age, location, driving record, and the insurance company's rates.

b.   It will cost higher because the insurance company provides more coverage in the event of an accident.

c.  The difference in cost between the two coverage amounts depends on factors such as the insurance provider's rates and the person's specific circumstances.

a. Insurance coverage of 50/100/10:

The coverage limits 50/100/10 is a representation of  the minimum liability coverage required by state laws.

$50,000 = coverage for bodily injury liability per person.

$100,000  = coverage for bodily injury liability per accident.

$10,000 = coverage for property damage liability per accident.

b. Insurance coverage of 100/300/25:

The coverage limits 100/300/25 represent higher liability coverage limits:

$100,000  = coverage for bodily injury liability per person.

$300,000  = coverage for bodily injury liability per accident.

$25,000  = coverage for property damage liability per accident.

c. Difference in cost:

The difference in cost between the two coverage levels is influenced by a number of variables, including the insurance company's rates and the individual's unique situation.

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The total number of possible arrangements when all the cubes are arranged in a line is 96.

To calculate the number of possible arrangements when all the cubes are arranged in a line.

we need to consider the total number of cubes and their quantities.

In this case, we have:

- 1 purple cube

- 2 blue cubes

- 2 red cubes

- 4 orange cubes

- 1 green cube

- 2 yellow cubes

To find the number of arrangements, we can use the concept of permutations. The formula for permutations is given by:

P(n) = n!

Where P(n) represents the number of permutations of n objects and n! denotes the factorial of n.

First, let's calculate the factorial of the total number of cubes:

[tex]n! = 1! * 2! * 2! * 4! * 1! * 2![/tex]

Calculating the factorials:

[tex]1! = 12! = 2 * 1 = 24! = 4 * 3 * 2 * 1 = 24[/tex]

Substituting the values back into the equation:

[tex]n! = 1 * 2 * 2 * 24 * 1 * 2 = 96[/tex]

Therefore, the total number of possible arrangements when all the cubes are arranged in a line is 96.

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The Transformation notation for transforming figure 1 to figure 2 is R y-axis T(-3, -2) R 180° T(2, -2).

The notation that describes the transformation of figure 1 to figure 2 is a combination of translation, reflection and rotation.To begin with, figure 2 is a mirror image of figure 1.

The mirror reflection transformation is represented by an ‘R’ in notation, followed by the line of reflection. In this case, the line of reflection is the y-axis. Therefore, the mirror reflection transformation notation is R y-axis.Next, the figure is translated or moved. The vertices (2, 3), (2, 6), (6, 6), (6, 4), (4, 4)

which forms the semi-cube have moved three units left and two units down. While the vertices (minus 2, minus 2), (minus 6, minus 2), (minus 6, minus 5), (minus 4, minus 4) and (minus 2, minus 4)

which forms the second semi-cube have moved two units right and two units down. Thus, the notation for this transformation is T(-3, -2) and T(2, -2).

Lastly, the figure is rotated 180 degrees counterclockwise around the origin. This transformation is represented by the notation R 180°.

Therefore, the transformation notation for transforming figure 1 to figure 2 is R y-axis T(-3, -2) R 180° T(2, -2).

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no sorry its way to hard to answer this

The length of BL is approximately 7.9 units.

In triangle ABL, we are given that AL = 12, TS = 7.75, and SL = 5.1. We need to find the length of BL.

Since TS is parallel to AL, we can use the concept of similar triangles to solve this problem.

By drawing a line parallel to BL through point T, we create two similar triangles: triangle TSL and triangle ABL. The corresponding sides of similar triangles are proportional.

Let's denote the length of BL as x. Then we can set up the following proportion:

TS/AL = SL/BL

Substituting the given values:

7.75/12 = 5.1/x

To solve for x, we can cross-multiply and solve the resulting equation:

7.75 * x = 12 * 5.1

7.75x = 61.2

Dividing both sides of the equation by 7.75:

x = 61.2 / 7.75

x ≈ 7.9

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If you earn $1 every 500 seconds and work for a normal 8-hour day, you would have Earned $57.

To calculate the amount of money earned in a normal workday, we need to determine the total number of seconds in 8 hours and then divide it by the time it takes to earn $1.

There are 60 seconds in a minute and 60 minutes in an hour. Therefore, there are 60 x 60 = 3600 seconds in an hour.

To find the total number of seconds in 8 hours, we multiply the number of seconds in an hour by 8:

8 hours x 3600 seconds/hour = 28,800 seconds.

Next, we need to determine how many times $1 can be earned in 28,800 seconds. Given that $1 is earned every 500 seconds, we divide 28,800 by 500:

28,800 seconds ÷ 500 seconds = 57.6.

Since we cannot earn a fraction of a dollar, we round down to the nearest whole number. Therefore, you would have earned 57 dollars during the 8-hour workday.

In summary, if you earn $1 every 500 seconds and work for a normal 8-hour day, you would have earned $57.

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The next step in drawing a 40° angle would be to: D. draw a mark on the paper at 40°

A protractor is a geometric tool used to measure and draw angles. It typically has a semi-circular shape with markings along the curved edge representing degrees or angles.

The next step in drawing a 40° angle after lining up the ray with the baseline and origin on the protractor is to draw a ray connecting the vertex (starting point) of the angle and the mark on the protractor corresponding to the 40° angle.

This ray will form the desired 40° angle with the baseline, completing the construction of the angle.

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The Wronskian of the set of functions {xln|xl|, x^2ln|xl|} is zero, indicating that the functions are linearly dependent.

To compute the Wronskian of a set of functions {y1, y2}, we arrange the functions as columns in a matrix and calculate the determinant of that matrix. In this case, we have the set of functions {y1, y2} = {xln|xl|, [tex]x^2[/tex]ln|xl|}.

Let's construct the matrix:

| xln|xl| x^2ln|xl| |

|---------------------|

| y1 y2 |

To calculate the Wronskian, we compute the determinant of this matrix:

W = | xln|xl| x^2ln|xl| |

|---------------------|

| y1 y2 |

Using the properties of determinants, we can expand this determinant along the first row:

W = (xln|xl|)(y2) - ([tex]x^2[/tex]ln|xl|)(y1)

Simplifying further, we have:

W = xy2ln|xl| - x^2y1ln|xl|

Now, substituting the given functions for y1 and y2, we have:

W = x(x^2ln|xl|)ln|xl| - x^2(xln|xl|)ln|xl|

Simplifying inside the parentheses:

W = x^3ln|xl|^2ln|xl| - x^3ln|xl|^2ln|xl|

Combining like terms:

W = 0

Therefore, the Wronskian of the set of functions {y1, y2} = {xln|xl|, x^2ln|xl|} is equal to zero. This implies that the functions are linearly dependent.

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Answer: 9/4

Step-by-step explanation:

Reciprocal means flip the fraction

The reciprocal of 4/9  is  9/4

Answer: the rciprocal is 9/4

Step-by-step explanation:

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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Answer:

2 is really answer it is this question bro than ka for good point

Step-by-step explanation:

hello shreekant thanks 886A bubs 2 is answr

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

A statistically significant test result (p-value ≤ 0.05) supports the rejection of the null hypothesis, while a p-value greater than 0.05 suggests that there is not enough evidence to reject the null hypothesis.

The statement provided is not entirely accurate. A statistically significant test result with a p-value ≤ 0.05 indicates that the observed effect is unlikely to have occurred by chance alone, and it provides evidence to reject the null hypothesis. It does not necessarily mean that the test hypothesis is false, but rather that the data collected supports an alternative hypothesis.

The p-value represents the probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true. When the p-value is smaller than the predetermined significance level (often set at 0.05), it suggests that the observed effect is statistically significant and not likely due to random chance.

Conversely, a p-value greater than 0.05 does not necessarily mean that no effect was observed. It simply means that the observed effect is not statistically significant at the chosen significance level, and there is insufficient evidence to reject the null hypothesis. However, it is important to consider the specific context and limitations of the study when interpreting the results.

In summary, a statistically significant test result (p-value ≤ 0.05) supports the rejection of the null hypothesis, while a p-value greater than 0.05 suggests that there is not enough evidence to reject the null hypothesis.

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The value of the missing angle using Cosine rule is 128.68°

Let :

a = 7

b = 10

c = 4

Missing angle = B

From Cosine rule :

CosB = (a² + c² - b²)/2ac

Substituting the values into the formula :

CosB = (7² + 4² - 10²)/2×7×4

CosB = -35/56

CosB = -0.625

Taking the cosine inverse of 0.625

B = 128.68

Therefore, the value of the missing angle is 128.68

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2 x 10^-8 is 5 x 10^-13 times smaller than 4 x 10^-4.In other words, 2 x 10^-8 is 500,000,000,000 (500 trillion) times Smaller than 4 x 10^-4.

To determine how many times smaller 2 x 10^-8 is than 4 x 10^-4, we can divide the two numbers and express the result in scientific notation.

First, let's divide 2 x 10^-8 by 4 x 10^-4:

(2 x 10^-8) / (4 x 10^-4)

To simplify this division, we can divide the numerical values and subtract the exponents:

2 / 4 = 0.5

10^-8 / 10^-4 = 10^(-8 - (-4)) = 10^-8 + 4 = 10^-12

Therefore, (2 x 10^-8) / (4 x 10^-4) simplifies to 0.5 x 10^-12.

Now, let's convert this result back to scientific notation:

0.5 x 10^-12 = 5 x 10^-13

Thus, 2 x 10^-8 is 5 x 10^-13 times smaller than 4 x 10^-4.

In other words, 2 x 10^-8 is 500,000,000,000 (500 trillion) times smaller than 4 x 10^-4.

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The limit lim ₓ → ₀ f(x) is 5

The squeeze theorem is used to evaluate a kind of limits. It is also known as the sandwich theorem.

To evaluate a limit lim ₓ → ₐ f(x), we usually substitute x = a into f(x) and if that leads to an indeterminate form, then we apply some algebraic methods.

But neither of them may work in evaluating some kind of limits such as lim ₓ → ∞ (sin x / x).

From the information given, we have that;

We know that lim ₓ → ₀ 5 - x² = 5 - 0²

lim ₓ → ₀ = 5

lim ₓ → ₀ 5 + x²

lim ₓ → ₀ = 5+ 0²

lim ₓ → ₀ = 5

Also, f(x) lies between 5 - x² and 5 + x².

Using the squeeze theorem, the limit for f(x) is;

lim ₓ → ₀ f(x) = 5.

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A graph that represent the data is shown below, with the x-axis labeled time and the y-axis labeled temperature.

In Mathematics and Geometry, a graph is a type of chart that is typically used for the graphical representation of data points, end points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

In this scenario, we would use an online graphing calculator to label the x-axis of the cartesian coordinate with time (measured as hours before or after midnight) while the y-axis of the cartesian coordinate would be labeled temperature (measured in degree Celsius), and then plot the data points as shown in the image attached below.

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Missing information:

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

The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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The histogram accurately displays the data collected from Question #1 and provides useful insights into the distribution and range of opinions among the survey population.

Question 1 data:

4, 2, 3, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1

From the histogram, it can be observed that the data is approximately normally distributed with a mean of around 3. The distribution appears to be somewhat symmetrical with the majority of the data being between 2 and 4. The frequency of the value '1' and '5' is the least which implies that the occurrence of these values is very low.

The analysis of the data shows that the majority of the people surveyed chose answers that were in the middle range of the scale, between 2 and 4. This could indicate that the survey question was not highly polarizing and that the survey population had similar opinions on the subject matter.

However, it is also worth noting that there were a few outliers at both ends of the scale. This suggests that there were a few people who had very strong opinions about the topic and did not fall within the norm of the survey population.

Overall, the histogram accurately displays the data collected from Question  and provides useful insights into the distribution and range of opinions among the survey population.

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Answer:

None of the answer choices

Step-by-step explanation:

Answer:

x ≥ 4

Step-by-step explanation:

The given statement is "The difference of 10 and a number is at most six".

Let "x" be the unknown number.

"The difference of 10 and a number" can be represented as either "10 - x" or "x - 10", depending on whether x < 10 or x > 10.

"Is at most six" means it is less than or equal to six.

Therefore, we have two potential cases:

[tex]\begin{minipage}{3 cm}\underline{\sf Case\;1}:\;\textsf{If $x < 10$}\\\\\boxed{10 - x \leq 6}\end{minipage} \qquad \qquad\begin{minipage}{3 cm}\underline{\sf Case\;2}:\;\textsf{If $x > 10$}\\\\\boxed{x-10 \leq 6}\end{minipage}[/tex]

Solving the inequalities:

[tex]\boxed{\begin{aligned}\underline{\sf Case\;1}\\\\10 - x &\leq 6\\10 - x-10 &\leq 6-10\\-x &\leq -4\\x &\geq 4\end{aligned}}[/tex]      [tex]\boxed{\begin{aligned}\underline{\sf Case\;2}\\\\x-10&\leq 6\\x-10+10 &\leq 6+10\\x &\leq 16\\\\\end{aligned}}[/tex]

[Remember that when dividing both sides of an inequality by a negative number, we have to reverse the inequality sign.]

Therefore, the two possible solutions are:

If we take the statement "the difference between 10 and a number" as "10 - x" then the solution is x ≥ 4.