Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.
After she rolls it 2,000 times, she finds that she rolled the number 2 a total of 187 times. Which of the following is true?
A. Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times.
B. Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability.
C. We cannot draw any conclusions from Joan's experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability.
D. We cannot draw any conclusions from Joan's experience with this die without also knowing how many times the other numbers appeared.

Assuming the distribution is bell-shaped, the estimated standard deviation is 10.

Since the range is 60 and the distribution is bell shaped the N or Number will be 6

Thus, to calculate the standard deviation:

60/6 = 10

The standard deviation is a statistic that expresses the degree of variation or dispersion among a set of values. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.

None of the standard deviations are "good" or "bad.". They serve as gauges of your data's dispersion. Sometimes, when using ratings scales, we want a wide spread because it shows that the range of the group we are rating is covered by our questions and ratings.

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The volume of the solid whose base is the region enclosed by the curve and the line is calculated as V = ∫ A(x) dx.

This solid has a base that is defined by a curve and a line, and its cross sections perpendicular to the x-axis are right isosceles triangles. We will use mathematical techniques to find the volume of this solid.

To find the volume of this solid, we need to use calculus. First, we need to determine the equation of the curve that forms the base of the solid. Once we have the equation, we can find the limits of integration that define the boundaries of the base region.

Next, we need to find an expression for the area of a cross section of the solid. We are given that these cross sections are right isosceles triangles. This means that the base and height of each triangle are equal. Let's call this length "a". Then, the area of each cross section is given by

=> A(x) = (1/2) * a²

To find the volume of the solid, we need to integrate the area of each cross section over the range of x values that define the base region. We can write the volume as V = ∫ A(x) dx.

To perform the integration, we need to determine the limits of integration. We can do this by finding the points where the curve intersects the line that defines the base region. Let's call these points (x1, y1) and (x2, y2). Then, the limits of integration are x1 and x2.

Finally, we need to substitute the expression for A(x) into the integral and evaluate it. The final result will give us the volume of the solid.

In summary, to find the volume of this solid, we need to use calculus. We first determine the equation of the curve that forms the base, then find an expression for the area of a cross section, and integrate this expression over the limits of integration that define the base region.

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The probability of success on the trial 7 for the given binomial experiment is 0.34.

An experiment utilizing a set number of independent trials with just two results is called a binomial experiment. There are two possible outcomes for these experiments: success and failure. Because of the nature of what is being tested, results in these studies can only ever be successes or failures.

Because there are only a limited number of outcomes that can occur during each trial of a binomial experiment, they are unique from other types of studies. Particularly, there can only ever be one of two outcomes in binomial experiments.

The probability of success and failure of a trial is same for every number of trials.

Given that,

n = 10 trials

Success = 0.34

Hence, the probability of success on the trial 7 for the given binomial experiment is 0.34.

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Step-by-step explanation:

I don't know car stuff, but that looks like its asking you to use the formula:

F1 x r1 = F2 x r2

Therefore, it will be:

175N x 200mm = 160N x 20mm

I hope this helps :)

The parameterization of the helix is:

[tex]r(t) = (7 cos(t), 7 sin(t), 33/(2*\pi ) * t)[/tex] & the arc length of one full turn of the helix is approximately 147.26 Å

where t is the parameter that varies from 0 to [tex]2\pi[/tex]

In this parameterization, the first two coordinates give the coordinates of a point on a circle of radius 7 that lies in the plane perpendicular to the helix axis, while the third coordinate gives the height of the point along the axis.

To find the arc length L of one full turn of the helix, we use the arc length formula:

[tex]L = ∫_0^(2π) ||r'(t)|| dt[/tex]

where r'(t) is the derivative of r(t) with respect to t, and || || denotes the Euclidean norm.

We have:

[tex]r'(t) = (-7 sin(t), 7 cos(t), 33/(2*pi))and||r'(t)|| = √[(-7 sin(t))^2 + (7 cos(t))^2 + (33/(2pi))^2] = 7√(2 + (33/(2pi))^2)So, we get:L = ∫_0^(2π) 7√(2 + (33/(2pi))^2) dt = 7√(2 + (33/(2pi))^2) * ∫_0^(2π) dt = 14π√(2 + (33/(2*pi))^2)[/tex]

(Note: the symbol "Å" represents angstrom, which is [tex]10^(-10)[/tex] meters, and it is used to express atomic distances.)

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The  answer of given question:   That we are using the fact that True is treated as 1 and False as 0 in Python, so the expression (lst[0] % 2 == 0) will evaluate to 1 if the first element of the list is even, and 0 otherwise.

Here's an implementation of the even count function using forward recursion in Python:

python

def even_count_fr(lst: list[int]) -> int:

   if not lst:

       return 0

   else:

       return (lst[0] % 2 == 0) + even_count_fr(lst[1:])

This function takes a list of integers as input, and returns the number of even integers found in the list.

The base case for the recursion is when the list is empty, in which case the function returns 0. Otherwise, the function checks if the first element of the list is even, and adds 1 to the result if it is. The function then makes a recursive call to the same function with the tail of the list (i.e., all the elements except the first one), and adds the result of that call to the result from the previous step.

The equation (lst[0]% 2 == 0) will evaluate to 1 if the first entry of the list is even and 0 otherwise. This is because we are exploiting the Python fact that True is considered as 1 and False as 0, respectively.

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The equation of the line parallel to the line passing through the points Y(5, 2) and Z(-3,-5) will be y = 7/8x + 4.5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line is passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5).

The equation of the line will be calculated as:-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -5 - 2 ) / ( -5 - 3 )

Slope = 7 / 8

The equation will be written as:-

y = 7/8x + c

The slope of the two parallel lines will be the same. The y-intercept of the parallel lines will be,

y = 7/8x + c

1 = (7/8 x -4 ) + c

c = 4.5

The equation will be:-

y = 7 / 8x + 4.5

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The number of denominations for the three single cards is 12 3 because there are 220 possible combinations of three cards from a deck, each combination representing a unique poker hand.

The number of denominations for the three single cards is 12 3 because it is impossible to have a poker hand with only two cards. The two-card hands can contain only one pair or two different cards, and neither of these hands are possible with only two cards. Therefore, the number of possible combinations of three cards is 12 3.

We can calculate this using the combination formula: nCr = n! / r!(n-r)!

For a hand of three cards, n = 12 (there are 12 denominations of cards) and r = 3. Therefore, 12 3 = 12! / 3!(12-3)! = 220. This means there are 220 possible combinations of three cards from a deck, each combination representing a unique poker hand.

The number of denominations for the three single cards is 12 3 because there are 220 possible combinations of three cards from a deck, each combination representing a unique poker hand.

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The total number of syringes that the ICU had is given as follows:

175.

The total number of syringes that the ICU had is obtained applying the proportions in the context of the problem.

20% of the total supply x is equivalent to 35 syringes, hence the equation is given as follows:

0.2x = 35

Solving the equation, the total number of syringes that the ICU had is given as follows:

x = 35/0.2

x = 175 syringes.

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A point that is located 8 units from Point A include the following: D. (-3,-1).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

By translating the coordinate of point A vertically downward by 8 units, the coordinates of the image of point A' include the following:

(x, y)                               →                          (x, y - 8)

Coordinate of point A = (-3, 7)   →    Coordinate of point A' (-3, 7 - 8) = (-3, -1)

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The average number of likes will be 16.5. the correct option is D.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is calculated by adding all the data points and dividing it by the total number of the data.

Given that Bethany has a photo website where she places photos that she has taken so others can see them. Below is how many likes each of her current photos was given: 10, 13, 15, 15, 17, 29.

The average will be calculated as:-

Mean = ( 10 + 13 + 15 + 15 + 17 + 29 ) / 6

Mean = 99 / 6

Mean = 16.5

Therefore, the average number of likes will be 16.5. the correct option is D.

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Answer:

x=2⁰ AED=78⁰

Step-by-step explanation:

180⁰-108⁰= 78⁰

angle AED= 78⁰

108⁰+50⁰= 158⁰

180⁰-158⁰=22⁰

22⁰+78⁰=100⁰

100⁰+ 78⁰=178⁰

180⁰-178⁰= 2⁰

x=2⁰

Answer:

15:30 or 3:30

Step-by-step explanation:

19:12=18:72

18:72-3:42= 15:30

15:30 or 3:30

The time when Grace started reading her chemistry book is calculated as  15:30 in 24-hour format.

To find out what time Grace started reading her chemistry book in 24-hour format,

Simply subtract 3 hours and 42 minutes from 19:12.

Convert 19:12 to minutes: 19 hours × 60 minutes/hour + 12 minutes

= 1152 minutes.

Subtract 3 hours and 42 minutes from 1152 minutes:

1152 minutes - (3 hours × 60 minutes/hour + 42 minutes)

= 1152 - (180 + 42)

= 930 minutes.

Convert the remaining minutes back to hours and minutes:

930 minutes ÷ 60 minutes/hour

= 15 hours with a remainder of 30 minutes.

Combine the results:

Grace started reading her chemistry book at 15:30 in 24-hour format.

Therefore, time when Grace start her reading of chemistry book is 15:30 in 24-hour format.

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The mathematical function describing the cost of car the next year is →

C{n + 1} = C{n} (1 - 3/20).

The depreciation rate is a rate at which the price of a quantity decreases every year.

Given is that the cost of a new car is $32,000 it depreciates at a rate of 15% per year.

We can understand it as follows.

After one year the cost would be -

{x} = 32000 - {15% of 32000}

{x} = 32000 - 4800

{x} = $27200

After second year the cost would be -

{x} = 27200 - {15% of 27200}

{x} = 27200 - 4080

{x} = $23120

This means that after every year, the value decrease by 15% of what it was a year before. We can write -

C{n + 1} = C{n} - (15/100) C{n}

C{n + 1} = C{n} (1 - 3/20)

Therefore, the mathematical function describing the cost of car the next year is →

C{n + 1} = C{n} (1 - 3/20).

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The solution is,  the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8.

This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.

The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.

Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.

In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.

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Answer:

2:1

Step-by-step explanation:

If we examine the two figures we see that the length of each side of Figure B is twice the length of the corresponding side of Figure A

For example side of length 44 in Figure B corresponds to side of length 22 in Figure A

Scale Factor: Final Dimension/Initial Dimension =

Length of Figure B side/Length of Figure A corresponding side

44/22 = 2/1 or 2:1

So the scale factor from A to B is 2 or 2:1

The number of bags of potatoes and carrots did the farmer sell in all is 75 bags.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, a farmer is selling  potatoes and carrots into bags, 3/5 were bags of potatoes and the rest were bags of carrots. He sold 45 bags of potatoes and 3/4 of the bags of carrots, and had 1/4 of the bags left.

The bags of potato = 3x/5

The bags of carrot = 2x/5

Therefore, according to question,

x-45-3x/5×2x/5 = x/4

7x/10-x/4 = 45

18x/40 = 45

x = 45×40/18

x = 100

Total bags sold = 100×2/5+3/5+45 = 75

Hence, the number of bags of potatoes and carrots did the farmer sell in all is 75 bags.

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[tex] \boxed{\sf Option \: A\text{:} \: \dfrac{1 + \sqrt{-32}}{4} = \dfrac{1}{4} + \sqrt{2}i} [/tex]

[tex] \\ \\ [/tex]

We are asked to express the given number in the form a + ib, also known as the algebraic form.

[tex] \\ \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \sf z = a + ib \\[/tex]

Where:

✰ a and b are real numbers and are the complex number's real part and imaginary part, respectively.

[tex] \\ \\ [/tex]

✰ i is the imaginary unit number and can be expressed as follows:

[tex] \\ \sf i= \sqrt{-1}[/tex]

[tex] \\ \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \sf z = \dfrac{1 + \sqrt{-32}}{4} = \dfrac{1 + \sqrt{32 \times (-1)}}{4} \\ \\ \\ \sf \diamond \: We \: know \: that \: \sqrt{ab} = \sqrt{a} \times \sqrt{b}. \\ \\ \implies \dfrac{1 + \sqrt{32 \times (-1)}}{4} = \dfrac{1 + \sqrt{32}\times \sqrt{-1}}{4}[/tex]

[tex] \\ \\ \sf \implies \dfrac{1 + \sqrt{32}\times \sqrt{-1}}{4} = \dfrac{1 + \sqrt{16 \times 2} \times \sqrt{-1}}{4} = \dfrac{1 + 4\sqrt{2} \times \sqrt{-1}}{4}[/tex]

[tex] \\ \\[/tex]

[tex] \diamond \: \sf Substitute \: \sqrt{-1} = i. \\ \\ \implies \sf \dfrac{1 + 4\sqrt{2}\times \sqrt{-1}}{4} = \dfrac{1 + 4\sqrt{2} \times i}{4} = \dfrac{1 + 4i\sqrt{2}}{4} [/tex]

[tex] \\ \\ \: \sf \diamond \: Simplify \: knowing \: that \: \dfrac{a + b}{c} = \dfrac{a}{c}+\dfrac{b}{c}. [/tex]

[tex] \\ \\ \\ \implies \: \sf \dfrac{1 + 4i\sqrt{2}}{4} = \dfrac{1}{4} + \dfrac{4i\sqrt{2}}{4} = \boxed{\sf \dfrac{1}{4} + \sqrt{2}i} [/tex]

[tex] \\ [/tex]

Therefore, the first option is correct.

[tex] \\ \\ \\ [/tex]

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The solution is, a = 0 & b = -15.

A complex number is a number of the form a + bi, where a and b are real numbers ; This way, a complex number is defined as a polynomial.

here, we have,

z₁ = 3 cis(pi) and z₂ =5 cis(pi/2)

we know, cisx = cosx + i sinx

so, we get,

z₁ = 3 cis(pi) = 3(-1)

and z₂ =5 cis(pi/2) = 5( i.1)

If z₁ x z₂ = a+bi.

or, -3 * 5i = a+ ib

or, -15i = a +ib

Hence, The solution is, a = 0 & b = -15.

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The given expressions are not equivalent. They are numerical expressions.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expressions are -18-(6 * 2) or (18 + 6)*2.

If the expressions are equivalent, then they will have the same values.

If they are not equivalent, then they will have different values.

-18-(6 * 2) = -18 - 12 = -30

(18 + 6)*2 = 24 * 2 = 48

Both the expressions are not equivalent.

Hence the expressions are not equivalent.

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Answer:

m<B = 58 degrees, m<C = 63 degrees

Step-by-step explanation:

let's find y!

angles B and A are complementary, so they should equal 90

therefore, B + A = 90

substitute

4y + 8y - 6 =90

12y = 96

y=8, and m<B = 8y-6; so m<B = 58

angles C and D are equal because of vertical angles

therefore, C = D

substitute

7x=5x+18

2x=18

x=9

m<C = 7x, so m<C = 63

Chebyshev's Theorem can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean.

Chebyshev's Theorem is a mathematical theorem that can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean. It states that for any distribution, no matter what its shape, at least a certain proportion of values will fall within a certain number of standard deviations from the mean. This proportion can be calculated using the formula 1-1/k², where k is the number of standard deviations. For example, if k is 3, then at least 75% of all data points will fall within three standard deviations of the mean. This theorem is particularly useful for distributions that are not normally distributed, since it provides a way to estimate the proportion of data points that fall within a certain range, even if the distribution is not symmetrical. Chebyshev's Theorem is an important tool for data analysis and can be used in a wide variety of contexts.

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In both cases, pulley C is the fastest one since its radius is the smallest one.

In this problem we find two cases of power transmition, the first example consists in a rigid transmition system formed only by pulleys and the second example consisting in a flexible transmition system formed by belts and pulleys.

Ideally, power is conserved throughout every system and rotational velocity of the pulley is inversely proportional to its radius. We need to determine does rotate faster in each case.

n ∝ 1 / R

Thus, we find the following results:

Case 1: Pulley C is the fastest pulley since it has the smallest radius.

Case 2: Pulley C is the fastest pulley since its has the smallest radius.

There is no additional information (i.e. any angular speed of pulley, geometric dimensions in the second case) that may allows us to determine whether if rigid transmition system or a flexible transmition system is faster.

The representation only allows us to determine what pulley is the fastest within a system.

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Answer:

36cm and 15cm

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

Divide the dimensions of the map by the given ratio.

After the first reduction the dimensions of the new map are:

Therefore, the new dimensions of the map are 36cm and 15cm.

The final dimensions of the map are 72 cm by 30 cm.

If the map is enlarged twice in the ratio 3:5, this means that both the length and the width are multiplied by the same factor. Let the scale factor of the enlargement be x. Then, we have:

x = ( 5 /  3) x 2

x = 10 / 3

To find the final dimensions of the map, we multiply the original dimensions by the scale factor.

Final length = 21.6 cm x ( 10 / 3 ) = 72 cm

Final width = 9 cm x ( 10 / 3 ) = 30 cm

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Answer:

Step-by-step explanation:

Set x miles Leo can travel, and his cost have to be no more than $20, so

1.75+0.75x =20

0.75x = 20-1.75

0.75x = 18.25

x = 18.25/0.75 = 24.333 miles

The number of bacteria after 8 hours is approximately 2,713.

Let's apply the exponential growth formula:

N = N0 * e(rt),

N is the number of bacteria at a particular period. N0 is the initial bacterial population, e is the mathematical constant (about equal to 2.71828), r is the growth rate, and t is the amount of time that has passed.

The information provided in the problem can be used to determine the growth rate:

N1 = N0 * e(r*2)

N2 = N0 * e(r*4)

To get eliminate N0, divide the second equation by the first equation:

N2/N1 = e(r4) / e(r2)

385/135 = e(r4) / e(r2)

If we condense this expression, we get:

e(r*2) = 385/135

e(r*2) = 2.8519

When we take the natural logarithm of both sides, we get:

r*2 = ln(2.8519)

r = ln(2.8519)/2

r = 0.5457 (rounded to 4 decimal places)

The number of bacteria after 8 hours can now be determined using the exponential growth algorithm once more:

N = N0 * e(rt)

N = 135 * e(0.5457*8)

N = 2,713 (rounded to the nearest whole number)

Therefore, the number of bacteria after 8 hours is approximately 2,713.

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To determine which statement is true, we need to compare the number of students who prefer each game relative to the total number of students surveyed.

The total number of students surveyed is:

14 + 16 + 28 + 14 + 8 = 80

A) To find the probability of a student preferring tic tac toe or connect 4 versus checker or jenga, we add the number of students who prefer tic tac toe or connect 4:

28 + 8 = 36

And add the number of students who prefer checker or jenga:

14 + 16 + 14 = 44

Therefore, statement A is false.

B) To find the probability of a student preferring connect 4 versus tic tac toe, we divide the number of students who prefer connect 4 by the number of students who prefer tic tac toe:

28/8 = 3.5

Therefore, statement B is false.

C) To find the probability of a student preferring tic tac toe versus checkers, we divide the number of students who prefer tic tac toe by the number of students who prefer checkers:

8/16 = 0.5

Therefore, statement C is true.

D) To find the probability of a student preferring jenga or tic tac toe versus checkers or bean bag toss, we add the number of students who prefer jenga or tic tac toe:

28 + 8 = 36

And add the number of students who prefer checkers or bean bag toss:

14 + 16 = 30

Therefore, statement D is true.

Therefore, the correct answer is option D: a student is less likely to prefer checkers or bean bag toss than jenga or tic tac toe.

The correct statement about the quadratic function is given as follows:

C. The second difference would be constant.

A quadratic function is modeled as follows:

y = ax² + bx + c.

Then the first difference, which is the first derivative of the quadratic function, is obtained as follows:

y = 2ax + b.

The second difference, which is the second derivative of the quadratic function, is obtained as follows:

y = 2a.

The coefficient a is a constant, hence the second difference would be constant and the correct option is given by option C.

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According to the information, the mean of these values would be: 169

To calculate the mena of this series of numbers we must add all the values and multiply them by the number of values available. In this case, we would have to divide it by 10. The procedure is shown below:

According to the above, the mean of this operation would be 169.

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