Akbar bought a watch at a discount of 5%. The original price of the watch was Rs 910. How much did Akbar pay for the watch?

Triangle ABC has side lengths of 8.2 cm, 5.6 cm, and 4.49 cm, and angles of approximately 77 degrees, 50.5 degrees, and 52.5 degrees.

We have,

To construct triangle ABC, follow these steps:

- Draw a line segment AB of length 8.2 cm.

- Draw point A, and using a protractor, draw an angle BAC of 77 degrees with AB as its base. Label the intersection of this angle and AB as point C.

- Draw a line segment AC of length 5.6 cm.

- Using a protractor, draw an angle BCA of 103 degrees with AC as its base. Label the intersection of this angle and AB as point B.

- Triangle ABC is now constructed with side lengths AB = 8.2 cm, AC = 5.6 cm, and BC as the unknown side.

To find the length of side BC, we can use the law of cosines:

BC² = AB² + AC² - 2(AB)(AC)cos(BAC)

Substituting in the known values.

BC² = 8.2² + 5.6² - 2(8.2)(5.6)cos(77°)

BC ≈ 4.49 cm

To find the other angles, we can use the law of sines:

sin(BAC) / AC = sin(BCA) / BC

Substituting in the known values.

sin(77°) / 5.6 = sin(103°) / 4.49

sin(BCA) ≈ 0.784

BCA ≈ 50.5°

Finally, we can find angle CAB by subtracting the sum of angles BAC and BCA from 180 degrees:

CAB ≈ 52.5°

Thus,

Triangle ABC has side lengths of 8.2 cm, 5.6 cm, and 4.49 cm, and angles of approximately 77 degrees, 50.5 degrees, and 52.5 degrees.

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The correct choice for the transformation of the function f (x) = (x + 3)² from the parent function f (x) = x² is,

⇒ Horizontal translation.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Here, Parent function is,

⇒ f (x) = x²

And, After translation the function is,

⇒ f (x) = (x + 3)²

Now, We can draw the graph of both function.

Hence, By graph we get;

The correct choice for the transformation of the function f (x) = (x + 3)² from the parent function f (x) = x² is,

⇒ Horizontal translation.

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The probability of randomly choosing a student who prefers the beach or the zoo is 57%.

A group of people or a sample of the population is "surveyed" in order to obtain information or data in order to gain insights or understanding about a certain topic or situation.

By multiplying the proportion of students who prefer the beach by the proportion who prefer the zoo, one may determine the likelihood of selecting a student who favors one of the two destinations:

33% + 24% = 57%

Therefore, the probability of randomly choosing a student who prefers the beach or the zoo is 57%.

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Answer:

A

Step-by-step explanation:

Hope this helps

The taste test conducted by the local chili Restaurant  of a Single-blind study because the customers do not know the type of chili they are tasting, while the test administrators do know which type of chili is being presented.

In a single-blind study, the participants or subjects do not know which group they are assigned to or what treatment they are receiving, while the experimenter or test administrator knows the type of treatment being given. In this case, the test administrators know which type of chili is being presented to the customers, but the customers are not aware of the type of chili they are tasting.

The use of a single-blind study is appropriate in this case because it helps to reduce the possibility of bias in the results. If the customers knew which type of chili they were tasting, it could influence their preferences based on preconceived notions or expectations. By not knowing the type of chili they are tasting, the customers are more likely to give their unbiased opinions and preferences.

Additionally, the experiment is not a double-blind study because the test administrators are aware of the type of chili that is being presented. In a double-blind study, both the participants and the experimenters are unaware of which group the participants are assigned to or which treatment they are receiving. This helps to reduce the potential for bias from both the participant and experimenter.

the taste test conducted by the local chili restaurant is an example of a single-blind study because the customers do not know the type of chili they are tasting, while the test administrators do know which type of chili is being presented.

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Answer:

Grandma can make 0.75 batches of cookies with only a half cup of milk.

Step-by-step explanation:

To solve this problem, we can set up a proportion.

[tex]\frac{2}{3}[/tex] = [tex]\frac{0.5}{x}[/tex]

We can use cross products to solve.

3(0.5)=1.5

2(x)=1.5

x=0.75

Therefore, Grandma can make 0.75 batches of cookies with only a half cup of milk.

Hope this helps!

The equation of h(x) in vertex form is: C. h(x) = (x + 1)² + 2.

In Mathematics and Geometry, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Next, we would create a system of equation by using the data points provided in the table above;

a(-3)² + b(-3) + c = 6

9a - 3b + c = 6     .....equation 1.

a(0)² + b(0) + c = 3

c = 3    .....equation 2.

a(1)² + b(1) + c = 6

a + b + c = 6    .....equation 3.

By solving the system of equations simultaneously, the values of a, b, and c are as follows;

a = 1

b = 2

c = 3

Therefore, the required quadratic function in vertex form is given by;

ax² + bx + c = 0

x² + 2x + 3 = 0

h(x) = x² + 2x + 3

h(x) = (x + 1)² + 2

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Answer:

A - 1/4

Step-by-step explanation: The probability of getting heads on the toss of a coin is 0.25. If we consider all possible outcomes of the toss of two coins as shown, there is only one outcome of the four in which both coins have come up heads, so the probability of getting heads on both coins is 0.25.

Answer:

reflect the parent function over the y-axis, and translate it 3 unit to the left

In situation a, the predictor variable is age, as it is being tested to see if it affects the outcome variable, which is the number of risky behaviors. So, age is the independent variable and the number of risky behaviors is the dependent variable.

In situation b, the predictor variable is the number of family members, as it is being tested to see if it affects the outcome variable, which is the level of education of children. So, the number of family members is the independent variable and the level of education of children is the dependent variable.

It is important to identify the predictor variable and the outcome variable in any study as this helps in understanding the relationship between the two variables and in interpreting the results accurately.

For situation A, the predictor variable is "age," and the outcome variable is "number of risky behaviors." As age increases, the study aims to see if the number of risky behaviors changes.

For situation B, the predictor variable is "number of family members," and the outcome variable is "level of education of children." The study examines whether the children's level of education changes based on the number of family members.

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The equation of the line in slope intercept form is y = -1/3 x - 6

Note that the Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is defined as the ratio of the rise to the run.

We are Given that the line passes through the points (0, -6) and (-6, -4)

The slope of the line is calculated by the formula given as;

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -4 + 6 ) / ( -6 - 0)

Slope = ( 2 / -6 )

Slope  = -1/3

Thus, the equation of the line in slope-intercept form is

y-y₁ = m(x-x₁)

y + 6 = -1/3(x)

y = -1/3 x - 6

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Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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To find the general solution of the second-order differential equation 5y'' + y' = 0, we can use the method of separation of variables.

Let's assume y = e^(mx), where m is a constant.

Taking the first and second derivatives of y with respect to x, we have:

y' = me^(mx)

y'' = m^2e^(mx)

Substituting these expressions into the differential equation, we get:

5(m^2e^(mx)) + (me^(mx)) = 0

Now, we can factor out e^(mx):

e^(mx) * (5m^2 + m) = 0

For this equation to hold true, either e^(mx) = 0 or 5m^2 + m = 0.

Since e^(mx) is never zero for any real value of x, we focus on the second equation:

5m^2 + m = 0

We can factor out m:

m(5m + 1) = 0

Setting each factor equal to zero, we have two possible solutions:

m = 0 or 5m + 1 = 0, which gives m = -1/5.

Therefore, the general solution of the given second-order differential equation is:

y(x) = C1e^(0x) + C2*e^((-1/5)*x)

Simplifying this expression, we have:

y(x) = C1 + C2*e^(-x/5)

Here, C1 and C2 are arbitrary constants that can be determined based on initial conditions or additional information about the problem.

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The repeating decimal 11.454545... can be expressed as the ratio of two integers: 1134/99.Simplifying the fraction, if possible, we find that:1134/99 = 114/11Hence, the repeating decimal 11.454545... can be written as the ratio 114/11.

To express the repeating decimal 11.454545... as a ratio of two integers, we can use algebraic manipulation to convert it into a fraction.

Let's denote the repeating decimal as x:

x = 11.454545...

Multiplying x by 100, we get:

100x = 1145.454545...

Subtracting the original equation from the multiplied equation, we have:

100x - x = 1145.454545... - 11.454545...

Simplifying both sides:

99x = 1134

Dividing both sides by 99:

x = 1134/99.

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Answer:

Sure, here are the answers to your questions:

a. The maximum value of f(x,y) is 674.

b. The point(s) where the function attains its maximum are (-6,3) and (6,3).

c. The minimum value of f(x,y) is -5.

d. The point(s) where the function attains its minimum are (0,0) and (-3,-1).

Here are the steps on how I got the answers:

First, we need to find the critical points of the function. This can be done by finding the points where the gradient is equal to zero.

The gradient of f(x,y) is given by the following vector:

∇f(x,y) = (4x - 4, 6y)

Setting this vector equal to zero, we get the following system of equations:

4x - 4 = 0

6y = 0

Solving this system of equations, we get the following critical points:

(-6,3)

(6,3)

Next, we need to evaluate the function at each critical point and at the boundary points of the domain.

The boundary points of the domain are given by the following points:

(-13,0)

(13,0)

(0,-13)

(0,13)

Evaluating the function at each of these points, we get the following values:

f(-13,0) = -674

f(13,0) = -674

f(0,-13) = -674

f(0,13) = -674

f(-6,3) = 674

f(6,3) = 674

f(0,0) = -5

f(-3,-1) = -5

Finally, we need to compare the values of the function at the critical points and at the boundary points to find the maximum and minimum values.

The maximum value of the function is 674, which is attained at the points (-6,3) and (6,3).

The minimum value of the function is -5, which is attained at the points (0,0) and (-3,-1)

Step-by-step explanation:

The approximate solution of x in log eˣ ⁻ ³ = 7 is 16

From the question, we have the following parameters that can be used in our computation:

log eˣ ⁻ ³ = 7

This can be expressed as

(x - 3)log(e) = 7

Divide both sides of the equation by log(e)

So, we have

x - 3 = 7/log(e)

Evaluate the quotient and approximate

x - 3 = 16

Add 3 to both sides of the equation

x = 19

This means that the approximate solution of x in log eˣ ⁻ ³ = 7 is 16

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Complete question

What is the solution to log eˣ ⁻ ³ = 7

The equivalent expressions of 3(2/3p+3-1/3p-5) is 2p - 6.

By simplifying 3(2/3p+3-1/3p-5), we first have to combine the constants in the parentheses:

2/3p + 3 - 1/3p - 5 = (2/3p - 1/3p) + (3 - 5) = (1/3p) - 2

Substituting this expression back into the original equation, we get:

3(2/3p+3-1/3p-5) = 3[(1/3p) - 2 + 3 - 5]

Simplifying inside the brackets, we have:

3[(1/3p) - 2 + 3 - 5] = 3[(1/3p) - 2 - 2]

Multiplying by 3, we get:

3[(1/3p) - 2 - 2] = (1/p) - 6

Therefore, the equivalent expression of 3(2/3p+3-1/3p-5) is (1/p) - 6.

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The measure of each of the angles are calculated as:

m<1 = 63 degrees.; m<2 = 49 degrees; m<3 = 87 degrees; m<4 = 44 degrees.

The measure of each angle can be calculated as explained below:

m<2 = 49 degrees [based on the vertical angles].

m<1 = 180 - m<2 - 68 [based on the triangle sum theorem]

Plug in the values:

m<1 = 180 - 49 - 68

m<1 = 63 degrees.

m<3 = 180 - 93 [linear pair theorem]

m<3 = 87 degrees.

m<4 = 180 - m<3 - 49 [based on the triangle sum theorem]

Substitute:

m<4 = 180 - 87 - 49

m<4 = 44 degrees.

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We have two possible solutions ∅ = 20.54 degrees and ∅ = -67.58 of the equation

We can start by using the trigonometric identities for the tangent and secant functions:

tan(∅+45°) = (tan∅ + tan45°)/(1 - tan∅ tan45°) = (tan∅ + 1)/(1 - tan∅)

tan(∅-45°) = (tan∅ - tan45°)/(1 + tan∅ tan45°) = (tan∅ - 1)/(1 + tan∅)

sec2∅ = 1/cos2∅ = 1/(1 - sin2∅) = 1/(1 - tan2∅)

Substituting these expressions into the original equation, we get:

[(tan∅ + 1)/(1 - tan∅)] - [(tan∅ - 1)/(1 + tan∅)] = 2/(1 - tan2∅)

Multiplying both sides by (1 - tan∅)(1 + tan∅), we obtain:

(tan∅ + 1)(1 + tan∅) - (tan∅ - 1)(1 - tan∅) = 2(1 - tan∅)(1 + tan∅)/(1 - tan∅)(1 + tan∅)

Simplifying and rearranging terms, we get:

4tan∅ = 2(1 - tan2∅)

2tan2∅ + 4tan∅ - 2 = 0

Dividing both sides by 2, we get:

tan2∅ + 2tan∅ - 1 = 0

Using the quadratic formula, we get:

tan∅ = (-2 ± √8)/2

tan∅ = -1 ± √2

Since the range of the tangent function is (-∞, ∞), both values of tan∅ are possible.

Therefore, we have two possible solutions ∅ = arctan(-1 + √2) = 0.358 radians ≈ 20.54 degrees

∅ = arctan(-1 - √2) = -1.179 radians = -67.58 degrees

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The number line will begin at point 8 and point in the negative direction, with the circle darkened.

Inequalities are expression not separated by an equal sign. Given the inequality expression below:

2x-5≤11

Add 5 to both sides

2x-5 + 5≤11 + 5

2x≤16

Divide both sides by 2

2x/2 ≤16/2

x≤8

The number line will start from the point 8 pointing towards the negative direction and the circle shaded.

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The distance between points A and B will be 6.71 units.

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

Where we have

A = (0, 0)

B = (6, 3)

This means that the point A is on the origin and point B will be (6, 3).

Then the distance between points A and B will be

D² = (6 - 0)² + (3 - 0)²

D² = 6² + 3²

D² = 36 + 9

D² = 45

D = √45 units

Evaluate

D = 6.71 units

Hence, the distance between points A and B will be 6.71 units.

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There are 36, coins of 50c out of a total of 120 coins.

Assume that

Quantity of 50 cent coin = x

Quantity of 20 cent coin = y

Then according to question,

50x + 20y = 3480 ...(i)

Now if the sum of the coins is 120,

x + y = 120  ...(ii)

Now use elimination method,

By 50 x (ii) - (i),

30y = 2520

y = 84  

Now put this value this into (ii);

x = 36

Hence,

Quantity of 50 cent coin = 36

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The expression that represents the change in the amount in Indira's account is: Negative 20 times 5 + 45.
To understand why, we need to break down the different actions that Indira took. So the overall change in Indira's account balance is negative $55.

First, she withdrew $20 from her account every day for 5 days. This means that she took out a total of 20 x 5 = $100 from her account. However, since she withdrew this money, the change in her account balance is negative.
Next, she deposited $45 into her account. This means that she added $45 to her account balance. Since this is a deposit, the change in her account balance is positive.
To calculate the overall change in her account balance, we need to subtract the negative change (from the withdrawals) from the positive change (from the deposit). This can be represented as:
Negative 20 times 5 + 45
Or, using order of operations:
-20 x 5 + 45 = -100 + 45 = -55
So the overall change in Indira's account balance is negative $55.

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The data in Table 1 are not proportional because it does not have a constant of proportionality.

The data in Table 2 are proportional because it has a constant of proportionality that is equal to 3.

The data in Table 3 are proportional because it has a constant of proportionality that is equal to 4.

The equation y = 3x - 2 is not proportional.

The equation y = 0.25x is proportional with a constant of proportionality that is equal to 0.25.

The equation y = x + 5 is not proportional.

An equation for the pay as you go phone is y = 10x and the constant of proportionality is 10.

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) based on the data points provided as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 6/2 = 9/3 = 12/4

Constant of proportionality, k = 3.

Therefore, the required equation is given by;

y = kx

y = 3x

For Jim's pay as you go phone, we have:

Constant of proportionality, k = y/x

Constant of proportionality, k = 10/1

Constant of proportionality, k = 10

Therefore, the required equation is given by;

y = kx

y = 10x

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Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile.

To test the claim that it takes the same time to ride each of the miles, we need to use a one-way ANOVA test.

Using the provided data, we calculate the mean time for each mile and find that Mile 2 has a significantly higher mean time than the other two miles. Therefore, it appears that Mile 2 has a hill.

Jeff Parent's data shows that there is a significant difference in the mean time it takes to ride each mile. Using a one-way ANOVA test with a 0.05 significance level, we found that Mile 2 has a significantly higher mean time than the other two miles. This indicates that there is a hill on Mile 2, which is causing the increased time.

Therefore, we reject the claim that it takes the same time to ride each of the miles and conclude that there is a hill on Mile 2.

Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile. This information can be useful for Jeff to adjust his training and race strategy accordingly.

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The sum of the given quantities that is 8kg+6g+200g+150g = 8356g or 8.356Kg.

To add the given portions, we need to convert them into the identical unit. One kilogram (kg) is the same as one thousand grams (g), so we can multiply 8 kg by using one thousand to get 8000 g. Then we can add 8000 g, 6 g, 200g, and 150g to get the total in grams.

The overall is 8356g. To convert it back to kilograms, we can divide it by a thousand to get 8.356 kg. Therefore, the solution is 8.356 kg.

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The correct question is:

Add the following. "8Kg+6g+200g+150g".

a) The monthly income tax is given as follows: $10,666.

b) The monthly take home salary is given as follows: $39,334.

The tax and the salary are obtained applying the proportions in the context of the problem.

The allowance is of $216,000 per year, hence the monthly allowance is given as follows:

216000/12 = $18,000.

Then the monthly tax is of 1/3 = 33 and 1/3% of 50000 - 18000 = $32,000, hence:

1/3 x 32000 = $10,666.

The take home salary is the remainder of the salary that is not paid in tax, hence:

50000 - 10666 = $39,334.

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For the following examples:

3. Dave's truck has a fuel capacity of 180 US gallons, but it is only one-quarter full, which means he needs 3/4 of 180 gallons = 135 gallons of diesel fuel.

To convert gallons to liters, multiply by 3.78541 (1 gallon = 3.78541 liters).

So Dave needs 135 gallons x 3.78541 liters/gallon = 511.66535 liters of diesel fuel.

The cost of diesel fuel is 94.9 C per liter, so the total cost for Dave to refill his truck is 511.66535 liters x 94.9 C/liter = $485.63.

4. To determine the volume of concrete Greg will need for his driveway, we first convert the dimensions to meters:

20 feet = 6.096 meters, 36 feet = 10.9728 meters, and 4 inches = 0.1016 meters.

Then use the formula for the volume of a rectangular solid: volume = length x width x height.

So the volume of concrete needed for Greg's driveway is 6.096 meters x 10.9728 meters x 0.1016 meters = 6.801 cubic meters.

The cost of the concrete is $135 per cubic meter, so the total cost for the concrete that he will need for his driveway is 6.801 cubic meters x $135/cubic meter = $918.14.

5. The volume of each planting box is 48 inches x 24 inches x 18 inches = 20736 cubic inches.

To convert cubic inches to cubic yards, divide by 46656 (1 cubic yard = 46656 cubic inches).

So each planter box requires 20736 cubic inches / 46656 cubic inches/cubic yard = 0.44444 cubic yards of potting soil.

Susan needs to build 35 planting boxes, so she will need 35 x 0.44444 cubic yards = 15.5554 cubic yards of potting soil.

Holland Growers charges $17 per cubic yard of potting soil, so the cost from them will be 15.5554 cubic yards x $17/cubic yard = $264.45.

Night Growers charges $21.50 per cubic meter of potting soil, which is equivalent to $16.34 per cubic yard (1 cubic meter = 1.30795 cubic yards).

So the cost from Night Growers will be 15.5554 cubic yards x $16.34/cubic yard = $254.36.

Therefore, the total cost of the topsoil she needs from each supplier is $264.45 from Holland Growers and $254.36 from Night Growers.

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Knowing whether the mean is more than or less than the median can give us information about the skewness of a distribution because the mean and median represent different aspects of the distribution's central tendency.

In a positively skewed distribution, the tail of the distribution extends towards higher values, meaning there are some extreme high values that pull the mean towards the right. In this case, the mean is greater than the median because it is influenced by those high values, shifting the central tendency towards the right.

On the other hand, in a negatively skewed distribution, the tail of the distribution extends towards lower values, indicating the presence of extreme low values that pull the mean towards the left. As a result, the mean is lower than the median because the central tendency is shifted towards the left by those low values.

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