Your friend asks you for help on a geometry exercise. Your​ friend's paper is shown to the right. What error did your friend​ make? Explain.
a.Your​ friend's paper does not name the triangles correctly for them to be congruent.
b. Your​ friend's paper shows that the SAS Postulate should be used to show congruence because a pair of congruent angles is included between two pairs of congruent sides.
c. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the triangles do not have two pairs of congruent angles.
d.
The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.

Hi there! :)

Answer:

\(\huge\boxed{L = 9 \text { units}}\)

Given:

Perimeter = 28

Let the breadth = x. The length is 4 units greater, so we can represent this as (x + 4).

Set up an expression. Remember that the formula for the perimeter of a rectangle is:

P = 2(l) + 2(w)

Substitute:

28 = 2(x) + 2(x+ 4)

Distribute:

28 = 2x + 2x + 8

Combine like terms and simplify:

28 = 4x + 8

20 = 4x

x = 5.

The length of the breadth is 5 units. Substitute in 5 to solve for the length:

(5) + 4 = 9 units.

The length of the rectangle is 9 units.

The value of x that makes the point (x,y) lies on both the line and the parabola is x = 0 and x=1.

The values of x for which the point (x,y) lies on both the line and the parabola, we set the equation of the line y = 4x equal to the equation of the parabola y^2 = 16x.

By substituting y = 4x into the equation of the parabola we get (4x)^2 = 16x and further simplifying it results in 16x^2 = 16x.

so x=1 and x=0

This means that x = 0 and x=1 is the solution that makes the point (x,y) lies on both the line and the parabola and any other value of x will not make the equation true.

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Complete question:

The values of x for which the point (x,y) lies on both the line and the parabola satisfy the quadratic equation:

The equation of line is y = 4x

equation of parabola is \(y^2\) = 16x

Answer:

this is confusing

Step-by-step explanation:

Answer:

0 because 0 times whatever is 0

Step-by-step explanation:

The length of the rectangular painting is equal to 76 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of a rectangular painting is 4636 cm². The width of the painting is equal to 61 cm.

The length of the painting is calculated as,

Area of rectangle = Length x Width

4636 = Length x 61

Length = 4636 / 61

Length = 76 cm

The length is 76 cm for the rectangle.

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The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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To determine whether there must be at least two cards of the same suit in a poker hand, we can apply the pigeonhole principle.

The pigeonhole principle states that if you distribute more objects into fewer containers (pigeonholes), at least one container must contain more than one object.

In this case, the pigeons are the cards in the poker hand, and the pigeonholes are the four different suits (hearts, diamonds, clubs, and spades). The rule assigning each pigeon to a pigeonhole is that each card is assigned to its corresponding suit pigeonhole.

Now, let's consider the situation. We have a poker hand consisting of 5 cards. Since there are only four suits available, at least one of the suits must have more than one card assigned to it. This is because if each of the four suits had only one card, we would have a total of 4 cards, which is fewer than the 5 cards in a hand.

By the pigeonhole principle, if one suit has more than one card, there must be at least two cards of the same suit in the poker hand. Therefore, it is guaranteed that in any poker hand, there will be at least two cards of the same suit.

This conclusion holds true regardless of the specific arrangement of the cards in the hand. The pigeonhole principle provides a logical reasoning that ensures the existence of at least two cards of the same suit in a poker hand, based solely on the number of cards and suits involved.

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The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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Answer:

\(12\) books

Step-by-step explanation:

\(62 \div 5 = 12remainder2\). Get rid of the the remainder (\(2\)) because it was specified that the books were split evenly, and then answer is \(12\).

Answer:

-9.75 or -39/4 or \(-9\frac{3}{4}\)

Answer:

Mr. Smith

Step-by-step explanation:

Mr Smith is using the better method because he is making use of a larger number of trials such that the result of his experiment whereby he plans to flip the coin 1,000 times, will be more accurate than the result of that of Mr Jones  that only plans to flip the coin only 10 times which allows for the large number correct outcome of the flipping of the coin to balance out the few inaccuracies. Whereby when only 10 trials are used, the few number of the inaccurate outcomes will have a larger impact on the correct result of the experiment.

The surface area A(S) is 64√2 - 128/3

What is a parametric equation?

A parametric equation is a mathematical representation of a curve or surface in terms of one or more parameters. Instead of defining the curve or surface directly in terms of x and y (or x, y, and z for three-dimensional surfaces), parametric equations express the coordinates as functions of one or more parameters.

What is surface area?

Surface area is a measure of the total area that covers the outer part of a three-dimensional object or surface. It represents the sum of all the areas of the individual faces or surfaces that make up the object.

To find the area of the surface given by the parametric equations, we first need to calculate the cross product of the partial derivatives of the vector function r(u, v). Then we will integrate the magnitude of the cross product over the parameter domain D.

Let's calculate the partial derivatives of r(u, v) with respect to u and v:

∂r/∂u = <2u, v, 0>

∂r/∂v = <0, u, v>

Now, let's calculate the cross product of these partial derivatives:

ru × rv = <2u, v, 0> × <0, u, v>

= <v(v), 0, -2u(u)>

The magnitude of ru × rv is |ru × rv| = √(v² + 4u²).

To find the surface area, we need to integrate |ru × rv| over the parameter domain D, which is given as 0 ≤ u ≤ 2 and 0 ≤ v ≤ 4.

A(S) = ∫∫D |ru × rv| dA

= ∫[0,4]∫[0,2] √(v² + 4u²) dudv

Integrating this expression will give us the surface area A(S).

A(S) = ∫[0,4]∫[0,2] √(v² + 4u²) dudv

We can start by integrating with respect to u:

∫[0,2] √(v² + 4u²) du

To integrate this expression, we can make a substitution by letting w = v² + 4u². Then dw/du = 8u, which implies du = (1/8u)dw.

When u = 0, w = v² + 4(0)² = v², and when u = 2, w = v² + 4(2)² = v² + 16.

The integral becomes:

∫[v², v²+16] √w (1/8u) dw

Since u = (w - v²) / (4u), we can rewrite the integral as:

(1/8) ∫[v², v²+16] √w / u dw

Now we can integrate with respect to w:

(1/8) ∫[v², v²+16] √w / ((w - v²) / (4u)) dw

(1/8) ∫[v², v²+16] (4u/ (w - v²)) √w dw

Let's simplify further:

(1/2) ∫[v², v²+16] (u/ (w - v²)) √w dw

We can now evaluate this integral with respect to w. The limits of integration are v² and v² + 16.

(1/2) ∫[v², v²+16] (u/ (w - v²)) √w dw

(1/2) u ∫[v², v²+16] (1/ √w) dw

Integrating (1/ √w) with respect to w gives 2√w.

(1/2) u [2√w] evaluated from v² to v²+16

(1/2) u [2√(v²+16) - 2√v²]

Now, let's evaluate the outer integral with respect to v:

∫[0,4] (1/2) u [2√(v²+16) - 2√v²] dv

To evaluate this integral, we substitute u = 2u:

∫[0,4] (1/2) 2u [2√(v²+16) - 2√v²] dv

∫[0,4] u [2√(v²+16) - 2√v²] dv

Now we can integrate with respect to v:

u ∫[0,4] [2√(v²+16) - 2√v²] dv

To evaluate this integral, we can apply the power rule for integration and simplify:

u [v√(v²+16) - (4/3)v\(^{3/2}\)] evaluated from 0 to 4

Now we substitute the limits of integration:

u [(4√(4²+16) - (4/3)4\(^{3/2}\)]

Simplifying further:

u [(4√(16+16) - (4/3)4\(^{3/2}\)]

u [(4√32 - (4/3)4\(^{3/2}\)]

We can simplify the expression inside the square root:

4√32 = 4√(16 * 2) = 4√16 * √2 = 4 * 4√2 = 16√2

The expression becomes:

u [(16√2 - (4/3)4\(^{3/2}\)]

Simplifying the second term:

(4/3)4\(^{3/2}\) = (4/3) * 4 * √4 = (4/3) * 4 * 2 = 32/3

The expression becomes:

u [(16√2 - 32/3)]

Now, let's substitute the limits of integration:

u [(16√2 - 32/3)] evaluated from 0 to 4

Plugging in the upper limit:

4 [(16√2 - 32/3)] = 4 * (16√2 - 32/3) = 64√2 - 128/3

Finally, let's subtract the value at the lower limit:

0 [(16√2 - 32/3)] = 0

Therefore, the surface area A(S) is:

A(S) = 64√2 - 128/3

Note: The units of area will depend on the units of the original parametric equations (x, y, z).

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When the amplitude of the oscillator gradually decreases with time, we say it is a damped oscillator. The oscillator's behavior is said to be undamped if the amplitude remains the same over time.

Suppose that both the undamped and damped systems are set in motion with the initial conditions

y(0) = y0 and y′(0) = v0.

The amplitude of the damped response is half that of the amplitude of the undamped response at a time t equal to: t = (1/ωd)ln(A0/A0d), where A0 is the amplitude of the undamped response, A0d is the amplitude of the damped response, and ωd is the damped angular frequency.

What is a damped oscillator?

A damped oscillator is an oscillator that gradually loses energy over time as a result of the energy dissipation mechanism present in the oscillator.

A spring-mass system immersed in a viscous fluid, a pendulum and a guitar string are examples of oscillatory systems. When the amplitude of the oscillator gradually decreases with time, we say it is a damped oscillator. The oscillator's behavior is said to be undamped if the amplitude remains the same over time.

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Answer:

75°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

let x be the sixth angle, then sum and equate to 720°

150 + 100 + 80 + 165 + 150 + x = 720

645 + x = 720 ( subtract 645 from both sides )

x = 75

The sixth interior angle is 75°

There are 9000 4-digit numbers from 1000 to 9999. There are 10,000 5-digit numbers that end in I. There are 1,000 5-digit numbers that end in 0. There are 10,000 5-digit numbers that are multiples of 10.

(a) To determine the number of 4-digit numbers from 1000 to 9999, we subtract the starting point (1000) from the ending point (9999) and add 1 since we're including both endpoints. Therefore, the number of 4-digit numbers is:

9999 - 1000 + 1 = 9000.

(b) To count the number of 5-digit numbers that end in I, we need to determine the possible values for the other four digits. For each of the other four digits, there are 10 possible choices (0-9). Therefore, the number of 5-digit numbers ending in I is:

10^4 = 10,000.

(c) To count the number of 5-digit numbers ending in 0, we again need to determine the possible values for the other four digits. For each of the other four digits, there are 10 possible choices (0-9). However, for the last digit, it must be 0. Therefore, the number of 5-digit numbers ending in 0 is:

10^3 = 1,000.

(d) To count the number of 5-digit numbers that are multiples of 10, we need to determine the possible values for the other four digits. For each of the other four digits, there are 10 possible choices (0-9). Again, the last digit must be 0 since it is a multiple of 10. Therefore, the number of 5-digit numbers that are multiples of 10 is:

10^4 = 10,000.

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Answer:

i think its B

Step-bi think iy-step explanation:

2+3+1+2+1= 9

3+1 = 4

4/9 simplified 2/3

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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Answer:

(-4,1)

Step-by-step explanation:

change the sign of the x value to a negative

(-1,3)

add 3 to the x value since it's horizontal

(-4.3)

subtract 2 from the y value, since it's vertical

(-4,1)

hope this helps.

The independent variable for Scenario A is given as follows:

a. The employee benefits package.

In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:

In the context of this problem, we have that the input and the output of the relation are given as follows:

Hence the independent variable for Scenario A is given as follows:

a. The employee benefits package.

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Answer:

Exponential decay

Step-by-step explanation:

The general form of an exponential function is

\(P=P_{0}a^t\), where P0 is the initial value, a is the base, and t is the exponent.

In your example, P0 is 1 and a is 4/5.

A function is experiencing exponential growth when a > 1.

A function is experiencing exponential decay when 0 < a < 1.

4/5 lies between 0 and 1, so the function is experiencing exponential decay.

The value of the expression \(343^{-4/3}\) is 1/2401.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(343^{-4/3}\)

This can be written as,

1/\(343^{4/3}\)

343 = 7³

= 1/\(7^{3\times4/3}\)

= 1/\(7^4\)

\(7^4\) = 7 x 7 x 7 x 7 = 49 x 49 = 2401

= 1/2401

Thus,

The value of the expression is 1/2401.

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Answer:

pretty sure its D

Step-by-step explanation:

A is definetly at 1 in weight (ounces), and definetly at 0.25 at cost.

Answer:

The answer is D

Step-by-step explanation:

If 2 is 50 cents, then 1 is 25 cents

(sorry i just wanted points <33)

1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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The value of x is 5, if a, b, and c are collinear points.

According to the given question.

a, b, and c are collinear points.

Which means points a, b, and c both lie in a same line.

b is between a nd c .

Also, ab = 12

bc = 5x - 2

and ac = 3x + 20

Since, b lies in between a and c

Therefore,

ab + bc = ac

12 + 5x - 2 = 3x + 20

⇒ 10 + 5x = 3x + 20

⇒ 5x - 3x = 20 - 10

⇒ 2x = 10

⇒ x = 10/ 2

⇒ x = 5

Therefore, the value of x is 5.

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The key features include random assignment of participants into two groups (drug A and placebo), administration of the drug or placebo without participants knowing which one they received, and comparison of outcomes (number of pain episodes) between the groups at the end of the treatment period.

This is a randomized controlled trial (RCT). An RCT is a type of research study where participants are randomly assigned to receive either the treatment (drug) or a placebo, and then the outcomes of both groups are compared. In this case, the study was conducted by the National Institutes of Health to investigate whether drug A can reduce the pain associated with sickle-cell disease. 150 sickle-cell sufferers were randomly assigned to receive the drug and another 150 were given placebos. The researchers took great care to ensure that the participants did not know whether they were receiving the drug or the placebo. At the end of the treatment period, the number of episodes of pain reported by each subject was counted. This study is important in helping researchers and healthcare professionals understand the effectiveness of the drug in reducing the pain associated with sickle-cell disease.

This study is a double-blind randomized controlled trial (RCT).

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Answer:

Inconsistent

Step-by-step explanation:

A system of linear equations that has at least one solution is called consistent, whereas a system of linear equations that has no solutions is called inconsistent.

A system of linear equations that has no solution is a set of inconsistent equations.

The correct answer is an option (B)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a set of equations for which we find a common solution."

"A system of equations is consistent if there is at least one set of values that satisfies each equation in the system."

"A system of equations is inconsistent if there is no solution to the given system of equations."

From the definition, we can see that the system of equations is inconsistent if a system of equations has no solution.

Therefore, A system of linear equations that has no solution is a set of inconsistent equations.

The correct answer is an option (B)

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The point (2, 4) is a solution to the system of equations 2x + y = 8 and 6x - y = 0.

A) (2, 4) for the system 2x + y = 8 and 6x - y = 0

Yes, (2, 4) is a solution to the system of equations. To prove this, we can substitute the values into the two equations. In the equation 2x + y = 8, substituting x = 2 and y = 4, we get 2(2) + 4 = 8. This statement is true, so the point (2, 4) is a solution to this equation. In the equation 6x - y = 0, substituting x = 2 and y = 4, we get 6(2) - 4 = 0. This statement is also true, so the point (2, 4) is also a solution to this equation. Therefore, (2, 4) is a solution to the system of equations 2x + y = 8 and 6x - y = 0.

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Answer:

the answer is -33 srry couldn't explain :(

Answer:

Step-by-step explanation:

(-12)-21= -33. Tienes q sumar porque son del mismo signo y se queda con el signo de negativo por que ambos números son negativos.

approximately 28.2 mg of the substance will remain after 9 hours.

We can use the formula for exponential decay to solve this problem:

N(t) = N0 * e^(-kt)

where:

N(t) = the amount of radioactive substance remaining after time t

N0 = the initial amount of radioactive substance

k = the decay constant

t = time elapsed

We are given that the initial amount of radioactive substance is 110 mg, and after 6 hours, 38 mg remains. So we can set up the following equation:

38 = 110 * e^(-6k)

To solve for the decay constant k, we can divide both sides by 110 and take the natural logarithm of both sides:

ln(38/110) = -6k

k = -ln(38/110) / 6

k ≈ 0.1664

Now we can use this value of k to find the amount of radioactive substance remaining after 9 hours:

N(9) = 110 * e^(-0.1664*9)

N(9) ≈ 28.2

what is exponential?

In mathematics, an exponential function is a function of the form f(x) = a^x, where a is a positive constant (called the base) and x is the variable. Exponential functions grow or decay at a constant percentage rate, which makes them useful for modeling various real-life phenomena, such as population growth, radioactive decay, compound interest, and the spread of epidemics. Exponential functions have a characteristic curve that starts out slowly, but eventually grows rapidly as x increases (in the case of exponential growth) or decreases (in the case of exponential decay).

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Answer:

The problem is about cases of diabetes in old people through months.

The variable is descrete , because it doesn't admit decimal numbers, it represents people, and people are whole numbers.

The frequency table would be

January                       24

February                     30

March                          20

April                             18

May                             28

June                             12

The total number of people is 132.

The mean would be the total number of people divided by the six months.

\(\mu = \frac{132}{6} =22\)

Therefore, the mean is 22 people per month.

Remember that the median is the value at the center of the data set, which is between March and April, so

\(\frac{20+18}{2}=19\)

Therefore, the mean is 19.

The third statistical value is determined by the major frequency. So, the data that repeats the most is February, which means that month encloses the majority of people.