. A middle school teacher conducted a survey of the 8th grade class and found that 43 students were athletes and 19 of those students drink soda. There were 33 students that were not athletes, but drank soda. Last, they found that 22 students were not athletes and did not drink soda. Given this information, how many students don't drink soda

The coordinates of point U are (-h, 0).

To find the coordinates of point U in the parallelogram RSTU, we can use the properties of parallelograms. In a parallelogram, opposite sides are parallel, and hence they have the same slope.

Given that point S is at (0, 0), we can calculate the slope of RS as follows:

Slope of RS = (y2 - y1) / (x2 - x1)

= (0 - g) / (0 - (-f)) (Substituting coordinates of R and S)

= g / f

Since RS and TU are opposite sides of the parallelogram, they must have the same slope. Thus, the slope of TU is also g / f.

Given that point T is at (h, 0), we can calculate the equation of the line TU in point-slope form using the slope we just found:

y - y1 = m(x - x1) (Point-slope form of a line)

where;

Plugging in the values, we get:

y - 0 = (g / f)(x - h)

Simplifying, we get:

y = (g / f)x + gh / f

Now, we can substitute the coordinates of point U, which are (x, y), into the equation we just found:

y = (g / f)x + gh / f

y = (g / f)x + gh / f

Since U lies on the x-axis (i.e., y = 0), we can set y = 0 in the equation and solve for x:

0 = (g / f)x + gh / f

(g / f)x = -gh / f

x = -h

So, the x-coordinate of point U is -h.

Now, we can substitute the value of x = -h into the equation we found earlier to get the y-coordinate of point U:

y = (g / f)x + gh / f

y = (g / f)(-h) + gh / f

y = -gh / f + gh / f

y = 0

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Answer: To find the sale price of the trampoline, you have to subtract 25% or a quarter of the original price ($68) from the original price ($68)

Step-by-step explanation:

To find a quarter of 68, you can simply divide this by 4 and now you have a quarter of the original price, $68. 68/4 = 17

Then you subtract a quarter of the original price from the original price.
68-17= sales price

68-17= 51

Sales Price = $51

Hope this helps :D

the perimeter of the rhombus is 20 inches, and the area is 24 square inches.

How to solve the question?

To find the perimeter of a rhombus, we need to know the length of one side. Fortunately, we can use the properties of a rhombus to find the length of the sides. A rhombus has two pairs of equal-length sides, so we can use the Pythagorean theorem to find the length of each side.

Let's label the diagonals of the rhombus as d1 and d2. The diagonals of a rhombus bisect each other at right angles, so we can draw a right triangle with half of each diagonal as the legs and a side of the rhombus as the hypotenuse. Using the Pythagorean theorem, we can find the length of the sides:

(1/2)d1 = 3 inches

(1/2)d2 = 4 inches

Side length = √((1/2)d1² + (1/2)d2²) = √(9 + 16) = 5 inches

Now that we know the length of the sides, we can find the perimeter:

Perimeter = 4 x side length = 4 x 5 = 20 inches

To find the area of the rhombus, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 x 8) / 2 = 24 square inches

So the perimeter of the rhombus is 20 inches, and the area is 24 square inches.

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Answer: The answer is 84

The total of the angels of the triangle always equals 180. So 62+34=96 therefor 96-180=84.

The calculated value of the percent error of the measurement is 18.7%.

Percent error is calculated by subtracting the measured value from the actual value, dividing the result by the actual value, and then multiplying by 100 to get a percentage.

Using this formula, we have:

Error = Actual Value - Measured Value = 13.4 - 10.9 = 2.5

So, we have

Percent Error = (Error / Actual Value) * 100 = (2.5 / 13.4) * 100 ≈ 18.7%

Therefore, the percent error of the measurement is approximately 18.7%.

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In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, in the given expert.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt.

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, the author lets readers peek inside the protagonist, Miriam, to understand her feelings and thoughts as they happen. For instance, readers can feel Miriam's mild dizziness 

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The probability of having at least one faulty component in your selection is 0.41 or 41%.

The probability of having at least one faulty component in a selection of 5 can be found by calculating the probability of having no faulty components and then subtracting this from 1.

The probability of having no faulty components in a selection of 5 is:

P(no faulty) = (0.9)^5 = 0.59

Therefore, the probability of having at least one faulty component in a selection of 5 is:

P(at least one faulty) = 1 - P(no faulty) = 1 - 0.59 = 0.41

So the probability of having at least one faulty component in your selection is 0.41 or 41%.

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--The complete Question is, You randomly pick 5 components from the bag of 30. What is the probability that you have at least one faulty component in your selection? --

Answer:

Answers down below!

Step-by-step explanation:

Mean: 38.2

Median: 34

Range: 56

Mode: 13 and 34

Hope this helps!

Answer:

Mrs. Ades is not being fair. The probability of Elias and Maha getting chosen should be equal, but Elias has a 6/10 chance of being chosen, while Maha only has a 4/10 chance of being chosen. This is because Elias has 6 tiles assigned to him, while Maha only has 4 tiles assigned to her.

Explanation:

To make it fair, Mrs. Ades should assign each person an equal number of tiles, or draw from a bag with the tiles numbered 1 through 5 twice, assigning one to Elias and one to Maha each time, and then draw from a bag with tiles numbered 6 through 10 twice, assigning one to Elias and one to Maha each time.

Answer:62.5

Step-by-step explanation:

There seems to be an error in the expression for P3(x). It appears to be missing an exponent for the second term.

Assuming that the correct expression is P3(x) = x^4 - 21x^2 + 20x, we can analyze its properties.

The degree of the polynomial P3(x) is 4, which means its graph will have at most 4 x-intercepts and at most 3 turning points.

To find the x-intercepts, we set P3(x) equal to zero and solve for x:

x^4 - 21x^2 + 20x = 0

x(x^3 - 21x + 20) = 0

Using the factor theorem or synthetic division, we can find that x = 0 is a root of the polynomial, so (x-0) is a factor. The remaining cubic factor can be factored as (x-1)(x-4)(x+5).

Therefore, the x-intercepts of the graph of P3(x) are x = 0, x = 1, x = 4, and x = -5.

As for the y-intercept, we can find it by setting x = 0:

P3(0) = 0^4 - 21(0)^2 + 20(0) = 0

So the y-intercept is (0,0).

To determine the turning points, we can find the critical points by taking the derivative of P3(x) and setting it equal to zero:

P3'(x) = 4x^3 - 42x + 20

4x^3 - 42x + 20 = 0

Solving this equation yields three critical points: x ≈ -1.23, x ≈ 0.58, and x ≈ 2.65.

We can use the second derivative test to determine the nature of these critical points. The second derivative is:

P3''(x) = 12x^2 - 42

At x ≈ -1.23 and x ≈ 2.65, the second derivative is negative, indicating that these are local maxima. At x ≈ 0.58, the second derivative is positive, indicating that this is a local minimum.

Therefore, the graph of P3(x) has a local maximum at (approximately) (-1.23, P3(-1.23)), a local minimum at (approximately) (0.58, P3(0.58)), and a local maximum at (approximately) (2.65, P3(2.65)).

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The trig function that meets the given criteria is determined as f(x) = 4sin(π/4x) + 9.4.

We can use the formula for a sinusoidal function of the form:

f(x) = Asin(Bx - C) + D

where:

We have A = 4 and K = 9.4, so we know that the midline of the function is at y = D = 9.4.

Since we don't have any information about the horizontal shift, we can assume that C = 0.

Then, the formula becomes:

f(x) = 4sin(Bx) + 9.4

Now, we need to find B so that the function has a period of 2π. Since the period is given by T = 2π/B, we have:

2π = TB = (13.4 - 5.4)B = 8B

Therefore, B = π/4. Finally, we can write the function as:

f(x) = 4sin(π/4x) + 9.4

This function has an amplitude of 4, a midline at y = 9.4, and a period of 2π.

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The area of the plot of land that has a top view as shown on a map above is calculated as: C. 112 square meters

The shape of the plot of land can be decomposed into two different triangles and 1 rectangle.

Area of triangle 1 = 1/2 * base * height

base = 8 m

height = 5 m

Area of triangle 1 = 1/2 * 8 * 5 = 20 square meters

Area of triangle 2 = 1/2 * base * height

base = 8 m

height = 7 m

Area of triangle 2 = 1/2 * 8 * 7 = 28 square meters

Area of the rectangle = length * width = 8 * 8

= 64 square meters.

Therefore, we have:

Area of the plot of land = 64 + 28 + 20

= 112 square meters.

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(a) To solve this problem, we need to apply the concept of combinations.  We can find the total number of combinations by using the formula:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we want to select.

Let's assume that we have x pennies, y nickels, z dimes, and w quarters. Since we want to select 25 coins, we can write the equation as x + y + z + w = 25

To find the number of ways to select 25 coins, we need to find the number of solutions to this equation. The total number of combinations is given by: (25 + 4 - 1)C(4 - 1) = 28C3

where we have 25 coins to select and four piles to choose from. Thus, the answer is 28C3.

(b) To solve this problem, we need to use the concept of counting with restrictions. Since we must select at least 5 quarters, we can assume that we have selected 5 quarters and we need to select the remaining 20 coins from the remaining piles. Let's assume that we have x pennies, y nickels, and z dimes. We can write it as x + y + z = 20

To find the number of ways to select 20 coins from the remaining piles, we can use the concept of combinations. The total number of combinations is (20 + 3 - 1)C(3 - 1) = 22C2

Thus, the total number of ways to select 25 coins with at least 5 quarters is given as 10C5 x 22C2

where we have selected 5 quarters from 10 quarters and 20 coins from the remaining piles.

(c)To solve this problem, we need to use the concept of counting with restrictions. Since we can select at most 10 quarters, we need to consider two cases:

(i) We select 10 quarters, and we need to select 15 coins from the remaining piles.

For case (i), we need to select 15 coins from the remaining piles. We can assume that we have x pennies, y nickels, and z dimes. We can write the equation as x + y + z = 15

The total number of ways to select 15 coins is (15 + 3 - 1)C(3 - 1) = 17C2

(ii) We select fewer than 10 quarters, and we need to select the remaining coins from the piles.

For case (ii), To calculate the number of ways, we can use the combination formula to select i quarters out of 10, where i can vary from 0 to 9, and select the remaining (25-i) coins from the remaining piles. We can then sum up the number of ways for all possible values of i to get the total number of ways to select 25 coins with at most 10 quarters.

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If cash is  54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills, the total deposit is $454.00.

To find the total deposit, we need to add up the amounts from the checks and cash, and then subtract the cash received.

First, let's add up the amounts from the checks:

$152.54 + $147.46 = $300.00

Next, let's add up the amounts from the cash:

54 one-dollar bills = $54.00

12 five-dollar bills = $60.00

6 ten-dollar bills = $60.00

Total cash = $174.00

Finally, we need to subtract the cash received:

$174.00 - $20.00 = $154.00

Therefore, the total deposit is $300.00 + $154.00 = $454.00.

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Complete question is:

Find the total deposit if you have: Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.

The Central Limit Theorem is an important tool that provides the information you will need to use sample means to make inferences about a population mean.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that if we take repeated random samples of size n from any population with a finite mean and variance, then the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

This means that if we take a large enough sample size from a population, the distribution of the sample means will be approximately normal, even if the population distribution is not normal. This is important because the normal distribution is well understood and has many useful properties that make it easier to work with in statistical analyses.

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Answer:

Step-by-step explanation:

Let X be the number of adults who had their faces painted.

Therefore, the number of kids who had their faces painted is 8*X.

Given that 56 kids had their faces painted, we can write an equation as:

8*X = 56

Solving for X:

X = 7

So, there were 7 adults who had their faces painted and 56 kids who had their faces painted.

Altogether, there were 7 + 56 = 63 people who had their faces painted.

The correct representations of the inequality is

- 6x + 15 < 10 - 5x  and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

We have the inequality -3(2x - 5) < 5(2 - x)

Now, simplifying each side of inequality

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

-3(2x - 5) = - 6x + 15

and, 5(2 - x) = 5(2) + 5(-x)

5(2 - x) = 10 - 5x

So, - 6x + 15 < 10 - 5x

Now, Subtract 15 from both sides

- 6x < -5 - 5x

- x < - 5

x > 5

The correct statements are:

- 6x + 15 < 10 - 5x  and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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The answer of the given question based on the cylinder is ,  the volume of the solid = 929.44  inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.

Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.

To find volume of  solid, we need to subtract  volume of  inner cylinder from  volume of outer cylinder.

Volume of the outer cylinder = πr²h

where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)

h = height of the outer cylinder = 23 inches

Volume of the outer cylinder = π(4)²(23) = 368π in³

Volume of the inner cylinder = πr²h

where r = radius of the inner cylinder = 2 inches

h = height of the inner cylinder = 18 inches

Volume of the inner cylinder = π(2)²(18) = 72π in³

So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder

= 368π - 72π

= 296π

= 929.44  inch³

The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.

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There are 813 minutes in between 17:53 to 7.26 .

Time can be represented in two formats, that is in a twelve - hour format and in a twenty four - hour format.

Here the time 17:53 and 7:26 is represented in twenty four - hour format where the day is divided in twenty four hours and time runs from midnight and ends at midnight.

(If the time 17:53 and 7:26 was represented in twelve - hour format then it would have AM and PM to denote if the time is from midnight till noon or noon till midnight, which is clearly not the case.)

Thus, from 17:53 to 7.26 there is 13 hours and 33 minutes.

We know one hour has 60 minutes. Therefore by method of conversion of hours to minutes we get,

Number of minutes between 17:53 to 7.26 = {(13*60) + 33} = 780+33 = 813

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The expanded form of (2x² + 5y)⁵ using the binomial theorem is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.

Given the expression in the question:

(2x² + 5y)⁵

To expand (2x² + 5y)⁵ using the binomial theorem, we need to apply the following formula:

(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + C(n, 2)a⁽ⁿ⁻²⁾ b² + ... + C(n, r)[tex]a^{(n-r)}[/tex] [tex]b^r[/tex] + ... + C(n, n)a⁰ bⁿ

Where C(n, r) is the binomial coefficient, which represents the number of ways to choose r items from a set of n distinct items.

(2x² + 5y)⁵

Here: a = 2x² and b = 5y, so we have:

Plug into the above formula

(2x² + 5y)⁵ = C(5, 0)(2x²)⁵ (5y)⁰ + C(5, 1)(2x²)⁴ (5y)¹ + C(5, 2)(2x²)³ (5y)² + C(5, 3)(2x²)² (5y)³ + C(5, 4)(2x²)¹ (5y)⁴ + C(5, 5)(2x²)⁰ (5y)⁵

Simplifying each term using the binomial coefficient formula C(n, r) = n! / (r! (n-r)!):

(2x² + 5y)⁵ = 1(32x¹⁰)1(1) + 5(16x⁸)1(5y)¹ + 10(8x⁶)2(25y²) + 10(4x⁴)3(125y³) + 5(2x²)4(625y⁴) + 1(1)5(3125y⁵)

Simplifying the coefficients and the exponents of x and y:

(2x² + 5y)⁵ = 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵

Therefore, the expanded form is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.

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Sampling methods that may be biased for finding the percentage of defective boards in a sawmill production are: selecting 30 consecutive boards, emailing customers and relying on their responses, and selecting every 40th board produced. So, the correct answer is A, B and D.

The biased sampling methods are Examining 30 consecutive boards one hour after production begins may be biased because it only captures a snapshot of the production at that specific time, and the boards selected may not be representative of the entire batch produced during the day.

Emailing customers to ask about defective boards may be biased because the response rate may vary among customers, and customers who experienced a higher or lower number of defective boards may be more likely to respond.

Selecting 20 boards at random each day for 5 days and examining them is less likely to be biased, as long as the selection process is truly random and representative of the entire production.

Selecting every 40th board produced over the course of one week is also less likely to be biased if the production process is consistent and there are no patterns or variations in the production that would affect the quality of every 40th board. So, the correct answer for biased is A, B and D.

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Justin made a total deposit of $1985.66.

A deposit is a sum of money that is added to an account or made available for use in a financial transaction. It can refer to money that is placed into a bank account, such as a savings or checking account, or to a payment made in advance for goods or services. Deposits are often required when b accounts, taking out loans, or making large purchases.

In the context of banking, deposits can earn interest, which can increase the amount of money in the account over time.

Let's start by adding up the bills:

Total amount of bills = 8 x 100 + 27 x 50 + 83 x 5 + 141 x 1

Total amount of bills = 800 + 1350 + 415 + 141

Total amount of bills = 1706

Next, let's add up the coins:

Total amount of coins = 13 x 0.25 + 117 x 0.05

Total amount of coins = 3.25 + 5.85

Total amount of coins = 9.10

Now, let's add up the checks:

Total amount of checks = 317.94 + 57.89 + 527.24 + 77.49

Total amount of checks = 980.56

Finally, let's add up the cash back:

Total amount of cash back = 30 x 20 + 11 x 10

Total amount of cash back = 600 + 110

Total amount of cash back = 710

To find the total deposit, we need to add up all the amounts:

Total deposit = Total amount of bills + Total amount of coins + Total amount of checks - Total amount of cash back

Total deposit = 1706 + 9.10 + 980.56 - 710

Total deposit = 1985.66

Therefore, Justin made a total deposit of $1985.66.

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The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3.

For this problem, the number of packs bought is the least common multiple of 10 and 12, which is obtained by factoring them into prime numbers as follows:

10 - 12|2

5 - 6|2

5 - 3|3

5- 1|5

1 - 1

Hence:

lcm(10, 12) = 2² x 3 x 5 = 60.

Hence:

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The expression that is equivalent by the Distributive Property is A 3x+12

this is the only answer that actually uses the distributive property.

The Distributive Property is a mathematical rule that applies to operations such as multiplication and addition or subtraction. It states that when you multiply a number by a sum or difference of two or more numbers, you can distribute the multiplication over each of the individual terms in the sum or difference.

3 can be multiplied by both x and 4 to get 3x+12 (which is using the distributive property)

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The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.

The probability of landing on a green section is 0/16, which simplifies to 0.

The probability of landing on a red section is 4/16, which simplifies to 1/4.

The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.

In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.

The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.

Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.

The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.

Since there are no green sections, the probability of landing on a green section is 0.

There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.

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The areas of the composite figures are listed below:

Case 6: A = 134.126 ft²

Case 7: A = 212.5 cm²

Case 8: A = 957.305 m²

Case 9: A = 316.643 in²

In this problem we find four cases of composite figure, that is, figures that are the result of adding and subtracting figures, whose area formulas are introduced below:

Semicircle

A = 0.5π · r²

Circle

A = π · r²

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we proceed to determine the area of each composite figure:

Case 6

A = (25 ft)² - π · (12.5 ft)²

A = 134.126 ft²

Case 7

A = (25 cm) · (14 cm) - 0.5 · (25 cm) · (11 cm)

A = 212.5 cm²

Case 8

A = 0.5π · [(21.6 m)² + (9 m)²] + 0.5 · (21.6 m) · (9 m)

A = 957.305 m²

Case 9

A = 0.5 · (20 in) · √[(25 in)² - (20 in)²] + (17 in) · √[(25 in)² - (20 in)²] - 0.5π · 0.25 · [(25 in)² - (20 in)²]

A = 316.643 in²

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Answer:

21.5

Step-by-step explanation:

1. Line the numbers from least to greatest:

20, 20, 21, 22, 23, 26

2. cross off one from one side then the other

(ex: 20, 20, 21, 22, 23, 26 --> 20, 21, 22, 23 --> 21, 22)

3. the number left is the median, but if there are 2 numbers left do step 4 and 5

4. find the middle of the 2 numbers (ex: 21 and 22's middle is 21.5)

5. The middle of the those 2 numbers is the median (which in this case is 21.5)