Answer: ddddddddddddddddddddddddddddddddddddddddddddddbddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
Step-by-step explanation:
which of the following numbers are irrational. -4.8237, pi/2, 3 to the rooted power of 4, or 4 + the square root of 25?
The irrational number for this problem are given as follows:
pi/2.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.
For this problem, we have that the number pi/2 is irrational, as pi is a non-terminating decimal, and the division of an irrational by a rational results in an irrational.
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The gradient of a curve at the point (x,y) is given by dy/dx=2(x+3)^1/2-x. The curve has a stationary point at (a,14), where a is a positive constant. Find the value of a.
Using the gradient of the curve given, the value of a is 6
What is the value of aThe stationary point of a curve is a point where the slope of the curve is equal to zero. So, to find the value of a, we need to set the derivative of the curve equal to zero and solve for x.
dy/dx = 2(x + 3)^(1/2) - x
Setting this equal to zero, we have:
2(x + 3)^(1/2) - x = 0
Expanding the square root and rearranging, we get:
x = 2(x + 3)^(1/2)
Squaring both sides of the equation, we have:
x^2 = 4(x + 3)
Expanding the right side and rearranging, we have:
x^2 - 4x - 12 = 0
Using the quadratic formula, we can find the values of x that satisfy this equation:
x = [-(-4) ± √((-4)^2 - 4(1)(-12))] / 2(1)
x = [4 ± √(16 + 48)] / 2
x = [4 ± √64] / 2
x = [4 ± 8] / 2
So, the two possible values of x are:
x = 6, x = -2
Since we are looking for a positive value of x, the only solution that works is x = 6.
Therefore, the value of a is equal to 6.
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if a data set is normally distributed what percent of the data will lie below the mean
Explanation:
The normal curve, aka bell curve, has mirror symmetry with the mean at the very center. Half of the data is below the mean, while the other half is above the mean.
About 68% of the data will lie below the mean in a normally distributed data set. This is known as the Empirical Rule, which states that if a data set is approximately normally distributed, then approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
mrs. starnes enjoys doing sudoku puzzles. the time she takes to complete an easy puzzle can be modeled by a normal distribution with mean 5.3 minutes and standard deviation 0.9 minute. what proportion of the time does mrs. starnes finish an easy sudoku puzzle in less than 3 minutes?
The proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes is approximately 0.0055, or 0.55%
We can use the normal distribution and the given mean and standard deviation to find the proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes.
First, we need to standardize the value of 3 minutes using the z-score formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (3 - 5.3) / 0.9 ≈ -2.56
Next, we can use a standard normal distribution table or a calculator to find the proportion of the area under the standard normal distribution curve that corresponds to a z-score of -2.56. This proportion represents the proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes.
Using a standard normal distribution table, we can find that the area to the left of z = -2.56 is approximately 0.0055.
Therefore,
The proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes is approximately 0.0055, or 0.55%.
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Write the equation in standard form of the line y=1/9x+5
The equation in standard form is x - 9y = -45.
What is the Equation of a Line in Standard Form?The equation of a line in standard form is Ax + By = C, where x and y are variables and A, B and C are integers.
Given equation is y = 1/9 x + 5.
Here 1/9 is not an integer.
So multiplying the equation throughout by 9, we get,
9y = x + (5 × 9)
9y = x + 45
Subtracting both sides by x,
9y - x = 45
-x + 9y = 45
Multiplying throughout by -1,
x - 9y = -45, which is in standard form.
Hence the equation is x - 9y = -45 in standard form.
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Help please it's urgent
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
The formula to describe the variation is F = 1.6d².
Option C is the correct answer.
What is an equation?An equation is made up of one or two variables with a constant connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
F is directly proportional to the square of d.
This can be written as,
F ∝ d²
F = kd² ____(1)
Now,
F = 40 when d = 5.
40 = k x 5²
k = 40/25
k = 8/5 _____(2)
Now,
From (1) and (2).
F = (8/5)d²
F = 1.6d²
Thus,
The formula to describe the variation is F = 1.6d².
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the mayor of a small city is trying to determine the number of judges needed to handle the judicial caseload. during each month of the year it is estimated that the number of judicial hours needed is provided in the table below. a). each judge works all 12 months and can handle as many as 120 hours per month caseload. to avoid creating a backlog all cases must be handled by the end of december. formulate an lp whose solution will determine how many judges the city needs to handle the caseload for the year.
Total hours handled by x judges in the year ≤ 12120x where x is the number of judges needed to handle the caseload for the year.
To formulate an LP for this problem, we can define the decision variables and the objective function and constraints.
Decision Variables:
Let x be the number of judges needed by the city to handle the caseload for the year.
Objective Function:
We want to minimize the number of judges needed, so our objective function is:
minimize x
Constraints:
Each judge can handle up to 120 hours of caseload per month, so the total number of hours that can be handled by x judges in a month is 120x. The total number of hours needed to handle the caseload for the year is given in the table. Therefore, we have the following constraints:
For January: 120x ≥ 100
For February: 120x ≥ 120
For March: 120x ≥ 90
For April: 120x ≥ 80
For May: 120x ≥ 110
For June: 120x ≥ 130
For July: 120x ≥ 140
For August: 120x ≥ 110
For September: 120x ≥ 100
For October: 120x ≥ 90
For November: 120x ≥ 80
For December: 120x ≥ 120
These constraints ensure that the total number of hours handled by the judges in each month is at least as much as the number of hours needed to handle the caseload in that month.
We also need to ensure that all cases are handled by the end of December. This can be expressed as follows:
Total hours handled by x judges in the year ≤ 12120x
This constraint ensures that the total number of hours handled by the judges in the year is less than or equal to the maximum possible number of hours that can be handled by x judges in a year.
Therefore, the LP can be formulated as follows:
minimize x
subject to:
120x ≥ 100
120x ≥ 120
120x ≥ 90
120x ≥ 80
120x ≥ 110
120x ≥ 130
120x ≥ 140
120x ≥ 110
120x ≥ 100
120x ≥ 90
120x ≥ 80
120x ≥ 120
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A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 5 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 2:8?
A. 4
B. 10
C. 16
D. 64
The required perimeter of the door on the scale drawing is 4 cm, which is option A.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
To find the perimeter of the door on the scale drawing, we need to first find the dimensions of the door on the scale drawing. We can use the scale 2:8 to convert the actual dimensions of the door to the corresponding dimensions on the scale drawing:
Height on scale drawing = (2/8) x 5 cm = 1.25 cm
Width on scale drawing = (2/8) x 3 cm = 0.75 cm
The perimeter on the scale drawing = 2 x (height on scale drawing + width on scale drawing)
Perimeter on scale drawing = 2 x (1.25 cm + 0.75 cm)
Perimeter on scale drawing = 2 x 2 cm
The perimeter on the scale drawing = 4 cm
Therefore, the perimeter of the door on the scale drawing is 4 cm, which is option A.
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Please help! Find the area of the shaded regions. give your answer a completely simplified exact value of the terms of pi (no approximations)
For given circle, Area of shaded region is 52π cm².
What exactly is a circle?
A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.
The equation for a circle in the plane is:
(x-h)^²+ (y-k)² = r²
When the coordinate points are (x, y)
(h, k) is the coordinate of a circle's center.
where r is the circumference of a circle.
where circle area = πr²
Circle circumference=2πr
Now,
Radius of biggest circle = 8cm
radius of unshaded circle= 4cm and
radius of smaller shaded circle= 2cm
Then,
Area of shaded region= Area of biggest circle - area of white circle + area of smaller shaded circle
=π*8² - π*4² + π*2²
=64π-16π+4π
=52π cm²
hence,
Area of shaded region is 52π cm².
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Edward and his little brother made up
a game using coins. They flip the coins
towards a cup and receive points for
every one that makes it in. Edward
starts with 20 points, and his little
brother starts with 18 points. Edward
gets 2 points for every successful
shot, and his brother, since he is
younger, gets 3 points for each
successful shot. Eventually, the
brothers will have a tied score in the
game. How many additional shots will
each brother have made? How many
points will they both have?
Edward and his brother will have each
made ________
shots, for a tied score
of ________
. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?
Answer:
26 meters,
hope this helps!
Segment has endpoints (−7, 14) and (11, 5). Point lies on at (−3, 12).
What is the ratio of to ?
Last time I asked the question Brainly decided to delete like 90% of my question.
The ratio of the coordinate point on the line is 2 to 7.
What is the ratio of the point on the coordinate?The ratio of the coordinate point on the line is calculated as follows;
Let the coordinate points = (xp, yp)
Let the ratio of the line = a:b
xp = x₁ + (a/(a+b) (x₂ - x₁)
yp = y₁ + (a/a+b) (y₂ - y₁)
-3 = -7 + ( a/a+b)(11 - - 7)
-3 = -7 + (a/a+b)(18)
-3(a + b) = -7(a+b) + 18a
7(a + b ) - 3(a+b) = 18a
7a + 7b - 3a - 3b = 18a
4b = 14a
4/14 = a/b
2/7 = a/b
2 : 7 = a : b
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if a seed is planted, it has a 69% chance of growing into a healthy plant. let x be the number of seeds grow into healthy plants when 75 seeds are planted. what is the distribution of x? x ~ ? (,) please show the following answers to 4 decimal places. what is the probability that exactly 44 seeds grow into healthy plants? what is the probability that at least 44 seeds grow into healthy plants? what is the probability that more than 44 seeds grow into healthy plants? what is the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants?
The probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
The probability distribution of x, where x is the number of seeds that grow into healthy plants when 75 seeds are planted, is a binomial distribution with parameters n = 75 and p = 0.69. The probability of x = 44 is calculated by using the formula for the probability mass function of the binomial distribution:
[tex]P(x=44) = (75 choose 44) * (0.69)^44 * (1-0.69)^(75-44) = 0.1578[/tex]
The probability of x >= 44 is calculated by using the formula for the cumulative probability function of the binomial distribution:
[tex]P(x > = 44) = 1 - P(x < = 43) = 1 - (75 choose 43) * (0.69)^43 * (1-0.69)^(75-43) = 0.7406[/tex]
The probability of x > 44 is calculated by subtracting the probability of x = 44 from the probability of x >= 44:
P(x > 44) = P(x >= 44) - P(x = 44) = 0.7406 - 0.1578 = 0.5828
The probability of 19 <= x <= 53 is calculated by subtracting the probability of x <= 18 from the probability of x <= 53:
[tex]P(19 < =x < =53) = P(x < =53) - P(x < =18) = 0.9994 - 0.0053 = 0.9941[/tex]
Therefore, the probability that exactly 44 seeds grow into healthy plants is 0.1578, the probability that at least 44 seeds grow into healthy plants is 0.7406, the probability that more than 44 seeds grow into healthy plants is 0.5828, and the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
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f(x) = -2x
g(x) = 8x² - 5x+7
Find (f g)(x).
O-16x³5x+7
O 16x4 + 10x³ - 14x²
O-16x² + 10x - 14x
O-16x³ + 10x² - 14x
Answer:
-16x² + 10x - 14.
Step-by-step explanation:
To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).
So, let's first evaluate g(x):
g(x) = 8x² - 5x + 7
Next, substitute g(x) into f(x):
(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14
Therefore, (f g)(x) = -16x² + 10x - 14.
Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:
Vertex = (1,-5)
Point = (5,-7)
G( x )= Answer field 1
(x- Answer field 2
)^2 +Answer field 3
The standard form of the equation of the quadratic function is y = -1/8x^2 + 1/4x - 41/8
How to find the standard form of the equation of the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
(h, k) = (1, -5)
(x, y) = (5, -7)
A quadratic function is represented as
y = a(x - h)^2 + k
So, we have
y = a(x - 1)^2 - 5
Given that
(x, y) = (5, -7)
We have
-7 = a(5 - 1)^2 - 5
This gives
16a = -2
So, we have
a = -1/8
Recall that
y = a(x - 1)^2 - 5
So, we have
y = -1/8(x - 1)^2 - 5
Expand
y = -1/8(x^2 - 2x + 1) - 5
This gives
y = -1/8x^2 + 1/4x - 41/8
So, the required equation is y = -1/8x^2 + 1/4x - 41/8
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Find the value of z.
108°
40°
z=[?]°
Answer: z is in the triangle all triangles -180 degrees so 108+40 = 148
180-148=32
Answer 32 degrees
Step-by-step explanation:
Answer: 20 for acellus
What is the volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters? Leave the answer in terms of π.
400π m3
1,600π m3
160π m3
1,256π m3
The volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters is 400π m³.
What is Volume?Volume is the amount of space occupied by an object in three dimensions. It is a measure of how much space is contained within a solid shape, such as a cube, sphere, or cylinder. The unit of volume can vary based on the system of measurement being used, but common units include cubic meters, cubic centimeters, liters, and gallons. Volume is calculated by multiplying the area of the base of the object by its height or depth, depending on the shape of the object.
The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
In words, the volume of a right circular cylinder is equal to the area of the circular base (πr²) multiplied by the height (h). This formula holds true regardless of the dimensions of the cylinder, as long as it has a circular base and straight sides that are perpendicular to the base.
The volume of a right circular cylinder is given by the formula V = πr²h, where r is the radius of the circular base and h is the height of the cylinder.
Since the diameter of the circular base is 10 meters, the radius is half of that, or 5 meters. The height of the cylinder is 16 meters.
Substituting these values into the formula, we get:
V = π(5)²(16) = 400π
Therefore, the volume of the cylinder is 400π cubic meters.
So the answer is 400π m³.
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What is the frequency of the function f(z)?
f(z)=-2 sin (2) +3
Express the answer in fraction form
Enter your answer in the box.
if 3 is subtracted to a number and the sum is multiplied by 5 the number thus obtained is 575 find the original number
Answer:
118
Step-by-step explanation:
Let the original number be x.
After subtracting 3, the result is x - 3.
When this result is multiplied by 5, we get (x - 3) * 5 = 575.
Expanding and solving for x, we have:
5x - 15 = 575
5x = 590
x = 118
So the original number was 118.
7. Find the value of w in the regular heptagon
whose interior angle has a measure of
(w + 8). Round your answer to the nearest
hundredth.
Answer: 96
The sum of the interior angles of a regular heptagon is equal to (n-2)180 degrees, where n is the number of sides of the polygon.
Since a regular heptagon has 7 sides, the sum of its interior angles is (7-2)180 = 720 degrees.
Therefore, the measure of each interior angle is 720 degrees / 7 = 104 degrees.
If the measure of an interior angle is (w + 8) degrees, then w + 8 = 104.
Solving for w, we get w = 96.
write x=[tex]\sqrt{y^2-3}[/tex] as a set of parametric equations with x =[tex]\sqrt{} t[/tex]
The set of parametric equations are
[tex]x=\sqrt{t}[/tex]
[tex]y=\sqrt{3+t[/tex]
Parametric Equations:A parametric equation uses a parameter, which is an independent variable (often represented by the notation t), and dependent variables, which are expressed as continuous functions of the parameter and are independent of other variables.
Using one or more independent variables known as parameters, a parametric equation defines a set of quantities as functions.
Given the equation:
[tex]x= \sqrt[]{y^{2}-3 }[/tex]
Let's find a set of parametric equation for the given equation given the parameter:
[tex]x = \sqrt{t}[/tex]
From the parameter:
[tex]x = \sqrt{t}[/tex]
Now, substitute [tex]\sqrt{t}[/tex] for x in the given equation:
[tex]x=\sqrt{y^2-3} \\\\\sqrt{t} = \sqrt{y^2 - 3} \\\\t=y^2-3\\\\y^2=3+t\\\\y=\sqrt{3+t}[/tex]
Therefore, the set of parametric equations is:
• [tex]x=\sqrt{t}[/tex]
• [tex]y=\sqrt{3+t}[/tex]
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The formula area of a trapezoid is A=1/2 h(b_1+b_2) solve for b_1
Please help ASAP
Answer: b1 = [tex]\frac{2A}{h} -b2[/tex]
Step-by-step explanation:
Algebra my friend...Algebra
So:
A = 0.5h(b1+b2)
A/(0.5h) =b1+b2
.: A/(0.5h) - b2 = b1
In other words:
b1 = [tex]\frac{A}{0.5h} -b2[/tex]
The 0.5 in the denominator can be rearranged to get the final answer:
b1 = [tex]\frac{2A}{h} -b2[/tex]
1. You need to dig a tunnel. You begin at the surface of the ground. The tunnel slopes downward for 83 meters. The final depth below ground is 52 meters. Find the angle of depression of the tunnel's descent. Round your answer to the nearest tenth. Draw a diagram to illustrate your problem.
Answer: 38.8°
Step-by-step explanation:
See the attached diagram:
From it we can tell that the tunnel forms a right triangle, with the length of a leg and the hypotenuse given. We can use the sine function to easily answer this, (letting θ be the angle we need to find)
sinθ = 52/83
.: θ = arcsin(52/83)
(Note: arcsin is the inverse of the sine function)
.: θ ≅ 38.8°
uppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52 . using the empirical rule, what percentage of american women have shoe sizes that are between 6.54 and 9.58 ?
Using the empirical rule, we can conclude that approximately 68% of American women have shoe sizes between 6.54 and 9.58.
Using the empirical rule, we can say that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
To find the percentage of American women who have shoe sizes between 6.54 and 9.58, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:
z1 = (6.54 - 8.06) / 1.52 = -1.00
z2 = (9.58 - 8.06) / 1.52 = 1.00
Now, we can use the empirical rule to find the percentage of women with shoe sizes between z = -1.00 and z = 1.00. Since this interval corresponds to one standard deviation from the mean, we know that approximately 68% of the data falls within this range.
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what are the lengths or each side?
Answer:
5
Step-by-step explanation:
The rule of the sides of a triangle is that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This rule is also known as the triangle inequality theorem.
16. The diagram shows a sketch of the graph y = ab^x where b>0
The curve passes through the points A (1, 10) and B (4,80).
The point C (-1, k) lies on the curve.
Find the value of k.
I don’t what exponential graphs are and I don’t understand what the question means!!!
Answer:
k is 2.5.
Step-by-step explanation:
To find the value of k, we can use the information given about points A and B to find the value of the parameters a and b. Since we know that the curve passes through A (1, 10) and B (4, 80), we can substitute these points into the equation y = ab^x to find the values of a and b.
Starting with point A:
10 = a * b^1
Next, using point B:
80 = a * b^4
We can now use these two equations to find the value of b:
10 = a * b^1
80 = a * b^4
Dividing the second equation by the first equation:
8 = b^3
Taking the cube root of both sides:
b = 2
We can now use either of the two equations to find the value of a:
10 = a * b^1
a = 10/2 = 5
Now that we have found the values of a and b, we can substitute the point C (-1, k) into the equation y = ab^x to find the value of k:
k = 5 * 2^(-1) = 5 * (1/2) = 2.5
So the value of k is 2.5.
A plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
Please input your answer:
Answer:
Step-by-step explanation:
Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.
Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.
Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:
5x + 27 = 11x + 15
Solving for x, we can find the length of each shorter piece:
6x = -12
x = -2
This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12
feet and is 10 feet tall. Which of the following best describes the volume of the sand?
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
What is the volume of the cone?Let h be the height of the cone and A be the base area of the cone.
Then the volume of the cone will be given as,
Volume = (1/3) × A × h
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12 feet and is 10 feet tall.
The base area of the cone is given as,
A = π × (d/2)²
A = 3.14 × (12 / 2)²
A = 3.14 × 36
A = 113.04 square feet
Then the volume of the cone is given as,
V = 1/3 × 113.04 × 10
V = 376.8 cubic feet
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
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In a family the oldest child is 7 years older than the youngest child what is a equation to represent this situation
The equation to represent the situation where the oldest child is 7 years older than the youngest child, using x for the age of the youngest child and y for the age of the oldest child, is y = x + 7.
If we let x represent the age of the youngest child in a family, then we can say that the oldest child is 7 years older than the youngest child. We can represent the age of the oldest child using the expression "x + 7", because if we add 7 to the age of the youngest child, we get the age of the oldest child.
Therefore, we can write an equation to represent this situation by equating the age of the oldest child to the age of the youngest child plus 7. This can be written as:
x + 7 = Oldest child's age
where x is the age of the youngest child, and "Oldest child's age" represents the age of the oldest child in the family. This equation tells us that if we know the age of the youngest child, we can find the age of the oldest child by adding 7 to it.
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Need this for a math lesson
The upper quartile score on the final exam is 83.
What is Upper quartile?Upper quartile, represented as Q₃, also known as third quartile is the value in a data set such that 75% of the points in the data set are below this value, after arranging in an ascending order.
Given data set is the scores for the final exam in an 8th grade math class.
58, 72, 74, 92, 84, 40, 74, 81, 76, 83.
First arrange the data in an ascending order.
40, 58, 72, 74, 74, 76, 81, 83, 84, 92.
Median is the middle element.
Median = (74 + 76) / 2 = 75
Upper quartile is the median of the second half.
Consider the second half.
76, 81, 83, 84, 92.
Median = 83
Third quartile = 83
Hence 83 is the upper quartile score on the final exam.
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