Answer:
Step-by-step explanation:
from the first ... 3y = 3x + 12 or
y = x + 4
This is the same as the second, so D
Dan and Matt's ages add up to 56. Dan is 13 times older than Matt. How old are they?
Dan is 52 years old and Matt is 4 years old.
What are their ages?The first step is to form a system of equations using the information provided in the question:
a + b = 56 equation 1
a = 13b equation 2
Where:
a = Dan's age
b = Matt's age
The substitution method would be used to determine the values.
Substitute for a in equation 1 using equation 2:
13b + b = 56 equation 3
14b = 56
b = 56 / 14
b = 4
Substitute for b in equation 2:
a = 13(4)
a = 13 x 4
= 52
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One angle of a triangle measures 35°. The other two angles are in a ratio of 10:19. What are the measures of those two angles?
95 and 50 are the measures of those two angles.
What are the properties of triangle?The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
given, One angle of a triangle measures 35°. The other two angles are in a ratio of 10:19.
Let second angle of the triangle is "x"
Thus, third angle of triangle will be = 10/19x
Since, sum of the three angles of triangle is 180 degrees
35 + x + 10/19x = 180
29x/19 = 145
x = 5 *19
x = 95
So, Second angle of triangle = x = 95
Third angle of triangle = 10/19x = 50
therefore, the measures of those two angles are 95 and 50.
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If point R has coordinates (x,y) and point S has coordinates (x + 1, y + 1), what is the distance between R and S?
The distance between the two points R and S is √2.
The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places.
The distance between the two points R and S can be calculated using the Pythagorean theorem. Given the coordinates (x, y) for point R and (x + 1, y + 1) for point S, the distance d between R and S is given by:
d = √((x + 1 - x)^2 + (y + 1 - y)^2) = √(1^2 + 1^2) = √2.
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pls help me with this equation
In contrast to the pair of following two triangles, the initial two triangles do not share any similarities.
What is meant by similar triangles?Two triangles are considered to be similar if the corresponding sides are proportionate and the corresponding angles are congruent. Or to put it another way, comparable triangles may not necessarily be the same size but they do have a similar shape. The triangles are also congruent if the lengths of their respective sides are the same.
We already know that the ratio of the two triangles' corresponding sides must match for them to be identical triangles.
A.) In the first pair of triangles,
The first pair of triangles to be similar,
[tex]$\frac{U S}{U D}=\frac{U T}{U E}=\frac{S T}{D E}$$[/tex]
The aforementioned ratio ought to be comparable, however as we can see,
[tex]$$\begin{aligned}& \frac{U S}{U D} \neq \frac{U T}{U E} \\& \frac{39}{16} \neq \frac{40}{16}\end{aligned}$$[/tex]
The two triangles supplied are not identical triangles because, as we can see, the ratio of the triangle's sides is not the same.
B.) In the second pair of triangles,
The second pair of triangles to be similar,
[tex]$\frac{A B}{H G}=\frac{B C}{G F}=\frac{C A}{F H}$$[/tex]
As we can see, the ratio should be comparable to the one above.
[tex]$\frac{72}{12}=\frac{48}{8}=\frac{84}{14}=6$$[/tex]
The two triangles supplied are similar triangles because, as we can see, the ratio of the triangle's sides is the same.
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If EF=8, FD=10, ED=11, IG=24, and HG=26.4, find the perimeter of GHI. Round your answer to the nearest tenth if necessary. Figures are not easily drawn to scale.
The perimeter of the given figure is 79.4 units.
What is perimeter:The perimeter of a polygon is defined as the length of the boundary around the sides of the polygon. The perimeter of a polygon can be calculated by calculating the sum of the lengths of the sides of the polygon.
Perimeter of polygon = Sum of sidesHere we have
EF = 8, FD = 10, ED = 11, IG = 24, and HG = 26.4
As we know,
Perimeter = Sum of all sides
The perimeter of GHI = (EF + FD + ED + IG + HG)
= 8 + 10 + 11 + 24 + 26.4
= 79.4 units
Therefore,
The perimeter of the given figure is 79.4 units.
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Find the 12th term of the geometric sequence 7, -21, 63, …
The 12th term of the geometric sequence 7, -21, 63 is -1240029, this is determined using the Geometric progression formula.
What is geometric progression?When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.
The geometric progression is given by the formula:
aₙ = arⁿ⁻¹
a = first term = 7
r = common ratio = - 21 / 7 = - 3
n = number of terms = 12
Therefore, substituting the values in the GP:
a₁₂ = 7 × -3¹²⁻¹
a₁₂ = 7 × -3¹¹
a₁₂ = 7 × -177147
a₁₂ = -1240029
Therefore, the 12th term of the geometric progression is -1240029.
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A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B.
(And please hurry.)
What objective function can be used to maximize the profit?
P = _a + _b
Let a = units of A produced
Let b = units of B produced
At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.
Therefore
a ≥ 30
b ≥ 10
a + b ≤ 80
Product A yields a profit of $15 and product B yields a profit of $8.
Therefore the objectve profit function is
P(a,b) = 15a + 8b
Answer:
The objective function is
P(a,b) = 15a + 8b, subject to
a >= 30; b>= 10; a+b <= 80
Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.
The maximum profit occurs when a=70 and b=10.
Answer:
P= 15a + 8b
Step-by-step explanation:
Can anyone help me with this problem
Answer:
-7
Step-by-step explanation:
angles in a triangle add up to 180⁰
90⁰+30⁰+(x+67)=180⁰
187+x=180⁰
x=180⁰-187⁰
x=-7
The area of this rectangle is at most 400 square centimeters, Write and solve an inequality to represent the possible values for the height, h, for this triangle. Show all steps of your work.
16cm h
An inequality to represent the possible values for the height, h, for this triangle is 1ft≤h≤25ft
The area of a rectangle is expressed as;
Area = Length * height
A = Lh
If the area of a rectangle is at most 400 square centimeters, this is expressed as;
A ≤400
≤ means at most that the area of the rectangle cannot be greater than 400
Substitute the given value into the inequality expression
Lh ≤ 400
Given
L = 16
16h ≤ 400
Divide both sides by 16
16h/16 ≤ 400/16
h ≤ 400/16
h ≤ 25
Hence the possible values of the height are within the range 1ft≤h≤25ft since we cannot have a negative value for the dimension.
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NEW ASSESSMENT QUESTION:
BASIC EDUCATION CERTIFICATE
SECTION A: OBJECTIVES
1. Divide 2.646 by 0.9. Give your answer to 1
d.p.
On applying the arithmetic operation of division, the expression 2.646 / 0.9 gives a result of 2.9.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The expression given is -
2.646 / 0.9
The expression is given in decimal form.
Use the arithmetic operation of division.
First remove the decimal points.
Multiply the numerator and denominator by 1000 as there are three decimal points in the numerator -
(2.646 × 1000) / (0.9 × 1000)
Now divide the expression -
2646 / 900
= 2.94
Rounding off to one decimal point gives 2.9.
Therefore, the value is obtained as 2.9.
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Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.
7cos(9x)−1=1
Answer:
To solve the equation 7cos(9x)−1=1, we first need to move the 1 to the left side of the equation:
7cos(9x) = 2
To find the solutions of the equation, we can divide both sides by 7:
cos(9x) = 2/7
Now we will use the inverse cosine function, denoted as arccos, to find the angle that has a cosine value of 2/7. Since the function cos is periodic with period 2Pi, it's range is [-1,1], we will look for the solutions between 0 and 2Pi.
x = (1/9)arccos(2/7) + (2kPi)/9 for k =0,1,2,....
we can also express the solution in degrees by multiplying the radian measure with 180/Pi.
x = (20/63)arccos(2/7) + (160*k) for k =0,1,2,....
or
x = (20/63) * arccos(2/7) * (180/pi) + (160*k) for k =0,1,2,....
where k is an integer.
So, x = (20/63) * arccos(2/7) * (180/pi) + (160*k) where k =0,1,2,.... is an expression that represents all solutions to the equation in degrees.
Please complete. Due today
3 (n+7)
Answer:
3(n+7) =
(3)(n) + (3)(7) =
3n + 21
Step-by-step explanation:
I hope this helps you :D
Copy the problem and write a statement/reason proof
Answer:
..........................
At the local Convenience store William and Sarah are getting snacks for the friends. William buys 3 soft drinks and 2 hot dogs at a cost of $7. 70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $ 4. 55.
Find the cost of 1 soft drink and 1 hot dog.
If at local Convenience store , William buys 3 soft drinks and 2 hot dogs for $7.70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $4.55 , then the cost of 1 soft drink is $1.4 and cost of 1 hot dog is $1.75 .
We will use system of equations to find cost of 1 soft drink and 1 hot dog. let the cost of 1 soft drink is = $x ; and
let the cost of 1 hot dog is = $y ;
So , for William the situation is represented as ;
⇒ 3x + 2y = 7.70 .....equation(1)
and for Sarah the situation is represented as ;
⇒ 2x + y = 4.55 ....equation(2)
we first solve equation(1) for y:
⇒ y = (7.70 - 3x)/2
We can substitute this expression for y in equation (2) and solve for x:
⇒ 2x + (7.70 - 3x)/2 = 4.55
⇒ 4x + (7.70 - 3x) = 4.55×2
⇒ 4x -3x = 9.1 - 7.70
⇒ x = 1.4
So, the cost of 1 soft drink is $1.4 ,
Now , We can use this value of x to find the cost of 1 hot dog:
⇒ y = (7.70 - 3x)/2
⇒ y = (7.70 - 3×1.4)/2
⇒ y = (7.70 - 4.2)/2
⇒ y = 3.5/2 ;
⇒ y = 1.75
So, the cost of 1 hot dog is $1.75 .
Therefore, one soft drink costs $1.4 and one hot dog costs $1.75 .
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Are these triangles similar? If so why?
In the given image the triangle POR and triangle FGH are not equal or similar to each other.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In ΔPQR, the line segment PQ measures 35 units.
In ΔPQR, the line segment PR measures 49 units.
In ΔPQR, the line segment QR measures 63 units.
In ΔFGH, the line segment FG measures 69 units.
In ΔFGH, the line segment GH measures 38 units.
In ΔFGH, the line segment HF measures 67 units.
These two triangles are not similar to each other.
Both these triangles have different measurements of line segments.
Both these triangles have no data available for their angles.
The only way the two triangles are similar is that they both are scalene triangles as they both have different measuring sides.
Therefore, the two triangles are not similar.
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a swimming pool can be filled using either a pipe, a hose, or both. using the pipe alone it takes 12 hours. using both it takes 8 4/7 hours. how long does it take using the hose alone?
It takes 30 hours using the hose alone to fill the swimming pool.
How to add and subtract fractions?Step 1: Make denominators the same
Step 2: Add or Subtract the numerators (keeping the denominator the same)
Step 3: Simplify the fraction
To add or subtract unlike fractions, the first step is to make denominators the same so that numerators can be added just like we do for like fractions.
Let [tex]x\\[/tex] represent the swimming pool be filled with hose alone.
Given that using the pipe alone it takes 12 hours. using both it takes 8 4/7 hours. According to given condition,
[tex]\frac{1}{x} + \frac{1}{12} = \frac{1}{8\frac{4}{7} } \\\frac{1}{x} = \frac{1}{\frac{60}{7} } - \frac{1}{12}[/tex]
[tex]\frac{1}{x} = \frac{7}{60} - \frac{1}{12}\\\\ \frac{1}{x} = \frac{7}{60} - \frac{5}{60}\\\\\frac{1}{x} = \frac{2}{60}\\\\ x = \frac{60}{2}\\\\\\ x= 30[/tex]
It takes 30 hours using the hose alone to fill the swimming pool.
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Peter expected to earn $425 in a week. In fact he earned $500. What was the percent of error?
The percent of error is 17.65% .
The percent of error is a way to measure the difference between the expected value and the actual value. In this case, Peter expected to earn $425 in a week but he actually earned $500.
So, the difference between the expected value and the actual value is $75. The percent of error is calculated by taking the difference between the actual value and the expected value, dividing that by the expected value, and multiplying the result by 100%.
In this case, (500-425)/425*100% = 17.65%, which means that Peter's actual earnings were 17.65% higher than what he expected to earn.
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Graph the solution to this inequality on the number line.
−4x≥12
Answer:
Solution set for x is x ≤ -3
First option
Step-by-step explanation:
We have the equation
- 4x ≥ 12
Divide both sides by 4:
- x ≥ 12/4
-x ≥ 3
Multiply by -1 to make x positive. When we multiply an inequality by a negative number the inequality sign changes: ≥ becomes ≤
Therefore we get
x ≤ 3
On the number line this is represented by the first choice
Note that the 3rd and 4th choices are easily eliminate since they represent ≥ -3 and > -3
Choice #2 has an unfilled circle at -3. This represents a < inequality
A filled circle represents a ≤ inequality
Answer
Solution set for x is x ≤ -3
First option
Solve using substitution.
y = -10
2x + y = −18
Answer:
try your best
Step-by-step explanation:
u can do it!!
To avoid using the variable "vi", which of the following equations should you use?
A) v² = v² + 2aAx
B) Ax = (v₁ + v₁)t
C) Vf = V₁ + at
D) Ax = vft – ⁄at²
In order to avoid using the variable "Vi", the equation which you should use include the following: D) Ax = Vft – 1/2at².
What is the second equation of motion?In Mathematics, the third equation of motion is represented by this mathematical expression:
Ax = Vit + ½at² ......equation 1.
Where:
Ax represents the distance travelled or covered.t represents the time.Vi represents the initial velocity.a represents the acceleration.From the first equation of motion, we have:
Vf = Vi + at
Making Vi the subject of formula, we have:
Vi = Vf - at ......equation 2.
Substituting the equation, we have:
Ax = (Vf - at)t + ½at²
Ax = Vft - at² + ½at²
Ax = Vft + ½at²
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A rectangle has a height of x+4x+4 and a width of x^2+3x+2
The area of rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.
Explain the term area of the rectangle?Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth. In other words, a rectangle's area is equal to the sum of its width and length.So, from the definition of the area of the rectangle.
Area = length x width
Given:
length/height = x+4x+4 = 5x + 4width = x^2+3x+2Thus,
Area = (5x + 4)(x^2+3x+2)
Simplifying,
Area = 5x(x^2+3x+2) + 4(x^2+3x+2)
Area = 5x³ + 19x² + 22x + 18
Thus, the area of the rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.
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The complete question is-
A rectangle has a height of x+4x+4 and a width of x^2+3x+2. Express the area of the entire rectangle.
Write a formula in the form
f (t) = A cos Bt+ k that models the surface temperature of the
lake.
Answer:
The formula is going to be 17 hrs
The hertz (Hz) is a unit of frequency that represents the number of complete cycles per second. It is used to measure repeating events, both scientific and general. For instance, a clock ticks at 1 Hz. One scientific application is the electromagnetic spectrum, or the range of all possible frequencies of electromagnetic waves. The spectrum includes frequencies from everyday contexts, such as radio and TV signals, microwaves, light (infrared, visible, and ultraviolet), and X-raysThe hertz (Hz) is a unit of frequency that represents.
For each question, use powers to write a mathematical expression. Then evaluate each expression.
Express your answer as a power.
a. How many hertz are in 1 gigahertz? 1 terahertz?
b. A television channel has a frequency of 60 megahertz. What is the channel’s frequency in hertz?
c. The frequency of a microwave is 30 gigahertz. What is the microwave’s frequency in hertz?
d. The frequency of a visible ray of light is 1000 terahertz. A radio station has a frequency of
100 megahertz. How many times greater is the frequency of the light than the frequency of the
radio station?
a. There are 10⁹ hertz in 1 giga hertz and 10^12 hertz in one terahertz
b. The channels frequency in hertz 6×10⁷hertz
c. The frequency of a microwave in hertz is 3× 10^10 hertz
d. The frequency of light is 10⁵ times greater than the frequency of the radio station
What is frequency?Frequency describes the number of waves that pass a fixed place in a given amount of time. So if the time it takes for a wave to pass is is 1/2 second, the frequency is 2 per second. If it takes 1/100 of an hour, the frequency is 100 per hour.
The S.I unit of frequency is hertz and it has other bigger unit stated as follows:
1 kilohertz = 10³hertz
1megahertz = 10⁶ hertz
1 gigahertz = 10⁹ hertz
1 tera hertz = 10^12 hertz
Therefore 60mega hertz = 60× 10⁶ = 6×10⁷
30 gigahertz = 30 × 10⁹ = 3 × 10^10
if the frequency of light is 1000 tera hertz and 100 mega hertz is the frequency of a radio station , then the frequency of light will be 1000×10^12 ÷ 100× 10⁶ = 10⁵ greater than the frequency of the radio station.
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In △feg , point h is between points e and f, point j is between points f and g, and hj¯¯¯¯¯∥eg¯¯¯¯¯ . eh=14 , hf=26 , and fg=60 . what is fj ? enter your answer in the box. fj =
The value of FJ is 39 units.
See the attached figure to better understand the problem
We know that
If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.
According to this problem,
△FEG is similar to △FHJ ( by AA Similarity Theorem)
so
[tex]\frac{FE}{FH} = \frac{FG}{FJ}[/tex]
We have,
FE = HF + EH = (26 + 14 ) units
FE= 40 units
FH = HF = 26 units
FG = 60 units
substitute the given values,
[tex]\frac{40}{26} = \frac{60}{FJ}[/tex]
[tex]FJ = \frac{26 * 60}{40}[/tex]
FJ = 39
So, the value of FJ is 39 units.
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the coordinates of three points are (2, 2), (4, 2), and (3, 3). what is the area of the triangle formed by connecting these three points?
The area of the triangle formed by connecting the three points is 6 square units. The result is obtained by using the determinant method.
How to find the area of a triangle in coordinate geometry?The area of a triangle in coordinate geometry can be found by using the determinant formula.
[tex]Area \: of \: triangle = \frac{1}{2} \left[\begin{array}{ccc}x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right][/tex]
The three points of a triangle are:
(x₁, y₁) = (2, 2)(x₂, y₂) = (4, 2)(x₃, y₃) = (3, 3)Using the determinant formula, the area of the triangle is
[tex]= \frac{1}{2} \left[\begin{array}{ccc}2&2&1\\4&2&1\\3&3&1\end{array}\right][/tex]
= ½ |2(2-(3)) - 4(2-(3)) + 3(2-2)|
= ½ |2(-6) - 4(-6) + 0|
= ½ |-12 + 24|
= ½ |12|
= 6 square units
Hence, the area of the triangle is 6 square units.
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fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0,a), where should the station be located so as to minimize the expected distance from the fire?
The fire station should be located at the midpoint (a/2) of the road to minimize the expected distance from the fire.
The total distance cost will be infinite if we start at one point on a given line at an infinite distance. However, as we move this point toward the given points, the total distance cost begins to decrease. After a while, it then increases once more, reaching infinite at the other infinite end of the line. Therefore, the distance cost curve resembles a U-curve, and its bottom value must be determined.
The fire station should be located at the midpoint (a/2) of the road (0,a) to minimize the expected distance from the fire.
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Answer? Please help.
Answer:
answer is no
Step-by-step explanation:
how to find a vector perpendicular to another vector
A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.
You can utilize methods based on the dot-product and cross-product of vectors to create a vector that is perpendicular to another supplied vector. The total of the products of the relevant components is the dot-product of the vectors A = (a1, a2, a3) and B = (b1, b2, b3):
AB = a1 b2 + a2 b2 + a3 b3. The dot product of two vectors that are perpendicular is equal to zero.
The formula for calculating the cross-product of two vectors is AB = (a2 b3 - a3 b2, a3 b1 - a1 b3, a1 b2 - a2*b1).
A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.
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Complete the stem-and-leaf plot of the data.
The stem-and-leaf plot for the data in this problem is given as follows:
0|5 8 91| 2 2 3 4 5 82|1 5.3|0.How to build the stem-and-leaf plot?The measures that are less than 10 are given as follows:
5, 8 and 9.
Hence they go on the plot as follows:
0|5 8 9
The measures that are between 10 and 19 are given as follows:
12, 12, 13, 14, 15, 18.
Hence they go on the plot as follows:
1| 2 2 3 4 5 8
The measures that are between 20 and 29 are given as follows:
21 and 25.
Hence they go on the plot as follows:
2|1 5.
The remaining measure is given as follows:
30.
Which goes on the plot as follows:
3|0.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Determine whether the underlined value is a parameter or a statistic_ The average score for a class of 28 students taking a calculus midterm exam was 72% Is the value a parameter or a statistic? A. The value is a statistic because the class of 28 students is a sample. b. The value is a parameter because the class of 28 students is a sample c. The value is a parameter because the class of 28 students is a population. d. The value is a statistic because the class of 28 students is a population.
The value is a parameter because the class of 28 students is a population.
A statistic is a measure calculated from a sample of the population, whereas a parameter is a measure that is calculated from the entire population. It is generally a numeric value that is used to characterise a population trait. A probability distribution is defined or described by a fixed value that is typically unknown.
The population's mean, variance, and standard deviation are just a few parameters. By employing statistical techniques like maximum likelihood estimation, these parameters are often calculated from a sample of data. In the given question, since from a class of 28, the average score was 72% of the population which is the total, this value is a parameter.
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