A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width. Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.
Answers
The option is (B) The entire solution region is viable is correct when both the inequalities are solved.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
Let's first translate the given information into mathematical inequalities -
The perimeter of the tabletop to be no more than 28 feet -
Perimeter = 2(length + width) ≤ 28
The length of the tabletop to be greater than or equal to the square of 2 feet less than its width -
Length ≥ (Width - 2)²
We can combine these two inequalities to form the system -
2(length + width) ≤ 28
Length ≥ (Width - 2)²
Now, let's solve for y in terms of x (so that we can graph the solution region) -
2(y + x) ≤ 28
y ≥ (x - 2)²
Simplifying the first inequality -
y ≤ -x + 14
Now graph both the inequalities -
The viable solutions are the points that satisfy both inequalities, which lie in the shaded region above.
Therefore, there is no part of the solution region that includes negative length or negative width.
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Related Questions
4. Compute the unadjusted cost of goods sold for the year. Do not include any underapplied or overapplied overhead in your answer.
5. Assume that the $70,000 ending balance in Work in Process includes $24,000 of direct materials. Given this assumption, supply the information missing below:
Answers
The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:
Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory
Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.
5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:
Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead
Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:
Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor
Without knowing the value for direct labor, we cannot compute the overhead cost.
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There are 10 roller coasters at 6 flags. If you only have time to ride 3 before the park closes. How many different ways can you create a path to 3 different roller coasters?.
Answers
There are 120 different ways to create a path to 3 different roller coasters at Six Flags.
There are a total of 10 choose 3 ways (120) to choose 3 roller coasters out of the 10 available at Six Flags. To calculate this, we can use the combination formula.
The combination formula is:
nCr = n!/(r!(n-r)!).In this case, n is 10 and r is 3, so the total number of possible combinations is
10!/3!7! = 120.To calculate the number of combinations without using a formula, we can use the following method: Start with the first roller coaster, then add a second roller coaster, then a third. There are 10 choices for the first roller coaster, then 9 for the second, and 8 for the third. This results in:
10x9x8 = 720 possible combinationswhich is 6 times more than the 120 calculated by the combination formula. This is because the combinations ABC and CBA are the same, and so are other combinations that are just permutations of each other.
Therefore, there are 120 different ways to create a path to 3 different roller coasters at Six Flags.
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(2x³-x + 1) / (x² + x + 1)
Answers
Answer:
Hopefully this is the answer you are looking for.
In the equation y=6x+1/4,which one is a “rate of change” and which is the initial value
Answers
Answer:
Step-by-step explanation:
6 is the rate of change and 1/4 is the initial value
Determine if the statement is true or false. Construct an argument that can be used to defend your solution.
An exterior angle of a triangle will always be obtuse.
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The statement "an exterior angle of a triangle will always be obtuse" is actually false.
Why it is?
An exterior angle of a triangle is formed by extending one of the sides of the triangle, and it is the angle between that extended side and the adjacent side of the triangle.
The measure of an exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
Now, consider a triangle with interior angles of 70, 60, and 50 degrees. If we extend the side opposite the 70-degree angle, we get an exterior angle of 110 degrees. However, 110 degrees is not obtuse, since an angle is obtuse if and only if it is greater than 90 degrees. Therefore, we have shown that an exterior angle of a triangle does not always have to be obtuse.
In summary, the statement "an exterior angle of a triangle will always be obtuse" is false, and we have provided a counterexample to show why this is the case.
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Bob has a total of 60 adventure cards for a game. The table shows the number of cards, c, distributed to p players. Which equation describes the pattern in the table?
p 2 3 4 5
c 30 20 15 12
c = 60 ÷ p
c = 60 – p
c = 60p
c = 60 + p
Answers
For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p
Describe probability. Describe using an example.Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.
The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.
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If the equations x² - 5x+6=0 and X² + ax +6=0 common roots, find the Value a
Answers
Answer:
Step-by-step explanation:
After a 27% decrease the value of a game card was now on sale for $34.00. What was the original price?
Answers
The original price of the game card was approximately $46.58.
What purpose does a game serve?When the game can be effectively described by a numerical "characteristic function," such as v(S), which expresses how much any coalition S of players may win with certainty, regardless of the behaviour of the other players, then we can most readily determine the value of the game.
Let x represent the game card's initial cost. So 1 - 0.27 = 0.73, the price would be 0.73x after a 27% drop.
We are aware that 34.00 = 0.73x. We can divide both sides by 0.73 to find x:
x = 34.00 ÷ 0.73
x ≈ 46.58
Thus, the game card's initial cost was only about $46.58.
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simple workingo ut :)
Answers
Answer: b = 82°
To solve for angle b, calculate using the given angles and the straight angle theorem.
Straight Angle TheoremThe straight angle theorem is a rule that says all straight lines are 180°.
Since the angle formed by XY is a straight line, it is also equal to 180°.
XY is divided into three separate angles, a, b and c.
If we add a, b, and c, it will equal to 180°.
Write an equationXY = a + b + c XY is the sum of a, b, and c.
180° = 46° + b + 52° Substitute what we know.
To solve for b using this equation, isolate.
180° - 46° = 46° + b + 52° - 46° Subtract 46° on both sides.
134° = b + 52°
134° - 52° = b + 52° - 52° Subtract 52 on both sides.
82° = b Keep the variable on the left.
b = 82° Final answer.
Therefore, angle b is 82°.
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Round to the closest whole number. 32% of the animals were males. If the herd had 112 animals how many were female?
Answers
Using arithmetic operations it is obtained that there were approximately 76 female animals in the herd.
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.
If 32% of the animals were males, then 100% - 32% = 68% of the animals were female.
To find the number of female animals in the herd of 112 animals, multiply the total number of animals by the percentage that were female -
68% = 68/100 = 0.68
Number of female animals = 0.68 x 112
Number of female animals = 76.16
Rounding this to the closest whole number gives -
Number of female animals ≈ 76
Therefore, the number of female animals is 76.
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find the value of a in the number 6a subtract 4 a+ 5a=210
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The value of "a" will be 30 for the given Algebraic expression.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, a algebraic expression 6a -4a +5a = 210
Simplifying the equation in terms of a
6a -4a +5a = 210
adding or subtracting the terms with the same variables
7a = 210
divide by 7 on both sides
a = 30
Therefore, the value of "a" will be 30 for the given Algebraic expression.
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Supreme Auto Parts produces components for motorcycle engines. It has plants in Amarillo, Texas, and Charlotte, North Carolina, and supply factories in Detroit and Atlanta. Production and cost data for a major component are as follows. Freight Costs Plant Detroit Atlanta Capacity Unit CostAmarillo $15 $9 $1,500 $110Charlotte $7 $5 $3,300 $120Demand 2,100 1,000 Formulate a transportation model to determine the best distribution plan. If the constant is equal to one, enter "1".Let: X11 = number of components produced in Amarillo and supplied to DetroitX12 = number of components produced in Amarillo and supplied to AtlantaX21 = number of components produced in Charlotte and supplied to DetroitX22 = number of components produced in Charlotte and supplied to Atlanta Min X11 + X12 + X21 + X22 Subject to the constraints X11 + X12 -Select-≤≥=Item 7 X21 + X22 -Select-≤≥=Item 11 + X21 -Select-≤≥=Item 15 X12 + X22 -Select-≤≥=Item 19 X11, X12, X21, X22 ≥ 0
Answers
According to the given information the Minimize equation is
Z = 110X11 + 120X12 + 120X21 + 130X22.
What is Statistics ?
Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It provides methods and techniques to make sense of complex data sets, to draw conclusions and make decisions based on the data. Statistics can be applied to a wide range of fields, including business, economics, social sciences, medicine, and many others. Some key topics in statistics include probability theory, hypothesis testing, regression analysis, and data visualization.
Minimize:
Z = 110X11 + 120X12 + 120X21 + 130X22
Subject to:
X11 + X12 ≤ 1500 (capacity constraint for Amarillo)
X21 + X22 ≤ 3300 (capacity constraint for Charlotte)
X11 + X21 ≥ 2100 (demand constraint for Detroit)
X12 + X22 ≥ 1000 (demand constraint for Atlanta)
where:
X11 = number of components produced in Amarillo and supplied to Detroit
X12 = number of components produced in Amarillo and supplied to Atlanta
X21 = number of components produced in Charlotte and supplied to Detroit
X22 = number of components produced in Charlotte and supplied to Atlanta
Therefore, according to the given information the Minimize equation is
Z = 110X11 + 120X12 + 120X21 + 130X22
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Approximate the area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2]
by calculating the sum of the areas of 4 rectangles with equal widths along the interval. The
rectangles should be placed on the x-axis and the heights should be the function values at the right
endpoint of each subinterval, as shown below.
Answers
The approximate area between the x-axis and the graph of f(x) =x² +3
over the interval [0, 2] is 9.75.
What is interval in function?introducing intervals, bounded collections of numerical values that are highly helpful in explaining domain and range. To demonstrate where a value lies in relation to two endpoints, we can use interval notation.
To approximate the area between the x-axis and the graph of
f(x) = x² + 3 over the interval [0, 2].
The heights of the rectangles in the right rectangle method are determined by the function's value at the right endpoint of each subinterval. The right endpoints of each subinterval would be 0.5, 1, 1.5, and 2 if the range [0, 2] were divided into 4 equal subintervals, each of width 0.5.
The height of the first rectangle
f(0.5) = 0.5² + 3
f(0.5) = 3.25
and, the height of the second rectangle
f(1) = 1² + 3
f(1) = 4
and, the height of the third rectangle
f(1.5) = 1.5² + 3
f(1.5) = 5.25
and, the height of the fourth rectangle
f(2) = 2² + 3
f(2) = 7
So, sum of the areas of the rectangles
= (0.5) × (3.25+4+5.25+7)
= (0.5) × 19.5
= 9.75
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I need help with this question.
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For the trapezoid ABCD following statements are true -
Statement 2: The length of AB can be found using 3²+4²=c².
Statement 3: The perimeter of the trapezoid shown is 22 units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
Statement 2 is true because AB is a horizontal side and its length can be found using the Pythagorean theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
AB = √((4 - 1)² + (7 - 3)²)
AB = √((3)² + (4)²)
AB = √(9 + 16)
AB = 5
Statement 3 is true because the perimeter of a trapezoid is the sum of the lengths of its four sides, so the perimeter of this trapezoid is
Perimeter = AB + BC + CD + DA
Perimeter = 5 + 5 + 4 + 8
Perimeter = 22
Therefore, second and third statement is true.
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Unexpected expenses have come up, and you want a cash advance on your credit card (which comes with a transaction fee of 2.5%). The limit on your credit card is $7,500, and you already have a balance of $2,200. What is your available credit? How much will you owe as a transaction fee if you want a cash advance on your available credit??
Please answer correctly and explain your answer…
Answers
To calculate your available credit, you need to subtract your current balance and the amount of cash advance you want from your credit limit:
Available credit = credit limit - current balance - cash advance amount
Given that your credit limit is $7,500 and your current balance is $2,200, the available credit can be calculated as follows:
Available credit = $7,500 - $2,200 - cash advance amount
Now, if you want a cash advance of $1,000, for example, your available credit will be:
Available credit = $7,500 - $2,200 - $1,000 = $4,300
Therefore, your available credit is $4,300 if you want a cash advance of $1,000.
To calculate the transaction fee, you need to multiply the cash advance amount by the transaction fee percentage. In this case, the transaction fee is 2.5%. So, if you want a cash advance of $1,000, the transaction fee will be:
Transaction fee = $1,000 x 0.025 = $25
Therefore, if you want a cash advance of $1,000, you will owe a transaction fee of $25. It's important to note that cash advances usually come with a higher interest rate than regular credit card purchases, so it's best to use them only when absolutely necessary and pay them off as soon as possible to avoid accruing interest charges.
Joe dreams of being a striker for Bafana Bajora some day. Every day, after school, he takes 100 practice goal kicks from various angles and distances. On the first day he only managed to kick 12 goals. On the second next day be kicked 14 goals, on the third day 16 and on the fourth day 18. If the pattern continues, how long will be huve to practice before he will kick 100 goals?
Answers
The number of days it will take for him to kick 100 goals is given as follows:
45 days.
How to define a linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which:
The slope m represents the increase of y per each unit of x.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
m = 2, as each day, the number of goals increased by two.b = 10, as on the first day, he managed to kick 12 goals, hence on the day zero, the amount was of 12 - 2 = 10.Hence the function giving the number of goals on day x is given as follows:
y = 2x + 10.
The number of days for him to score 100 goals is then obtained as follows:
100 = 2x + 10
2x = 90
x = 90/2
x = 45 days.
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Pls help solve this math
Answers
The constant of proportionality (k) for the graph is 11.7.
The proportional equation for the graph is y = 11.7x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for money earned per hour as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 35.1/3 = 81.9/7
Constant of proportionality, k = 11.7.
Therefore, the required equation is given by:
y = kx
y = 11.7x
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Suppose that, in 2006, Germany produced 13.239 million bikes. The total world production that year totaled 84 million bikes. What percent of the world's total production of bikes is contributed by Germany? Round your answer to the nearest tenth of a percent.
Answers
Answer:
15.8%
Step-by-step explanation:
You want the percentage of world bike production represented by 13.239 million bikes out of a world production of 84 million bikes.
PercentageA fraction is converted to a percentage by multiplying it by 100%.
13.239/84 × 100% ≈ 15.8%
Germany contributed about 15.8% of the world's bike production in 2006.
Antonio has 3 different colored shirts, he wants to share them with his 2 brothers. How many times can all 3 boys trade shirts without wearing them twice?
Answers
Answer:
6 times
HOPE THE ANSWER HELPS
PLSSSS HELP ASAP!!! 50 POINTS BIG BALLER
Find the value of x.
2xdegree symbol
20degree symbol
A.10
B.45
C.35
D.80
Plss help and also if you put a random answer or a answer just for the points just remember that report button looks really nice today !
Answers
A number cube is rolled three times. An outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.
Answers
Answer:16/10
Step-by-step explanation:
add 4/5+4/5=16/10
so the answer is 16/10
Write the equation of the circle given center: (1,-3) and diameter:20
I put it as (x-1)^2+(y+3)^2=400
Answers
Answer:
(x - 1)^2 + (y + 3)^2 = 400.
Step-by-step explanation:
Your equation is correct.
The center of the circle is (1, -3), which is the midpoint of the diameter. The diameter is 20, so the radius is 10. The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values, we get:
(x - 1)^2 + (y + 3)^2 = 10^2
Simplifying the right side, we get:
(x - 1)^2 + (y + 3)^2 = 100
Therefore, the equation of the circle is (x - 1)^2 + (y + 3)^2 = 400.
Can someone please help.
Answers
The sinusoidal function is y = 2sin(2x) - 1
How to determine the sinusoidal functionThe general form of a sinusoidal function is given by:
y = A sin(Bx + C) + D
where:
A is the amplitudeB is the frequencyC is the phase shiftD is the vertical shiftWe know that the period is π and the amplitude is 2.
So, we have
A = 2
B = (2π)/(π) = 2
So, we have
y = 2sin(2x + C) + D
The point (-11π/4, 1) implies that, the function is shifted down by 1 unit
So, we have
y = 2sin(2x) - 1
Hence, the function is y = 2sin(2x) - 1
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if you have to go to school 3 days from tuesday what day will you go back to school
Answers
Answer:
Three days from Tuesday is Friday.
Return on Total Assets
A company reports the following income statement and
balance sheet information for the current year:
Net income
Interest expense
Average total assets
$386,760
68,250
5,230,000
Determine the return on total assets. If required, round
the answer to one decimal place.
6, Incorrect
Answers
The return on total assets (ROTA) can be calculated using the formula:
ROTA = Net Income / Average Total Assets
Using the given information, we have:
ROTA = $386,760 / $5,230,000 = 0.0739 or 7.39%
Therefore, the return on total assets for the company is 7.39%. Note that this answer is rounded to two decimal places.
Sampling considerations. A statistics class has 10 graduate students and 40 undergraduate students. You want to randomly sample 10% of the students in the class. One graduate student and four undergraduate students are selected at random. Which of the following is not correct? and why?
(a) Because each student has a 10% chance of being selected, this is a simple random sample.
(b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.
(c) It is possible to get a sample that contains only graduate students.
(d) It is possible to get a sample that contains only undergraduate students.
Answers
The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.
Simple random sample:A simple random sample is a type of probability sampling method used in statistics, where each member of a population has an equal chance of being selected for the sample.
In other words, in a simple random sample, every possible sample of a given data will have has an equal probability of being selected from the population.
Here we have
A statistics class has 10 graduate and 40 undergraduate students.
We want to randomly sample 10% of the students in the class.
Even though one graduate student and four undergraduate students are selected at random, the percentage selecting both categories is the same.
Hence, this is a simple random sample.
Therefore,
The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.
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(a) Select each constant that is definitely positive.
(b) Select each constant that is definitely between 0 and 1.
(c) Select each constant that could be between 0 and 1 or is definitely between 0 and 1.
(d) Which two of these constants are definitely equal?
(e) Which one of the following pairs of constants could be equal?
Answers
The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.
What is an exponent?Let 'a' is the leading coefficient and 'b' is the factor.
The exponent is given as,
y = a(b)ˣ
Some points regarding the exponent function:
If the value of 'b' is greater than one, then the graph will be increasing in nature.If the value of 'b' is less than one, then the graph will be decreasing in nature.If the value of 'b' is equal to one, then the graph will be constant in nature.If 'a' is positive, the graph will be above the line.If 'a' is negative, the graph will be below the line.If 'a' is the same for two exponent equations, then the graph has the same y-intercept.The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.
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WILL VOTE 75 POINTSSS
Which of the following can sine squared theta over the quantity 1 plus cosine theta end quantity be simplified to?
cos θ
1 + cos θ
1 − cos θ
sin θ + tan θ
Answers
Answer:
The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".
Answer:
1 - cos θ
Step-by-step explanation:
41 is what percent of 120
Answers
Answer: Approximately 34.17%.
Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%
classify the following as point , line , and or plane ________1 Corner of a Vaccinatopn room ________2 Face mask ________3 Long chain of children for pediatric vaccination
Answers
1. Point - Corner of a Vaccination room
2. Plane - Face mask
3. Line - The long chain of children for pediatric vaccination
What are points, lines, and planes:Point:
A point is represented as a "dot" on paper. There will be no length, width, or height existing for a point. It simply identifies a certain position. Zero dimensions apply to it.
Line:
The line is a one-dimensional shape in geometry. A line, thus, has length but neither width nor height. In any direction, a line never stops. Two end points of lines act as the fundamental determinants of a line.
Plane:
The coordinate plane, which is used to plot points in algebra, is an example of a plane. The number lines on the coordinate plane stretch eternally from left to right and from up to down, respectively. The coordinate plane cannot be seen entirely.
Here we have
Corner of a Vaccination room, Face mask, The long chain of children for pediatric vaccination
Where
The corner of a Vaccination room represents a point.
Face mask represents a plane
The long chain of children for pediatric vaccination represents a line.
Therefore,
1. Point - Corner of a Vaccination room
2. Plane - Face mask
3. Line - The long chain of children for pediatric vaccination
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