Solution of 1- 2y/3 - y + 2y = 1/y + 2, Please.

It is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.

An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.

For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.

Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".

Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.

To compare the cost of driving the old truck to the diesel truck, we need to know the fuel efficiency of the old truck. Let's assume that the old truck uses gasoline and has a fuel efficiency of 20 miles per gallon.

To drive 60 miles, the old truck will use 60/20 = 3 gallons of gasoline.

At $3.86 per gallon, the cost of 3 gallons of gasoline is 3 * $3.86 = $11.58.

The diesel truck uses 4 gallons of diesel to drive 60 miles. The cost of diesel is not given in the problem, so we'll assume it's the same as the cost of gasoline, $3.86 per gallon.

At $3.86 per gallon, the cost of 4 gallons of diesel is 4 * $3.86 = $15.44.

Therefore, it is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.

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The Total Surface area of cardboard in the box is 992 cm².

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given:

length= 20 cm

width = 12 cm

height= 8 cm

So, the TSA of Cuboid

= 2(lw + wh + lh)

=2( 20 x 12 + 12 x 8 + 8 x 20)

=2( 240 + 96 + 160)

= 2(496)

= 992 cm²

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The solution is, the function is  g(x) = (x -5)² + 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

we know that,

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

"a" is the vertical stretch

-a is a reflection over the x-axis

h is the horizontal shift (positive = right, negative = left)

k is the vertical shift (positive = up, negative = down)

given that,

f(x) = (x-2)² + 1

now we have,

Given: 3 units left   -->   h = -3

so, we get,          

g(x) = (x - 2- 3)² +1

       =(x-5)² + 1

Hence, The solution is, the function is  g(x) = (x -5)² + 1.

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Answer:

Step-by-step explanation:

the optimal point is (40,000, 40,000, 20,000), which gives an annual income of $680,000. The slack for the first, second, and fourth constraints is 0, and the slack for the third constraint is also 0.

Answer:

88 days

Step-by-step explanation:

inversely proportional means for a response y and input x, we have the formula

y = k/x

10 days = k/44 workers

multiply both sides by 44 to find k

44 workers * 10 days = k

k = 440 workers * days

y = k/x

x = 5 workers

440 workers * days / 5 workers = y

88 days = y

The mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The number of patients experiencing side effects in a sample of 100 patients as a binomial distribution with n = 100 and p = 0.20.

The mean of a binomial distribution is given by:

μ = np

Substituting n = 100 and p = 0.20, we get:

μ = 100 × 0.20 = 20

Therefore, the mean is 20.

The variance of a binomial distribution is given by:

σ²= np(1 - p)

Substituting n = 100 and p = 0.20, we get:

σ² = 100 × 0.20 × (1 - 0.20) = 16

Therefore, the variance of the number of patients experiencing side effects in a sample of 100 patients is 16.

The standard deviation of a binomial distribution is the square root of its variance:

σ =√Variance

=√16

= 4

Hence, the mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

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The direct distance between the White House and the Pentagon is approximately 3.067 miles.

Distance is a measure of how far apart two objects or points are from each other. It is a fundamental concept in mathematics, physics, and other scientific disciplines, and plays a crucial role in our everyday lives.

Distance can be measured in various units, such as meters, kilometers, miles, feet, and inches, depending on the context and application. In mathematics, the distance between two points in a plane can be found using the Pythagorean theorem, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:

distance = √((x2-x1)² + (y2-y1)²)

In this formula, the square of the difference in the x-coordinates and the y-coordinates of the two points are added and then the square root of the sum is taken to obtain the distance.

Using the distance formula, the direct distance between the two buildings is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

where (x1, y1) = (-8,-6) and (x2, y2) = (-1,10)

d = sqrt[(-1 - (-8))^2 + (10 - (-6))^2]

d = sqrt[7^2 + 16^2]

d = sqrt(49 + 256)

d = sqrt(305)

Since each unit on the grid represents 0.125 miles, we can convert the answer to miles by multiplying by 0.125:

d = sqrt(305) * 0.125

d = 3.067 miles (rounded to 3 decimal places)

Therefore, the direct distance between the White House and the Pentagon is approximately 3.067 miles.

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Answer:

the answer is A. 11 1/4

Step-by-step explanation:

the base times height for the triangle divided by 2 plus the bxh of the rectangle.

3x3/2 + 1 1/2 x 4 1/2

Answer:

Step-by-step explanation:

Here is a more detailed explanation:

We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:

x   f(x)   g(x)

1    3      5

4    9      20

To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.

For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

So the equation of f(x) is y = 2x + 1.

Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:

y - 5 = 5(x - 1)

y - 5 = 5x - 5

y = 5x

So the equation of g(x) is y = 5x.

To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:

2x + 1 = 5x

3x = 1

x = 1/3

Substituting this value of x back into either equation, we can find the corresponding value of y:

y = 2(1/3) + 1 = 7/3

So the point of intersection is (1/3, 7/3).

Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.

The percentage of the decrease in the value of the XYZ Company stock is 16%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The decrease in the value of the stock is $25 - $21 = $4.

To find the percent decrease, we need to divide the decrease by the original value and then multiply by 100:

Percent decrease = (Decrease / Original value) x 100

In this case, the original value is $25, so:

Percent decrease = (4 / 25) x 100 = 16%

Therefore, the percentage of the decrease in the value of the XYZ Company stock is 16%.

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Answer:

the formula for this is y=mx+b

b stands for the y, m is the slope of the line,  and x stands for the x axis!

Step-by-step explanation:

i am pretty sure your answer is -1.4

hope this helps I to help you out attached a screenshot

The stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.

Given that, 600, 600, 600, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 612, 620, 620, 625, 629, 631, 635, 638, 640, 640, 645, 646, 650, 651, 660, 660, 665, 671, 671, 674, 680, 693, 700, 705, 706, 707, 707, 715, 715, 719,  720,  725, 727, 732, 738, 739 and 745.

a) Split between hundreds place and the tens place.

60|  0   0   0

61|  1    1    1    1    1    1    1    1    1    1    1    2

62|  0   0   5   9

63|   1    5   8  

64|  0    0   5   6

65|  0    1

66|  0    0   5

67|   1     1    4

68|  0

69|  3

70|  0  5   6   7   7

71 |   5  5  9

72|   0  5  7

73|   2  8  9

74|   5

b) Split between the tens place and the ones place.

6|   00  00   00  10   10  10   10   10   10  10  10  10  10  10   12   20   20   25 29   31   35   38   40   40   45   46   50   51   60   60   65   71   71   74   80   93

7|    00   05   06   07   07   15   15   19  20  25  27  32  38  39  45

Therefore, stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

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Answer:

0

Step-by-step explanation:

Probability (also known as chance) is the number that indicates how likely an event is to occur. If something has a low probability, it is unlikely to happen. If something has a high probability, it is likely to happen.

If we look at a phone keypad, you will see the numbers 0-9, but you will never see a number greater than 9.

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the numbers, but none are greater than 9.

The solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 is (-2, 3)

Isolate x in the first equation:

x + 3y = 7

x = 7 - 3y

Use the substitution method, Substitute the value for x into the second equation:

2x + 4y = 8

2(7 - 3y) + 4y = 8

Solve for y:

14 - 6y + 4y = 8

-2y = -6

y = 3

Substitute y into either original equation:

x + 3y = 7

x + 3(3) = 7

x + 9 = 7

x = -2

Write the solution as an ordered pair:

The solution is (-2, 3).

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The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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Answer:

3.

a.4 feet

b.77 feet

c.8 seconds

Step-by-step explanation:

We can start by noting that the given equation, d(p) = 1/4p^2 - 2p, represents the depth (in feet) at a given point in time as you swim underwater, where p is the time in seconds since you started swimming.

a. To find the deepest point underwater, we need to find the maximum of the function d(p). We can do this by finding the vertex of the parabola. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = 1/4 and b = -2, so the x-coordinate of the vertex is:

x = -b/2a = -(-2)/(2(1/4)) = 4

So the deepest point underwater occurs at p = 4 seconds. To find the depth at this point, we can substitute p = 4 into the equation:

d(4) = 1/4(4)^2 - 2(4) = -4 feet

Therefore, the deepest point underwater is 4 feet below the surface.

b. To find the depth when you have held your breath for 22 seconds, we need to evaluate the function d(p) at p = 22. We can round our answer to the nearest foot.

d(22) = 1/4(22)^2 - 2(22) = 77 feet

Therefore, the depth when you have held your breath for 22 seconds is approximately 77 feet below the surface.

c. To find how long you hold your breath to make the swim, we need to find the time it takes to swim from one side of the pool to the other. We can do this by finding the roots of the equation d(p) = 0, which represent the times when you reach the other side of the pool (i.e., when the depth is zero). We can use the quadratic formula to solve for p:

p = (-b ± sqrt(b^2 - 4ac))/2a

In this case, a = 1/4, b = -2, and c = 0, so the formula becomes:

p = (-(-2) ± sqrt((-2)^2 - 4(1/4)(0)))/(2(1/4)) = 8 or 0

The root p = 0 corresponds to the start of the swim, so the time it takes to make the swim is:

p = 8 - 0 = 8 seconds

Therefore, you hold your breath for 8 seconds to make the swim from one side of the pool to the other.

The completed balance sheet is given below:

A balance sheet is a financial statement that shows the financial position of a company at a specific point in time. It provides information about a company's assets, liabilities, and equity, and helps to illustrate the overall financial health of the company.

The Balance Sheet

Sheffield company

balance sheet (partial)

December 31, 2023

Plant Assets

Land $3,926,000

Building $28,650,000

Less: Accumulated Depreciation (14,396,250)

Net Building $14,253,750

Equipment $49,569,000

Less: Accumulated Depreciation (4,127,795)

Net Equipment $45,441,205

Total Plant Assets $63,620,955

Note that the buildings and equipment are shown at their net book value, which is the original cost less the accumulated depreciation.

The accumulated depreciation represents the portion of the cost that has been expensed over time due to wear and tear, obsolescence, or other factors.

The land is not depreciated, so its original cost is shown.

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Answer:

Look at the screenshot.

The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Years, prices, prices as a percentage of 1990 price, price index 1990=100

Now,

The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.

It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.

Therefore, by ratio the answer will be  Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.

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The area that will be frosted on the bottom layer 680

What are the basic mathematical operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

1. Find the smaller cake first with (lw*amount of sides) and then add it to the larger cake using the same formula.

6*6*6+10*10*6

This equals 816

2. Find the amount not frosted. The bottom and the connection. Simply, (lw).

6*6+10*10

This equals 136

3. Subtract 136 from 816.

816-136= 680 sq inches

Hence, The area that will be frosted on the bottom layer 680

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The answer here would be D. In choice A, this would be incorrect because he would divide the millage cost before the passenger fee. In choice B, this would be incorrect because he would add the passenger fee, when it is required to subtract it. Choice C would be incorrect, because yet again, you are not supposed to add the passenger fee. This leaves choice D, which is correct.

Answer:

Are we supposed to give the answer in fractions?

The solution of the system x + y ≥ 75 and 2.5x + 10.5y ≤ 800  of the equation is

The system of equation x + y ≥ 75 and 2.5x + 10.5y ≤ 800 will have a solution that is as written in the equation.

This is done by substituting each value

Using (250, 10)

250 + 10 ≥ 75

260 ≥ 75 correct

2.5x + 10.5y ≤ 800

2.5 * 250 + 10.5 * 10 ≤ 800

730 ≤ 800 correct

since the the values are correct for the equations,  (250, 10) is the solution

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On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to find the equivalent value for the division as -

"153 ÷ 4"

On dividing 153 by 4, we can write the result as follows -

{x} = 153/4

{x} = 38.25

{x} = 38[tex]\frac{1}{4}[/tex]

Therefore, On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].

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{Question in english -

What is the remainder when 153 is divided by 4?}

There are 160 tree in each row.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

To calculate the number of students in the seventh grade, you must divide the number of students in the Environmental Club by the percentage they represent. The answer is 8 divided by 0.05, which equals 160. Therefore, there are 160 students in the seventh grade.

The Environmental Club provides students with an opportunity to learn more about the natural environment and how to help protect it. The club members work together to come up with ideas to promote environmental awareness and action in their school and community. They plan activities such as tree-planting, trash clean-ups, and educational presentations. The club also participates in activities like field trips to local parks and nature preserves.

By joining the Environmental Club, students can gain a better understanding of their local environment and how to protect it. This can help them become more aware of their actions and how they can make a difference in the world. They can also develop leadership and communication skills, as well as an understanding of the importance of teamwork. Furthermore, they can make friendships and connections with other students who share the same values and interests.

Overall, the Environmental Club is an important part of the school community and provides great benefits to its members. It allows students to gain knowledge, build skills, and make a positive difference in their communities.

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a. The period of y = 2tan(4x) on the interval [0,pi] is pi/2.

Justification: The period of a tangent function is pi/b where b is the coefficient of x. Therefore, the period of 2tan(4x) is pi/4, and the function completes two periods on the interval [0,pi], giving a total period of pi/2.

b. The location of vertical asymptotes for y = 2tan(4x) on the interval [0,pi] is x = (2n + 1)pi/8 where n is an integer.

Justification: The vertical asymptotes of a tangent function occur where the cosine of the angle in the argument is equal to zero. In this case, the cosine is equal to zero at (2n + 1)pi/8, giving the location of the vertical asymptotes.

c. The domain of y = 2tan(4x) on the interval [0,pi] is [0, pi/4) U (pi/4, pi/2) U (pi/2, 3pi/4) U (3pi/4, pi].

Justification: The tangent function has vertical asymptotes at odd multiples of pi/2, so the function is undefined at these points, and thus excluded from the domain.

d. The range of y = 2tan(4x) on the interval [0,pi] is (-∞, ∞).

Justification: The range of the tangent function is the set of all real numbers.

e. The x-intercepts of y = 2tan(4x) on the interval [0,pi] are x = k(pi/8), where k is an integer.

Justification: The x-intercepts of a tangent function occur where the function is equal to zero, which happens at integer multiples of pi.

f. The y-intercept of y = 2tan(4x) on the interval [0,pi] is (0,0).

Justification: The y-intercept of a function occurs where x=0, so the y-intercept of this function is (0, 0), as 2tan(4*0) = 0.

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The baseball team won 87.5% of their games in that month.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.

The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.

Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.

Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance

To find the percentage of games won, we need to divide the number of games won by the total number of games played and multiply by 100%:

percentage of games won = (number of games won / total games played) x 100%

total games played = number of games won + number of games lost = 21 + 3 = 24

percentage of games won = (21 / 24) x 100%

percentage of games won = 87.5%

Therefore, the baseball team won 87.5% of their games in that month.

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The surface area of the rectangular prism, found by summing the surface areas of the six rectangular faces is about 2,600 square inches

A rectangular prism is a three dimensional solid with six rectangular faces, such that faces of the prism that face each other are parallel and congruent.

The surface area of the rectangular prism is the sum of the surface areas of the six rectangular faces of the prism

The area of the rectangles that make up the surface are;

A₁ = 8 inches × 36 inches = 288 square inches

A₂ = 23 inches × 8 inches = 184 square inches

A₃ = 23 inches × 36 inches = 828 square inches

A₄ = 23 inches × 8 inches = 184 square inches

A₅ = 8 inches × 36 inches = 288 square inches

A₆ = 23 inches × 36 inches = 828 square inches

The surface area of the rectangular prism, A, is therefore;

A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆

Therefore;

A = 288 + 184 + 828 + 184 + 288 + 828 = 2600

The surface area of the rectangular prism is 2,600 square inches

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1. Point - Corner of a Vaccination room

2. Plane  - Face mask

3. Line - The long chain of children for pediatric vaccination

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

Learn more about Planes at

https://brainly.com/question/17608790

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