What did you learn, observe and discover in this pr

Answer:

C \(\displaystyle x = 15\)

Step-by-step explanation:

Use the Pythagorean Theorem to define the hypotenuse:

\(\displaystyle a^2 + b^2 = c^2 \\ \\ 12^2 + 9^2 = x^2 \hookrightarrow 144 + 81 = x^2 \hookrightarrow \sqrt{225} = \sqrt{x^2} \\ \\ \boxed{15 = x}\)

I am joyous to assist you at any time.

\( \huge \underline\text{ Hello There}\)

\( \text{We know, Pythagoras Theorem}\)

\(\implies \text{ (Hypotenuse)²= (Base)² + (Altitude)²}\)

\( \text{Here, \red{Hypotenuse}= x, \red{Base}= 9, \red{Altitude}= 12}\)

\( \underline \text{To Find, } \text{Value of'x'}\)

\( \huge \underline\text \red {Solution}\)

\((x) {}^{2} = (9) {}^{2} + ({12})^{2} \\ \implies (x) { }^{2} = 81 + 144 \\ \implies (x) {}^{2} = 225 \\ \implies x = \sqrt{225} \\ \implies x = 15\)

\( \tt{So \: The \: Value \: of'x'= 15}\)

\( \bold{\therefore Hypotenuse= 15}\)

\( \text{Correct Opt. C= x =15}\)

Step-by-step explanation:

Ratio is dividing ( over ) of 2 no. but it must be in the same unit so our given unit is cat and dog .

So it doesn't has ratio but if it has 11:2 is their ratio .

The row space of matrix A, obtained from given vectors X1 to X4, has a dimension of 2. The rank is 2, and the nullity is 1.

To find the row space of matrix A, we need to determine the linearly independent rows of A. We can construct matrix A using the given vectors as its rows: A = [X1, X2, X3, X4].

Row reducing matrix A using Gaussian elimination, we obtain the row echelon form R. The non-zero rows of R form the row space of A. In this case, the row space of A consists of two linearly independent rows.

The dimension of the row space is the number of linearly independent rows, which is 2. The rank of A is also 2, which is equal to the dimension of the row space.

The nullity of A can be found by subtracting the rank from the number of columns in A, which gives 3 - 2 = 1. Therefore, the nullity of A is 1.

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Step-by-step explanation:

Greetings !

Firstly, write down the given expression

\(g(x) = 2x + 8x - 1\)

simplify it to be more accurate where 2+8=10

\(g(x) = 10x - 1\)

plug in -3 in the value of x and simplify the expression

\(g( -3 ) = 10( - 3) - 1 \\ g( - 3) = - 30 - 1\)

Thus, subtract the numbers

\(g( - 3) = - 31\)

Hope it helps!

Explanation:

x = max number of gallons the tank can hold

Greg's car starts off 1/3 full, so (1/3)x = x/3 number gallons is in the car.

Add on 11 more gallons to get (x/3) + 11 = x/3+33/3 = (x+33)/3

The expression (x+33)/3 represents the number of gallons he has after buying 11 gallons of gas. This is equal to (5/6)x since this represents the idea of the tank being 5/6 full

The equation we need to solve is (x+33)/3 = (5/6)x

Let's do so to get...

(x+33)/3 = (5/6)x

(x+33)/3 = (5x)/6

6(x+33) = 3*5x

6x+198 = 15x

198 = 15x-6x

198 = 9x

9x = 198

x = 198/9

x = 22

His tank can hold up to 22 gallons.

Haruka hiked about 14 kilometres in total.

According to the question

We don't know precisely how many kilometres Haruka travelled in the morning, but she hiked several kilometres in the morning and six kilometres in the afternoon. We may utilise the information provided—that her afternoon hike was 25% shorter than her morning trip—to solve the problem.

The unknown quantity (the number of kilometres hiked in the morning) may be represented as X in algebra. We may express the equation as follows if Haruka travelled 6 kilometres in the afternoon, which was 25% less than her morning hike:

6 = X - 0.25X

This equation can be simplified to:

6 = 0.75X

And finally, by solving for X, we get:

X = 8

In the morning, Haruka walked 8 kilometres. The distance travelled in the morning and afternoon are simply added together to provide the total number of kilometres hiked:

8 + 6 = 14 kilometers

Thus, during the course of the two excursions, Haruka covered a distance of 14 kilometres.

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Haruka hiked about 14 kilometres in total.

According to the question

We don't know precisely how many kilometres Haruka travelled in the morning, but she hiked several kilometres in the morning and six kilometres in the afternoon. We may utilise the information provided—that her afternoon hike was 25% shorter than her morning trip—to solve the problem.

The unknown quantity (the number of kilometres hiked in the morning) may be represented as X in algebra. We may express the equation as follows if Haruka travelled 6 kilometres in the afternoon, which was 25% less than her morning hike:

6 = X - 0.25X

This equation can be simplified to:

6 = 0.75X

And finally, by solving for X, we get:

X = 8

In the morning, Haruka walked 8 kilometres. The distance travelled in the morning and afternoon are simply added together to provide the total number of kilometres hiked:

8 + 6 = 14 kilometers

Thus, during the course of the two excursions, Haruka covered a distance of 14 kilometres.

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Answer:

true

Step-by-step explanation:

Answer:

This is true. Hope this helps!

Step-by-step explanation:

To produce an annual interest income of $335,250 by investing $500,000 between Fund A and Fund B, you should invest approximately $370,833 in Fund A and $129,167 in Fund B.

Let's assume the amount invested in Fund A is denoted by S, and the amount invested in Fund B is denoted by (500,000 - S), as the total investment is $500,000.

The interest income from Fund A can be calculated as (S * 0.053), and the interest income from Fund B can be calculated as ((500,000 - S) * 0.078).

According to the given information, the total annual interest income should be $335,250. Therefore, we can set up the equation:

(S * 0.053) + ((500,000 - S) * 0.078) = 335,250

Simplifying and solving the equation, we find:

0.053S + 39,000 - 0.078S = 335,250

-0.025S + 39,000 = 335,250

-0.025S = 296,250

S ≈ 370,833

So, you should invest approximately $370,833 in Fund A and the remaining amount, $500,000 - $370,833 = $129,167, in Fund B. Therefore, to produce an annual interest income of $335,250, you should invest around $370,833 in Fund A and $129,167 in Fund B.

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After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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The average velocity when the position of an object is given by s(t) = - 18t² + 180t are:

(a) For interval [1, 10] = - 18 m/s.

(b) For interval [1, 9] = 0 m/s.

(c) For interval [1, 8] = 18 m/s.

(d) For interval [1, 1 + h] = (144 - 18h) m/s

We know that the average velocity is = (Initial velocity + Final velocity)/2

Given the function that represents the position of the object moving along the line is,

s(t) = - 18t² + 180t

Differentiating the above function with respect to 't' we get,

d/dt [s(t)] = d/dt [- 18t² + 180t]

s'(t) = - 36t + 180

v(t) = - 36t + 180

So at the time t the function of velocity is, v(t) = - 36t + 180

(a) For the interval [1, 10]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(10) = - 180

So the average velocity for [1, 10] = (144 + (-180))/2 = - 18 m/s.

(b) For the interval [1, 9]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(9) = - 324 + 180 = - 144

So the average velocity for [1, 9] = (144 + (-144))/2 = 0 m/s.

(c) For the interval [1, 8]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(8) = - 288 + 144 = - 108

So the average velocity for [1, 8] = (144 + (-108))/2 = 36/2 = 18 m/s.

(d) For the interval [1, 1 + h]:

Initial velocity = v(1) = - 36 + 180 = 144

Final Velocity = v(1 + h) = - 36 - 36h + 180 = 144 - 36h

So the average velocity = (144 + (144 - 36h))/2 = (288 - 36h)/2 = (144 - 18h) m/s.

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Answer:

x + 6

Step-by-step explanation:

Sum means to add the 2 terms , so

x + 6 ← represents the sum of 6 and x

We get the cartesian equation of the plane:

-48x - 28y + 20z = -240

To find the cartesian equation of a plane using the given vectors u and v, we need to find a normal vector to the plane. A normal vector is a vector that is perpendicular to the plane. We can find a normal vector by taking the cross product of u and v. The cross product of two vectors u and v is given by:

n = u x v = <(u2*v3 - u3*v2), (u3*v1 - u1*v3), (u1*v2 - u2*v1)>

Plugging in the values for u and v, we get:

n = <-6,8,4> x <2,-6,-9> = <(8*-9 - 4*-6), (4*2 - -6*-6), (-6*-6 - 8*2)>

n = <-72+24, 8-36, 36-16> = <-48, -28, 20>

Now that we have a normal vector to the plane, we can use it to find the cartesian equation of the plane. The cartesian equation of a plane is given by:

n1(x-x0) + n2(y-y0) + n3(z-z0) = 0

where n =  is the normal vector and (x0, y0, z0) is a point on the plane. We can use the vector u as a point on the plane, so (x0, y0, z0) = (-6, 8, 4). Plugging in the values for n and (x0, y0, z0), we get:

-48(x+6) - 28(y-8) + 20(z-4) = 0

Simplifying, we get the cartesian equation of the plane:

-48x - 28y + 20z = -240

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Answer:

Step-by-step explanation:

Step one:

given data

we are given that the linear function for the cost is  c=3.5t

c is the cost and

t is the number of tickets.

We are told that t=15, to find c, let us put the value of t in the linear function for the cost

\(c=3.5(15)\\\\c=52.5\)

This shows that 15 tickets will cost $52.5

Answer:

-5

Step-by-step explanation:

Answer:a) 322 MILES  B) 34.391 ( The price per gallon was not given in units ) but if price of I gallon = lets say $2.89, then for 11.5 Gallons will be $34.391

Step-by-step explanation:

a)

M r Jones car needs 28 miles for 1 gallon = 28 MILES= 1 Gallon

Number of miles he can drive withe 11.5 gallons

1 Gallon = 28 miles

11.5 gallons = 11.5 x 28miles = 322 miles

b)  IF 1 gallon costs 2.89

11.5 gallons will  cost= 11.5 x 2.89= 34.391

Probability of an event is the measure of its chance of occurrence. The correct probabilities are:

Suppose that the sample space is S. Out of which there are two events, A and B, subsets of S.

Then, we can interpret P(A|B) as the probability of that part of A which is in B, with the new sample space as B. (assuming probabililty of B isn't 0).

Symbolically, we write it as:

\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\)

For three sets, A, B and C:

\(n(A \cup B \cup C) = n(A) + P(B) + P(C) - n(A\cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)\)

The problem is incomplete. The corresponding venn diagram is attached below.

We can symbolize the venn diagram as:

\(n(A) = 12+8+6+5 =31\\n(B) = 11+8+5+3 = 27\\n(C) = 4+8+6+3 = 21\\n(A \cap B) = 5+8=13\\n(B\cap C) = 3+8=11\\n(A \cap C) = 6+8=14\\n(A \cap B \cap C) = 8\)

S = sample space = collection of all unique elements.

S is union of A, B and C.

\(n(S) = n(A \cup B\cup C) = 31 + 27 + 21 -13-11-14+8 = 49\)

Checking all the options for their correctness:

We have:

\(P(A|C) = P(A\cap C)/P(C) = \dfrac{n(A\cap C)/n(S)}{n(C)/n(S)} = \dfrac{n(A \cap C)}{n(C)} = \dfrac{14}{21} =\dfrac{2}{3}\)

Thus, its correct.

\(P(C|B) = P(C\cap B)/P(B) = \dfrac{n(C\cap B)/n(S)}{n(B)/n(S)} = \dfrac{n(C \cap B)}{n(B)} = \dfrac{11}{27} \neq \dfrac{8}{27}\)

Thus, this option is incorrect.

Thus, this option is incorrect.

\(P(C) = \dfrac{n(C)}{n(S)}= \dfrac{21}{49} =\dfrac{3}{7}\)

Thus, its correct.

\(P(B|A) = P(B\cap A)/P(A) = \dfrac{n(B\cap A)/n(S)}{n(A)/n(S)} = \dfrac{n(B\cap A)}{n(A)} = \dfrac{13}{31} \neq \dfrac{13}{27}\)

Thus, this option is incorrect.

Thus, the correct probabilities are:

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The value of the calculated ending balance would be $141.

From the question, we have the following parameters that can be used in our computation:

Starting balance = $80

Checks = 4 at $10 each

Bills = 3 at $7 each

Using the above as a guide, we have the following:

Ending balance = 80 + 4 * 10 + 3 * 7

Evaluate

Ending balance = 141

Hence, the value of the ending balance is $141

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Answer:

t ≤ 8

Step-by-step explanation:

26 + 3t ≤ 50

3t ≤ 50 - 26

3t ≤ 24

t ≤ 8

When dividing the result of 2x³ + x² - 2x + 8 by x + 2, the result will be B. 2x² - 3x + 4.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. A polynomial is an expression made up of terms, exponents, constants, and variables (or indeterminate).

In this case, it should be noted that the multiplication of 2x² - 3x + 4 by x + 2 will be:

(2x² - 3x + 4) (x + 2)

2x³ + 4x² - 3x² - 6x + 4x + 8

= 2x³ + x² - 2x + 8

Therefore, the correct option is B.

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The mathematical program will help the user to provide the data on the Excel sheet and solve accordingly.

The mathematical program to minimize the total cost of constructing the wastewater treatment plants can be expressed as follows:

Minimize z = 50x1 + 100x2 + 100x3 + 50x4 + 50x5 + 100x6 + 100x7

Subject to:

x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 4 (1)

x1 + x2 + x3 + x4 + x5 + x6 + x7 >= 1 (2)

x1 + x4 <= 1 (3)

x2 + x4 <= 1 (4)

x3 + x4 <= 1 (5)

x4 + x5 <= 1 (6)

x4 + x6 <= 1 (7)

x4 + x7 <= 1 (8)

x1, x2, x3, x4, x5, x6, x7 are binary variables (i.e. they can only take on the values 0 or 1)

The objective function (1) minimizes the total cost of constructing the wastewater treatment plants, where the cost of constructing a plant in each city is given in the table. The constraints (2)-(8) ensure that at most four wastewater treatment plants are constructed and that each city is served by at most one wastewater treatment plant.

To solve this problem with Excel, we can create a spreadsheet with columns for the names of the cities, the corresponding costs of constructing a wastewater treatment plant, and the binary variables x1, x2, x3, x4, x5, x6, x7. We can then use Excel's solver tool to minimize the objective function subject to the constraints. The solver tool can be found under the Data tab in the Analyze group.

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Answer:

4

Step-by-step explanation:

Mark me brainleist please!

Answer:

Step-by-step explanation:

Pictograph

Pictograms are a powerful tool for visualizing data and are widely used in a variety of different fields, from marketing and advertising to science and education.

A pictogram is a type of chart that uses symbols instead of words or numbers to portray data. Pictograms are often used in data visualization and are particularly useful for presenting complex information in a simple and easily understandable way. Pictograms can be used to represent a wide range of data, including statistical information, demographic data, and geographical information. They are also commonly used in advertising and marketing, as they are a powerful tool for communicating ideas and concepts quickly and effectively. Pictograms can be created using a variety of different techniques, including hand-drawn illustrations, computer-generated graphics, and photographs. They are typically presented in a grid format, with each symbol representing a single data point. Pictograms can be used to show trends, compare data sets, and highlight key points. They are also a great way to make data more engaging and interactive, as users can explore the data by clicking on individual symbols or groups of symbols.

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Where the above are given,

10. The nurse should give 2.45ml of the liquid medication.

11. The nurse can give 24ml of meperidine in 24 hours.

12. The patient should take 42 tablets of the antibiotic.

13. The IV rate is 100ml/hr at 1500gtt/min with a 15gtt/ml drip factor.

14. Each dose of codeine contains 15000mg.

15. The patient should be given 2.67oz (approximately) of the cough syrup.

10. To determine how much   of the liquid should be given, we can set up a  proportion

1g/3.5ml = 700mg/x

Cross-multiplying,

1g * x = 700mg * 3.5ml

x = (700mg * 3.5ml) / 1g

x = 2450mg*ml/g

Therefore, the amount of liquid to be given is 2.45ml.

11. The order states meperidine 75mg IM every 6 hours PRN pain, and the pharmacy sends a vial that contains 25mg/2ml. To calculate how many ml can be given in 24 hours, we need to consider the frequency and duration.

In 24 hours, there are 24/6 = 4 doses to be given. Each dose contains 75mg of meperidine.

To find the volume (ml) of each dose, we can set up a proportion  -

25mg/2ml = 75mg/x

25mg * x = 75mg * 2ml

x = (75mg * 2ml) / 25mg

x = 6ml

12.  To calculate the number of tablets the patient should take, we need to consider the dosage and the duration.

Each tablet contains 250mg of the antibiotic.

To find the number of tablets for the total dosage, we can set up a proportion  -

250mg/1 tab = 0.75g/x

250mg * x = 0.75g * 1 tab

x = (0.75g * 1 tab) / 250mg

x = 0.003 tab

Since we cannot take a fraction of a tablet, the patient should take 1 tablet every 4 hours for 7 days, resulting in a total of 1 * 6 * 7

= 42 tablets.

13.  To determine the IV rate, we need to calculate the number of drops per minute.

The formula to calculate the IV rate in drops per minute (gtt/min) is -

IV rate (ml/hr) = Total volume (ml) / Total time (hr)

IV rate (gtt/min) = IV rate (ml/hr) * Drop factor (gtt/ml)

IV rate (ml/hr) = 1000ml / 10hr = 100ml/hr

IV rate (gtt/min) = 100ml/hr * 15gtt/ml =

1500gtt/min

Therefore, the IV rate is 100ml/hr at 1500gtt/min.

14. To determine the   amount of milligrams of  codeine in each dose, we need to convert grams to milligrams.

1  gram (g) = 1000   milligrams (mg)

15 grams (gr) = 15 * 1000mg = 15000mg

Therefore, each dose contains 15000mg of codeine.

15. To calculate how much cough syrup should be given in ml's, we can set up a proportion -

225mg/1oz = x ml/600mg

225mg * x = 1oz * 600mg

x = (1oz * 600mg) / 225mg

x = 2.67oz

Therefore, 2.67oz of cough syrup should be given in ml's.

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The weekly payroll for these three employees can be represented by the expression: h + a * 36 + r/2 dollars per week.

To calculate the weekly payroll for these three employees, we need to determine the total amount paid to each employee and then sum them up.

Let's break it down:

1. Dental Hygienist:

  The dental hygienist is paid h dollars per week.

2. Dental Assistant:

  The dental assistant works 36 hours per week at a dollars per hour. To calculate their weekly pay, we multiply the hourly rate by the number of hours worked:

  Weekly pay for dental assistant = a dollars/hour × 36 hours/week

3. Receptionist:

  The receptionist works 40 hours per week and receives r dollars every other week. To calculate their weekly pay, we divide the bi-weekly pay by 2:

  Weekly pay for receptionist = (r dollars/2 weeks) ÷ (1 week/2 weeks) = r/2 dollars/week

Now, we can calculate the total weekly payroll by summing up the pay for each employee:

Total Weekly Payroll = Pay for Dental Hygienist + Pay for Dental Assistant + Pay for Receptionist

The weekly payroll for these three employees is h + a * 36 + r/2 dollars.

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Answer:

4

Step-by-step explanation:

Step-by-step explanation:

c

Answer:

12.53 miles

Step-by-step explanation:

6² + 11² = x²

36 + 121 = x²

157 = x²

x = 12.53 miles

The distance from town A to town C would be; 12.53 miles.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We are given that Town B is 6 miles due north of town A, and town C is due east of town A. It is 11 miles from town B to town C.

Therefore,

6² + 11² = x²

36 + 121 = x²

157 = x²

x = 12.53 miles

Hence, the distance from town A to town C would be; 12.53 miles.

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Answer:

1. Most people without iphones have MP3 Players (first correlation), meaning that if you have an iphone you most likely don't NEED a MP3 player (this may not be a fact just a thought). Also having a iphone most of been pretty common during this time, cause only 12 out of 50 people didn't have one.

2. I gathered the percents of how many people with iphones and a MP3 player, and how many without iphones have a MP3 player. About 53% of people with iphones have a MP3 player while a whopping 67% of people without iphones had a MP3 player. This helped with the correlation and can also help the gathering of data be more useful to other questions. For example, "What percentage of people have an iphone?".

Step-by-step explanation:

Answer:

x = 6°

y= 25°

Step-by-step explanation:

in a cyclic quadrilateral, sum of opposite angles is 180° . So here sum of the angles B and D will be 180° . Similarly sum of angles W and C will be 180° . We can write a equation as ,

ang. W + ang. C = 180

2y + 89 + 8x + 3 = 180

8x + 2y + 92 = 180

8x + 2y = 180 - 82

8x + 2y = 98 . . . . . (1)

Again , we have;

10x - 6 + 2y + 76 = 180

10x + 2y +70 = 180

10x + 2y = 180 - 70

10x + 2y = 110 . . . . . (2)

Subtract equation (1) and (2) to eliminate y,

10x - 8x +2y -2y = 110 - 98

2x = 12

x = 12/2

x = 6

plug this value in equation (1) ,

8*6 + 2y = 98

48 + 2y = 98

2y = 98 - 48

2y = 50

y = 50/2

y = 25

and we are done!

Answer:

The total number of students that voted is 25.

Step-by-step explanation:

18 students = 72% of the students who voted

Divide the percentage of students by 100.

72% ÷ 100 = 0.72%

Then, divide 18 by 0.72%.

18 ÷ 0.72% = 25

So, the total number of students that voted is 25 students.

Hope this helped !