Need help with this question quickly

The true Statements are : π is the area of the circle of radius 1 and π is the circumference of diameter 1.

What is Area of a Circle ?

The area of a circle is pi times the radius squared (A = π r²)

Putting r =1 ,we get

A = π×(1)² = π

What is Circumference of a Circle ?

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

C = π×D

putting D =1 , we get

C = π

Hence,  π is the area of the circle of radius 1 and π is the circumference of diameter 1.

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Answer:

2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

simplifying

[tex]\sqrt{45}[/tex]

= [tex]\sqrt{9(5)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]

= 3[tex]\sqrt{5}[/tex]

Then

[tex]\sqrt{45}[/tex] - [tex]\sqrt{5}[/tex]

= 3[tex]\sqrt{5}[/tex] - [tex]\sqrt{5}[/tex]

= 2[tex]\sqrt{5}[/tex]

Negative one-sixth times the quantity 3 minus 15 times the quantity one-third squared end quantity is C. negative two ninths.

Fractions: A fraction can represent any number of equal parts or a portion of a whole. A fraction is a word used in everyday English to indicate the number of parts of a given size, such as one-half, eight-fifths, or three-quarters.

we will compute the expression,

The expression will be, based on the information provided:

= 1/6 ×( 3 - 15 ) × (1/3)²

= -1/6 × -12 × 1/9

= -2 × 1/9

= -2/9

thus, we can conclude that a negative two-ninth is the correct answer to the expression.

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4s2 4p1 - electronic configuration corresponds to gallium

Periodic table has 4 different blocks, which are s block, d block, p block, and f block. Each block has corresponding elements which gives its electron configuration

What is group and period?

Prediction of Period ⟶ In electronic configuration of an atom, principal quantum number (n) of valence electrons represents the period of an element.

Prediction of Block ⟶ The orbital out of s,p,d and f which receives last electron represents block of an element

Prediction of Group ⟶ The group prediction occurs with help of block as:-

(1) For s block: Group Number = Number of valence e-

(2) For d block: Group Number = Number of e- in (n−1)d subshell + number of e- in ns subshell

(3) For p block: Group Number = Number of valence

e- + 10

(4) For f-block: Group Number = 3

Lets take an ex of chlorine ( Z= 17 )

Electronic configuration = 1s2 2s2 2p6 3s2 3p5

Since the last e- enters in p - subshell:

(i) Therefore Block will be "p "

(ii) For group we have element in p-block

∴ Group number = 10 + Valence e- in s subshell + Valence e- in p subshell

Group Number = 10+2+5=17

(iii) For period

Quantum number of valence e- =3

∴ Period number = 3

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a) √2 t |1, -1>

b ) t√0 |0, 1>=0

c) 2t² |1, -1> are the eigenstates of S² with the appropriate eigen value.

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it. The associated eigenvalue, generally indicated by lambda, is the factor by which the eigenvector is scaled.

Eigenvalues and eigenvectors play an important role in the analysis of linear transformations. The prefix eigen- comes from the German word eigen, which means "property," "characteristic," or "own."

a) S- |1,0>= t√(1+0)(1-0+1) |1, 0-1>

=t√2 |1, -1>

=√2 t |1, -1>

∴S±(s, m>=t√(s±m)(s±m+1) |s, m±1>

b) S₊ |0, 0>= t√(0-0)(0+0+1) |0, +1>

=t√0 |0, 1>=0

S₋ |0, 0>=t√(0+0)(0-0+1_) |0. -1>

c) S² |1, 1>= 1(1+1)t² |1, 1>

=2t² |1, -1>

∴ S² |s, m>=s(s+1)t² |s, m>

Hence, |1, -1> and |1, -1> are eigen function of S² with eigen value 2t²s.

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Answer:

16

Step-by-step explanation:

You have to know which theorem applies. This theorem only works because we know line m and line n are parallel.

Alternate Exterior Angles theorem says 111 degrees and 7x-1 are congruent.

This means we can set them equal to each other:

7x - 1 = 111

Solve for x:

7x = 112

112 / 7 = x

x = 16

Answer: -15

Step-by-step explanation:

do 17-32= -15

The probability of a bill exceeding $300 is 0.0091.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

For normal distribution z score = (X-μ)/σ

here mean= μ = 196

std deviation  = σ = 44.0000

probability of a bill exceeding

$300  = P(X>300)

          =P(Z>(300-196)/44)  

          =P(Z>2.36)

          =0.0091

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The total percentage of athletes who enjoy cycling is given by:

74.5%.

A percentage is the division of an amount by a total amount, which is then multiplied by 100%.

In this problem, the percentages are already given for the entire population.

The percentage of athletes who enjoy cycling is divided into two nodes, as follows:

The percentages associated from each node are given on the text as follows:

Hence the proportion of athletes who enjoy cycling is given as follows:

0.45 x 0.80 + 0.55 x 0.70 = 0.745.

Then the percentage is of:

0.745 x 100% = 74.5%.

Which means that the last option is correct.

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The dollar interval would be ± 6.70 to present in order to obtain a probability of 0.500.

What is probability?

Probability is a branch of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of error in research by using probability.

z value for the probability of 0.5  is 0.67

standard error = sd/√n = 80/√64 =10

dollar interval = z*se

                      = 0.67*10

                       =6.70

Hence, the dollar interval would be ±6.70.

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After solving, her total finance charge was $11.65.

In the given question we have to find her total finance charge.

Mrs. stevens bought identical gifts for her children = 5

Each gift value = $80

So, Total cost = $80×5

Total cost = $400

She paid total 1/2 cost.

Financed the remaining balance through her credit union for 18 months at 9 % interest.

the money is paid 1/2

The rest amount is converted into EMIs.

P = $200

r= 9% = 0.09

n =18 months

[tex]\text{EMI}=P\times\frac{r}{n}\left [ \frac{(1+\frac{r}{n})^n}{(1+\frac{r}{n})^n-1} \right ][/tex]

Put the values.

[tex]\text{EMI}=200\times\frac{0.09}{18}\left [ \frac{(1+\frac{0.09}{18})^{18}}{(1+\frac{0.09}{18})^{18}-1} \right ][/tex]

After solving

EMI = $11.65

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We apply permutation formula to the number of participants considering that there are no ties and find out that there are 60 different outcomes possible if there are no ties.

It is given to us that -

There are 5 participants - Abe, Bobby, Charles, Devin, and Edwin

We have to find out the number of different 1st - 2nd - 3rd place outcomes that are possible if there are no ties.

Considering that there should be no ties,

If we select one person, say Abe, then there are 4 different ways remaining for the second place in the race.

Similarly, assuming that Abe ranked 1st in the race and Bobby ranked 2nd in the race, there are 3 different ways remaining for the third place in the race.

Continuing like this, the 5 different participants can be ranked accordingly such that there are no ties.

For this situation, we have to find the permutation where -

Total number of objects (in this case, participants) = n = 5

and, total number of objects selected = r = 3

We know that the formula for permutation is -

[tex]P = \frac{n!}{(n-r)!}\\[/tex]

Substituting the values of 'n' and 'r' in the above equation, we have

[tex]P = \frac{n!}{(n-r)!}\\= > P = \frac{5!}{(5-3)!}\\= > P = 60[/tex]

Thus, by applying permutation formula, we find out that there are 60 different outcomes possible if there are no ties.

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(a) The mean is 32, and the standard error is 0.068 (b) The expected shape will be approximately normal (c) The probability of scoring less than 60% is 0.278

As the number of questions (n) is 50 and the probability of getting the correct answer (p) is 0.64, the mean can be calculated as follows;

E(x) = np

E(x) = 50 × 0.64

E(x) = 32

The standard error is calculated as follows;

SE = √p×(1-p) ÷ n

SE = √0.64 × (1-0.64) ÷ 50

SE = √0.004608

SE = 0.068

Therefore, the mean is calculated to be 32, and the standard error is 0.068

As the sample size is large therefore the expected shape will be approximately normal

To calculate the probability of scoring less than 60%, we first calculate the z-score using:

z = (x – μ) / σ

z = (0.60 - 0.64) / 0.068

z = -0.588

So we have;

P (x < 60%) = P (z < -0.588)

P (x < 60%) = 0.278

Therefore the probability of scoring less than 60% is 0.278

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The length of fence  is 170feet if a rectangular garden measures 60 feet by 25 feet. Fencing is used to cover the garden from any unwanted animals.

A fence is defined as the structure that encloses an area, typically outdoors, and is usually constructed from the posts that are connected by boards, wire, rails or netting.

We know very well that the length of the fencing can be found by the perimeter of rectangle.

Perimeter of rectangle is given by =2×(length + breadth) or

=>P=2L +2W

if L is the length of rectangle and W is the width of rectnagle

Now, here we have length of rectangular garden as 60 feet and width as 25 feet

=>P=2×60+2×25

=>P=120+50

=>P=170feet

Hence, required length of fence is 170 feet.

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The equation of the line is y = 7x + 6 when  the line crooses the y-axis at the point (0,6) and has a slope of 7

The line crosses the y-axis at the point (0,6)

The slope of the line is 7

The equation of a line in slope point form is

y - y' = m(x - x')

Where m stands for the slope of the line and x' y' are the coordinates of the point through which the line passes.

So, the point x',y' is 0, 6 and the slope m is 7

y - y' = m(x - x')

y - 6 = 7 (x - 0)

y - 6 = 7x

y = 7x + 6

Therefore, the equation of the line which  crosses the y-axis at the point (0,6) and has a slope of 7 is y = 7x + 6

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The compound inequality describes the possible lengths for the third side, x is -4< c< 14.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.

A triangle with A, B, and C vertices is symbolized by ΔABC

The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:

(a - b) < c < (a + b)

As a result, let a = 5 and b = 9

(5-9) <c (5+9)

-4< c< 14

As a result, the third side of the triangle must follow the inequality, which is -4< c <14

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The average speed of a car is 93.34 km/h

Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time.

Average speed formula is the average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as: Total distance travelled / total speed

According to the equation,

A car covers the road from city A to city B, 40 km, in 30 minutes, and the road from city B to C, 30 km, in 15 minutes

Total distance a car covers is 40 + 30

= 70km

Total time a car takes is 30 + 15

= 45minutes = 0.75 hours

Average speed = total distance / total time

Average speed = 70 / 0.75

= 93.34 km/h

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Example of  linear inequalities; y ≤ x – 1 and y < –2x + 1

A combination of linear inequality equations with the same variables is referred to as a system of linear inequalities.

There are five inequality symbols used to represent equations of inequality.

These are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.

Example of  linear inequalities;

Graph the following system of linear inequalities:

y ≤ x – 1 and y < –2x + 1

Graph the first inequality y ≤ x − 1.

We will draw a solid border and shade below the line due to the "less than or equal to" mark.

On the same x-y axis, graph the second inequality, y -2x + 1.

In this instance, the less-than symbol will cause our boundaries to be dashed or dotted. Under the border, cast a shade.

As a result, the darker-colored zone extending indefinitely downward is the solution to this inequality problem, as seen below.

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Answer:

16

Step-by-step explanation:

The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is  4x+y-6=0.

The line's equation is expressed in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

The slope intercept form is used to calculate the y-intercept and slope of a straight line.

We know that the equation of the line is, y= mx +b

4x+y-1=0 is the same as y= -4x+1

For this equation, b=1, but for a line with slope -4 passing through the point (1,2), the y-intercept changes.

y= -4x+b

The above line is passing through the point (1, 2)

2=-4(1)+b

Now, we have to solve for b value we get b=6.

The equation that we get is,

y= -4x+6 or 4x+y-6=0.

The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is  4x+y-6=0.

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The 3 ways to prove two triangles are similar are AA, SSS and SAS Similarity Postulate.

In the given question we have to explain the 3 ways to prove two triangles are similar.

Similar triangles are described as having the same shape but varying sizes. Examples of related objects include squares with any side length and all equilateral triangles. Alternatively put, if two triangles are similar, their corresponding sides will be proportionately equal and their corresponding angles will be congruent.

The 3 ways to prove two triangles are similar are:

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24 hours takes all five machines to fill the same production order.

Given,

Four machines take 30 hours to fill a certain production order.

[tex]Rate = \frac{Work}{Time}[/tex]

Let, Total work = 1 unit

The rate of 4 machines = [tex]\frac{1}{30}[/tex]

We can let the rate of 5 machines be n and create the equation:

[tex]\frac{4}{\frac{1}{30} }=\frac{5}{n}[/tex]

[tex]120=\frac{5}{n}[/tex]

[tex]120n = 5[/tex]

[tex]n=\frac{5}{120}[/tex]

[tex]n=\frac{1}{24}[/tex]

Time taken by five machines = [tex]\frac{1}{\frac{1}{24} }[/tex]

Time is taken by five machines = 24 hours

Hence, 24 hours takes all five machines to fill the same production order.

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An exponential function is a mathematical function in which the output of the function increases (or decreases) at a rate that is proportional to the current value of the output.

Exponential functions have an “asymptote”, which is a line that the graph approaches but never crosses. This asymptote is often a horizontal line, and it can be used to identify exponential functions.

To determine if a graph is an exponential function, look for a curve that rises or falls steeply and then levels off. The curve should be smooth and symmetrical, and the points should lie along a straight line when plotted on a logarithmic scale. The equation for the graph should also have an exponential form, such as y=ab^x. If these characteristics are present, then the graph is an exponential function.

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The inverse of the 4 × 4 matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] found using an online matrix tool  is presented as follows;

[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\begin{bmatrix}\dfrac{1}{a} & 0& 0 &0 \\\\ 0& \dfrac{1}{b} & 0 & 0\\\\0 &0 &\dfrac{1}{c} & \\\\0 &0 &0 &\dfrac{1}{d} \\\end{bmatrix}[/tex]

The inverse, A⁻¹ of a matrix, A, can be found using the formula;

[tex]A^{-1}=\dfrac{adj \, A}{det\, A}[/tex]

The adjugate of the specified matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] is found using an online tool as follows;

[tex]adj\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}=\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}[/tex]

The value of the determinant of the matrix found using an online calculator is presented as follows;

[tex]det\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix} = a\cdot b \cdot c\cdot d[/tex]

The inverse of the matrix in the question is therefore;

[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\dfrac{\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}}{a\cdot b\cdot c \cdot d} = \begin{bmatrix}\dfrac{1}{a} &0 &0 &0 \\ \\0& \dfrac{1}{b} & 0& 0 \\ \\0&0 &\dfrac{1}{c} &0 \\\\ 0& 0& 0& \dfrac{1}{b} \\\end{bmatrix}[/tex]

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It will take Chad 12 hours to drive 672 miles and he will need 24 gallons of gasoline

Given that: Chad is planning a 672–mile road trip

Chad’s car can travel 308 miles with 11 gallons of gas. We can use this information to calculate the miles 1 gallon can cover. Thus:

Number of miles per gallon =   308/11 = 28 miles per gallon

Also, Chad plans to drive 168 miles every 3 hours. We can use this information to calculate Chad's speed. Thus:

Speed = 168/3 =  56 miles per hour

To determine how many hours it will take Chad to drive 672 miles:

Speed = distance/time

=> time = distance/speed    

Speed = 56 miles per hour and distance =  672 miles

time = 672/56 = 12 hours

Number of gallons = distance / Number of miles per gallon

Number of gallons = 672/28 = 24 gallons

Therefore, it will take Chad 12 hours to drive 672 miles and he will need 24 gallons of gasoline

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Answer:

14

Step-by-step explanation:

-2(-12)/3-(-2+(-4))

=24/3-(-2+(-4))

=8-(-2+(-4))

=8-(-2-4)

=8-(-6)

=8+6

=14

The sum of and diffrence identities to find the exact values of sine cosine and tangent are calculated below :

Given that,

1. 75º = 30° + 45 2. 15º = 45° - 30° 3. 105° = 60° + 450 4. 165º = 135° + 30° 5. 195º = 225º – 30° 6. 255 – 300

To find them we need to know the respective formulas:

In relation to the illustration above, the key sin,cos,tan formulas are:

sin A = Opposite side/Hypotenuse = BC/AB

cos A = Adjacent side/Hypotenuse = AC/AB

tan A = Opposite side of triangle /Adjacent side of triangle = BC/AC

1) 75°

sin(75°)= 0.966

cos(75°)=0.259

tan(75°)=3.732

2) 105°

sin(105°)=0.966

cos(105°)= -0.259

tan(105°)= -3.732

3) 175°

sin(175°)=-0.259

cos(175°)= -0.966

tan(175 )=0.268

4) 11π/12

sin(11π/12)=0.050

cos(11π/12)=0.999

tan(11π/12)=0.050

5) 17π/12

sin(17π/12)=0.078

cos(17π/12)=0.997

tan(17π/12)=0.078

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Answer:

D

E

Step-by-step explanation:

Prime factorize 252.

252 = 2 * 2 * 3 * 3 * 7

[tex]\sf \sqrt{252}=\sqrt{2*2*3*3*7}[/tex]

        [tex]\sf = 2*3\sqrt{7}\\\\=6\sqrt{7}[/tex]

D

[tex]\sf \text{The exponent form of } \ \sqrt{252}=252^{\frac{1}{2}}[/tex]

E

Step-by-step explanation:

so, first, let's see the factors of 252 :

252 / 2 = 126

126 / 2 = 63

63 / 2 no

63 / 3 = 21

21 / 3 = 7

so, 252 = 2×2×3×3×7 =

= 4×9×7 =

= 36×7 =

= 42×6 =

= 18×14

and others. but these are closest to the given answer options.

A. is wrong. 126^(1/2) is the same as sqrt(126). that is of course not the same as sqrt(252).

B. is wrong. to leave 6 in the square root, the remaining factor is 42. and sqrt(42) is not 7.

C. is wrong. to leave 7 in the square root, the remaining factor is 36. and sqrt(36) is not 18.

D. is correct. see C. sqrt(36) = 6. so, sqrt(252) = sqrt(36×7) = 6×sqrt(7).

E. is correct. 252^(1/2) is exactly the same as sqrt(252). an exponent of 1/n means the nth root.

The area of the shaded portion of the inscribed hexagon is; 3.395 ft²

We are given;

Diameter of circle = 5 ft

Thus;

radius; r = 5/2 = 2.5 ft

Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;

a = d/2

where d is the length of the long diagonal

Formula for area of hexagon is;

A = (3/2) * √3 * a²

Thus;

A =  (3/2) * √3 * 2.5²

A = 16.24 ft²

Area of circle is gotten from the formula;

A = πr²

A = π * 2.5²

A = 19.635 ft²

Thus;

Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²

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The minimum sample size needed is 93.

Given:

A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.

here

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

[tex]n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }[/tex]

On submitting and solving using calculator

n = 93

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