[tex] {2x}^{4} = 50 \\ = > {x}^{4} = \frac{50}{2} \\ = > {x}^{4} = 25 \\ = > {x}^{4} - 25 = 0 \\ = > ( {x}^{2} + 5)( {x}^{2} - 5) = 0 \\ = > {x}^{2} - 5 = 0 \\ > (x - 5)(x + 5) = 0 \\ = > x = 5 \: \: and \: \: - 5[/tex]
Answer:
5, -5
Hope it helps.
Please send your query through comment section.
A mall independent movie company determine the profit, P, for producing n DVD copie of a recent releae i P=-0. 02n^23. 4n-16. P i the profit in thouand of dollar and n i in thouand of unit
The equation P = -0.02n^2 + 3.4n - 16 represents the profit, P, in thousands of dollars for a small independent movie company as a function of the number of DVD copies produced, n, in thousands.
The equation is a quadratic equation, which means it is a polynomial equation of degree 2. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants and x is the variable. In this case, the equation can be written as P = -0.02n^2 + 3.4n - 16, where P is the variable, and -0.02, 3.4, and -16 are the constants.
The first term in the equation is -0.02n^2, which represents the cost of producing the DVD copies. As n increases, the cost of production also increases, and the coefficient -0.02 represents that the cost of production is directly proportional to n^2. The negative sign in front of the term indicates that as the number of copies increases, the cost of production also increases and thus the profit decreases.
The second term in the equation is 3.4n, which represents the revenue generated by the sale of the DVD copies. As n increases, the revenue generated also increases, and the coefficient 3.4 represents that the revenue is directly proportional to n. The positive sign in front of the term indicates that as the number of copies increases, the revenue generated also increases and thus the profit increases.
The last term in the equation, -16, represents the fixed costs associated with producing the DVD copies, such as overhead costs, marketing and distribution costs, etc. These costs are not directly related to the number of copies produced and are constant regardless of how many copies are produced.
In summary, the equation P = -0.02n^2 + 3.4n - 16 represents the profit for a small independent movie company as a function of the number of DVD copies produced. The profit is affected by the cost of production, revenue generated from sales, and fixed costs. As the number of copies increases, the cost of production increases, the revenue generated increases, and the fixed costs remain constant. The profit is the difference between the revenue generated and the costs incurred.
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Prove that the two lines represented by the following equations are perpendicular to each other.
a)6x²-5xy-6y² = 0
b) x²-y²+x+y=0
c) x² - y² = 0
Two lines represented by the following equations are perpendicular to each other. Explanation is given below.
What is a perpendicular line?Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.
We have the equations:
a)6x²-5xy-6y² = 0
b) x²-y²+x+y=0
c) x² - y² = 0
The above lines are the product of two separate lines.
To prove that the two lines represented by the following equations are perpendicular to each other:
We have drawn the graphs of all the three equations.
The attached images are equation 1, equation 2, equation 3 are in the order of a, b and c.
And we can clearly see that the lines are perpendicular.
The general formula of the equation,
ah²+ 2hk + bk² = 0.
When a+b = 0,
Then the lines are perpendicular.
The sum of the coefficients of order 2 variable is zero.
a). 6 - 6 = 0
b). 1-1 = 0
c). 1-1 = 0
Therefore, the proof is given above.
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A line segment can be drawn from each vertex of a polygon to every other vertex, forming the sides and diagonals of the polygon. A square, for example, has 4 sides and 2 diagonals. Using combinations, write an expression that would give you the total number of sides and diagonals for a polygon with n sides.
The total number of sides and diagonals for a polygon with n sides is given by the equation n(n - 3)/2.
What is polygon?In geometry, a polygon is a two-dimensional closed object with straight sides that is flat or planar. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the spots where two sides meet.
Here,
A square has 4 sides and 2 diagonals.
Now, a pentagon will have 5 sides and 5 diagonals
A hexagonal when drawn will have 6 sides and 9 diagonals
Thus, we see that;
When n = 4, d = 2
When n = 5, d = 5
When n = 6, d = 9
Using combination, we will find number of pairs of 2 vertices that can possibly be formed from n-vertices. Thereafter we will subtract n from that since it's neighboring vertices can't combine with the current one.
Thus, we have;
C(n, 2) - n
This gives s;
(n(n-1)/2) - n
Simplifying this gives;
(n(n - 1) - 2n)/2
(n² - n - 2n)/2
(n² - 3n)/2
n(n - 3)/2
The expression that would give you the total number of sides and diagonals for a polygon with n sides is n(n - 3)/2.
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jessie uses a graph to record deposits into her savings account. her account starts with $80 deposits. she adds $25 per week to the account
Camera search
Answer: y=25x+80
Step-by-step explanation:
what is the function f(x)=x^0 when x=129
Answer:
The function f(x) = x^0 when x = 129 would be equal to 1.
The exponent of 0 for any value of x, means that the result will always be 1.
Answer:
well my sweet wife
any thing with power zero always equal to 1.
Communication Explain how to use algebra to find two numbers whose difference is 8 and whose product is a minimum.
The two numbers are 4 and -4, and their product is 4 * -4 = -16, which is the minimum value.
What is algebra?Generally, To find two numbers whose difference is 8 and whose product is a minimum, we can use algebra. Let's call the two numbers x and y. We know that:
x - y = 8 (the difference between the two numbers is 8)
To find the product of the two numbers, we can multiply x and y:
xy = x(x - 8) = x^2 - 8x
To find the minimum value of the product, we can take the derivative of this expression with respect to x and set it equal to 0:
d(xy)/dx = 2x - 8 = 0
Solving for x, we find that x = 4.
Therefore, one of the numbers is 4. We can use the equation x - y = 8 to find the other number:
4 - y = 8
y = -4
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The scatter plot shows the maximum noise level when different numbers of people are in a stadium. the linear model is given by the equation
y = 1.5x +22.7, where y represents maximum noise level and x represents the number of people, in thousands, in the stadium.
the slope of the linear model is 1.5. what does this mean in terms of the maximum noise level and the number of people?
The starting value of the noisy at the y-axis is represented by the equation's 22.7 y-intercept.
How is slope determined?To calculate the % slope, multiply the percent elevation difference between two locations by the distance between them. The change in grade between two places is referred to as a "rise." The distance between the sites is known as the run. Therefore, the formula for percent slope is (increase/jog) x 100.
Given that such scatter plot depicts the stadium's loudest conditions depending on the amount of spectators present The linear model is provided more by equation y=1.5x+22.7, where x is the number of spectators in the stadium, expressed in thousands, and y is the maximum noise level. y=1.5x+22.7
y=1.5x+22.7 is the expression for the highest noise. The gradient in the following equation is 1.5. The starting value of such noise somewhere at y-axis is represented by the y-intercept of something like the equation, which is 22.7.
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what does it mean to say that experimental conditions are controlled? what does it mean to say that experimental conditions are controlled? all physical conditions except for one are identical for all groups tested. there is no difference in outcome between the control and experimental treatment. the null hypothesis is correct. the test groups consist of the same individuals.
A controlled experiment is a scientific test conducted under controlled conditions. That is, change only one (or a few) factors at a time and keep all others constant.
Control Experiment:
Controls eliminate alternative explanations for experimental results, particularly experimental error and experimenter bias. Many controls, like molecular markers used in SDS-PAGE experiments, are specific to the type of experiment being performed and may simply have the purpose of confirming that the instrument is functioning properly. I have. Choosing and using appropriate controls and ensuring that experimental results are valid (eg, no confounding variables) can be very difficult. Control measurements can also be used for other purposes. For example, measuring the background noise of a microphone in the absence of a signal allows the noise to be subtracted from later signal measurements to produce a higher quality processed signal.
For example, if a researcher fed a laboratory artificial sweetener to 60 laboratory rats and observed that 10 of them subsequently became ill, the underlying cause could be the sweetener itself or could be something else. Other variables that may not be immediately apparent can interfere with experimental design. For example, an artificial sweetener can be mixed with a diluent, and it could be the diluent that causes the effect.To see the effect of the diluent, he does the same test twice. A diluent with artificial sweeteners and a diluent-only version in the same way. Here the experiment is checked for diluent and the experimenter can distinguish between sweetener, diluent and no treatment. Controls are usually required when confounding factors cannot be easily separated from the primary treatment. For example, a tractor may need to be used to spread manure when there is no other practical way to spread it. The simplest solution is for the tractor to drive over the plot without spreading fertilizer and control the effects of tractor traffic.
The simplest types of controls are negative and positive controls, both of which are found in many different types of experiments. If both are successful, these two controls usually have the most latency. sufficient to eliminate significant confounding variables. That is, an experiment produces a negative result when a negative result is expected and a positive result when a positive result is expected.
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and 49 are complementary . If m angle3=3x-7 and m angle9=4x-1 , find m angle3 .
Answer: m angle3 = 3x - 7 = 3(14) - 7 = 37 degrees
Step-by-step explanation:
Since angles 3 and 9 are complementary, their measures add up to 90 degrees. So, we can set up the equation:
m angle3 + m angle9 = 90
We can substitute in the given values for the measures of each angle:
(3x - 7) + (4x - 1) = 90
Solving for x:
7x - 8 = 90
7x = 98
x = 14
a therapist wanted to determine if yoga or meditation is better for relieving stress. the therapist recruited 100 of her high-stress patients. fifty of them were randomly assigned to take weekly yoga classes and the other 50 were assigned weekly meditation classes. after one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. the therapist wants to construct a 95% confidence interval for the difference in proportions of patients experiencing stress relief after yoga and after meditation. are the conditions for inference met?
The required Confidence interval for the given data is CI = 0.6 - 0.7 ± 1.96[tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex].
What is hypothesis test?Hypothesis testing is a methodical process for determining whether research study findings are consistent with a specific idea that pertains to a population. To evaluate a hypothesis about a population, hypothesis testing uses sample data.
According to question:We have,
x1 = 30, x2 = 35
n1 = 50, n2 = 50
p1 = x1/n1 = 30/50 = 0.6
p2 = x2/n2 = 35/50 = 0.7
Then,
at α= 0.05, the critical value taken by table of z
Zc = 1.96
CI =[tex]P_{1}-P_{2}[/tex] ±[tex]\sqrt{\frac{P_{1}(1-P_{1})}{n_{1}}+\frac{P_{2}((1-P_{2})}{n_{2}} }[/tex]
CI = 0.6 - 0.7 ± 1.96 [tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex]
This is our needed answer,So option (D) is correct.
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Help quickly please! (Worth 20 points) The more hours Randall works, the more wages he earns. Randall's wage is the ___________ variable. The hours he works is the __________ variable. 1. independent; dependent, 2. dependent; independent
Answer:
Randall's wage is the dependent variable. The hours he works is the independent variable.
Step-by-step explanation:
Use the Law of Sines to solve the triangle. (Round your answers to two decimal places.)
B = 2° 45', b = 6.4, c= 5.3
Answer: 20
Step-by-step explanation:
If a road map has a scale of 3 in: 100 mi, find the following distances
How far is it between Cardwell and Claremont if they are 4.5 inches apart on the map?
The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
If a road map has a scale of 3 inches to 100 miles.
Then the scale factor is given as,
Sclar factor = 100 / 3
Sclar factor = 33.33 miles per inch
Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,
Distance = 33.33 x 4.5
Distance = 150 miles
The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.
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Which of the following equations has 2 as a root ?
A. 2x² - 7x + 6 = 0
B. x² - 4x + 5 = 0
C. x² + 3x - 12 = 0
D. 3x² - 6x - 2 = 0
A. (A)
B. (B)
C. (C)
D. (D)
The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option A)
The roots of a quadratic equation is equal to its solution.
If x = 2 is the solution of an equation, then f(2) = 0.
Let's check for the given functions:
A. 2x² - 7x + 6 = 0
f(2) = 2(2)² - 7(2)+ 6
f(2) = 2(4) - 14 + 6 = 0
Hence, x = 2 is its root.
B. x² - 4x + 5 = 0
f(2) = 2² - 4(2) + 5
f(2) = 4 - 8 + 5 = 1
Since f(2) ≠ 0, hence 2 is not its root.
C. x² + 3x - 12 = 0
f(2) = 2² + 3(2) - 12
f(2) = 4 + 6 - 12 = -2
Since f(2) ≠ 0, hence 2 is not its root.
D. 3x² - 6x - 2 = 0
f(2) = 3(2)² - 6(2) - 2
f(2) = 12 - 12 - 2 = -2
Since f(2) ≠ 0, hence 2 is not its root.
Hence, the correct option is A. 2x² - 7x + 6 = 0
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Express
2x² + 8x + 3
in the form 2(x + p)² + q
Answer:
2x^2 + 8x + 3 in 2( x + 2 )^2 + q form is 2( x + 2 )^2 - 5
a collector offers to buy state quarters for $2000\%$ of their face value. the face value of each quarter is $25$ cents. at that rate how many dollars will bryden get for his four state quarters?
A collector offers to buy state quarters for 2000% of their face value. The face value of each quarter is 25 cents. At that rate 20 dollars Bryden will get for his four state quarters.
In the given question, a collector offers to buy state quarters for 2000% of their face value.
The face value of each quarter is 25 cents.
We have to find at that rate how many dollars Bryden will get for his four state quarters.
As given that,
Collector buy state quarters = 2000% of their face value
We can write 2000% as 20×100%.
It means that state quarters is 20 times of their face value.
As we know that, 4 quarter is equal to the one dollar. So,
Bryden get for his four state quarters = 20×1 dollars
Bryden get for his four state quarters = 20 dollars
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what is the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise?
The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).
What is rotation?
The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.
Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then
=> (x , y) = (-8,0)
Now 270 degrees counter clockwise rotation then,
=> (y,-x) = (0,-(-8))
=> (y,-x)=(0,8)
Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).
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you need to find the height of the cylinder
TSA = 2πrh + πr² (r = 40/2 = 20)
4715 = 40πh + 400π
4715/(40π) = h + 10
≈ 37.5 = h + 10
h = 27.5 cm
Hope this helped.
Answer:-
h = 17.52cm
Step-by-step explanation:
To find the height, we'll use the formula for a surface area of a cylinder.
[tex]\boxed{\sf SA=2\pi rh+2\pi r^2}[/tex]
Since the diameter is 40 cm, than the radius is :-
[tex]\sf r=\cfrac{d}{2}[/tex][tex]\sf r=\cfrac{40\;cm}{2}[/tex][tex]\sf r=20cm[/tex]Now, let's substitute the values to the SA formula:-
[tex]\sf 4715\;cm^2=2\pi (20cm)h+2\pi (20cm)^2[/tex]
[tex]\sf 4715cm^2=40\pi cmh+800cm^2\pi[/tex]
[tex]\sf \cfrac{4715cm^2-800cm^2\pi }{40\pi cm} =\cfrac{40\pi cm(h)}{40\pi cm}[/tex]
[tex]\sf h=\cfrac{2,201.725877cm^2}{40\pi cm}[/tex]
[tex]\sf h=17.52\; cm[/tex]
____________________
Hope this helps!
Have a great day!
what is the x value of the solution to this system of equations? 2x-3y=8 4x+5y=2
Answer: y=18
Step-by-step explanation:
a car rental company charges an initial fee of $42 and a daily fee of $12. a customer pays a total of $138. how many days did the customer rent the car?
The customer rented the car for 8 days.
The total amount paid by the customer, $138, is made up of the initial fee and the daily fee multiplied by the number of days the car was rented.
We can set up the equation as:
138 = 42 + 12x (where x is the number of days the car was rented)
To find the number of days, we can subtract the initial fee from both sides of the equation:
138 - 42 = 12x
96 = 12x
Then we can divide both sides by 12 to solve for x:
x = 8
So the customer rented the car for 8 days.
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answer the gaps/questions attached
The Venn diagram that indicates the number of students that study a language and the probability of two student chosen study Spanish are as follows;
a) Please find attached the drawing of the completed Venn diagram created with MS Word
b) The probability that two student chosen at random study Spanish is 17/66
What is the probability of an event?The probability of the occurrence of an event is the likelihood that an event takes place from within a number of possible event.
The probability that two student
a) The number of students that study French and Spanish but not German = 18 - 13 = 5
The number of students that study only French = 0
The number of student that study only French and German = 25 - 13 - 5 = 7
Number of students that study only only German = 40 - 19 - 13 - 7 = 1
The number of students that study only Spanish = 100 - 19 - 13 - 5 - 1 - 7 - 41 = 14
Please find attached the completed Venn diagram created with MS Word
b) The number of students that study Spanish = 19 + 13 + 5 + 14 = 51
The probability that the first student chosen studies Spanish = 51/100
The probability that the second student chosen = 50/99
Therefore, the probability that the two student chosen at random, without replacement, study Spanish = (51/100) × (50/99) = 17/66
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How do you find the ratio of a line segment?
P=(m+nmx2+nx1,m+nmy2+ny1). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.
What is the segment ratio formula?
P=(m+nmx2+nx1,m+nmy2+ny1). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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managers must make a number of important decisions about the use of control charts. what are they? multiple select question. what size samples to take how often samples should be taken how many control charts to use to monitor the process what type of control chart to use what tools to use to take measurements at what points in the process to use control charts
Managers must make all the given vital decisions from the options, hence, d) All of the above is the correct answer.
Managers must make a number of important decisions about the use of control charts, some of which include:
What size samples to takeHow often samples should be takenHow many control charts to use to monitor the processWhat type of control chart to use (e.g. X-bar chart, R chart, etc.)What tools to use to take measurementsAt what points in the process to use control charts.These are all important decisions that managers need to make when using control charts to monitor and improve processes in an organization. The right decisions can help ensure that control charts are effective in detecting and addressing issues with processes, while the wrong decisions can lead to control charts being ineffective or even counterproductive.
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The complete question is -
Managers must make a number of important decisions about the use of control charts. what are they?
multiple select questions.
a) what size samples to take and how often samples should be taken.
b) how many control charts to use to monitor the process.
c) what type of control chart to use.
d) what tools to use to take measurements at what points in the process to use control charts.
e) All of the above.
a manager receives 9 applications for a specific position. she wants to narrow it down to 4. in how many ways can she rank 4 applications?
The number of ways that can she rank 9 applications should be 126.
What is the definition of combination in math?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
Calculation of the number of ways:
Since A manager receives 9 applications for a specific position. She wants to narrow it down to 4.
So here we do apply the permutation here:
9*8*7*6/ 4*3*2
=126
Hence, The number of ways that can she rank 4 applications should be 126
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Which of the following conditions make triangle ADB sinilar to triangle ABC? PLS HELP
Answer: A
Step-by-step explanation:
A.
It makes an AA similarity(both share 1 angle, and both have right angles)
Starting from 1.5 miles away, a car drives towards a speed check point and then passes it. the car travels at a constant rate of 53 miles per hour. the distance of the car from the check point is given by d=|1.5-53t|. at what times is the car 0.1 miles from the check point?
The time at which the car is 0.1 miles from the checkpoint is 95.1s and 108.7s.
The speed of the car is 53 miles per hour.
The distance of the car from the checkpoint is given by d = |1.5 - 53t|
To be 0.1 miles away from the checkpoint, the car has to travel 1.4 miles OR 1.6 miles.
53 miles = 60 minutes
1.4 miles = 1.4 / 53 × 60
= 1.5849056 minutes
= 1.5849056 × 60 seconds
= 95.1 seconds
1.6 miles = 1.6 /53 × 60
= 1.8113207 minutes
= 1.8113207 × 60 seconds
= 108.7 seconds
So the required time is 95.1s and 108.7s.
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A quadrilateral has two angles that measure 175° and 85°. The other two angles are in a ratio of 3:17.
What are the measures of those two angles?
The measure of the other two angles of the quadrilateral are 15 and 85.
What are the angles of a quadrilateral?
Angles in a quadrilateral are the four angles that occur at each vertex within a four-sided shape; these angles are called interior angles of a quadrilateral. The sum of the interior angles of any quadrilateral is 360 360°. We can prove this using the angle sum of a triangle.
A quadrilateral is a polygon having four sides, four angles, and four vertices. When we draw the diagonals to the quadrilateral, it forms two triangles. Both these triangles have an angle sum of 180°. Therefore, the total angle sum of the quadrilateral is 360°
Given, two angles of quadrilateral as 175° and 85°.
Let other 2 angles be x and y.
x + y + 175 + 85 = 360
x + y = 100
Given x/y = 3/17
x= 3/17(y)
So,
3y/17 + y = 100
20y = 1700
y = 85
x = 100 - 85 = 15
Hence other two angles of the quadrilateral are 15 and 85.
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The circle below has center o, and its radius is 5 in. Given that mzAOB=30°, find the
length of the minor arc AB.
Give an exact answer in terms of , and be sure to include the correct unit in your
answer.
This is all I coulf find hope it helps! :')
An online game award player 12 point for every puzzle olved correctly. Bryce correctly olved 98 puzzle. How many point wa Bryce awarded?
The required number of points win by the player on correctly solve the puzzle are 1176.
What is Online game?Games referred to as "online" are those that are played through a computer network, most frequently the Internet. Online games can range from straightforward text-based games to those with intricate visuals and multiplayer virtual worlds.
According to question:Player is getting 12 points on correctly solving the puzzle,
He plays 98 puzzle games,
Total number of points
98(12)
= 1176 points
Thus, required number of winning points are 1176.
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a small pilot study estimated that 34% of americans do not like the taste of cilantro. how large would the random sample need to be to obtain a margin of error of at most 0.03 with 95%?
The size of the random sample needed to obtain a margin of error of at most 0.03 with 95% confidence would be around 1,912 people.
What is error?Error in math is a mistake made in a mathematical process or calculation. It can be caused by a single incorrect step or an incorrect understanding of a concept. Error in math can take many forms, such as incorrect answers, incorrect equations, wrong calculations, and incorrect logic. It is important to identify and address errors in math in order to get the correct answer or solution.
This is because the formula for calculating the sample size for a given margin of error is:
Sample size = (Zα/2)2 * p*(1-p) / m2
Where Zα/2 is the critical value for a 95% confidence level (1.96), p is the estimated proportion of the population that doesn’t like cilantro (34%), and m is the margin of error (0.03).
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