Why do we use p hat in statistics?

Answers

Answer 1

In statistics, p hat is used as an estimator of the population proportion (p) of a categorical variable. It is the sample proportion of the variable, which is calculated as the number of occurrences of a particular category in the sample divided by the total sample size.

The reason why p hat is used is that it provides an estimate of the unknown population proportion based on a representative sample. By using p hat, we can draw inferences about the population proportion with a certain level of confidence. This is important in hypothesis testing and confidence interval estimation, where we want to make statements about the population based on the information gathered from a sample.

Using p hat as an estimator of p is also beneficial because it has desirable statistical properties, such as being an unbiased estimator, having a sampling distribution that approaches normality, and having a known standard error.

Learn more about variables here: brainly.com/question/29583350

#SPJ4


Related Questions

What is the value of x, given that the two prisms are similar?

Answers

Answer:

A. 10

Step-by-step explanation:

2/4 = x/20

1/2 = x/20

2x = 20

x = 10

Answer: 10

Write the equation of the line that passes through the points (4, -3) and (8,5). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.

Answers

An equation of the line that passes through the points (4, -3) and (8,5) is y + 3 = 2(x - 4).

What is the point-slope form?

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.x and y are the points.

At data points (4, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-3) = (5 - (-3))/(8 - 4)(x - 4)

y + 3 = 8/4(x - 4)

y + 3 = 2(x - 4)

Read more on slope here: brainly.com/question/16897180

#SPJ1

what is convergence radius calculator

Answers

A convergence radius calculator is a tool used in calculus to calculate the radius of convergence for a power series using the ratio test.

To calculate the convergence radius of a power series, one can use a formula known as the "ratio test". The ratio test involves taking the limit of the absolute value of the ratio of successive terms in the series, as n approaches infinity. If this limit exists and is less than 1, then the series converges absolutely. The convergence radius can then be found as the reciprocal of this limit.

For example, given the power series:

∑(n=0 to infinity) [tex](x-2)^n / n^2[/tex]

we can use the ratio test to find the convergence radius as follows:

[tex]|(x-2)^(n+1) / (n+1)^2| / |(x-2)^n / n^2|[/tex]

= [tex]|(x-2) / (n+1)|^2 * (n^2 / (x-2)^2)[/tex]

= [tex](n^2 / (n+1)^2) * (1 / (x-2)^2)[/tex]

= [tex]n^2 / ((n+1)^2 * (x-2)^2)[/tex]

Taking the limit of this expression as n approaches infinity, we get:

[tex]lim(n- > ∞) (n^2 / ((n+1)^2 * (x-2)^2))[/tex]

= [tex]1 / (x-2)^2[/tex]

Since this limit exists and is less than 1 for all x except x=2, the power series converges absolutely for all values of x within a radius of [tex]1/(x-2)^2[/tex] centered at x=2. Therefore, the convergence radius of the power series is 1.

To learn more about convergence radius please click on below link        

https://brainly.com/question/18763238

#SPJ4

Use the drop-down menus to order the decimals from greatest to least.
8.31, 8.296, 8.06, 8.3

Answers

Answer:

8.31, 8.3, 8.296, 8.06

Step-by-step explanation:

8.31, 8.296, 8.06, 8.3

The order of decimals from greatest to least is

8.31, 8.3, 8.296, 8.06

Bonnie bakes a pan of brownies and cut them into 12 equal pieces after lunch 8/12 of the brownies are left her friends eat half of those brownies with dinner what fraction of the whole pan of brownies do they eat with dinner

Answers

Answer:

4/12

Step-by-step explanation:

8/12 ÷ 2 = 4/12

Answer: 1/3

Step-by-step explanation:

8/12 divided by 2 is 1/3

What is 200 Micrograms (mcg) in Milligrams (mg)?

Answers

To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms, 200 micrograms (mcg) is equal to 0.2 milligrams (mg).

When we want to convert a unit of measurement to another unit of measurement, we use conversion factors to make the conversion. In the case of converting micrograms (mcg) to milligrams (mg), we need to know that 1 milligram is equal to 1000 micrograms. This means that to convert any value from micrograms to milligrams, we need to divide by 1000.

To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms.

So, to convert 200 mcg to mg, we divide 200 by 1000:

200 mcg ÷ 1000 = 0.2 mg

Therefore, 200 micrograms (mcg) is equal to 0.2 milligrams (mg)

It is important to understand the concept of unit conversions because it is a crucial aspect of many scientific and engineering calculations. Knowing how to convert units of measurement allows us to work with data that is expressed in different units and compare results from different experiments. In addition, being able to convert units is a valuable skill for everyday life, such as when reading nutrition labels or measuring medication dosages.

To learn more about measurement Click here:

brainly.com/question/4725561

#SPJ4

can yall help me with this question immediately pls?

Answers

The diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.

What is diameter?

Diameter is the line jwhich passes through the center of a circle and joins two points on the circumference of the circle.

To find the diameter of the Ferris wheel which is a circle, we see that the grpah gives the height of a passenger on the Ferris wheel as a function of the number of complete cycles since the ride started.

Now, the diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.

Learn more about diameter here:

https://brainly.com/question/28428702

#SPJ1

The image of a trapezoid is shown.

An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.

What is the area of the trapezoid?

70 m2
38 m2
35 m2
19 m2

Answers

Answer: 35m2

Step-by-step explanation:took the test and i got it right

An isosceles trapezoid with a short base of 3 meters and a height of 5 meters then the area of the trapezoid is 35 m²

What is the area of the trapezoid?

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

We can start by finding the length of the long base. Since the trapezoid is isosceles, we know that the length of the portion of the large base from the left vertex to the perpendicular is equal to the length of the portion from the right vertex to the perpendicular. Let's call the length of the long base "x":

x = 4 + 7 = 11 meters

Now we can use the formula for the area of a trapezoid:

Area = (1/2) * (short base + long base) * height

Substituting the values we have:

Area = (1/2) * (3 + 11) * 5

Area = 7 * 5

Area = 35 m²

Therefore, the area of the trapezoid is 35 m².

To learn more about the area of the trapezoid visit:

https://brainly.com/question/1463152

#SPJ1

An ice cream store charges 75 cents for each scoop of ice cream and 25 cents for each cone. The formula c=0.75x+0.25
can be used to determine c, the total cost for an ice cream cone with x scoops of ice cream. According to the formula, how much should it cost to buy an ice cream cone with 4 scoops of ice cream?

Responses

Answers

$3.25 for an ice cream

You substitute the variable x for 4 and you solve the equation after.

c=0.75(4)+0.25
c=3+0.25
c=3.25

Write an equation in slope-intercept form for the line that passes through the points (0, 5) and (1, 3)?

Answers

Answer:

Step-by-step explanation:

y= -2x + 5

Which function is the inverse of g (z) = (²-1)³ — 3?
Of(1) = √2+6+1
Of(1) = 2√2+3+1
O f(1) = 2√1+1+3
O f(1) = √21+2+3

Answers

The inverse of function is  f(x) = (x - 4)³/8 + 3

What is inverse function?

A function that reverses the results of another function is known as an inverse function. If y = f(x), then x = g(y), then a function g is the opposite of a function f. To put it another way, applying f and then g is equivalent to doing nothing. This can be expressed as g(f(x)) = x in terms of how f and g are made up.

Given g(x) = 2(∛x-3)+4

let g(x) = y

y = 2(∛x-3)+4

change the variables since options are in form of x

x =  2(∛y-3)+4

simplify for y

subtract 4 from both side

x - 4 = 2(∛y-3)+4 - 4

x - 4 = 2(∛y-3)

divide both side by 2

(x - 4)/2 = (2(∛y-3))/2

(x - 4)/2 = (∛y-3)

cube both side

((x - 4)/2)³ = ((∛y-3))³

(x - 4)³/8 = y - 3

(x - 4)³/8 + 3 = y

Hence  the value f(x) =  (x - 4)³/8 + 3 .

Learn more about inverse function;

brainly.com/question/2541698

#SPJ9

Vector u = (-3, 8), and vector v = (-14, 6). Match each vector operation with the magnitude of its resultant vector

Answers

The magnitude of given operations of vectors are found.

What are Vectors?

Quantities with the independent characteristics of magnitude and direction are called vectors.

Given:

u = (-3, 8) and v = (-14, 6)

So, 3u = (-9, 24) and 2v = (-28, 12)

3u - 2v = (-9+28, 24-12)

3u - 2v = (19, 12)

Magnitude of 3u - 2v = √19² + 12²  = √505 units

2u = (-6, 16) and 3v = (-42, 18)

2u - 3v = (36, -2)

Magnitude = √36² + (-2)²  = √1300 units

u = (-3, 8) and 4v = (-56, 24)

u + 4v = (-59, 32)

Magnitude = √(-59)² + 32²  = √4505  units

5u = (-15, 40) and v = (-14, 6)

5u - v = (-1, 34)

Magnitude = √1157  units

7u = (-21, 56) and 2v = (-28, 12)

7u - 2v = (7, 44)

Magnitude = √1985 units.

Learn more about Vectors here :

brainly.com/question/13322477

#SPJ9

A 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association, so some suggested that having male pattern baldness might somehow cause a person to have a severe reaction to COVID-19 (since they had been bald before catching COVID-19, so that the disease could not have caused their baldness). Which option below was most likely a lurking variable?

Age

Diet

Height

Weight

Answers

If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.

What is a  lurking variable?

In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.

Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.

Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness

Therefore, age is the most likely lurking variable in this scenario.

Learn more about lurking variable here:https://brainly.com/question/30419202

#SPJ1

HELP ASAP!!
Simplify the expression.


the expression negative one fifth j plus three fourths minus the expression five halves j plus seven eighths

Answers

The simplified expression is given as follows:

-27j/10 - 1/8.

How to simplify the expression?

The expression for this problem is defined as follows:

-j/5 + 3/4 - (5j/2 + 7/8).

The negative sign means that every term in the parenthesis has the signal exchanged, hence:

-j/5 + 3/4 - 5j/2 - 7/8.

Then the expression is simplified combining the like terms, as follows:

With j: -j/5 - 5j/2 = -2j/10 - 25j/10 = -27j/10.Constant: 3/4 - 7/8 = 6/8 - 7/8 = -1/8.

Meaning that the expression is of:

-27j/10 - 1/8.

More can be learned about simplification of expressions at https://brainly.com/question/11975096

#SPJ1

Write the following ratio in simplest form: 32 min : 36 min (1 point) a. 8 : 9 b. 8 : 36 c. 32 : 9 d. 128 : 144

Answers

The simplest form of the given ratio 32 min : 36 min is equal to  

option a. 8 : 9.

Ratio  is equal to

32 min : 36 min

Factors of 32 are = 1, 2, 4, 8, 16, 32

Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36

Greatest common factor of 32 and 36 is equal to 4

Simplest form of the given ratio is equal to

32 min : 36 min

= ( 8 × 4 ) min : ( 9 × 4 ) min

'4' get cancelled with other we get,

= 8 min : 9 min

Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .

Learn more about ratio here

brainly.com/question/13419413

#SPJ4

2.
(5x-2)(2x
+ 7)
= (5x)(2x) - 2(7)
= 10x² - 14

A.10x14
B.10x² +31x 14
C.7x + 5
D.10x + 5

Answers

The resultant of the given expression (5x-2)(2x+7) is  10x² + 31x - 14

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.

For example, the expression "3x + 2" is an algebraic expression that contains the variable "x", the numbers "3" and "2", and the mathematical operations of addition and multiplication.

Given expression ,

(5x-2)(2x+7)

= (5x-2)(2x+7) = 5x(2x) + 5x(7) - 2(2x) - 2(7)

= 10x² + 35x - 4x - 14

= 10x² + 31x - 14

Therefore, The resultant of the given expression (5x-2)(2x+7) is  10x² + 31x - 14

To learn more about Algebraic expression from given link.

https://brainly.com/question/953809

#SPJ1

What is the LCM of 3 and 5 and 3?

Answers

Answer:15

Step-by-step explanation:

sketch a graph for days 0-9

Answers

According to the information in the table, the graph would look like the one in the attached image.

How to graph the information in the table?

To graph the information in the table we must carefully observe the information. In this case, the relationship is decreasing because the number of infected is decreasing as time increases. In accordance with the above, the curve that shows this relationship is a decreasing curve.

In this case, we must locate the time on the x axis and the infected on the y axis and mark a point in the areas where the data coincide. Later we must graph a line that joins the points and our graph would be finished.

Learn more about charts at: https://brainly.com/question/15507084

#SPJ1

HELP ME PLEASE!!!!! FAST ASAP HELP
PICTURE ATTACHED

A company logo is made up of a desire and two identical triangles as shown in this image
What is the area of the logo

Answers

The area of the logo is given as 139 cm

How to solve for the area

In order to get the area of the shape, i would have to get the area of the triangles first

area of a triangle = 1/2 b * h

base = 9 / 2 = 4.5

h = 6

area = 1/2 * 9 * 6

= 27

Area of 2 triangle = 2 x 27

= 58

The are aof the square = a * a

= 9 * 9

= 81

The total area of the logo is given as 81 + 58

= 139 cm

Read more on area of a triangle here"https://brainly.com/question/17335144

#SPJ1

What is the simplest form of the radical expression?
√2+√5/√2-√5

Answers

Exact Form: - 7+2√10/3

What is 20% off 250000 ?

Answers

From the given information provided, 20% off 250000 is 50000, and the discounted price is 200000.

The formula for calculating percentage is:

percentage = (part/whole) x 100

Here's an example:

Let's say you got 35 out of 50 questions correct on a test. To calculate the percentage of questions you answered correctly, you would use the formula as follows:

percentage = (35/50) x 100

percentage = 0.7 x 100

percentage = 70%

To calculate 20% off 250000, you can multiply 250000 by 20% (which is 0.20 in decimal form) and then subtract the result from 250000:

250000 - (0.20 x 250000) = 250000 - 50000 = 200000

Learn more about percentage here: brainly.com/question/24877689

#SPJ4

A loan of $25,000 has an annual simple interest rate of 5.5%. The total cost of the loan is $38,750. How much total interest will you pay?

Answers

The solution is,  total interest will you pay is  $13750.

What is Subtraction?

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

A loan of $25,000 has an annual simple interest rate of 5.5%.

The total cost of the loan is $38,750.

so, total interest will you pay = $(38750 - 25000)

                                                 = $13750

Hence, The solution is,  total interest will you pay is  $13750.

To learn more on subtraction click:

brainly.com/question/2346316

#SPJ9

the population of a school is 800 students and is increasing at a rate of 2%per year.

Answers

Answer: Increases by 16 students per year

Step-by-step explanation:

100% = 800

2% = x

So between 100% and 2%, the scale factor would be 50 since 100 / 2 = 50

Then 800 / 50 would be 16

So..

1 Year = 816 students

2 Years = 832 students

3 Years = 848 students

4 Years = 864

And so on..

If f(1) = 0, what are all the roots of the function ? use the remainder theorem.

Answers

By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.

A root of a function is a value for x that makes the function equal to zero.

In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.

The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.

So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.

Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.

The roots of f(x) will be the values of x that we used as factors in each step of the division process.

This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.

Complete Question

If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.

To know more about function here.

https://brainly.com/question/28193995

#SPJ4

What are the math topics covered in the grade 6 math worksheets?

Answers

The math topics covered in the grade 6 math worksheets are algebra,geometry,measurement, number operation.


1. Number sense and operations: This includes understanding numbers, fractions, decimals, and integers, as well as performing operations with them.


2. Algebra: This includes understanding algebraic expressions and equations, and using them to solve problems.


3. Geometry: This includes understanding basic geometric concepts, such as lines, angles, and shapes, and using them to solve problems.


4. Measurement: This includes understanding measurement concepts, such as length, area, and volume, and using them to solve problems.


5. Data analysis and probability: This includes understanding basic concepts of statistics, such as mean, median, and mode, and using them to analyze data and make predictions.

To know more about algebraic expressions click on below link:

https://brainly.com/question/953809#

#SPJ11

Write the linear equation for the graph below.

Answers

Answer:

y = 6x

Step-by-step explanation:

The line is sloping up at a rate of 6 y units per 1 x unit. So the slope is 6/1 (6x)

How do you find the two largest numbers in an array in Matlab?

Answers

To find the two largest numbers in an array in Matlab, you can use the sort function and indexing to access the two largest elements.

Here's an example:

array = [3, 8, 2, 10, 5];

sorted_array = sort(array, 'descend');

largest_number = sorted_array(1);

second_largest_number = sorted_array(2);

In this example, we have an array of numbers called array. We use the sort function to sort the array in descending order, which means that the largest numbers will be at the beginning of the array. The resulting sorted array is assigned to a new variable called sorted_array.

We then use indexing to access the first and second elements of the sorted array, which will be the two largest numbers. These numbers are assigned to the variables largest_number and second_largest_number, respectively.

It's important to note that if the array contains duplicate values, this method will return the two largest unique values. If you want to find the two largest values including duplicates, you can use the max function twice with the 'omitnan' parameter to handle any NaN values in the array:

array = [3, 8, 2, 10, 5, 10];

largest_number = max(array, [], 'omitnan');

array_without_largest_number = array(array < largest_number);

second_largest_number = max(array_without_largest_number, [], 'omitnan');

In this example, we first find the largest number in the array using the max function with the 'omitnan' parameter to ignore any NaN values. We then create a new array that excludes the largest number, and use the max function again to find the second largest number in the new array.

To know more about array in Matlab, click here:

brainly.com/question/14699216

#SPJ4

Solve for x
Show proofs
Help

Answers

The length of the rise x is 25.5

How to determine the value of the side length x

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

Length = 17

Angle = 27 degrees

The rise, x is then calculated using the following laws of tangent

tan(27) = 13/x

Make x the subject

So, we have the following representation

x = 13/tan(27)

Evaluate the expression

This gives

x = 25.5

Hence, the value of x is 25.5

Read more about triangles at

https://brainly.com/question/14285697

#SPJ1



Analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary
line.
Warm-Up
y> -1.4x +7
y> 3x-2
y <19-5x
y>-x-42
y < 3x
y<-3.5x+2.8
Solution Set Shaded Above
Solution Set Shaded Below

Answers

Answer:

The graph in the attached figure

we have

----> inequality A

The solution of the inequality A is the shaded area below the dashed line

The slope of the dashed line A is  positive m=2

The y-intercept of the dashed line A is (0,-5)

The x-intercept of the dashed line A is (2.5,0)

----> inequality B

The solution of the inequality B is the shaded area above the dashed line

The slope of the dashed line B is  negative m=-3

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (1/3,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

using a graphing tool

The graph in the attached figure

GIVE ME BRAINLIEST IF IM CORRECT :)

F(x)=4x+2 FIND THE INVERS SHOW WORK

Answers

Given    To find    Solution:  First, we replace  with  and  with :      Now, we finally replace  with   Therefore, the inverse of  is

Answer:y=(x-2)/4

Step-by-step explanation:

y=4x+2

4x=y-2

x=(y-2)/4

y=(x-2)/4

Other Questions
write 5x10^3 x 9x10^7in stanadred form What does schadenfreude mean? The following data show the ages of recent award-winning male actors at the time when they won their award. Make a frequency table for the data, using bins of 20-29, 30-39, and so on.Click the icon to view the ages of male actors.Complete the table below.Age20-2930-3940-4950-5960-6970-79No. of actors What was one way that James Watt's steam technology contributed to the Industrial Revolution?Steam engines improved the shipping of goods and raw materials. A virus is spreading around brookfield. At the moment, 685 people are infected. If the virus is spreading at a rate of 13% each day, how many people in all will have caught the virus in 3 days?. Write a function where y should vary directly with x, then give a real world example for it. Which benefit of citizenship from this list most appeals to you? Explain your answer. cite an example of a thesis statement for an argumentative essay? how does the elevation of mexico city affect its climate? Which interpersonal role involves serving as a link among people?(A) Leader(B) Figurehead(C) Liaison(D) Negotiator(E) Spokesperson What is the role of mitochondria in red blood cells? Sort the Pavlovian conditioning phases in the correct order of acquisition, extinction, and spontaneous recovery.1. Light alone - pecking slowly diminishes 2. Light alone - pecking returns3. Light + food - pecking occurs to both4. Rest period without light or food Given that syn addition of H2H2 occurs from both sides of a trigonal planar double bond, draw allstereoisomers formed when each alkene is treated with H2H2. 3^3x=9^9Find the answer for x in the following equation............................... A broker needs to train affiliated licensees on properly following disclosure requirements. Which of these strategies will help the training initiative be most effective?a. Offer multiple classes so that new licensees are trained separately from experienced salespeople.b. Have all associates take a multiple choice exam at the end of the training.c. Use a "scared straight" approach by asking licensees who have been disciplined for disclosure errors to speak at the training.d. Create a document listing the disclosure rules and require all associates to sign an acknowledgment of receipt. Ex 2: Matt bowled games of 162, 170, and 148. What must he bowl in the next game tohave an average of 155? What is the sum of all frequencies in a frequency distribution? and why is the sum of all____ There is a strong relationship between the mood-elevating effect of caffine and the extent to which it will keep an individual awake. Large doses of caffeine have been shown to produce panic attacks in individuals with a history of panic disorder. True or False What does the residual plot tell you about the line of best fit? Can someone please help me. I am doing this project where I need to create a motto for a superhero based on 1 of the 6 essential nutrients (protein, vitamins, minerals, water, fats, and carbohydrates. I chose protein.) Thanks.