A sidewalk is 40 meters long. Each section of sidewalk is 8 decimeter long . How many sections of sidewalk are there?

The Bell Curve is a symmetrical curve that represents the probability distribution of a random variable.

The Bell Curve, also known as the normal distribution or Gaussian distribution, is a statistical concept used to describe the distribution of a set of data. The Bell Curve is a symmetrical curve that represents the probability distribution of a random variable.

The Bell Curve is often used to describe the distribution of scores on a test or exam. In this context, the Bell Curve is used to represent the distribution of scores across a population. The mean score (average score) is represented by the highest point on the curve, and the standard deviation is represented by the width of the curve.

In terms of percentages, the Bell Curve can be divided into different standard deviations, with each standard deviation representing a certain percentage of the population. The percentages of the population within each standard deviation are as follows:

68.27% of the population falls within one standard deviation of the mean.

95.45% of the population falls within two standard deviations of the mean.

99.73% of the population falls within three standard deviations of the mean.

These percentages are useful for understanding how scores or data are distributed across a population and can be used to set cutoff scores or define performance categories.

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Answer: (a) If the order of the choices is not taken into consideration, we want to count the number of combinations of 6 colors chosen from 10 distinct colors. The formula for the number of combinations of k objects chosen from a set of n distinct objects is:

n choose k = n! / (k! * (n-k)!)

So, the number of ways to choose 6 colors from 10 distinct colors, without replacement and without considering the order, is:

10 choose 6 = 10! / (6! * (10-6)!) = 210

Therefore, there are 210 ways to choose 6 colors from 10 distinct colors without considering the order.

(b) If the order of the choices is taken into consideration, then each choice can be made in 10 ways, and there are 6 choices to be made. Thus, the total number of ways to choose 6 colors from 10 distinct colors, with replacement and considering the order, is:

10 * 10 * 10 * 10 * 10 * 10 = 10^6 = 1,000,000

Therefore, there are 1,000,000 ways to choose 6 colors from 10 distinct colors, considering the order.

Step-by-step explanation:

The word "ml" stands for millilitre, a unit of measurement used to gauge a liquid's capacity.

One millilitre, or 0.001 litres, is equal to one thousandth of a litre. In scientific and medical settings, the volume of drugs, syrups, or even other liquids is frequently measured in millilitres.

On either hand, "milligrammes" (mg) is a weight or mass unit which is used to determine how much of a substance is present. One milligramme, or 0.001 grammes, is equivalent to one thousandth of a gramme. Milligrams are frequently used to express the percentage of a drug in a solution or to quantify the dosage of pharmaceuticals.

The conversion of ml to milligrams depends on the density of the substance being measured. Density is the measure of how much mass is contained in a given volume. Therefore, if you know the density of the substance, you can use it to convert ml to milligrams.

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a) The mean number of cars owned for this sample is, 77.75

b) The standard deviation of cars owned for this sample is, 12.44

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The following table shows the number of people that have either 0, 1, 2 or 3 cars registered in their name, from a sample of 311 people.

x       n

0      79

1       79

2      59

3      94

a) Now, the mean number of cars owned for this sample is,

⇒ Mean = (79 + 79 + 59 + 94) / 4

             = 77.75

Thus, the mean number of cars owned for this sample is, 77.75.

We know that;

Standard deviation = √ (xₐ - μ)² / N

Where, xₐ is each value from the population, μ is mean and N is number of points on data set.

Now, For a = 0, 1, 2, 3

Standard deviation = √ (xₐ - μ)² / N

Standard deviation = √(79 - 77.8)² + (79 - 77.8)²+ (59 - 77.8)²+ (94 - 77.8)²/4

Standard deviation = √1.44 + 1.44 + 353.44 + 262.44 / 4

Standard deviation = √154.69

Standard deviation = 12.44

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When rotated about its center, a regular hexagon has 6 rotational symmetries. In addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

Geometry is a branch of mathematics that deals with the study of spatial relationships and properties of shapes, sizes, positions, and dimensions of objects. It is concerned with points, lines, angles, curves, surfaces, and solids in both two and three-dimensional space. Geometry has practical applications in fields such as engineering, architecture, computer graphics, and physics. It is also a fundamental part of mathematical education, helping students develop skills such as logical reasoning, problem-solving, and spatial visualization. Finally, geometry has a rich history, dating back to ancient civilizations such as the Greeks, Egyptians, and Babylonians.

When rotated about its center, a regular hexagon has 6 rotational symmetries. In addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry, where each line passes through a vertex and the midpoint of the opposite side.

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To solve for y, isolate y on one side of the equation by performing inverse operations, and simplify the expression as much as possible.

To solve for y online, input the equation into an equation solver or a mathematical software tool, and select the "solve for y" option. This will allow you to isolate the variable y and solve for it algebraically. There are many online equation solvers and mathematical software tools available that can perform this task quickly and easily. Simply input the equation, select "solve for y," and the tool will generate the solution set for the equation in terms of y.

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Answer:

28 daisies

Step-by-step explanation:

4:2 = daisies:carnations

4:6 = daisies:total flowers

4/6 = x/42    x=number of daisies

6x = 4(42) = 168

x = 168/6 = 28

y = number of carnations = 42 - 28 = 14

Double check the answer:

28/14 = 4/2    ratio is correct!

Answer:

The FOIL method is a technique used to multiply two binomials. The word "FOIL" is an acronym that stands for "First, Outer, Inner, Last." I will dive in it briefly for u!

Step-by-step explanation:

To use the FOIL method, you multiply the first term of the first binomial with the first term of the second binomial. Then, you multiply the outer terms (first term of the first binomial and the second term of the second binomial), followed by the inner terms (second term of the first binomial and the first term of the second binomial), and finally the last terms (second term of both binomials). You then combine the like terms to simplify the result.

The FOIL method is especially useful when multiplying polynomials, which are expressions with one or more terms involving variables with various powers. For example, to multiply the binomials (x + 3) and (x - 2), you would use the FOIL method as follows:

First: x × x = x²

Outer: x × (-2) = -2x

Inner: 3 × x = 3x

Last: 3 × (-2) = -6

Combine the like terms: x² - 2x + 3x - 6 = x² + x - 6

Thus, the product of (x + 3) and (x - 2) is x² + x - 6.

Answer:

The FOIL method is a mnemonic device used to multiply two binomials. It stands for "First, Outer, Inner, Last" and it is a step-by-step process that helps to remember the order of operations for multiplying binomials. When multiplying two binomials, the FOIL method involves multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms, and then adding the resulting terms together to simplify the expression.

The FOIL method is used in polynomial algebra because it is an efficient way to multiply two polynomials of degree one, also known as binomials. When multiplying two binomials, we can use the FOIL method to distribute each term in the first binomial to each term in the second binomial, resulting in a new polynomial expression. This method allows us to simplify polynomial expressions and solve equations by factoring, which is a crucial skill in algebra and calculus.

In summary, the FOIL method is a mnemonic device used to multiply two binomials by remembering the order of operations for each term. This method is commonly used in polynomial algebra because it is an efficient way to simplify polynomial expressions and solve equations by factoring.

An irrational number of the numbers are,

⇒ √150

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Given that;

All the numbers are,

A) √121

B) √150

C) √400

D) √1,000,000

Now, We can simplify as;

A) √121 = 11

Hence, It is a rational number.

B) √150 = 12.2474..

Hence, It is a irrational number.

C) √400 = 20

Hence, It is a rational number.

D) √1,000,000 = 1,000

Hence, It is a rational number.

Thus, An irrational number of the numbers are,

⇒ √150

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Answer:

answer asap!!!!!!!!!!!

Hey, I’m not sure how to do clue number 5, im rly rly sorry, but I’ve shown how to do #6 below, hope this helped :

f(x) = a(1+r)^x

f(x) = 320(1+ 0.042)^x

f(60) = 320 ( 1 + 0.042)^60

f(60) = 3778

answer : 3778

The value on converting 169 lbs to Kilograms (Kg) is  equivalent to 76.65 Kg .

The Pound (lbs) and Kilogram (Kg) are both the units of measurement used for weight or mass.

They both belong to different systems of measurement. Pound is a unit of measurement in the Imperial and US Customary systems, whereas kilogram is a unit of measurement in the International System of Units (SI).

We know that One pound is = 0.4535 kilograms,

We have to convert 169 lbs to Kg ,

We write ;

⇒ 169 lbs = 169 × 0.4535 Kg ;

⇒ 169 lbs = 76.6415 Kg ≈ 76.65 Kg .

Therefore , 169 lbs is approximately equal to 76.65 Kg .

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Answer:

Para encontrar la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6, primero debemos encontrar la pendiente de la línea 3x - 2y = 6.

La forma estándar de la ecuación de una línea es y = mx + b, donde m es la pendiente y b es la intersección en y. Podemos reescribir la ecuación 3x - 2y = 6 en esta forma:

3x - 2y = 6

-2 años

Por lo tanto, la pendiente de la línea 3x - 2y = 6 es 3/2.

Dado que la línea L es paralela a esta línea, también tiene una pendiente de 3/2. Ente

y - y1 = m(x - x1)

donde m es la pendiente y (x1, y1) es un punto en la línea. Nos

y - 4 = (3/2)(x - (-2))

Simplificando esta ecuación, obtenemos:

y - 4 = (3/2)x + 3

y = (3/2)x + 7

Por lo tanto, la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6 es y = (3/2)x + 7.

Step-by-step explanation:

espero te sirva, traducelo si no puedes español.

Answer:

Option 2

 x     y

−3     0

−1      3

 0     4

 3     0

4 3

Step-by-step explanation:

For a relation x →  y to be a function, there can be one and only one value of y for a value of x

Looking at the tables we see that option 1 is out since all x values are 2 andthere are multiple values of y

The last option is out because for x = 0 there are two values of y=-2 and y = 2

Correct choice is the second option which has a unique y value for each value of x

Answer:

option 2 im doing it rn

Step-by-step explanation:

The correct statement is B. For all b, the equation Ax=b has a solution.

Since the columns of A are linearly independent, then the matrix A has full rank, and its column space is equal to the entire vector space in which it resides. This means that for any given vector b, we can find a linear combination of the columns of A that is equal to b, and therefore the equation Ax=b has a solution for all b.

Option A is incorrect, as there may be certain b vectors for which Ax=b has a solution.

Option C is incorrect, as the equation Ax=b may have a solution even when A has fewer columns than rows.

Option D is incorrect, as we can determine whether or not the equation Ax=b has a solution for all b by checking the rank of A.

Option E is incorrect, as the equation Ax=b may have a solution even when A has more columns than rows.

Option F is incorrect, as a square matrix may or may not have linearly independent columns, and therefore may or may not have a solution for all b.

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The area of the rectangle will be 18a³b^6

The area of the circle will be 25x^6π

The area of the triangle will be 12a³c⁴

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The area of the rectangle will be:

= Length × Width

= 6a²b⁴ × 3ab²

= 18a³b^6

The area of the circle will be:

= πr²

= π × (5x³)

= 25x^6π

The area of the triangle will be:

= 1/2 × base × height

= 1/2 × 4a²c × 6ac³

= 2a²c × 6ac³.

= 12a³c⁴

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Answer: Let's use algebra to solve this problem.

Let C be Clot's present age and S be Soup's present age. Then, according to the problem:

One year ago, Clot was C-1 years old, and four times Soup's age at that time was 4(S-1).

Clot's age one year ago was one-third of four times Soup's age, so we have:

C - 1 = (1/3) * 4(S - 1)

Simplifying this equation, we get:

C - 1 = (4/3)(S - 1)

C = (4/3)(S - 1) + 1

One year from now, Clot will be C + 1 years old, and Soup will be S + 1 years old. The sum of their ages will be 21, so we have:

(C + 1) + (S + 1) = 21

C + S + 2 = 21

C + S = 19

Now we have two equations with two unknowns. We can substitute the expression for C from the first equation into the second equation to get an equation in terms of S:

(4/3)(S - 1) + 1 + S = 19

Simplifying and solving for S, we get:

S = 6

Substituting S = 6 into the equation C + S = 19, we get:

C + 6 = 19

C = 13

Therefore, Clot's present age is 13 and Soup's present age is 6.

Step-by-step explanation:

The value of the 5y coefficient is 5 and The constant is 4 in the formula 4.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

5y+b+4

You can decompose the equation 5y+b+4 into the terms 5y, b, and 4.

Coefficients are a type of numerical element that multiply a variable. The term 5y is used to multiply the variable y, so the coefficient is 5. That 5 is a coefficient, as Jake claims, is therefore true.

Constants are numbers with no variables. As 4 contains only a constant and no variables, the answer is 4. Hence, 4 is a constant.

Hence The value of the 5y coefficient is 5 and The constant is 4 in the formula 4.

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a) The probability of finding oil is 0.70, or 70%.

b) The new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is  1.00 or 100% .

(a) The probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, since both of these outcomes are considered positive for the oil company:

P(find oil) = P(high-quality oil) + P(medium-quality oil) = 0.50 + 0.20 = 0.70

Therefore, the probability of finding oil is 0.70, or 70%.

(b) To interpret the soil test, we can use Bayes' theorem:

P(Ai | S) = P(S | Ai) * P(Ai) / P(S)

where P(Ai | S) is the updated probability of finding oil given the soil test, P(S | Ai) is the probability of observing the soil test result given that there is oil of the corresponding quality, P(Ai) is the prior probability of finding oil of the corresponding quality, and P(S) is the probability of observing the soil test result regardless of the presence of oil.

Using the given probabilities, we can calculate:

P(S) = P(high-quality oil) * P(S | high-quality oil) + P(medium-quality oil) * P(S | medium-quality oil) + P(no oil) * P(S | no oil)

= 0.50 * 0.20 + 0.20 * 0.80 + 0.30 * 0.20

= 0.26

Now we can calculate the updated probabilities for each quality of oil:

P(high-quality oil | S) = P(S | high-quality oil) * P(high-quality oil) / P(S)

= 0.20 * 0.50 / 0.26

= 0.3846 or 0.38 (rounded to two decimal places)

P(medium-quality oil | S) = P(S | medium-quality oil) * P(medium-quality oil) / P(S)

= 0.80 * 0.20 / 0.26

= 0.6154 or 0.62 (rounded to two decimal places)

P(no oil | S) = P(S | no oil) * P(no oil) / P(S)

= 0.20 * 0.30 / 0.26

= 0.2308 or 0.23 (rounded to two decimal places)

The oil company should interpret the soil test as providing evidence for the presence of medium-quality oil, since the updated probability for this outcome is higher than the updated probability for high-quality oil. The revised probabilities for finding oil are:

P(find high-quality oil | S) = P(high-quality oil | S) = 0.38

P(find medium-quality oil | S) = P(medium-quality oil | S) = 0.62

P(find no oil | S) = P(no oil | S) = 0.23

Therefore, the new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is:

P(find oil | S) = P(find high-quality oil | S) + P(find medium-quality oil | S)

= 0.38 + 0.62

= 1.00 or 100% (rounded to two decimal places)

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The probability that Ben will find two worthless $10 bills in his wallet is practically impossible.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

The probability that each bill will be a worthless $10 bill is very low. This is because the US Federal Reserve has discontinued the production of $10 bills in 2006, so the likelihood of finding two of them in circulation is highly unlikely. Additionally, bills are often replaced after a certain amount of time due to wear and tear, so the probability of finding two bills in circulation that are both from the discontinued series is even lower.

The chances of finding two $10 bills from the discontinued series in circulation is so extremely rare that it has been estimated to be one in ten million. Even though it is possible to find two bills from the discontinued series, it is extremely unlikely that one would carry two of them in their wallet. Therefore, the probability that Ben will find two worthless $10 bills in his wallet is practically impossible.

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The area of the shaded region is 5π  

The sector of a circle refers to the region enclosed by two radii of a circle and the arc between them. It is a part of the whole circle, and its area can be calculated using the following formula:

where θ is the central angle (in degrees) of the sector, r is the radius.  

Here we have

The length of arc FG = 5/3 π  and measure of ∠FEG = 50°

As we know Arc Length = θ × (π/180) × r  

=> Length of arc FG = 50 × (π/180) × r

From the given data,

=> 50 × (π/180) × r = 5π/3

=> 5 × (1/18) × r = 5/3

=>  (1/6) × r = 1

=> r = 6 units  

Hence, the radius of the circle is 6 units

By using the formula,

Area of a Sector of Circle = (θ/360°) × πr²

Area of shaded region = (50/360) × π(6)²  

= (5/36) × π(36)

= (5/36) × π(36)

= 5π  

The area of the shaded region is 5π  

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The error in the solution is that, In step 2, the Distributive Property was applied incorrectly.

Equations are mathematical expressions consisting of two or more variables and constants on two sides connected by an equal to sign.

Solution of the equation is the value of the variable that the equation holds true.

Given equation is,

8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Using the multiplication property of equality, multiplying whole equation by 2,

(2 × 8) - a = 6 (4 - 5a)

16 - a = 6 (4 - 5a)

Distributive property states that, for three numbers or expressions, a, b and c,

a (b + c) = ab + ac

Applying that,

6 (4 - 5a) = (6 × 4) - (6 × 5a) = 24 - 30a

But the student didn't multiply 6 with 5a, and thus he got 24 - 5a in step 2.

Hence the incorrect step is step 2 because of incorrect use of distributive property.

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Your question is a bit confusing. The complete question with an image is given below.

A student provided the steps for solving an equation. Which statement describes the error in the solution?

Equation : 8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

If function [tex]f(x) = 7x - 8[/tex]  and  [tex]g(x) =4[/tex] then the answer is [tex](fog)(-1) = -36.[/tex]

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behaviour of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

We need to find (fog)(-1) = f(g(-1)).

First, we find g(-1):

g(-1) = 4(-1) = -4

Then, we plug in g(-1) into f:

f(g(-1)) = f(-4) = 7(-4) - 8 = -36

Therefore, (fog)(-1) = -36.

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If 0 is not an eigenvalue of a matrix, then it means that the matrix is invertible it implies that the matrix has a unique inverse .

The Eigenvalues are defined as the values which is associated with a square matrix.  

A non-zero vector is said to have an eigenvector of a matrix if when the matrix is multiplied by the vector, the result is a scalar multiple of the vector and that scalar multiple is known as the eigenvalue.

If a matrix has an eigenvalue of 0, it means that there exists a non-zero vector such that when the matrix is multiplied by the vector, the result is the zero vector. Such a matrix is said to be singular or non-invertible.

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The Lagrange multipliers fail to solve the problem because  g = 0 at the coordinates (x, y) = (0, 1) where f reaches its minimum on g = 0,

The Italian mathematician Joseph-Louis Lagrange is honoured by having his multiplier method named after him. In order to apply the derivative test of an unconstrained problem to a constrained problem, it is necessary to convert it into a different form.

Moreover, this technique is frequently employed in mathematical optimization. When a function of the form f(x, y, and z) is subject to equality constraints of the form g(x, y, and z) = k or g(x, y, and z) = 0, one useful technique is the method of Lagrange's multipliers. This means that it depends on the values of the desired variable exactly satisfying the terms of one or more equations.

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One centimeters is equal to 0.01 meters. Centimeter (cm) and meter (m) are both units of length in the International System of Units (SI).

One centimeter is equal to 0.01 meters.

This can be derived by using the conversion factor that 1 meter is equal to 100 centimeters:

1 meter = 100 centimeters

Dividing both sides by 100, we get:

1 centimeter = 1/100 meters

Simplifying this, we get:

1 centimeter = 0.01 meters

Therefore, one centimeter is equal to 0.01 meters.

A centimetre is a metric length unit that equals one tenth of a metre. It is typically used to measure short distances, such as an object's length or width, or a person's height.

A metre, on the other hand, is the SI system's base unit of length and is defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second. Larger distances, such as the length of a room, a building, or a road, are measured with it.

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We can convert 162 cm to feet by multiplying by the conversion factor to get , 162 cm equivalent to 5.32 feet .

The length or the distance between two points is measured with the help of units such as : meter , centimeter , inches , feet .

We have to convert the length of 162 centimeter to feet ;

We know that , 1 centimeter is approximately equal to 0.0328 feet ;

So , the conversion factor is 0.0328 ;

So , for the conversion  we multiply the given length by 0.0328 ;

On multiplication we get ;

⇒ 162 centimeter = 162 × 0.0328 ;

⇒ 162 centimeter = 5.3136 feet .

Therefore , 162 cm is approximately equal to 5.32 feet .

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The mean of the distribution of  [tex]\bar{x}[/tex] and [tex]\bar{p}[/tex] are [tex]\mu_{\bar{x}}=\mu[/tex] and [tex]\mu_{\bar{p}}=p[/tex]. The standard deviation of the distribution of  [tex]\bar{x}[/tex] and [tex]\bar{p}[/tex] are [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex] and [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]. So a suitable option is option D.

A distribution is the collection of all potential values for terms that reflect specified events in statistics. It is possible to calculate the expected value or mean of a statistical distribution by integrating the product of the variable's probability and the distribution's definition of that probability. This is represented by the symbol μ.

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean and a higher standard deviation shows that the data are more dispersed. This is represented by the symbol σ.

Here, the expected value for [tex]\bar{x}[/tex] is written as    [tex]\mu_{\bar{x}}=\mu[/tex] , and the standard deviation for [tex]\bar{x}[/tex] is written as [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]. Similarly, the expected value for [tex]\bar{p}[/tex] is written as [tex]\mu_{\bar{p}}=p[/tex], and the standard deviation for [tex]\bar{p}[/tex] is written as  [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]. Therefore, the correct option for this will be D.

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The complete question is -

Which answer shows

i. The mean of the distribution of [tex]\bar{x}[/tex].

ii. The standard deviation of the distribution of [tex]\bar{x}[/tex].

iii. The mean of the distribution of [tex]\bar{p}[/tex].

iv. The standard deviation of the distribution of [tex]\bar{p}[/tex].

A.

i. [tex]\mu_{\bar{x}}=np[/tex]

ii. [tex]\sigma_{\bar{x}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

iii. [tex]\mu_{\hat{p}}=np[/tex]

iv. [tex]\sqrt{np(1-p)}[/tex]

B.

   i. [tex]\mu_{\hat{p}}=np[/tex]

ii. [tex]\sigma_{\bar{x}}=\sqrt{np(1-p)}[/tex]

iii. [tex]\mu_{\hat{p}}=\sqrt{np(1-p)}[/tex]

iv. [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

C.

i. [tex]\mu_{\bar{x}}=p[/tex]

ii. [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]

iii. [tex]\mu_{\hat{p}}=\bar{x}[/tex]

iv. [tex]\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

D.

i. [tex]\mu_{\bar{x}}=\mu[/tex]

ii. [tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]

iii. [tex]\mu_{\bar{p}}=p[/tex]

iv. [tex]\sigma_{\bar{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

E.

i. [tex]\mu_{\bar{x}}=\mu[/tex]

ii. [tex]\sigma_{\bar{x}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

iii. [tex]\mu_{\bar{p}}=p[/tex]

iv. [tex]\sigma_{\hat{p}}=\frac{\sigma}{\sqrt{n}}[/tex]

Answer:

1) x=5, y=5sqrt(2)

2) x=14

3) 7sqrt(2)

Step-by-step explanation:

I will give you a quick lesson.

The formula is a² + b² = c²

The longest line(usually the bottom) is C

If something is squared, multiply it by itself, for example, 6² is 36, multiply 6 by 6(6 x 6).

Do the same thing with a and b.

Then add a and b after you square them.

To make the number smaller, square root it.

Then you will get your answer, don't forget the exponent.

Sorry for not giving you the answer, but I hope this quick lesson helped you, this is how I learned, I hope this makes it easier for you. Have a GOOD DAY!

If the whole number n is such that n * (n+28) is a prime number.  the prime number is 29.

We can start by expanding the expression n × (n+28) to get n^2 + 28n. Notice that n^2 + 28n is a quadratic expression that can be factored as n(n+28). Therefore, if n × (n+28) is a prime number, then n and n+28 must be either 1 and the prime number or the prime number and 1 (since a prime number has only two positive factors, 1 and itself).

If n = 1, then n+28 = 29, and n × (n+28) = 1 × 29 = 29, which is a prime number.

If n+28 = 1, then n = -27, which is not a whole number.

Therefore, the prime number in question is n × (n+28) = 29.

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