The mean s recorded by 27 candidates happened to be 64%. During inspection it was found that one candidate actually scored 74% s instead of 47% recorded in the result sheet. What will be the correct mean?

​

The simplified expression is  c²a³ - 3[tex]a^4[/tex]c +  a²bc² - a³bc  - 3[tex]a^4[/tex]b+ 4ab²c² - 22a²b²c + 36a³b + 12a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²).

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

c +6b/(-2bc-6ab- 3a²) + 2b/(a² + 2ab) - b/(ac - 3a²)

Now, simplifying

(c+ 6b) (a² + 2ab)(ac - 3a²) + 2b(-2bc-6ab- 3a²)(ac - 3a²)- b (-2bc-6ab- 3a²)(a² + 2ab) / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= ca² + abc + 6a²b + ab² (ac - 3a²) + (4b²c - 12ab² - 6a²b)(ac - 3a²) - ( -2b²c - 6ab² - 3a²b)(a² + 2ab) / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= c²a³ - 3[tex]a^4[/tex]c + a²bc² - 3a³bc + 6a³bc - 18[tex]a^4[/tex]b + 4ab²c² - 12a²b²c - 12 a²b²c+ 36a³b - 6a³bc + 18[tex]a^4[/tex]b + 2a²b²c +  4a³bc + 6a³b² + 12a²b³  - 3[tex]a^4[/tex]b + 6a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= c²a³ - 3[tex]a^4[/tex]c +  a²bc² - a³bc  - 3[tex]a^4[/tex]b+ 4ab²c² - 22a²b²c + 36a³b + 12a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

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The critical value is 13.28 when the distribution of final marks in the statistics department.

Given that,

According to a teacher, the distribution of final marks in the statistics department is: A, 25%; B, 25%; C, 40%; D, 5%; and F, 5%. The following number of grades were recorded at the conclusion of a randomly chosen semester.

We have to recognize the important value.

We know that,

Given a=0.01,

The critical value of chi-square with 0.99,

df=n-1=4  is

13.28 (From chi-square table)

Therefore, The critical value is 13.28 when the distribution of final marks in the statistics department.

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y = mx + b where m is the rate of change and b is the y-intercept, describes the linear relationship between rise in temperature (y) and change in time (x) from 6 to 24 minutes.

To calculate the linear equation, we can use the Point-Slope Form of a Line formula, y = mx + b. To find the slope (m), we must calculate the rise (change in the y-value) over the run (change in the x-value). We must calculate the temperature difference between 6 minutes (T1) and 24 minutes (T2). Then, divide the temperature difference by the time difference of 18 minutes. The y-intercept (b) can be found by plugging in the known x and y values of 6 minutes and T1 respectively into the equation y = mx + b. Once we have the slope and y-intercept, we can plug them into the equation y = mx + b to calculate the equation that describes the linear relationship between the rise in temperature (y) and change in time (x) from 6 to 24 minutes.

y = mx + b, where

m = (T2 - T1)/(24 - 6) = (T2 - T1)/18

b = T1 - (m*6)

Therefore,

y = (T2 - T1)/18 * x + (T1 - (m*6))

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The expected value of the game that you play will be negative 0.21.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

A pack contains 3 gold marbles, 6 silver marbles, and 29 dark marbles. Somebody offers to play this game: You haphazardly select one marble from the pack. Assuming it is gold, you win $3. Assuming it is silver, you win $2. Assuming it is dark, you lose $1.

The expected value is given as,

E(x) = 3(3/38) + 2(6/38) - 1(29/38)

E(x) = 0.2368 + 0.3158 - 0.7632

E(x) = -0.21

The expected value of the game that you play will be negative 0.21.

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The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 foot

The surface area of the box = [tex]225[/tex] [tex]ft^{2}[/tex]

Weight of the metal = 1125 kg

According to the question,

Given value = [tex]500[/tex] [tex]ft^{3}[/tex] tanks is to be built which has to be a square-based rectangle steel holding tank.

For this, we have to know the total surface area of the box,

Surface area (A) = 4 x sides of the rectangle + square base -- equation 1

Let's take the width of the square base = p

And let height = h

Since we know that,

Rectangle sides = p x h

Square base ⇒ p x p = [tex]p^{2}[/tex]

Substituting these values in equation 1,

Surface area ( A ) = 4 x ( p x h ) + [tex]p^{2}[/tex] ---- equation 2

The formula for calculating the volume of the box,

V = p x p x h

V = [tex]p^{2}[/tex] x h --- equation 3

Referring to the question that the value of the volume is already given such that volume = [tex]500[/tex] [tex]ft^{3}[/tex]

So, V = [tex]500[/tex] [tex]ft^{3}[/tex]

Putting the value of V in equation 3,

500 = [tex]p^{2}[/tex] x h

h = [tex]\frac{500}{p^{2} }[/tex] ---- equation 4

Substituting the value of h from equation 4 to equation 2,

A = 4 x ( p x [tex]\frac{500}{p^{2} }[/tex] ) + [tex]p^{2}[/tex]

⇒ A = [tex]\frac{2000}{P}[/tex] + [tex]p^{2}[/tex]

We will be taking the derivative of the above equation,

⇒ A' = - [tex]\frac{2000}{p^{2} }[/tex] + 2p

Now we will be minimizing A,

⇒ 0 = - [tex]\frac{2000}{p^{2} }[/tex] + 2[tex]p[/tex]

⇒ [tex]\frac{2000}{p^{2} }[/tex] = 2[tex]p[/tex]

⇒ 2000 = 2[tex]p^{3}[/tex]

⇒ 1000 = [tex]p^{3}[/tex]

⇒ p = [tex]\sqrt[3]{1000}[/tex]

⇒ p = 10 foot

Substituting the value of p in equation 4,

⇒ h = [tex]\frac{500}{10^{2} }[/tex]

⇒ h = [tex]\frac{500}{100}[/tex]

⇒ h = 5 foot

Substituting values in the area of the square box,

A = 4 x (10 x 5) + [tex]5^{2}[/tex]

A = 200 + 25

A = 225 [tex]ft^{2}[/tex]

The weight of the metal,

⇒ weight = A x weight per square foot

⇒ weight = 225 x 5

⇒ weight = 1125 kg

Therefore, The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 feet

The surface area of the box = 225 [tex]ft^{2}[/tex]

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2- T-distribution with 58 degrees of freedom

When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.

[tex]t[/tex] = Student's t-distribution

[tex]X{i}[/tex] = sample mean

μ = population mean

[tex]s[/tex] = sample standard deviation

[tex]n[/tex] = sample size

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The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.

When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.

Answer: Part A: Yes there is. As the number of workers increases, so does the production.

Part B:    y = 5x + 2

Part C: The slope indicates that for every person there is 5 units being produced, and the y-intercept indicates that 2 units are being made every day, regardless of if there are no workers ( this, however is unrealistic but it is how the data is )

Step-by-step explanation:

The doubling time is approximately 83 years. This means that it will take approximately 83 years for the squirrel population to double from its initial size of 450 squirrels.

What is an exponential function?

An exponential function is a function in which the variable appears in the exponent. Exponential functions have the form y = ab^x, where a and b are constants and x is the variable. The constant b is called the base of the exponential function.

The given information states that the squirrel population P(t) follows a logistic growth model with a growth constant k = 0.8 yr-1 and a carrying capacity of 1800 squirrels. The formula for the squirrel population P(t) can be found using the logistic growth model:

P(t) = K / (1 + (K/P0 - 1) * e^(-kt))

where P0 is the initial population of squirrels, K is the carrying capacity, and t is time in years.

Substituting the given values into the formula, we get:

P(t) = 1800 / (1 + (1800/450 - 1) * e^(-0.8t))

Simplifying the equation, we get:

P(t) = 1800 / (1 + 3e^(-0.8t))

This is the formula for the squirrel population P(t).

To find the doubling time (the time it takes for the squirrel population to double), we need to find the time t at which the squirrel population reaches twice the initial population of 450 squirrels. This can be represented by the equation:

2 * 450 = 1800 / (1 + 3e^(-0.8t))

Solving for t, we get:

0.8t = ln(3)

t = ln(3) / 0.8

Hence, the doubling time is approximately 83 years. This means that it will take approximately 83 years for the squirrel population to double from its initial size of 450 squirrels.

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The answer is false. The covariance statistic gauges how closely two variables are related to one another.

a connection between two quantitative variables in which the corresponding values of the second variable tend to rise when the value of the first variable tends to rise (or fall) (or decrease).

The direction of the link between two variables is measured by covariance. A positive covariance indicates that both variables frequently exhibit high or low values together. While two variables have a negative covariance, they are often low when one is high.

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The eigenvalue for this coefficient matrix is c, the eigenvector is (1, 0) and the generalized eigenvector is (1, -4).The most general real-valued solution to the linear system of differential equations is given by:y(x) = c1e^(-4x) + c2xe^(-4x),

To find the eigenvalue, we need to solve the characteristic equation of the coefficient matrix, which is given by det(A - cI) = 0. In this case, the characteristic equation is -c^2 + 4c = 0, which has a single solution of c = 4. Thus, the eigenvalue is c = 4.

To find the eigenvector, we need to solve the linear system (A - cI)v = 0. For this coefficient matrix, the linear system is (A - 4I)v = 0, which has the solution v = (1, 0). Thus, the eigenvector is (1, 0).

To find the generalized eigenvector, we need to solve the linear system (A - cI)w = v, where v is the eigenvector. In this case, the linear system is (A - 4I)w = (1, 0), which has the solution w = (1, -4). Thus, the generalized eigenvector is (1, -4).

Finally, the most general real-valued solution to the linear system of differential equations is given by y(x) = c1e^(-4x) + c2xe^(-4x), where c1 and c2 are arbitrary constants.

Characteristic equation: det(A - cI) = 0

-c2 + 4c = 0

c = 4

Eigenvector: (A - 4I)v = 0

v = (1, 0)

Generalized eigenvector: (A - 4I)w = v

w = (1, -4)

Most general solution: y(x) = c1e^(-4x) + c2xe^(-4x), where c1 and c2 are arbitrary constants.

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Answer:

y- intercept = - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{5}{3}[/tex] x - 6 ← is in slope- intercept form

with y- intercept c = - 6

The probability that the student is from Section I, given that he or she is a mathematics major, is 0.214 and the probability that the student is from Section 1, is 0.294.

In the give question;

There are three sections of English 101.

In Section 1, there are 25 students, of whom 3 are mathematics majors.

In Section II, there are 20 students, of whom 7 are mathematics majors.

In Section lIl, there are 40 students, of whom 4 are mathematics majors.

We have to find the probability that the student is from Section I, given that he or she is a mathematics major and the probability that the student is from Section 1.

Total number of students in all sections = 25+20+40 = 85

Total number of students major in mathematics = 3+7+4 = 14

The probability that the student is from Section I, given that he or she is a mathematics major is represented as

P(I | M) = P(I∩M)/P(M)

P(I∩M) = (Student in section II - Student in section III)/Total student in all sections

P(I∩M) = (7 - 4)/85 = 3/85

P(M) = Total student of mathematics/Total student in all sections

P(M) = 14/85

Now putting the values

P(I | M) = (3/85)/(14/85)

P(I | M) = 3/14

P(I | M) = 0.214

Now finding the probability that the student is from Section 1.

Probability that student is from section I = Total students in section I/ total students

Probability that student is from section I = 25/85

Probability that student is from section I = 0.294

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The right question is:

There are three sections of English 101. In Section 1, there are 25 students, of whom 3 are mathematics majors, In Section II, there are 20 students, of whom 7 are mathematics majors. In Section lil, there are 40 students, of whom 4 are mathematics majors. A student in English 101 is chosen at random. Find the probability that the student is from Section I, given that he or she is a mathematics major. The probability that the student is from Section 1 is (Simplify your answer. Round to three decimal places as needed.)

The charge for cutting a board into 8 equal pieces is $1.2

Equate charges for cutting board : Number of equal pieces

0.60 : 4 = x : 8

0.60/4 = x / 8

cross product

0.60 × 8 = 4 × x

4.8 = 4x

divide both sides by 4

x = 4.8 / 4

x = 1.2

Therefore, it will cost $1.2 for cutting a board into 8 equal pieces.

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The method that would be the most straight forward for her to use would be the substitution method because you can easily solve one equation for a variable. That is option A.

The substitution method for solving equations is the method that can be used in a quadratic equation whereby one equation is solved and substituted into the next equation.

The given equation such as;

4x - 5y = 7 ---> eq 1

4X -9y = -4---> eq 2

From eq1 make 4x the subject of formula

4x = 7 + 5y

Substitute for 4x in equation 2;

7 + 5y - 9y = -4

7 - 4y = -4

7+4 = 4y

11 = 4y

y = 11/4

y = 2.75

Then substitute y = 2.75 into equation 1;

4x - 5y = 7

4x - 5(2.75) = 7

4x - 13.75 = 7

4x = 7 + 13.75

4x = 20.75

X = 20.75/4

X = 5.2

Therefore with the substitution method the value of X and y can be determined.

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Answer:

D

Step-by-step explanation:

Since this we have rose petal, the equation will be either

[tex]r = a \sin(n \alpha ) [/tex]

or

[tex]r = a \cos( n\alpha ) [/tex]

Since we have 3 petals, which is a odd number, n=3

so the answer must be either

[tex]r = a \cos(3a) [/tex]

[tex]r = a \sin(3 \alpha ) [/tex]

Where a is some constant real number.

So D is the answer

The answer is √7.

What is Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Step-by-step explanation:

Using the pythagorean theorem, we know that

     a^2 + b^2 = c^2

In this case,

c = 4, which means that a^2 + b^2 = 16

Since we know that a = 3, this means that a^2 is also 9. So, we know that b^2 = 16-9

Therefore, b^2 = 7

So, the answer is √7.

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Answer:

C)  The range of the function is all real numbers less than or equal to 0.

Step-by-step explanation:

Given function:

[tex]f(x)=-\sqrt{x}[/tex]

Domain

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, x ≥ 0.

Therefore, the domain of the function is all real numbers greater than or equal to 0.

Range

The range of a function is the set of all possible output values (y-values).

As the domain is x ≥ 0, the range of the function is all real numbers less than or equal to 0.

Answer:

C) The range of the function is all real numbers less than or equal to 0.

Answer:1 carrot cost .75 cents and a mango cost 1.40

Step-by-step explanation:

12 carrots + 10 mangoes = 23$

4 carrots + 5 mangoes = 10$

I know to get from 5 mangoes to 10 mangoes you have to multiply twice. so it wil come up to 20 dollars

8 carrots + 10 mangoes = 20$

divide by 2

that will leave 4 carrots and 3 dollars.

4/3 = .75

17 dollars is left

so 10 carrots is equal to 14 dollars

14/10 = 1.4 dollars

Answer:

Step-by-step explanation:

what is your question?

The value of b must be equal to -14, so that the function has at least one inflection point. Hence, option B is correct.

Expressions are mathematical operations that involve at least two terms connected by an operator and can be either integers, variables, or both. The operations with reflection coefficients are addition, subtraction, multiplication, and division. 

As per the instruction given in the question,

The given function,

f(x) = x⁴ + bx² + 1

Differentiate with respect to x,

f'(x) = 4x³ + 2xb

Again differentiate with respect to x,

f''(x) = 12x² + 2b

For inflection point, f''(x) = 0

12x² + 2b = 0

2b = -12x²

b = -6x²

x = √-b/6, x ∈ [1, 2]

Let's assume that b = -28

x = √-(-28)/6

x = √28/6

x = √14/3, here x ∉ [1, 2], hence it is incorrect.

If b = -14

x = √-(-14)/6

x = √14/6

x = √7/3 ≈ 1.82, here x ∈ [1, 2], hence it is correct.

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The regular polygon has 20 sides.

The regular pentagon is a regular polygon with five sides

The regular decagon is a regular decagon with ten sides

The angle sum around a point adds to 360 degrees.

Each interior angle of the square is 90 degrees

Each interior angle of the regular pentagon is 108 degrees.

The Interior angle of our unknown polygon is 360 - 108 - 90 = 162 degrees.

A quick calculation shows us that the exterior angle of this polygon is 18 degrees.

The sum of the external angles of any regular polygon is 360 degrees

Divide 360 by 18 and you get 20 times.

Thus our unknown polygon has 20 sides.

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The function f in slope - intercept form is y = -3x + 6 .

Given :

For linear function f, f(2)=0 and f(4)=-6.

Examples :

f(5)=0 means (5,0) is a point on the line.

f(3)=-2 means (3,-2) is a point on the line.

so f ( 2 ) = 0 means ( 2 , 0 )

f ( 4 ) = -6 means ( 4 , -6 )

slope m = -6 - 0 / 4 - 2

= -6 / 2

= -3

substitute m and ( 2 , 0 ) in y = mx  + b

0 = -3 * 2 + b

b = 6

substitute m and b value

y = -3x + 6

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The expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.

Here, we are assuming that the dishwasher is replaced in the first 2 years in order to calculate the expected value of the extended warranty.

Because there is 14% chance of replacement:

Value of warranty = 14%*$800 - $112.10

Value of warranty = $112.00 - $112.10

Value of warranty = -$0.10

Now, because it is assumed that replacement will be done in first 2 years, then,

Value of warranty will increase to $687.90 ($800 - $112.10).

Therefore, the expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.

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H0: There is no link between state and preferred sport.

H1: There is a connection between state and preferred sport.

Given,

The question to be answered is whether the factor "state" and the factor "sporting choice" are related.

Therefore, the focus of the study is on "association" and whether or not state-to-state variations in athletic preference distributions exist. The most appropriate test in this instance is the test for association.

Unless there is evidence to the contrary, two things are assumed to not be related. Since the null hypothesis is assumed to be true, the following two hypotheses are the proper pair:

H0: There is no connection between a person's state and their preferred sport.

H1: The choice for sports and state are related.

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The best measure of center for the frequency of the data is Mean. The value of the measure of the center is 30.

The Mean value refers to an intermediate value between a discrete set of numbers. It is a measure of central tendency in a data set. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean of a set of observed data is defined as being equal to the sum of the numerical values of each and every observation, divided by the total number of observations. Fifty part time college students were asked how many hours they work per week.

Frequency 12 10 81 6 0 10 30 40 0 10 30 40 20 Hours 20 Hours.

we can calculate mean by adding all the frequencies and then divide it by the number of observations.

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Answer: x=3y-1/2 or y=(x+1/2)/3

Step-by-step explanation:

f^-1(x) is just the inverse so all you need to do is switch x and y.

right now you have y=3x-1/2

so switch the x and y to get your answer of x=3y-1/2

if you're asked to solve for y, follow these steps:

1. x +1/2 = 3y-1/2 +1/2 -> x+1/2=3y

2. divide both sides by 3 -> (x+1/2)/3=y

Answer:

Step-by-step explanation

sec x = -9/5.

cos x = 1/ secx

So, here

cos x = 1 / -9/5

         = -5/9

sin x = √(1 - cos^2 x)

        = √(1 - 25/81)

        = √(56/81)

        = √56/9

tan x = sinx / cos x

         = √56/9 / -5/9

         = -√56/5

cosec x = 1 / sin x

             = 1 / √56/9

             = 9/√56.

cot x = 1/tanx

         = 1/-√56/5

         = -5/√56

Answer:

Step-by-step explanation:

in similar triangles

sides are proportional.