Alex tracked the number of cups of coffee he drank each day for the following month and

created a new probability distribution.

Number of Cups of Coffee, X 0

1 2 3 4

Relative Frequency, P(X) 0.035 0.579 0.286 0.080 0.020

According this new data, Alex is expected to drink 1.471 cups per day.

4. Calculate s(X) of Alex's new probability distribution. (1 point)

0.599

0.775

1.471

4.223

Answer:

To answer these questions, we need to know the par value, coupon rate, and number of debentures issued by Charter Corp. Based on the information provided, Charter Corp. issued 2,500 debentures with a $1,000 par value and a 7% coupon rate.

a. The dollar amount of interest per bond that an investor can expect to receive each year from Charter is calculated by multiplying the par value by the coupon rate. In this case, the interest per bond would be $1,000 x 7% = $70.

b. The total interest expense per year associated with this bond issue can be calculated by multiplying the number of bonds by the interest per bond. In this case, the total interest expense would be 2,500 x $70 = $175,000.

c. The company's net after-tax interest cost associated with this bond issue can be calculated by multiplying the total interest expense by the corporate tax rate. In this case, the net after-tax interest cost would be $175,000 x 21% = $36,750.

The probability that we have at least one customer buying 2 or more books before having two customers buying no books is 0.984.

Here is a possible MATLAB code to solve the problem:

%START

% Set the rate of the Poisson process

lambda = 4;

% Set the probabilities of N taking different values

p0 = 0.2;

p1 = 0.4;

p2 = 0.2;

% Compute the probability of having at least one customer buying 2 or more books

% before having two customers buying no books

prob = poisscdf(2-1, lambda*p0) - poisscdf(1-1, lambda*p0);

% Display the result

fprintf('Probability of having at least one customer buying 2 or more books before having two customers buying no books: %.4f\n', prob);

%END

This code uses the poisscdf function to compute the probability of having a certain number of events (customers buying 2 or more books or customers buying no books) in a given time period (one hour), assuming that the events occur according to a Poisson process with the given rate (4 customers per hour).

The probability of having at least one customer buying 2 or more books before having two customers buying no books is then computed as the probability of having 2 or more customers buying 2 or more books minus the probability of having 1 or more customers buying 2 or more books. The result is displayed using the fprintf function.

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Answer:

  120

Step-by-step explanation:

You want to know the measure of the third arc of a circle where one of the arcs is labeled 114°, and a second arc is intercepted by a 63° inscribed angle.

The measure of an inscribed angle (63°) is half the measure of the arc it intercepts:

  (1/2)(arc) = 63°

  arc = 2·63° = 126° . . . . . arc opposite the 63° angle

The total of arcs of a circle total 360°.

  114° +126° +x° = 360°

  x° = 120° . . . . . . . . . subtract 240°

The value of x is 120.

The number of litres of water the tank can hold is 48 litres

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Volume can be measured in cubic units, litres and gallons.

If the rate of pump is 8minutes per minute, therefore in 15 minutes, 15×8 = 120 litres is in the tank.

120 litres is 5/2 full

the volume of the tank will be 120×2/5

= 240/5

= 48litres

Therefore the volume of the tank is 48litres

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Answer:

[tex]f(x)=2.6(4)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the formula to create two equations:

[tex]\implies 10.4=ab[/tex]

[tex]\implies 665.6=ab^4[/tex]

Divide the second equation by the first to eliminate a, then solve for b:

[tex]\implies \dfrac{665.6}{10.4}=\dfrac{ab^4}{ab}[/tex]

[tex]\implies 64=\dfrac{b^4}{b}[/tex]

[tex]\implies 64=b^3[/tex]

[tex]\implies b=\sqrt[3]{64}[/tex]

[tex]\implies b=4[/tex]

Substitute the found value of b into the first equation and solve for a:

[tex]\implies 10.4=4a[/tex]

[tex]\implies a=2.6[/tex]

Therefore, the exponential function is:

[tex]f(x)=2.6(4)^x[/tex]

As per the binomial distribution, the value of var(Y) is 0.00008

What is meant by binomial distribution?

In math, the Binomial distribution counts the number of successes in n trials, where sampling is done with replacement or the probability of success is constant from trial to trial

Here we have given that,  X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample.

And we need to find the value of var(Y).

Here we know that the value of n = 6 and the value of x is 4 and the probability is 0.05.

Then as per the binomial distribution formula, it can be calculated as,

By using a calculator, you can enter trials=6, p=0.05, and X=4 into a binomial probability distribution function (PDF). If doing this by hand, apply the binomial probability formula:

=> [6!/4!(6-4)!] x 0.05⁴ x (1- 0.05)⁶⁻⁴

=> 0.00008

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The monomials with a GCF of 7x³y with degree 5 are 7x⁴y and 14x³y².

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

As per the given GCF as 7x³y,

The GCF of 14 and 7 is 7.

The GCF of x⁴y and x³y² will be x³y.

Thus,

GCF of 7x⁴y and 14x³y² = 7x³y

So monomials are 7x⁴y and 14x³y².

Hence "The monomials are 7x⁴y and 14x³y²".

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The probability density function fr(r) of the distance from a uniformly randomly chosen point in the unit disk to the origin is r, and the cumulative distribution function Fr(r) is (r² / 2).

To find the probability density function (PDF) and cumulative distribution function (CDF) of the distance from a uniformly randomly chosen point in the unit disk to the origin, we can first find the area of the unit disk and the area of the annulus centered at the origin and bounded by two circles with radii r and r + dr. The PDF is then the ratio of the area of the annulus to the total area of the unit disk, and the CDF is the ratio of the area of the annulus to the total area of the unit disk up to radius r.

The area of the unit disk is simply the area of a circle with radius 1, which is pi. The area of the annulus centered at the origin and bounded by two circles with radii r and r + dr is equal to the difference between the areas of the two circles, which is pi(r + dr)² - pi(r²). Therefore, the PDF of r is:

fr(r) = [pi(r + dr)² - pi(r²)] / pi = r + dr²

The CDF of r is the sum of the PDFs up to radius r, which is:

Fr(r) = ∫fr(t)dt from 0 to r = ∫(t + dt²)dt from 0 to r = (r² / 2) + (r × dt) + (dt³ / 3)

We can take the limit as dt approaches 0 to get the final expression for the CDF:

Fr(r) = (r² / 2)

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The p-value (0.0324) < α (0.10), & There is sufficient proof that the best ski area is dependent on the level of the skier.

What is the p-value?

The p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.

(a) Hypotheses:          

H1 : Best ski area is independent of the level of the skier      

H2 : Best ski area is dependent on the level of the skier      

(b) Expected counts:          

                                              Beginner     Intermediate    Advanced     Total  

Tahoe     Observed                 20          30               40          90

             Expected               12.41            31.03            46.55   90.00

Utah     Observed                 10             30             60    100

             Expected              13.79           34.48           51.72  100.00

Colorado    Observed                 10             40             50    100

             Expected                13.79            34.48           51.72  100.00

Total     Observed                  40             100             150  290

             Expected               40.00          100.00       150.00     290.00

(c)

All the expected counts are > 5, so we can apply the test      

(d) Test statistic:

Square Contingency Table Test for Independence  

                                              Beginner     Intermediate    Advanced     Total

Tahoe     Observed                 20          30               40          90

             Expected               12.41            31.03            46.55   90.00

              O - E                       7.59            -1.03          -6.55   0.00

             (O - E)² / E               4.64              0.03           0.92   5.59

Utah     Observed                 10             30             60    100

             Expected              13.79           34.48           51.72  100.00

                      O - E               -3.79            -4.48          8.28   0.00

             (O - E)² / E               1.04              0.58           1.32    2.95

Colorado    Observed                 10             40             50    100

             Expected                13.79            34.48           51.72  100.00

                      O - E               -3.79            5.52          -1.72   0.00

             (O - E)² / E               1.04              0.88           0.06        1.98

Total     Observed                  40             100             150  290

             Expected               40.00          100.00       150.00     290.00

                      O - E               0.00            0.00          0.00    0.00

             (O - E)² / E               6.72               1.50            2.30        10.53

                                         10.53         chi-square    

                                                 4           df    

                                      0.0324           p-value  

x² = 10.53 and p-value = 0.0324        

(e) Since the p-value (0.0324) < α (0.10), we reject H1. There is sufficient evidence that the best ski area is dependent on the level of the skier.

Hence, the p-value (0.0324) < α (0.10), & There is sufficient proof that the best ski area is dependent on the level of the skier.

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The required solutions following the sequence are given as,
(a) By the distance formula,
(b) By the addition of property,
(c) By the slope formula slopes of parallel lines are equal.

Here,
The coordinates of point D are (4, 5) and the coordinates of point E are (5, 3)
The distance formula is given as,

D = √[[x₂ - x₁]² + [y₂+ - y₁]²]

By distance formula,
DE = √5

Segment DE is half the length of segment AC
AC = DE + DE
AC = 2DE
AC = 2√5

The property used is an addition property.

Segment DE is parallel to segment AC,
By the slope formula slopes of parallel lines are equal.

Thus, the complete reasoning of the solution is shown above.

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Answer:

Prime numbers are odd that are greater than 2. Prime numbers are numbers that are not divisible by anything. EXAMPLE: 33 is not prime because if you take 3 times 11 then you get 33.

Step-by-step explanation:

Answer:

Lisa's original weight was 172.9 pounds.

Step-by-step explanation:

Let w be Lisa's original weight and l be the weight she lost. Since Lisa lost 27% of her original weight, we have:

0.27w = l

Substituting the known value of l, we get:

0.27w = 46.71

w = 46.71 / 0.27

w = 172.9

Thus, Lisa's original weight was 172.9 pounds.

Answer:

  about 323.9 mph

Step-by-step explanation:

You want the speed of a plane that travels 750 miles in 2 hours with the wind and in 2.75 hours against the wind.

The relation between time, distance, and speed is ...

  speed = distance/time

If p represents the speed of the plane, and w represents the speed of the wind, then we have ...

  p +w = 750/2 . . . . . . miles/hour with the wind

  p -w = 750/2.75 . . . . speed against the wind

Adding these two equations gives ...

  2p = 750(1/2 +1/2.75) = 750(4.75/5.50)

Dividing by 2, we have ...

  p = 375(19/22) ≈ 323.9 . . . . . miles per hour

The plane was flying about 323.9 miles per hour.

__

Additional comment

The wind speed was about 51.1 miles per hour.

The 90% confidence interval for the true mean proportion is given by

[-0.049 , -0.001]

Given values of the problem are:

P₁ = 12.9%

P₂ = 14.9%

n₁ = 1250

n₂ = 1000

hence the 90 % confidence interval can be calculated by using the formula for p-value and test statistic .

[tex]z = (P_1 - P_2 ) \pm z\times \sqrt{\frac{P_1\times(1-p_1)}{n_1}+\frac{P_2\times(1-{P_2})}{n_2}}[/tex]

Now we will put the above values in the equation to calculate the values of z .

Using the normal distribution table we can get the z-values.

Upper limit = - 0.049

Lower limit = - 0.001

Hence the 90% confidence interval can be calculated by [-0.049 , -0.001]

When employing common statistical procedures, confidence intervals are usually created using standardized techniques. The methods will have been created to fulfil a number of desired characteristics if the underlying presumptions are accurate. These desired properties include things like validity, optimality, and invariance.

Validity is the most important of the three, followed closely by "optimality." "Invariance" may be viewed as a characteristic of the procedure used to produce the confidence interval rather than a characteristic of the rule for generating the interval. In non-standard applications, the same desired attributes would be sought.

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Answer:

Rate= I*100/P*T

R= 1120 * 100/2000*7

R= 112000/14000

R= 8%

12090 people are there after 30 days when the growth rate of the population of a culture of bacteria, p(t).

Given that,

The growth rate of the population of a culture of bacteria, p(t), where t is the number of days, is 0.2 and is proportionate to the population's growth. Initially, there are 30 people.

We have to find how many people are there after 30 days. (Stop rounding your response.) and when will there be a population doubling.

We know that,

dp//dt directly proportional p

dp/dt=kp

Here,

k=0.2

dp/p=0.2dt

Integrating on both sides.

[tex]\int {1/p} \, dp =\int {0.2} \, dt[/tex]

logp=0.2t+c

p=c[tex]e^{0.2t}[/tex]

Here,

t=30

c=30

So,

p=30[tex]e^{0.2(30)}[/tex]

p=30×403

p=12090

Therefore, 12090 people are there after 30 days when the growth rate of the population of a culture of bacteria, p(t).

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99 many edges must be included in any tree with 100 vertices.

This is because, in a tree, there must be one fewer edge than vertices. This is because each edge connects two vertices, so the total number of edges must be lower than the total number of vertices. Additionally, a tree is a connected graph, meaning there must be at least one edge between any two vertices. The number of edges must also be acyclic, meaning there can be no loops or cycles in the graph. Therefore, any tree with 100 vertices must have 99 edges in order to satisfy these conditions.

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Answer:

5/12 of a pizza

Step-by-step explanation:

Answer:

It does not represent a proportional relationship

Step-by-step explanation:

Answer:

It does not represent a proportional relationship

Step-by-step explanation For a line, the constant of proportionality is a fancy way to say the slope. It makes more sense without the intercept: y=2xclearly, the constant of proportionality is 2.

Answer:

Step-by-step explanation:

To determine who was closer to the state record, we need to compare the distances of the jumps to the state records. To do this, we need to convert both distances to the same unit of measurement. We can convert inches to feet by dividing by 12. 38 feet 11 2/3 inches is equal to 38 + 11 2/3/12 = 38 + 0.9583333 feet = 39.9583333 feet.

Now we can compare the distances to the state records. The eighth-grade record is 40.17 feet and Alex jumped 39.9583333 feet, so he was closer to the record. The seventh-grade record is 38 feet 1 3/5 inches, which is equal to 38 + 1 3/5/12 = 38 + 0.292 feet = 38.292 feet. Eric jumped 36.89 feet, so he was not as close to the record as Alex. Therefore, the eighth graders should be awarded 100 points.

To find the number of seventh graders who participated in the competition, we need to first find the total number of seventh graders by multiplying the total number of students by 3/5. 595 x 3/5 = 357. Then, we multiply the number of seventh graders by 5/8 to find the number of seventh graders who participated in the competition. 357 x 5/8 = 214.625, or about 215 seventh graders participated in the competition.

To find the number of eighth graders who participated in the competition, we need to first find the total number of eighth graders by multiplying the total number of students by 2/5. 595 x 2/5 = 238. Then, we multiply the number of eighth graders by 7/8 to find the number of eighth graders who participated in the competition. 238 x 7/8 = 205.75, or about 206 eighth graders participated in the competition.

Victor decide to go abroad and do a missionary work.

so, the correct option is A.

What happens in Frankenstein Chapter 21?

When the court learns of Victor's residence on the Orkney Islands, Kirwin mounts a spirited defence of Victor and secures Victor's release. Victor's presence in his lab in Orkney at the time of the murder proves that he did not commit the crime. Victor is taken home by Alphonse.

Where does Victor run into his creature again, and why does the creature claim to be satisfied?

After meeting with the magistrate, where does Victor meet his creature again, and why does the b say he is satisfied? They cross paths again in the cemetery. Victor is now b because he feels as miserable and alone as the monster.

Was Victor convicted at his trial?

In a federal trial, Sheriff Victor Hill was found guilty of civil rights violations. He was found guilty on six of b federal charges, including violating the civil rights of inmates.

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The Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).

What is Green's function?

Green's function is an important mathematical tool used to solve differential equations. It is defined as a solution to a homogeneous linear differential equation with a source, or delta, function as its input. Green's functions are also known as impulse response functions and can be used to describe the response of a system to an arbitrary input. Green's functions provide a way to solve differential equations without having to solve the entire equation all at once. They are particularly useful for solving equations with boundary conditions that are difficult to solve without the use of Green's functions. Green's functions can also be used to solve integral equations and provide a powerful tool for solving many physical problems.

The reflection method for finding a Green's function for a problem on a semicircular region can be used as follows. First, we solve the problem on the half-plane by finding a Green's function G(x, xo) that satisfies the boundary conditions given. Then, we reflect the solution across the boundary of the semicircle, namely T1 and T2, to obtain the Green's function on the entire semicircle.
The Green's function on the half-plane is given by G(x, xo) = მ (x-xo). Using this solution, we can reflect it across the boundary of the semicircle. For T1, the reflected solution is given by G(x, xo) = მ (x-xo)cos(θ), where θ is the angle between the normal vector to T1 and the vector from xo to x. For T2, the reflected solution is given by G(x, xo) = მ (x-xo)sin(θ), where θ is the angle between the normal vector to T2 and the vector from xo to x.
Therefore, the Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).

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The correct option is D , as the number of shares issued is 80000.

What is stock ?

In finance, stock consists of all the shares by that possession of an organization or company is split. one share of the stock means that fractional possession of the corporation in proportion to the whole range of shares.

Main body:

as per the information given in the question , Common Stock, $1 par value, $80000 which means  the number of shares issued is 80000.

hence ,correct option is D as the number of shares issued is 80000.

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(a) Sandy picked  [tex]1\frac{1}{2}[/tex] more buckets than Keith  .

(b) Jason have saved money for total of [tex]3\frac{3}{4}[/tex] months .

In the question ,,

Part(a)  ,

it is given that

number of buckets of apples Keith picked is =  [tex]2\frac{5}{6}[/tex] buckets ,

number of buckets of apples Sandy picked is = [tex]4\frac{1}{3}[/tex] buckets

number of more buckets picked by Sandy is = (buckets picked by Sandy) - (buckets picked by Keith) .

= [tex]4\frac{1}{3}[/tex]  -  [tex]2\frac{5}{6}[/tex]  

= 13/3 - 17/6  = 3/2 = [tex]1\frac{1}{2}[/tex] buckets .

Part(b)

number of months that Jason saved money in account = [tex]2\frac{1}{2}[/tex] months

number of months that Jason saved money in cash =  [tex]1\frac{1}{4}[/tex] months

total number of months for which money is saved is =  [tex]2\frac{1}{2}[/tex] +  [tex]1\frac{1}{4}[/tex]

Simplifying further ,

we get,

= 5/2 + 5/4

= 15/4

=  [tex]3\frac{3}{4}[/tex] months .

Therefore , (a) Sandy picked  [tex]1\frac{1}{2}[/tex] more buckets  and (b) Jason saved money for [tex]3\frac{3}{4}[/tex] months .

The given question is incomplete , the complete question is

(a) Keith picked [tex]2\frac{5}{6}[/tex] buckets of apples and Sandy picked [tex]4\frac{1}{3}[/tex] buckets. How many more buckets of apples did sandy pick ?

(b) Jayson has [tex]2\frac{1}{2}[/tex] months worth of pay saved in his account. He has [tex]1\frac{1}{4}[/tex] months worth of pay saved in cash. Altogether, how many months of  money has Jayson saved ?

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Answer:

16 more blue birds

Step-by-step explanation:

If the total number of blue birds is 48

The total number of red birds is 32

then through simple subtraction we get to know that 16 more blue birds are present in the tree than the red birds

Extra Blue birds = 48-32

= 16

True, Building more movie theaters will cause the homicide rate to rise.There is a significant linear correlation.

What does a statistical correlation mean?

A statistical metric known as correlation, which is given as a number, describes the strength and direction of a relationship between two or more variables.

                Although there may be a correlation between two variables, this does not necessarily imply that the change in one variable is what led to the change in the values of the other variable.

Correlation does not always indicate cause. Many factors, such as multi colinearity between movie theaters and the number of killings, which both tend to rise with population, can contribute to a strong connection. In general, there are numerous factors that could account for the parallels between the two.

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The dimensions say (x,y,z) of a rectangular box of maximum volume is ( c/12, c/12, c/12).

The volume of a rectangular box is defined by the product of length, width, and height. For the maximum value of the rectangular box volume, simplify the expression by setting the first derivative of the rectangular box volume to zero in each dimension.

Let x, y, and z be the dimensions of the rectangular box. Since, the sum of the lengths of its 12 edges is a constant c. This implies

4x + 4y + 4z = c

=> x + y + z = c/4 --(1)

The volume of rectangular box = xyz

Consider xyz + lamda(x + y + z - c/4) where λ is Lagrange multiplier.

let f( x,y,z) = xyz + λ(x + y + z - c/4) --(*)

compute the partial derivatives of f( x,y,z) as

fx = yz + λ(1) = yz + λ

fy = xz + λ(1) = xz + λ

fz = xy + λ(1) = xy + λ

For critical points, set the partial derivatives equals to zero.

fx = yz + λ = 0

fy = xz + λ = 0

fz = xy + λ =0

=> xz = yz = xy = - λ

So, x = y = z

then, from equation (1) we get,

x + x + x = c/4

=> 3x = c/4 => x = c/12

thus, x = c/12, y = c/12, z = c/12

Thus, the dimensions of the rectangular box are x = y = z = c/12 or ( c/12, c/12, c/12) and

Maximum volume of rectangular box = xyz

= c³/1728

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If f(x,y,z) is a vector field rather than a scalar function. A vector-valued function is one that has a vector value and a calculable curl. Therefore, if we calculate this value, it will once more be a vector-valued function. The right response in this case is option B.

The following considerations must be made in order to answer this question: It is specified that the divergence of a vector field is a scalar-valued function.

A vector field's specified and actual curl is a vector field. A scalar field's divergence/Curl is not specified. A scalar field's gradient is a vector field that has a definite definition. A vector field's gradient is not known.

Since F is a vector-valued function, we may discover its divergence, which will be a scalar-valued function, and since the gradient of the scalar-valued function will be a vector-valued function, this calculation is attempting to compute the gradient of the divergence of the vector field F.

Complete question:

Let f(x,y,z) be a scalar-valued function, and F(x,y,z) be a vector field. Is the following defined? If it is defined, is it a scalar-valued function or a vector field? (You are only allowed one attempt for each part of this problem.)

(a) V (Vn Defined- it is a scalar-valued function O Defined - it is a vector field O Not defined

(b) VV F) O Defined - it is a scalar-valued function Defined - it is a vector field O Not defined

(c) V (V F) Defined it is a scalar-valued function Defined - it is a vector field Not defined

(d) V (V x F) Defined it is a scalar-valued function Defined it is a vector field Not defined

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The required simplified value o the given expression is 53.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 8 - m/n + p²

Now, put m = 8 n = 2 and p = 7

So,
= 8 - 8 / 2 + 7²
= 8 - 4 + 49

= 4 + 49

= 53

Thus, the required simplified value o the given expression is 53.

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A unit increase in gender will result in decrement of -52.73 in wage provided holding all other parameter constant.

What is parameter?

A parameter is a piece of information that an equation passes on. In terms of statistics, it means something different. In contrast to statistics, which only provide information about a small portion of the population, this value provides information about the entire population.

A parameter is constant because it was determined by surveying everyone (or everything). The average age of the students in your class, for instance, might be of interest to you. Maybe after asking everyone, you discovered that the average age was 25. Given that you polled the entire class, that qualifies as a parameter. Let's say you were curious about the median age of your grade or year.

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