About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? . (A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability

The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.

Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.

Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".

The formula for Spearman's rank correlation coefficient:

Rs = 1 - {6Σd₂}/{n(n₂-1)}

Where, Σd₂ = the sum of the squared differences between ranks.

n = sample size

Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.

To know more about the "Spearman rank correlation": https://brainly.com/question/14646555

#SPJ11

In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.

A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:

2000 - 872 - 173 = 955

Therefore, the missing number is 955.

B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:

9180 ÷ 102 = 90

Therefore, the missing number is 90.

C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:

706 + 99 = 805

Therefore, the missing number is 805.

To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.

A) 3 + (5x7) - 2 = 40

B) (3 + 5) × 7 - 2 = 54

C) 3 + (5 × (7-2)) = 28

Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.

An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..

To learn more about Equation visit here:

brainly.com/question/29538993

#SPJ4

Complete Question: -

Find unknown numbers of these operations

A ) 872 +. + 173 = 2000

B ) 9180:. = 102

C ). -99 = 706

With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.

A ) 3 + 5 x 7-2 = 40

B ) 3 + 5 × 7-2 = 54

C ) 3 + 5 × 7-2 = 28

IT'S FOR TODAY PLEASE ☹, CAN DO IN A LEAF OR WRITE ASI BUT EXPLAIN WELL!!!!!!HELP IF THEY DON'T KNOW NO RESPOND

The expected value of cases in which juries got the right decision is 150, and the variance is 375.

1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.

See more about variance at: https://brainly.com/question/9304306

#SPJ11

Answer:

Zeros: x = -10 and x = -3

Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Step-by-step explanation:

We are given the following function:
f(x) = -(x+3)(x+10)

We want to find the zeros and the vertex of the parabola.

The zeros are the values of the function where f(x) = 0.

So, in order to find the zeros, we can set f(x) = 0.

0 = -(x+3)(x+10)

We can divide both sides by -1, to get:

0 = (x+3)(x+10)

To solve this, we will use zero product property.
Split and solve:

x+3 = 0

x = -3

x+10=0

x = -10

Now, to find the vertex, we first get the average of the zeros.

Add the values of the zeros together, then divide by two:

[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]

Now, we plug this in for x to get the y value (found through f(x)) of the vertex.

[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]

So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Answer:

Isiah Thomas

Step-by-step explanation:

I amazing fact

Answer:

the correct answer is 4

Step-by-step explanation:

yea sorry i don’t know step-by-step

Answer:

y = 2x/15 + 6

Step-by-step explanation:

3y/2 = x/5 + 9

3y = (x/5 + 9) (2)    The 2 that was dividing goes on to multiply on the other side.

3y= 2x/5 + 18

y = (2x/5 + 18) / 3   The 3 that was multiplying goes on to divide on the other side.

y = 2x/15 + 6

The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459

The acceleration vector can be found from the following formula:

[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]

To find the tangential component of the acceleration vector, we first need the velocity vector v(t).

[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]

Next, we need to normalize the velocity vector using the following formula:

[tex]T(t) = v(t) / ||v(t)||,[/tex]

Where ||v(t)|| is the magnitude of the velocity vector.

[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]

Then, the tangential component of a(1) is:

[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]

To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.

[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)}  = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]

Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:

[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]

See more information about acceleration vector in: https://brainly.com/question/29811580

#SPJ11

Answer:

She will draw 120 times for a red marble

Step-by-step explanation:

The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.

By comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.

Comparing the probabilities of the three players, we can see that:

Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.

Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.

Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.

Therefore, the statement that is true is: Player 2 has the   of getting a hit in their at-bats.

Learn more about probabilities at https://brainly.com/question/24756209

#SPJ1

After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.

Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.

The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.

If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.

The number of generations (n) in seven hours is calculated as:

n = t/g

n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations

The number of cells in the cream pie after 7 hours is calculated as :

N = N₀ × 2ⁿ

N = 6 cells × 2⁷

N = 768 cells

Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.

Learn more about Number of generations here:

https://brainly.com/question/17045618

#SPJ11

The required ratio of the surface area of the given pyramids is (A) 3:2.

A ratio can be used to show a relationship or to compare two numbers of the same type.

To compare things of the same type, ratios are utilized.

We might use a ratio, for example, to compare the proportion of boys to girls in your class.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.

A proportion is an equation that equalizes two ratios.

For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)

So, the given surface area is:

- 21 in

- 14 in

Now, calculate the ratio as:

= 21/14

= 3/2

= 3:2

Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.

Know more about ratios here:

https://brainly.com/question/2328454

#SPJ1

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

To learn more about square root, click here:

brainly.com/question/29286039

#SPJ4

The probability that both tests yield the same result is 7.7%.

Simply put, probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
It is predicated on the likelihood that something will occur. The justification for probability serves as the primary foundation for theoretical probability. For instance, the theoretical chance of receiving a head when tossing a coin is 12.
Let's break it down:-
90% don't have of those 99%
5% will be positive
1% positive of those 1%
90% positive
10% negative.
Well we need it to be the same, so 99*(.05*.05+.95*.95)+.01*(.9*.9+.1*.1)= 90.4%.
If both tests are positive, we have:-

0.99*0.05*0.05 and 0.01*0.9*0.9 for being positive, so :-

[tex]\frac{carrier}{positive} = \frac{0.01*0.9*0.9}{(0.99*0.05*0.05+0.01*0.9*0.9)} = 7.7[/tex]

hence, the probability of the two tests yield the same result is 7.7%.

To know more about probability go through:-

https://brainly.com/question/13604758

#SPJ4

In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.

The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.

Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.

Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.

For more such questions on Parabola

https://brainly.com/question/29635857

#SPJ11

Answer: 2 solutions

Step-by-step explanation:

To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)

Setting them equal, we get (180n-360)/n = 1680.

Multiplying by n on both sides, we get 180n-360 = 1680n.

Solving, we get 1500n = 360.

n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.

The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.

Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.

Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest:

A = P*e^(rt)

where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).

For Sophie's account, we have:

P = $92,000

r = 6 1/8% = 0.06125 (as a decimal)

t = 14 years

A = 92000*e^(0.06125*14)

A = $219,499.70 (rounded to the nearest cent)

For Damian's account, we have:

P = $92,000

r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)

t = 14*12 = 168 months

A = 92000*(1+0.005521)^168

A = $288,947.46 (rounded to the nearest cent)

Now we can subtract Sophie's final amount from Damian's final amount to find the difference:

Difference = $288,947.46 - $219,499.70

Difference = $69,447.76

Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.

The first 4 terms of the sequence represented by the expression 3n + 5

is 8, 11, 14 and 17.

Sequence:

In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given, aₙ = (3n+5).

First four terms can be obtained by putting n=1,2,3,4

a 1=(3×1+5) = 8

a 2 =(3×2+5) = 11

a 3 =(3×3+5) = 14

a 4 =(3×4+5) = 17

First 4 terms in the sequence are 8, 11, 14, 17.

Learn more about Sequence:

https://brainly.com/question/30262438

#SPJ4

Answer:

Correct option is C)

Simple interest =

100

3000×6×2

=360

Compound interest =3000(1+

100

6

)

2

−3000=18×20.6=370.8

∴ Difference is Rs.10.8.

you can convert this value to $$

or simply the answer will be 2. $10

(hob-evzw-zjw) come

Answer:

B is your answer.
10.80$ which you just round to 10. 10 is your answer.

Step-by-step explanation:

For simple interest, the formula is:

Simple Interest = Principal × Rate × Time

For compound interest, the formula is:

Compound Interest = Principal × (1 + Rate)^Time - Principal

Let's calculate the values:

Principal = $3,000

Rate = 6% or 0.06

Time = 2 years

Simple Interest = $3,000 × 0.06 × 2 = $360

To calculate compound interest, we need to use the formula:

Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000

= $3,000 × (1.06)^2 - $3,000

= $3,000 × 1.1236 - $3,000

= $3,370.80 - $3,000

= $370.80

The difference between simple and compound interest is:

$370.80 - $360 = $10.80

In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.

a) The probability that an individual will wait more than 7 minutes can be found as follows:

Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.

Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.

b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.

For more such questions on probability

https://brainly.com/question/24756209

#SPJ11


Answer:

The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.

Step-by-step explanation:

qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]

where r = |z| = magnitude of z and theta = arg(z) = argument of z.

Calculate the magnitude of z:

|r| = sqrt((3)^2 + (4)^2) = 5

And the argument of z:

theta = arctan(4/3) = 0.93 radians

Now, find the two square roots of z:

sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]

= +/- 1.58 * [cos(0.47) + i sin(0.47)]

= +/- 1.58 * [0.89 + i*0.46]

Using a calculator, simplify this expression to:

sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8

Answer:

Starting with the left side of the equation:

cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)

= cosθ + sinθ

Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.

To solve the question asked, you can say:  So, the other angle of the figure is 49 degree.

In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.  

here the given angles are as -

107 + (180-156) + x = 180

as total angle sum of a triangle is 180

so,

x = 180 - 131

x = 49

So, the other angle of the figure is 49 degree.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]

The probability that there are no repeated digits in a 3-digit pin number is 0.72.

Formula used:

[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]

There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.

Therefore, the total number of possible 3-digit pin numbers with no repeated digits is

[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]

The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].

Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]

Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.

Learn more about probability below

https://brainly.com/question/13604758

The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378

First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.

The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.

The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).

To learn more about probability refer :

https://brainly.com/question/21200970

#SPJ11

In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.

Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.

Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799

In light of this, the insurance provider should impose a premium of: Premium = 400/n

$501.88 is the premium ($Premium = 400/0.799)

To know more about return visit:

https://brainly.com/question/28562900

#SPJ1

The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0

Given that

Center = (5, 0)

Point on the circle = (5. 9/2)

The equation of a circle can be expressed as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

So, we have

(x - 5)² + (y - 0)² = r²

Calculating the radius, we have

(5 - 5)² + (9/2 - 0)² = r²

Evaluate

r = 9/2

So, we have

(x - 5)² + (y - 0)² = (9/2)²

Expand

x² - 10x + 25 + y² = 81/4

Multiply through by 4

4x² - 40x + 100 + 4y² = 81

So, we have

4x² + 4y² - 40x + 19 = 0

Hence, the equation is 4x² + 4y² - 40x + 19 = 0

Read more about circle equation at

https://brainly.com/question/1506955

#SPJ1

Answer:

436g

Step-by-step explanation:

1kg=1000g

3kg=3000g

3000+52=3052

3052÷7=436

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the lower right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]  ( cross- multiply )

x = 4[tex]\sqrt{2}[/tex]

Answer: 165

Step-by-step explanation:

55 x 3 = 165

As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.

Let Arun's age be m years.

Let Arun's mother's age be n years.

From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.

To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:

n / m = (4m + 6) / m

To solve for n, we can cross-multiply to get:

n = m x (4m + 6)

Expanding the right-hand side of the equation, we get:

n = 4m² + 6m

Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:

n = 2m(2m + 3)

This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.

If Arun is 3 years old (m = 15), then his mother's age would be:

n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4