Find 10^(5^101) (mod 21).

note: 10^(5^101) is not 10^(501)

Answer:

14.7 and 16.9

Step-by-step explanation:

We want to find the confidence interval for the mean when the population standard deviation [tex]\sigma[/tex], is known so we use the [tex]z[/tex] confidence interval for the mean.

The following assumptions are also met;

The z confidence interval for the mean is given by:

[tex]\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:<\:\mu\:<\bar X+z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )[/tex]

The appropriate z-value for 95% confidence interval is 1.96 (read from the standard normal z-distribution table)....See attachment.

From the question, we have [tex]n=49[/tex], [tex]\sigma=3.8[/tex] and [tex]\bar X=15.8[/tex]

We substitute all these values to get:

[tex]15.8-1.96(\frac{3.8}{\sqrt{49} } )\:<\:\mu\:<\bar 15.8+1.96(\frac{3.8}{\sqrt{49} } )[/tex]

[tex]15.8-1.96(\frac{3.8}{7 } )\:<\:\mu\:<15.8+1.96(\frac{3.8}{7} )[/tex]

[tex]14.7\:<\:\mu\:< 16.9[/tex] correct to one decimal place.

To calculate the 95% confidence interval for the population mean of truck weights on I-475, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / Square Root of Sample Size). Plugging in the given values, we find that the 95% confidence interval is approximately 14.7 to 16.9 tons.

To calculate the 95% confidence interval for the population mean, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / Square Root of Sample Size). In this case, the sample mean is 15.8 tons, the population standard deviation is 3.8 tons, and the sample size is 49. The critical value for a 95% confidence level is approximately 1.96. Plugging in these values, we get:

Confidence Interval = 15.8 ± (1.96) * (3.8 / √49)

Confidence Interval ≈ 15.8 ± (1.96) * (3.8 / 7)

Confidence Interval ≈ 15.8 ± (1.96) * 0.543

Confidence Interval ≈ 15.8 ± 1.06

Therefore, the 95% confidence interval for the population mean is approximately 14.7 to 16.9 tons.

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Answer:

81 lots of 5,000 square feet fits in the property.

Step-by-step explanation:

The first step is calculate the square feet of the minimum area:

[tex]50 \: feets \times 100 \: feet = 5,000 \:square \: feet[/tex]

Second, from the ten acres we subtract the 26,000 feets of roads:

[tex]1 \: acre = 60 \: feet \times 660\:feet = 43,560\:square\:feet\\43,560 \times 10 = 435,600\\435,600 - 26,000 = 409,600 \:square \: feet\:available[/tex]

Third, we divide the lot area over the available square feet

[tex]\frac{409,600}{5,000} = 81.92[/tex]

81 lots of 5,000 square feet fits in the property.

Answer:

So the y-intercept is 2 while the slope is -7/2.

Step-by-step explanation:

We are going to write this in slope-intercept form because it tells us the slope,m, and the y-intercept,b.

Slope-intercept form is y=mx+b.

So our goal is to solve for y.

-7x-2y=-4

Add 7x on both sides:

   -2y=7x-4

Divide both sides by -2:

   [tex]y=\frac{7x-4}{-2}[/tex]

Separate the fraction:

[tex]y=\frac{7x}{-2}+\frac{-4}{-2}[/tex]

Simplify:

[tex]y=\frac{-7}{2}x+2[/tex]

If we compare this to y=mx+b, we see m is -7/2 and b is 2.

So the y-intercept is 2 while the slope is -7/2.

Answer:

the slope m is:

[tex]m = -\frac{7}{2}[/tex]

The y-intersection is:

[tex]b = 2[/tex]

Step-by-step explanation:

For the equation of a line written in the form

[tex]y = mx + b[/tex]

m is the slope and b is the intersection with y-axis.

In this case we have the equation

[tex]-7x - 2y = -4[/tex]

So we rewrite the equation and we have to:

[tex]2y = -7x + 4[/tex]

[tex]y = -\frac{7}{2}x + 2[/tex]

the slope m is:

[tex]m = -\frac{7}{2}[/tex]

the y-intersection is:

[tex]b = 2[/tex]

To maximize the area, a 2m length of wire should be used for the square and the rest for the triangle. To minimize the area, nearly all the wire should be used for the triangle, leaving a negligible amount for the square.

The problem described is a classic example of Mathematics optimization. In this case, we have two geometric shapes, a square and an equilateral triangle. To answer this question effectively, one needs to understand the relationship between the perimeter and area of these two shapes.

For the square, the area is given by A=s2, where s is the length of a side. For the equilateral triangle, the area is given by A=0.433*s2, where s is the length of a side. We want to understand how to divide the 6m wire so that we either maximize or minimize the total area of these two shapes.

The total length of wire used is fixed at 6m. Let's designate x as the length of wire used for the square. This means the length for the triangle would be 6-x. For the maximum area, the result generally comes around 2m for the square and 4m for the triangle. However, for the minimum area, the answer would be essentially 0m for the square and 6m for the triangle.

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(a) For maximizing total area, use [tex]\( s \approx 3.76 \)[/tex] meters in square.
(b) For minimizing area, use [tex]\( s = 0 \)[/tex] for maximum utilization of wire to the triangle, least yielding area near zero or minimal non-zero.

(a) Maximizing the Total Area

To maximize the total area, we need to determine the length of the wire to be used for the square [tex](\( s \))[/tex] and the length used for the equilateral triangle [tex](\( t \))[/tex].

(b) Minimizing the Total Area

To minimize the total area, confirm whether interiors of boundary values might be critical points. Specifically, see if using all the wire for one shape minimizes the area.

Answer:

Height = 56 cm

Step-by-step explanation:  

let the width of photograph  be = 'w' cm

let the Height of photograph be = 'h' cm

Now it is given that height is 40 cm greater than width

=> h = w + 40 cm.............................(i)

Now it is given that area of photograph = [tex]896cm^{2}[/tex]

We know that area = [tex]Width^{}[/tex]x[tex]Height^{}[/tex]

Thus we have [tex]h^{}[/tex] x [tex]w^{}[/tex]=[tex]896cm^{2}[/tex]

Applying value of 'h' from equation i we get

[tex](w+40^{})[/tex]x[tex]w^{}[/tex]=[tex]896cm^{2}[/tex]

[tex]w^{2} +40w=896cm^{2}[/tex]

This is a quadratic equation in 'w' whose solution in standard form is given by

w=[tex]\frac{-b\mp\sqrt{b^{2}-4ac}}{2a}[/tex]

upon comparing with standard equation  we see that

a =1

b=40

c=896

applying values in the formula we get

w=[tex]\frac{-40\mp\sqrt{40^{2}-4\times 1\times- 896}}{2 \times1 }[/tex]

w1 = 16 cm

w2 = -56 cm

We discard -56 cm since length cannot be negative thus

width = 16 cm

Height = 40+16 cm = 56 cm  

"in front of the [tex]y,z[/tex] plane" probably means [tex]x\ge0[/tex], in which case

[tex]4x^2-4y^2-z^2=4\implies x=\sqrt{1+y^2+\dfrac{z^2}4}[/tex]

We can then parameterize the surface by setting [tex]y(u,v)=u[/tex] and [tex]z(u,v)=v[/tex], so that [tex]x=\sqrt{1+u^2+\dfrac{v^2}4}[/tex].

The part of the hyperboloid in front of the yz-plane is represented parametrically by x(u,v)=2*cos(u), y(u,v)=-2*sinh(v), and z(u,v)=sinh(u).

The surface of the hyperboloid lies in front of the yz-plane and is described by the equation 4x² − 4y² − z² = 4. A common form of parameterization for this type of surface uses hyperbolic functions. Therefore, a parametrization for the part of the hyperboloid lying in front of the yz-plane can be given in terms of u and v as follows:

In this parametric form, u can range over all real numbers to cover the entire surface in front of the yz-plane, while v can oscillate between -∞ to +∞ to provide a full representation of the surface.

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Answer: 1406

Step-by-step explanation:

Given Table :

Admissions   Probability

1,040                0.3

1,320                0.2

1,660                0.5

Now, the expected number of admissions for the fall semester is given by :-

[tex]E(x)=p_1x_1+p_2x_2+p_3x_3\\\\\Rightarrow\ E(x)=0.3\times1040+0.2\times1320+0.5\times1660\\\\\Rightarrow\ E(x)=1406[/tex]

Hence, the expected number of admissions for the fall semester = 1406

Answer:

The probability is 0.001001.

Step-by-step explanation:

Players are selling raffle tickets for $500 worth of groceries at a local store.

You bought a $1 ticket for yourself and one for your mother.

The children eventually sold 1000 tickets.

We have to find the probability that you will win first place while your mother wins second place.

We can find this as :

P(winning) =[tex]1/999=0.001001[/tex]

Answer:

The expected earnings of the attendant for this particular period are: $12.66

Step-by-step explanation:

We have to calculate expected mean here:

So,

E(x) = ∑x*f(x)

[tex]E(X) = \{(7 * \frac{1}{12} )+(9 * \frac{1}{12} )+(11 * \frac{1}{4} )+(13 * \frac{1}{4} )+(15 * \frac{1}{6} )+(17 * \frac{1}{6})\\= 0.58+0.75+2.75+3.25+2.5+2.83\\=12.66\ dollars[/tex]

Therefore, the expected earnings of the attendant for this particular period are: $12.66 ..

Considering the discrete distribution, it is found that the attendant’s expected earnings for this particular period are of $12.67.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence, considering the probability of each earning amount, the expected earnings are of the attendant is given by:

[tex]E(X) = 7\frac{1]{12} + 9\frac{1}{12} + 11\frac{1}{4} + 13\frac{1}{4} + 15\frac{1}{6} + 17\frac{1}{6} = \frac{7 + 9 + 33 + 39 + 30 + 34}{12} = 12.67[/tex]

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Answer: Inductive argument.

Step-by-step explanation:

The arguments are of two types : Inductive  (uses pattern or signs to get a conclusion ) and deductive (Uses general facts or defines or theory to decide any conclusion)

The given argument : The road map indicates that it is 10 miles from Vacaville to Fairfield. From the information on the road map, it follows that Vacaville and Fairfield really are 10 miles apart.

The given argument is the argument that is based on signs (maps are signs) which comes under inductive arguments.

Thus, the given argument is an inductive argument.

The argument which concludes that Vacaville and Fairfield are 10 miles apart based on the information from a road map is an example of a deductive argument, specifically, a syllogism.

The argument you're describing here falls under the category of a deductive argument. Specifically, it is an example of a syllogism, which is a form of deductive reasoning consisting of two premises and a conclusion. The premises in this case are 'The map says there are 10 miles between Vacaville and Fairfield' and 'The map is correct'. Therefore, the conclusion is 'There are 10 miles between Vacaville and Fairfield'.

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Answer:

Elga is 37 years old.

Step-by-step explanation:

Let 'x' be the age of elga.

Alvin's age is: x + 15

Given that the sum of their ages is 89, we have that:

x + 15 + x = 89

2x = 89 - 15

2x = 74

x = 74/2 = 37

Elga is 37 years old.

Answer:

Elga is 37 years old.

Step-by-step explanation:

Alvin (A) is 15 years older than Elga (E).

The sum their anges (A and E) is 89.

So the system we have is:

A=15+E

A+E=89

We are going to input 15+E for A in A+E=89 since first equation says A+15+E.

A+E=89 with A=15+E

(15+E)+E=89

15+E+E=89

15+2E=89

Subtract 15 on both sides:

2E=89-15

2E=74

Divide both sides by 2:

2E/2=74/2

E=74/2

E=37

Elga is 37 years old.

A=15+E=15+37=52 so Alvin is 52 yeard old.

52+37=89.

and

52=15+37.

Answer:

a) The probability is the number of favorable outcomes divided by the number of possible outcomes. There are 52 cards in a deck.

Step-by-step explanation

hope this helps.

Answer:

The monthly payment is $35.10.

Step-by-step explanation:

p = 510

r = [tex]13.9/12/100=0.011583[/tex]

n = [tex]12+4=16[/tex]

The EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

Now putting the values in formula we get;

[tex]\frac{510\times0.011583\times(1+0.011583)^{16} }{(1+0.011583)^{16}-1 }[/tex]

=> [tex]\frac{510\times0.011583\times(1.011583)^{16} }{(1.011583)^{16}-1 }[/tex]

= $35.10

Therefore, the monthly payment is $35.10.

Answer:

The number would be 11.

Step-by-step explanation:

Dividend = Divisor × Quotient + Remainder

Given,

"n" is divided by 3, the remainder is 2,

So, the number = 3n + 2,

"n" is divided by 5, the remainder is 1,

So, the number = 5n + 1

Thus, we can write,

3n + 2 = 5n + 1

-2n = -1

n = 0.5,

Therefore, number must be the multiple of 0.5 but is not divided by 3 or 5,

Possible numbers = { 1, 2, 4, 7, 8, 11...... }

Since, 1 and 4 do not give the remainder 2 after divided by 3,

And, 2, 7 and 8 do not give the remainder 1 after divided by 5,

Hence, the least positive integer number that gives remainder 2 and 1 after divided by 3 and 5 respectively is 11.

Answer:

1388 dollars 77 cents.

Step-by-step explanation:

Since, the amount formula in compound interest is,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where, P is the principal amount,

r is the annual rate,

n is the number of periods in a year,

t is the number of years,

Given,

P = $ 1,282,

r = 1 % = 0.01,

n = 353,

t = 8 years,

Hence, the amount after 8 years would be,

[tex]A=1282(1+\frac{0.01}{353})^{2824}[/tex]

[tex]=\$ 1388.77244711[/tex]

[tex]\approx \$ 1388.77[/tex]

= 1388 dollars 77 cents.

Answer:

[tex]A_{38} = 350[/tex]

Step-by-step explanation:

The 5th term of the arithmetic sequence is 53. We can write the equation:

[tex]a + 4d = 53...(1)[/tex]

The 6th term of the arithmetic sequence is 62. We can write the equation:

[tex]a + 5d = 62...(2)[/tex]

Subtract the first equation from the second one to get:

[tex]5d - 4d = 62 - 53[/tex]

[tex]d = 9[/tex]

The first term is

[tex]a + 4(9) = 53[/tex]

[tex]a + 36 = 53[/tex]

[tex]a = 53 - 36[/tex]

[tex]a = 17[/tex]

The 38th term of the sequence is given by:

[tex] A_{38} = a + 37d[/tex]

[tex]A_{38} = 17+ 37(9)[/tex]

[tex]A_{38} = 350[/tex]

Answer:

[tex]A_{38}=386[/tex]

Step-by-step explanation:

We have been given an arithmetic sequence gas [tex]A_1,A_2,A_3,A_4[/tex] as :53,62,71,80. We are asked to find [tex]A _{38}[/tex].

We know that an arithmetic sequence is in format [tex]a_n=a_1+(n-1)d[/tex], where,

[tex]a_n[/tex] = nth term,

[tex]a_1[/tex] = 1st term of sequence,

n = Number of terms,

d = Common difference.

We have been given that 1st term of our given sequence is 53.

Now, we will find d by subtracting 71 from 80 as:

[tex]d=80-71=9[/tex]

[tex]A_{38}=53+(38-1)9[/tex]

[tex]A_{38}=53+(37)9[/tex]

[tex]A_{38}=53+333[/tex]

[tex]A_{38}=386[/tex]

Therefore, [tex]A_{38}=386[/tex].

To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Using the formula for permutations, it is found that there are 3003 different ways the members of the cabinet can be appointed.

To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Since there are 15 eligible candidates for the remaining 5 spots, and the order in which the members are appointed matters, we can use the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of candidates and r is the number of spots available. In this case, we have:

P(15, 5) = 15! / (15 - 5)!

Calculating this gives us:

P(15, 5) = 15! / 10!

P(15, 5) = (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)

P(15, 5) = 3003

Therefore, there are 3003 different ways the members of the cabinet can be appointed.

Answer:

2 possible towers

Step-by-step explanation:

2 possible towers

Step-by-step explanation:

The height of the tower required is 10 cm, and that height may be obtained by 'x' number of blocks A and 'y' number of blocks, knowing its respective height, so 'x' and 'y' must accomplish the equation:

[tex] 10 = 2x + 3y [/ tex]

The maximum value for 'x' is 5; a higher value will give a higher than 10 cm height as a result. So, the possible answers for 'x' are: (0,1,2,3,4,5). Note that both 'x' and 'y' values ​​must be integers, and the only numbers that satisfy that condition are (x = 2, y = 2) and (x = 5, y = 0). The other options for 'x' will give a noninteger value for 'y' because of the equation above.

So, there are just two options.

Answer: 1.75

Step-by-step explanation:

To find the value of [tex]\sqrt{3}[/tex]

[tex]\text{Let , }y=\sqrt{x}[/tex]

[tex]\text{And Let x = 4 and }\Delta x=-1[/tex]

Now,

[tex]\Delta y=\sqrt{x+\Delta x}-\sqrt{x}\\\\=\sqrt{3}-\sqrt{4}=\sqrt{3}-2\\\\\Rightarrow\ \sqrt{3}=\Delta y+2[/tex]

Since dy is approximately equals to [tex]\Delta y[/tex] then ,

[tex]dy=\dfrac{dy}{dx}\Delta x\\\\=\dfrac{1}{2\sqrt{x}}\times(-1)=\dfrac{1}{2\sqrt{4}}\times(-1)=-0.25[/tex]

Thus , the approximate value of  [tex]\sqrt{3}=-0.25+2=1.75[/tex]

Answer:

yes they are linearly independent

Step-by-step explanation:

By definition of linear dependence we have if  f(x) and g(x) be 2 functions

if they are linearly dependent then we can write

f(x) = αg(x)...........(i) where α is an arbitrary constant

in our case we can see that the range of sin(x) is only from [-1,+1] while as [tex]e^{x}[/tex] has range from [0,∞]

thus we cannot find any value of α for which (i) is valid

The situation can be modelled by the linear function r = $5.50t/10 + $8, where 't' is time and 'r' is cost. For a $25 rental, approximately 31 minutes can be rented. A linear model is appropriate as the cost increases steadily with time.

In this case, the independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. Here, 't' is the time on the computer, and 'r' is the total cost.

The linear function for this situation would be r = $5.50t/10 + $8. Note that $5.50t/10 is the cost per minute (as the rate is $5.50 every 10 minutes), and $8 is the setup fee.

To calculate how much time can be rented for $25, we solve for 't' when r = $25. $25 = $5.50t/10 + $8 gives t = (25 - 8) x 10/5.5, or roughly t = 31 minutes.

A linear model is reasonable for this situation as the cost of renting the computer increases steadily with time.

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The correct option is B.  The independent variable is time​ (t), in​ minutes, and the dependent variable is rental cost​ (r), in dollars. The linear function that models this situation is r equals . The cost equation is r = 8 + 0.55t, with t as the independent variable and r as the dependent variable. For $25, approximately 31 minutes can be rented.

The given situation can be modeled by a linear function where the total rental cost depends on the time rented. Here, the independent variable is time (t) in minutes, and the dependent variable is rental cost (r) in dollars.

Option B: The linear function that models this situation is:

→ r = 8 + 0.55t

To find the time that can be rented for $25:

→ Set r = 25 and solve for t:

→ 25 = 8 + 0.55t

Subtract 8 from both sides:

→ 17 = 0.55t

Divide both sides by 0.55:

→ t = 30.91 (approximately)

Rounding to the nearest minute, the time that can be rented is 31 minutes.

Answer:

Step-by-step explanation:

If each day equal chance then p = Prob that a person is borne on a particular day = 1/365

Each person is independent of the other and there are two outcomes either borne in July or not

p = prob for one person not borne in July = (365-31)/365 = 334/365

a)Hence prob that no one from n people borne in July = [tex](\frac{334}{365} )^n[/tex]

b) p = prob of any one borne in July or Aug = [tex]\frac{(31+31) }{365} =\frac{62}{365}[/tex]=0.1698

X- no of people borne in July or Aug

n =15

P(X>=2) =[tex]15C2 (0.1698)^2*(1-0.1698)^{13} +15C3 (0.1698)^3*(1-0.1698)^{12} +...+15C15 (0.1698)^{15}[/tex]

=0.7505

Answer: [tex]\dfrac{1}{59049}[/tex]

Step-by-step explanation:

The number of keys on the keypad = 9

The number of digits in the required pin code = 4

If repetition is allowed then , the number of possible codes will be

[tex](9)^5=59049[/tex]

Then , the probability that the choosen pin code is correct is given by :-

[tex]\dfrac{1}{59049}[/tex]

The probability of Geometric distribution formula :

[tex]P(X=x)=(1-p)^{x-1}p[/tex], where p is the probability of success and x is the number of attempt.

Using geometric probability , the probability of a correct guess on the first​ try is given by :-

[tex]P(X=1)=(1-\dfrac{1}{59049})^{1-1}(\dfrac{1}{59049})=\dfrac{1}{59049}[/tex]

Answer:

Skewed

Step-by-step explanation:

A project manager can interpret several things in a histogram. If something unusual happening, the histogram is said to Skewed. When the histogram is Skewed it means that many of the values of the graph are falling on only one side of the mean. It can be either on left side( left skewed) or on the right side called right skewed

Check the Wronskian determinant:

[tex]W(e^{x/2},xe^{x/2})=\begin{vmatrix}e^{x/2}&xe^{x/2}\\\frac12e^{x/2}&\left(1+\frac x2\right)e^{x/2}\end{vmatrix}=\left(1+\frac x2\right)e^x-\frac x2e^x=e^x\neq0[/tex]

The determinant is not zero, so the solutions are indeed linearly independent.

To verify a fundamental set of solutions for the given differential equation, one must demonstrate that the functions e^{x/2} and xe^{x/2} satisfy the equation and that their Wronskian is non-zero, indicating linear independence.

The student's question pertains to verifying whether a given set of functions, e^{x/2} and xe^{x/2}, form a fundamental set of solutions for the differential equation 4y'' - 4y' + y = 0. A set of solutions is fundamental if the functions are linearly independent and satisfy the differential equation. Linear independence can be proved by calculating the Wronskian, which must be non-zero over the given interval. To show that these functions are solutions, they must be substituted into the differential equation to check if it holds true.

To check for linear independence, we can compute the Wronskian:

which simplifies to e^{x} (1 - (x/2)) that is non-zero for all real numbers x, proving linear independence.

To verify if the functions satisfy the differential equation, we substitute each function into the equation. The derivatives of e^{x/2} and xe^{x/2} are taken, and then these are plugged into the equation to confirm that it yields zero.

Answer:

The total number of luxury cars are 43.

Step-by-step explanation:

Consider the provided information.

It is given that there are 260 cars in the parking lot out of 1/2 are SUVs.

Total number of SUV cars = [tex]260\times{\frac{1}{2}=130}[/tex]

Out of 260 cars 1/3 are sub compact cars.

Total number of sub compact cars = [tex]260\times{\frac{1}{3}}=86.66\approx{87}[/tex]

Therefore the total number of luxury cars are:

260 - 130 - 87 = 43

Therefore, the total number of luxury cars are 43.

Answer:

d

Step-by-step explanation:

Self-interest assumption means that an action taken by a person can be termed as self interest if he or she has any basis or reason behind taking such action.  The individual always looks for profit and self benefit.Hence they can be treated as selfish.

So, if a person sacrifices his or her own interest so that others can be punished then such act can be termed as self-interest as person concerned is taking such action with a reason behind such act.

Hence, the correct answer is the option (d).