find an equation of the tangent line to the given curve at the specified point. y = e^x /x , at the point (1, e)
An equation of the tangent line to the given curve at the specified point will be y = e(x - 1) + e.
Given the equation y = e^x /x and the point (1, e), the goal is to find an equation of the tangent line at this point.
To do this, we need to find the derivative of the equation at the point (1, e). Taking the derivative with respect to x gives us:
y' = (e^x * (1 - 1/x) - e^x/x^2) / x^2
Since we are looking for the derivative at the point (1, e), we can plug in x = 1 to get the derivative at this point:
y' = (e - e/1) / 1^2
y' = e
Therefore, the equation of the tangent line at the point (1, e) is y = e(x - 1) + e.
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4x+9=101 what is the value of x
Answer: x = 23
Step-by-step explanation:
Move all terms that don't contain
x
to the right side and solve.
Hope this helps :)
the radius of a sphere is increasing at a constant rate of 8 meters per second. at the instant when the radius of the sphere is 22 meters, what is the rate of change of the volume? the volume of a sphere can be found with the equation v
So, on solving the provided question we can say that the rate of change of the volume with respect to radius = [tex]1770 = 4/3 \pi r^3S = 4 \pi r^2[/tex] [tex]dS/dt = 8 \pi r dr/dt[/tex]
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.
Taking the derivative of the volume formula
[tex]DV/dt = 4\pi r*2 dr/dt\\5471 = 4 \pi r*2 dr/dt[/tex]
This equation r and dr/dt
We can solve for r...
sphere is 1770 cubic inches
[tex]1770 = 4/3 \pi r^3S = 4 \pi r^2dS/dt = 8 \pi r dr/dt[/tex]
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For every pound a company spends on advertising, it spends £0.24 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answer:
25:6
Step-by-step explanation:
1/0.24
100/24
50/12
25/6
h(x)=−3x+1
g(x)=2x
Find h(g(x))
Answer:
h(g)x)) = - 6x + 1
Step-by-step explanation:
to find h(g(x)), substitute x = g(x) into h(x) , that is
h(g(x))
= h(2x)
= - 3(2x) + 1
= - 6x + 1
What is half of 1 2 US?
Answer: 6
12 divided by 2 is 6 or 6 + 6 = 12
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 7 0-9 3 10 9 ; 2=lambda = 7, 10 0 0 10
The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).
what is matrix ?Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array. In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.
given
Eigen values ( λ )
| A - λI | = 0
= ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0
= λ = 7 , 11 , 11
eigen vector for λ = 7
( A - IB ) X = 0
= Let y = 1 , n1 = ( -1 1 0 )
eigen vector for λ = 11
( A - λI ) X = 0
n2 = ( 0 1 0 ) let n3= ( -2 0 1 )
D = ( 7 0 0 , 0 11 0 , 0 0 11 )
The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).
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Write a method that takes two circles, and returns the sum of the areas of the circles. This method must be named areaSum() and it must have two Circle parameters. This method must return a double. For example suppose two Circle objects were initialized as shown:
The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double.
Circle c1 = new Circle(5);
Circle c2 = new Circle(7);
[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]
1. Create a public static method named areaSum that takes two Circle objects as parameters.
2. The method should return a double.
3. Inside the method, use the getArea() method of the Circle class to get the area of both circles.
4. Return the sum of the areas of both circles.
5. The method should look like this:
[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]
The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double. The method uses the getArea() method of the Circle class to get the area of both circles and returns the sum of the areas.
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The input and output values of a function f (x) are shown in the table.
X
-4
-3
-2
-1
0
f (x)
2
1
0
1
2
If g (x) = 2f (x), then which table shows the input and output values of g (x)?
The table which shows the input and output values of g (x) is,
f (x) g(x)
2 4
1 2
0 0
1 2
2 4
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The input and output values of a function f (x) are shown in the table.
X f (x)
-4 2
-3 1
-2 0
-1 1
0 2
Here, We have;
⇒ g (x) = 2f (x),
Hence, The table which shows the input and output values of g (x) is,
f (x) g(x)
2 2×2 = 4
1 1×2 = 2
0 0×2 = 0
1 2×1 = 2
2 2×2 = 4
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12 in ,10 in 8 in what type of triangle is
The type of triangle that is given by the dimensions, is a Scalene triangle.
What are types of triangles ?A scalene triangle has sides that are all measured differently. In such a triangle, no side will be the same length as any other side. Every interior angle in a scalene triangle is also unique.
The lengths of two of the three sides in an isosceles triangle are equal. The angles that are opposite the equal sides are therefore equal. An isosceles triangle, in other words, has two equal sides and two equal angles.
Each side of an equilateral triangle has an equal length. Each internal angle in this scenario will be 60 degrees in length. An equilateral triangle is often referred to as an equiangular triangle since its angles are equal.
The dimensions here are not the same which means that all the sides are not equal and so this is a scalene triangle.
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Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
10 jars
Answer: I'm pretty sure there was suppose to be a 4th option that is not included here, none of these are correct, Lorraine can fill 8 jars.
Step-by-step explanation: First, we need to convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then we divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
⚠️Please verify inthe comments if there was indeed a 4th option⚠️
Answer:
8
Step-by-step explanation:
convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
whats the answer for this question
By the Pythagorean theorem, [tex]y=\sqrt{6^2-3^2}=3\sqrt{3}[/tex].
By the geometric mean theorem, [tex]y^2=3x \implies x=9[/tex].
Answer the screenshot
The polynomial of degree 3 with the given zeros and a leading coefficient of 1 is:
P(x) = x^3 - 5x^2 - 14x
How to find the polynomial?Remember to do one post per question, I will answer the first one.
We know that for a polynomial of degree N with the given N zeros:
{x₁, x₂, ..., xₙ}
We can write the polynomial as:
P(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Where the leading coefficient is a.
Here the degree of the polynomial is 3, and the 3 zeros are:
-2, 0, 7
And the leading coefficient is 1.
Then we can write it as:
P(x) = 1*(x + 2)*(x - 0)*(x - 7)
P(x) = (x^2 + 2x)*(x - 7)
P(x) = x^3 + 2x^2 - 7x^2 - 14x
P(x) = x^3 - 5x^2 - 14x
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Help would be greatly appreciated. Image below.
Answer: Part A. a student must find the missing length by using the Pythagorean theorem.
The answer should come out to be x=2√26 or x=−2√26 (Decimal: 10.19803902…, -10.19803902…) or (Rounded to the nearest tenth: 10.20, -10.20)
Step-by-step explanation:
Let's make x the missing length. The Pythagorean theorem says the way to set up this equation is the leg^2 + leg^2 = hypotnues^2.
Set up the problem and solve, I'll show you how to do it: x²+11²2=15²
Step 1: Simplify both sides of the equation.
x² + 121=225
Step 2: Subtract 121 from both sides.
x² + 121−121=225−121
x² = 104
Step 3: Take square root.
x = ± √104
The answer should come out to be x = 2√26 or x = −2√26 (Decimal: 10.19803902…, -10.19803902…) or (Rounded to the nearest tenth: 10.20, -10.20)
alberto sold half of his comic books. and then bought nineteen more. he now has 43. with how many did he start with
Answer:
48
Step-by-step explanation:
First you should subtract 43 and 19
then you get a answer 24
Multiply it by 2
you get 48
Answer:
no. of books =48 books
Step-by-step explanation:
lets say that he started with
x
books so,
(X÷2)-19=43
X÷2=24
X=48
Frank joined a fitness club. He paid a $50 registration fee, and dues are $12 per month. Which expression can be used to find the average monthly cost of an x-month membership at the club? y=50+12/xy=50+12x/x y= 50x+12/x y= (50+12)x/x
As per the unitary method, the expression can be used to find the average monthly cost of an x-month membership at the club is written as
(50 + 12x)/x.
The expression in math is known as the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Here we have given that Frank has to pay $50 as the registration fee and here we also given that this amount is compulsory to be paid
And we have also given that dues for $12 months is calculated as.
Then let us consider that the due to be paid every month be $x then the dues to be paid for 12 months will be 12x
Then the expression for the average monthly cost for x-month will be written as,
=> expression = total cost / total months
Then we have to apply the values on it, then it can be rewritten as,
=> (50 + 12x)/x
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As a farmer, suppose you want to fence off a rectangular field that borders a river. You wish to find out the dimensions of the field that occupies the largest area, if you have 1500 feet of fencing. Remember that a square maximizes area, so use a square in your work.
-Draw several diagrams to express the situation and calculate the area for each configuration, then estimate the dimension of largest possible field.
-Find the function that models the area in terms of one of its sides.
-Find the point that maximizes the function you found in the second bulleted item.
-Calculate the area of the field at the point you found in the third bulleted item, and then compare your results with the results in the first bulleted item.
According to the area of rectangle, the maximum area is given by a 300 × 500 ft rectangle that is being half of a square
The formula to calculate the area of square is written as
A = l x b
where l refers the length and b refers the breadth in rectangle.
Here we have know that if there were no river then the maximum area would be given by a square configuration since increasing the length and decreasing the width of a square by the same value t will decrease the area by a square with sides of length t.
Here we have to add the river on one side.
As we all know that we need to fence in a rectangle on one side of the river and then here we have imagine an identical rectangle on the other side of the river.
Then the maximum area is given when the two rectangles form a square that is when we have a rectangle twice as long as wide is written as
=> 1500 feet of fence then the rectangle has fenced sides written as 500feet and 300feet.
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A man is 38 years old, and his daughter is 14 years old. How many years will it be before the man's age is just twice the age of his daughter?
This is an algebraic word problem and it evaluated to be 10 years time before the age of the man will be twice the age of the daughter.
Algebraic word problemIn algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.
We shall represent the number of years it will be before the age of the man will be twice the age of the daughter with the letter x so that;
38 + x = 2(14 + x) {open bracket}
38 + x = 28 + 2x
38 - 28 = 2x - x {collect like terms}
10 = x
also x = 10.
Therefore, the agebraic word problem have a solution of 10 years before the age of the man will be twice the age of the daughter.
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your favorite restaurant has a promotion where you can win free food. you will roll 2 dice. the sum of the 2 dice will determine which prize you receive. 2-column table with 11 rows. column 1, outcome, entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. column 2, probability, entries startfraction 1 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 6 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 1 over 36 endfraction. which scenario uses the addition rule for mutually exclusive events? p(rolling a sum of 4) p(rolling a sum of 4 or rolling a sum of 5) p(rolling a sum of 12 or rolling a double 6) p(rolling a sum of 11 and rolling a sum of 12)
Answer: P(rolling a sum of 4 or rolling a sum of 5)
Step-by-step explanation: edge2023
The scenario that uses the addition rule for mutually exclusive events is:
p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)
This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.
The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36
The other scenarios do not use the addition rule for mutually exclusive events:
p(rolling a sum of 4) is a single event and does not involve a second event.
p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.
p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.
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Based upon the input from Units 1 and 2, you have just received your next assignment that will contribute to your next decision. For the outdoor sporting goods client, based upon your prior decision on whether or not to expand to the next market or retain your current position, justify your decision further utilizing the chi-square distribution tool. One key criterion point: You do not have adequate data to formulate a full chi-square for the outdoor sporting goods client. However, you have sufficient data to initiate this process. You are charged to demonstrate the initial steps of a nonparametric test that are qualitative. Utilizing the null and alternative hypotheses, further present your justifications for your selection and what it means beyond the mere formulas. What is this going to tell the Board of Directors and contribute to the decision-making process? The following information may be helpful in understanding chi-square and hypothesis testing: Please review this helpful video. The presenter uses flipping a coin and rolling a die. These are examples and analogies used in the CTU resources. The following are assumptions that might make the assignment more helpful and make the responses more uniform: Continue to utilize the Big D scenario. Work under the assumption that the sample is based upon 2 different proposed product lines. Additionally, work under the assumption that the same demographics are utilized for each product.
My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.
Because we put our alternative hypothesis equal to what we wish to show, you should continue to hold the stance you already hold. The opposite hypothesis, or null hypothesis, is a claim that there is no difference. For instance,There is no discernible difference between the mean and sample population, according to the null hypothesis.Alternative Hypothesis H1: The mean and sample population differ significantly.Level of significance: A: If there is no difference in the sample as well as population means, there is a 5% chance that the null hypothesis will be rejected. In a non-parametric test, rankings are considered as a test statistic after being translated from the observed sample. We utilize the rankings to calculate the test statistic in non-parametric testing. The choice of accepting or the null hypothesis being rejected will be decided when the levels of liberty and crucial values have been defined. Chi square is used since there are only two choices to compare. As soon as we get our data, we can calculate the chi squared value x2 and determine the crucial values from table of freedom levels with 95% certainty.To know more about hypothesis visit:
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if the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score e(x y)?
The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y).
e(x+y)
e = expected
x = points earned on part 1
y = points earned on part 2
So, the expected recorded score is the total of points earned on both parts: e(x+y).
The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y). This formula is useful for quickly calculating the total score of an assignment, allowing the grade book to be updated quickly and accurately.
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Think about how you can use a graph to help you out in someway in your daily life. what data from your life are you going to use? what kind of graph would you use to track this data? how will you use this graph to help you? explain.
The graph to represent this data is pie chart.
What is a Graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
The graph used to represent the data is shown in the figure;
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the length of a rectangle is 4 inches shorter than its width. the perimeter of the rectangle is 80 inches. what are the length and width of the rectangle?
If length of a rectangle is 4 inches shorter than its width and perimeter of rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .
The Perimeter of rectangle can be calculated by using formula : [tex]2(l+w)[/tex] ;
let the width of rectangle be = w ,
it is given that the length is 4 inches shorter than width , that means ;
the width of rectangle is ⇒ [tex]w-4[/tex] ;
So , the perimeter becomes ⇒ [tex]80=2(l+w)[/tex]
⇒ [tex]80=2(w-4+w)[/tex]
⇒ [tex]40=2w-4[/tex] ;
⇒ [tex]2w=44[/tex] ;
⇒ [tex]w=22[/tex] ;
and substituting [tex]w=22[/tex] , we get [tex]l=22-4 = 18[/tex] in
Therefore , the length of rectangle is 18 in and width is 22 in .
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Marcus is making homemade barbecue sauce. The recipe calls for 3 cups of ketchup for every 1/2 of mustard. What is the rate in cups of ketchup per cup of mustard
The rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.
What are expression models?The expression model is defined as the model of the given situation in the form of an expression using variables and constants.
Here,
The recipe calls for 3 cups of ketchup for every 1/2 of mustard.
Now,
The rate in cups of ketchup per cup of mustard = ketchup/mustard
= 3 / [1/2]
= 3 × 2 = 6 / 1
Thus, the rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.
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a closed rectangular container with a square base is to have a volume of 2000 cm3. it costs twice as much per square centimeter for the top and bottom as it does for the sides. find the dimensions of the container of least cost
Answer:
C(220^2 + 420*2.5) = 800C + 200C = 1000C
Step-by-step explanation:
Let the length of the square base be L cm, and then the height of the container will be H cm. The volume of the container is given by the formula V = L^2 * H = 2000 cm3.
The cost of the top and bottom is 2C, where C is the cost per square centimeter for the sides. The cost for the top and bottom is 2 * L^2 * C. The cost for the sides is 4LH * C.
So the total cost is C(2L^2 + 4LH).
We can use the volume equation to find the height in terms of the length (H = 2000/L^2) and substitute it back into the cost equation.
C(2L^2 + 4L(2000/L^2)) = C(2L^2 + 8000/L)
To minimize the cost, we need to minimize the function 2L^2 + 8000/L, so we need to find the value of L that minimizes it.
Take the derivative of the function and make it equal to 0, then solve for L.
d/dL(2L^2 + 8000/L) = 4L - 8000/L^2 = 0
4L = 8000/L^2
L^3 = 2000
L = (2000)^(1/3) = 20
Therefore, the square base of the container should have a length of 20 cm, and the height of the container will be 2000/L^2 = 2000/20^2 = 2.5 cm.
The lowest cost would be C(220^2 + 420*2.5) = 800C + 200C = 1000C
a machine manufactures a part in 11 minutes. a newer machine can manufacture the same part 1.5 minutes faster. write an equation that models how many parts p each machine can manufacture in any number of minutes m
The equation that models how many parts p each machine can manufacture in any number of minutes m is m = 1.5p
The term equation in math is defined as a mathematical sentence that has two equal sides separated by an equal sign
Here we have given that a machine manufactures a part in 11 minutes and here we have also know that a newer machine can manufacture the same part 1.5 minutes faster.
Let us consider that p refers the number of parts for old machine and m refers the time taken for manufacturing.
Then the equation can be written as,
=> m = 1.5p
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Determine the probability of tossing two heads in a row by:
Listing all possible outcomes ((H,T), (H,H) and so on) and circling the desired outcome.
Calculating desired outcome
--—----------------
Total number of outcomes
Answer:
4
Step-by-step explanation:
(H,H) (T,T)(T,H)(H,T)
A coin-operated coffee vending machine dipene, on the average, 6 oz of coffee per cup. Can thi tatement be true of a vending machine that occaion
It is possible for this statement to be true for a vending machine that occasionally dispenses more or less than 6 oz of coffee per cup.
The term "on average" or "on the average" refers to the mean or expected value of a distribution. The vending machine may have some variations in the amount of coffee it dispenses, but on average it dispenses 6 oz of coffee per cup.
It is possible that the vending machine may dispense more or less than 6 oz of coffee per cup due to machine variations, incorrect calibration, or maintenance issues. However, as long as the mean or average amount of coffee dispensed over a certain period of time is 6 oz per cup, the statement is considered true.
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What are the 5 methods of solving a linear equation?
There are mainly 6 methods used to solve a linear equation depending on the complexity and form of the equation.
A linear equation is represented as the equation of first order or variable having power 1 and can be written in the general form of Ax+By+C= 0, where A, B, and C are real numbers. And its simplest form is y= mx+b, where m is the slope or ratio of change in y and change in x, and b is the y-intercept. The following are the methods used to solve the linear equation:
1. Graphical Method.
2. Elimination Method.
3. Substitution Method.
4. Cross Multiplication Method.
5. Matrix Method.
6. Determinants Method
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a classroom of children has 11 boys and 18 girls in which five students are chosen to do presentations. what is the probability that at least four boys are chosen?
The total Number of ways to select five students out of 11 boys and 18 girls will be=104642
We have, total number of boys = 11, while the total number of girls = 18
Let us assume that,
X = total number of boys chosen
As it is given,
P(X>=4)=1
-P(X<=3)
Where, P(at most 3 boys are chosen) needs to be found out
As we know,
Here, the total number of ways to get at most 3 boys= Number of ways to get three boys and two girls + number of ways to get one boy and four girls + Number of ways to get two boys and three girls + Number of ways to get zero boys and five girls
Making the combination as per above arrangements:
We will get it as:
=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5
As we know,
The formula of combination is:
[tex]$${ }_n C_r=\frac{n !}{r !(n-r) !}$$[/tex]
[tex]${ }_n C_r=$[/tex] number of combinations
n= total number of objects in the set
r= number of choosing objects from the set
So, applying the concept of combination in the above,
=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5
[tex]= \frac{11!}{8! \times 3!} \times \frac{18!}{16! \times 2!}+\frac{11!}{9! \times 2!} \times \frac{18!}{15! \times 3!}+\frac{11!}{10! \times 1!} \times \frac{18!}{14! \times 4!}+\frac{11!}{11! \times 0!} \times \frac{18!}{13! \times 5!}[/tex]
[tex][\frac{11 \times 10\times9\times8! }{8!\times 6} \times \frac{18\times17\times16!}{16!\times2}]+[\frac{11\times10\times9!}{9!\times2} \times \frac{18\times17\times16\times15!}{15!\times6}]+[\frac{11\times10!}{10!} \times \frac{18\times17\times16\times15\times14!}{14!\times24}]+[\frac{1}{1} \times \frac{18\times17\times16\times15\times14\times13!}{13!\times120}][/tex]
[tex]=(165 \times153)+(55\times816)+(11\times3060)+(1\times856.8)[/tex]
=25245+44880+33660+856.8
=104641.8 = 104642 (approx)
For more questions on Permutation and Combination
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