Phil takes out a bank loan of $150 000 to buy a house, at an annual interest rate of 3.5%. The interest is calculated at the end of each year and added to the amount outstanding. Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.

Answer:

Height: 6

Base: 14

Step-by-step explanation:

Area=42 in^2

height=x-1

base=2x

bh/2=42

Substitute in the values:

2x(x-1)/2=42

The 2s cancel out each other.

x(x-1)=42

x^2 - x =42

x^2 - x - 42=0

When we factor that, we get:

(x-7)(x+6)=0

x=7 or x=-6

We will take the positive answer.

height= x-1 = 7-1 = 6

base= 2x = 2(7) = 14

Now let's double check if we are correct.

6(14)/2

=84/2

=42

We are correct!

Answer:

Base: 14 and height: 6 OR Base: -12 and height -7

Step-by-step explanation:

First, set up a proportion. (base x height) divided by 2 on one side and 42 over 1 on the other.

[tex]\frac{2x(x-1)}{2}=\frac{42}{1}[/tex]          Next, cross multiply. This involves taking the numerator of

                            one side (top) and multiplying it by the denominator

                            (bottom) of the other side.

84=2x(x-1)            42*2=84 and anything multiplied by 1 equals itself. Next,

                            distribute (multiply) the 2x by each term in the

                            parentheses.

84=2[tex]x^2[/tex]-2x            2x*x=2[tex]x^2[/tex]. 2x*-1=-2x. Next, subtract 84 from both sides.

0=2[tex]x^2[/tex]-2x-84        Now, you can simplify this by dividing by 2 on both sides.

0=[tex]x^2[/tex]-x-42             This is a quadratic equation, which means you have to

                             factor or use the quadratic formula. In this case, you can

                             factor by using product and sum. You have to find what

                             multiplies to -42 and adds to -1. Those numbers would be

                              -7 and 6. -7*6=-42 and -7+6=-1 Therefore, you will have

                              x-7 and x+6

0=(x-7)(x+6)           Next, solve each equation with each binomial set equal

                              to 0. For x-7=0, x=7 because you add 7 to both sides. For

                              x+6=0, x=-6 because you subtract 6 from both sides.

x=7   x=-6

You can check if these values work by plugging them into the formula.

[tex]\frac{2x(x-1)}{2}- > \frac{2*7(7-1)}{2}- > \frac{14(6)}{2}- > \frac{84}{2}- > 42[/tex]. x can be 7.

[tex]\frac{2x(x-1)}{2}- > \frac{2*-6(-6-1)}{2}- > \frac{-12(-7)}{2}- > \frac{84}{2}- > 42[/tex]   x can be -6

The base and height are the numbers in the numerator of the equation after the 3rd arrow for both processes.

Due to construction, approximately 5 minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit.

Given that,

length of highway is 8 miles

Reduced length is 55 miles

Hours taken is 35 miles per hour.

Let t₁ is time taken is 55 mph

t₁ = 8/55

Let t₂ is time taken is 35 mph

t₂ = 8/35

Difference in time = 8/35 - 8/55

= 8 × 20 / (35 * 55) hour

= 160 × 60 / (35 × 55) mins

= 4.7

= 5 minutes (approximately)

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The GCF can be applied to problems requiring the division of something into equal groups or an equal number of groups, as well as problems requiring the simplification of a fraction.

The LCM can be used to solve problems involving the overlap of two activities or something similar, as well as problems involving the addition of two or more fractions with different denominators.

The greatest common factor of two or more integers that are not all zero in mathematics is the largest positive integer that divides each of the integers.

A set's greatest common factor (GCF) is the largest factor that all of the numbers share.

For example, the numbers 12, 20, and 24 all have two common factors: 2 and 4. The greatest is 4, so the GCF of 12, 20, and 24 is 4. The LCM, or smallest common multiple, is the smallest common number or multiple of any two numbers. The least common multiple of 3 and 5 is 15, for example.

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The largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  for all positive even integers is 15

The correct answer is an option (d)

In this question, we need to find the largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  for all positive even integers n.

We can observe that (n + 1), (n + 3), (n + 5), (n + 7) and (n + 9)  are 5 consecutive odd integers

In every 5 consecutive odd positive integers, one of them is always divisible by 3 and one of them is always divisible by 5.

This means, (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5

i.e., (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15 (3 * 5 = 15)

Therefore, the largest integer that is a divisior of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  = 15

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The length of the median of the trapezoid ABCD is  12 .

In the question ,

it is given that ,

the area of the trapezoid ABCD is = 60 ,

the height of the trapezoid ABCD is = 5 ,

let one base of the trapezoid ABCD be = a ,

So, b = a + 4 ,

Substituting the value in the formula for Area of the trapezoid = A =(a+b)h/2

(a + a + 4)5/2 = 60

(2a + 4)5 = 120

2a + 4 = 120/5

2a + 4 = 24

2a = 24 - 4

2a = 20

a = 20/2

a = 10 units

and other base = 10 + 4 = 14 units

So , the length of the median will be = (10 + 14)/2

= 24/2 = 12 units

Therefore , the length of median is = 12  .

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Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.

According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.

At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.

Given that,

Elouise and Marcus are 20 km apart (AB)

There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)

Now, according to a Pythagoras theorem,

(AC)² + (AB)² = (BC)²

or, (AC)² = (BC)²- (AB)²

or, (AC)² = (10√3)² - (20)²

or, AC = [tex]\sqrt{500}[/tex]

or, AC = 22.36 km

So, distance bearing of Marcus from Elouise is 22.36 km.

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For the function, [tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex], the value of h(4) is h(4) ≈ 8.7

From the question, we are to determine the value of h(4) in the given function.

The given function is

[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]

To determine the value of h(4), substitute 4 for x in the given function

[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]

[tex]h(4) = \frac{50}{5.5 + 8e^{-0.9(4)} }[/tex]

[tex]h(4) = \frac{50}{5.5 + 8e^{-3.6} }[/tex]

[tex]h(4) = \frac{50}{5.5 + 8(0.0273237) }[/tex]

[tex]h(4) = \frac{50}{5.5 + 0.21859 }[/tex]

[tex]h(4) = \frac{50}{5.71859 }[/tex]

h(4) = 8.7434

h(4) ≈ 8.7

Hence, the value of h(4) is 8.7

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Answer:

120°

Step-by-step explanation:

The 3 angle measures of a triangle will always equal 180.

Since we've already got two angles, all we need to do is a simple equation to get our missing angle:

180-(50+70)=60

Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:

180-60=120

And there's your answer, 120°

There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!

Answer:130.09

Step-by-step explanation:

Using the formulas

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving forA

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·7.2+8·7.2+3.5·7.2+1

2·﹣54+2·(5·8)2+2·(5·3.5)2﹣84+2·(8·3.5)2﹣3.54≈130.08536

Answer:

Step-by-step explanation:

kakaka

Answer: 2 degrees.

Step-by-step explanation: If it is -4 degrees in Iceland at 7 am and the temperature increases by 6 degrees, the new temperature would be -4 + 6 = 2 degrees.

Determine the distance covered by a car traveling 80 km/h for each unit and time given. The answer should be in meter in one hour.

What is a kilometer?

1,000 meters is one metric unit of measurement (approximately 0.62 miles).

The car is travelling at the speed of 80 kilometers per hour.

One hour is  60 minutes.

So car will travel in ideal conditions 80 kilometers in one hour which is 60 minutes.

So just convert the kilometers into meters.

1 kilometer = 1000 meters,

Thus,

80 kilometers = 80,000 meters.

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if x is an integer it does not show the median of the 5 numbers to be greater than the average of the 5 numbers

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the center, making it the median of 4, 1 and 7.

(1) x must be higher than one or three. It will be the median if it is 8 or fewer.

Consequently, if x = 7, then the list is 1, 3, 7, 8, 12, and median is 7, while the average is 31/5, which equals 6.2, and the answer is YES.

The list is 1, 3, 8, 8, 12, and the median is 8 if x = 8. Average = 32/5 = 6.4; if x = REALLY BIG, the list is 1, 3, 8, 12, and x; and the median is 8; the answer is YES. The answer to the question is NO since the average is REALLY BIG.

insufficient

(2) According to the aforementioned findings, x must be at least 9.

Depending on the amount of x, the list is either 1, 3, 8, x, 12, or 1, 3, 8, x.

The median and mean expressions are the same, regardless of whether order is appropriate:

Mean (average): 8 median = (1 + 3 + 8 + 12 + x)/5 = (24 + x)/5 mean (average):

The mean is at least (24 + 9)/5 = 33/5 = 6.6 since x is at least 9.

This is not convincing because the mean might be either millions or 6.6 (if x = 9) (if x is huge).

insufficient

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At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, the value of a margin of error of x is 1.534%.

In the given question, at a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, then we have to explain how should we interpret that.

The given confidence interval = 95%.

We can write it as CI = 0.95.

An approval rating is 55%.

We can write it as(p) = 0.55

A margin of error is x.

Let the value of sample size n = 1000.

So the margin of error;

ME = z× {p(1-p)}/√n

The value of z for confidence interval of 95% is 1.96.

Now putting the value

x = 1.96× {0.55(1-0.55)}/√1000

x = 1.96× {0.55×0.45}/31.623

x = 1.96× 0.2475/31.623

x = 1.96×0.00783

x = 0.01534

x = 1.534%

So the margin of error should be 1.534%.

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The right question is:

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?

Answer:

would it not be 26? I honestly don't know

Answer:

$40.8

Step-by-step explanation:

You would do 3.40 * 12 because a dozen is 12 roses.

So 3.40 × 12 = 40.8

Could you please give me brainliest for this? Thank you!

Answer:

Irrational, rational, rational, rational, rational.

Step-by-step explanation:

√23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.

104.42 this is a rational number! An irrational number has repeating values or just random numbers after the decimal point.

Here's an example...

Tell, does this number look rational?

4.2359712309458730495870192354870394587234098657293085412364781236409584790853467923456790324785098234570923845702398547 (and it goes on forever...and ever...and ever......)

√64 is a rational number. As we know that √64 = 8, a rational number.

49.396 with the 6 repeating is rational because we can express 49.39 as:

49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with

49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.

10.97846727460 is rational because the decimal places stop, it is rational. Remember, an Irrational number is non-repeating and non-terminating. Since the number terminates, it is rational

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

(7, 5) are the required coordinates of the diner.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

You do the reverse to determine a point's coordinates in a coordinate system.

Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there.

To find the y-coordinate, repeat the previous step while adhering to a horizontal line.

So, we must discover the halfway point between Lan's house and Joe's house in order to get the diner's coordinates.

The following equation will determine the midway between any two points:

M(x1 + x2/2, y1 + y2/2)

There are (4, 4), the point, and the point replaces the specified values:

M(4+10/2, 4+6/2)

M(7, 5)

Therefore, (7, 5) are the required coordinates of the diner.

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2,598,960 many different hands consisting of four queens and one king.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

To choose 4 kings, there is only one way, and to choose a queen, there are four.

Thus, there are 4 different methods to draw the 5 cards as instructed.

The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.

= 52!/(47!)(5!) = 2,598,960.

Hence,  2,598,960 many different hands consisting of four queens and one king.

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The mean and standard deviation of sampling distribution are 0.0187 and 0.010 respectively

The mean is a measure of location which tells us the average of observation.

Standard deviation tells us how dispersed a data is or how much variation our data contains.

According to question,

The population size : N = 1500

Number of fraudulent in a month : 28

Population proportion : P = 28/1500

=> P = 0.0187

Sample size: n = 180

Sample proportion : p = 28 / 180

=> p = 0.156

Therefore The mean of sampling distribution for the sample size 28,

μ = P

=> μ = 0.0187

The standard deviation will be

=> σ = [tex]\sqrt{\frac{p(1-p)}{n}}[/tex]

Substituting the value,

=>  σ = [tex]\sqrt{\frac{0.0187(1-0.0187)}{180}}[/tex]

=>  σ  = 0.010

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The values for random variables in a Monte Carlo simulation area that were chosen at random from probability distributions are the right answer.

What is Monte Carlo Simulation ?

The Monte Carlo Method, also referred to as the Monte Carlo Simulation or a multiple probability simulation, is a mathematical method for predicting potential outcomes of an uncertain event. To help people make better decisions when faced with uncertainty, John von Neumann and Stanislaw Ulam developed the Monte Carlo Method during World War II.

Therefore, the values for random variables in a Monte Carlo simulation area that were generated at random from probability distributions are the right answer.

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The correct response is the set of values for random variables in a Monte Carlo simulation region that were randomly selected from probability distributions.

In order to represent uncertainty in a model that represents a real system and computes the values of model outputs, a Monte Carlo technique is used. During World War II, John von Neumann and Stanislaw Ulam created the Monte Carlo Method to aid people in making better judgments when faced with uncertainty.

As a result, the correct response is the random values for random variables that were produced using probability distributions in a Monte Carlo simulation area.

It is true, that the most level of confidence used in creating confidence intervals is 90%.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

We have given,

Given n = 93, u =24, x' = 23, α=5.5

z = x'- u / α(/√n) = 1.645

Hence the answer choice is true.

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Answer: 1 1/5

Step-by-step explanation: you can write it as 1.5/1 times 4/5.

multiply by numerator and denominator so 1.5*4 which is 6

and 1*5 which is 5.

Now you have 6/5

6 can go into 5 once and you have 1 extra so 1 1/5

The value of c that will make the expression x² + 24x + c  a perfect trinomial is 144.

The perfect squared trinomial as a perfect binomial is (x + 12)²

An expression obtained from the square of the binomial equation is a perfect square trinomial.

In other words, perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.

If a trinomial is in the form ax² + bx + c is said to be a perfect square, if and only if it satisfies the condition b² = 4ac.

Therefore,

x² + 24x + c

where

Therefore,

b² = 4ac

24² = 4 × 1 × c

4c = 576

divide both sides by 4

c = 576 / 4

c = 144

Therefore,

c = 144

The perfect squared trinomial as a perfect binomial is as follows:

x² + 24x + 144

x² + 12x + 12x + 144

x(x + 12) + 12(x + 12)

(x + 12)(x + 12)

(x + 12)

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A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.

The value of x is 47

The value of y is 10.6

The four angles for the given quadrilateral are,

96, 94, 76, and 94.

A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.

We have,

A an isoceles trapezium.

Where one pair of sides are equal and parallel.

Two angles are equal.

Now,

94 = 2x

x = 47

Now,

The four angles sum is 360.

94 + 94 + 96 + 3y + 44 = 360

328 + 3y = 360

3y = 360 - 328

3y = 32

y = 32/3

y = 10.7

Now,

3y + 44 = 3 x 10.7 + 44 = 32 + 44 = 76

Thus,

The four angles for the given quadrilateral are,

96, 94, 76, and 94.

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If there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

If there are 58 nominees, and Blackhawk can give only four scholarships then the number of ways is =

                        [tex]=^nC_r\\\\=^{58}C_4\\\\=\frac{58!}{4!*54!}\\\\=\frac{58 * 57 * 56 * 55}{4 * 3 * 2 *1}\\\\=4,24,270[/tex]

Hence, if there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.

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Dilating a triangle by - 3 with vertices (3, 4), (3, 5), and (5, 5) will be

(- 9, - 12), (- 9, - 15) and (- 15, - 15).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A triangle with vertices (3, 4), (3, 5) and (5, 5).

Now dilating by a scale factor of - 3 will have every point multiplied by - 3 and the new vertices will be (- 9, - 12), (- 9, - 15) and (- 15, - 15).

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The year 2029 written as a roman numeral is MMXXIX.

Roman numerals are mathematical representations of numbers in the Roman alphabet. Roman numerals are a numeral system that originated in ancient Rome and remained the standard way of writing numbers in Europe until the late Middle Ages.

Roman numerals are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, which stand for 1, 5, 10, 50, 100, 500, and 1,000, respectively.

In this case, it should be noted that 2029 is MMXXIX.

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Answer:

Y = 7x + 51

Step-by-step explanation:

Point-slope form is in this form: y = mx + b where b is the y-intercept and m is the slope. We have the slope, and we already have a point that must be on the line. The only thing we need is the y-intercept, so we can plug in the given point and the slope to solve for b.

Plug in (-7, 2) for x and y and the slope(7) for m. This gives: [tex]2 = 7*-7 + b[/tex], or [tex]2 = -49 + b[/tex]. Now add 49 to both sides to isolate x, and we get that [tex]b = 51[/tex]. We have everything we need for the equation now, so plug in the slope and y-intercept for m and b, giving us y = 7x + 51.\

Hope this helps!

Applying the formula of the lateral surface area of a cylinder, the number of gallons needed to paint the top and the lateral surface is: 314,901 gallons.

The lateral surface area of a cylinder = 2πrh, where h is the height, r is the radius of the cylinder.

Given the following:

Lateral surface area of the cylinder = 2 × π × 1.5 × 24 = 226.19 yards²

Area of the top = area of circle = πr² = π(1.5²) = 7.07 yards²

Area to be painted = 226.19 + 7.07 = 233.26 yards²

Convert square yards to square feet:

1 square yard = 1 square feet

233.26 square yards = 2099.34 square feet

Gallons of paint needed = 2099.34 × 150 = 314,901 gallons.

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The total ways in which the student can readd the books are 1512 ways.

What is Combination?

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant (unlike permutations).

Solution:

Since reading 2 american novels is compulsory

The student therefore needs to read only two more novels

It can be either American Novels or English Novels

Ways to read American Novel = 7C2

Ways to read English Novel = 7C2

Total Ways = 9C2 * (7C2 + 7C2)

Total Ways = 36 * (42)

Total Ways = 1512 ways

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