Choose Yes or No to tell if the fraction
4
9
4
9
will make each equation true.

63
×
□
=
28
63
×
□
=
28


18
×
□
=
8
18
×
□
=
8


96
×
□
=
42
96
×
□
=
42


36
×
□
=
16
36
×
□
=
16

Answer:

two out of how many there is.

Step-by-step explanation:

The result of blending 50 percent of each animation of the pairs that follow will be a new animation that combines the features of both animations. This is known as "root motion blending" and is used to create smooth transitions between different animations.

The new animation will have a duration that is the average of the two animations being blended (for example, blending IDLE and WALK_1 will result in a 3s duration animation) and will include features from both animations. For example, blending WALK_1 and WALK_2 will result in a walking animation that is at a pace between relaxed and fast. Similarly, blending SPRINT_1 and SPRINT_2 will result in a sprinting animation that includes both a straight sprint and a slight right turn. The root motion of the new animation will be the average of the root motions of the two animations being blended.

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Answer:

Step-by-step explanation:

You can use simple algebraic principles for this. First we distribute:

5(y + 2/5) = -13

5y + 10/5 = -13

5y + 2 = -13

Now we isolate the variable term:

5y + 2 = -13

5y = -15

Now we divide to isolate the variable itself:

5y = -15

y = -3

Hope this helps!

Answer:

[tex]\huge\boxed{\sf \angle A = 43\°}[/tex]

[tex]\huge\boxed{\sf \angle B = 59\°}[/tex]

Step-by-step explanation:

In ΔDBC,

98 + ∠B + 31 = 180°

∠B + 121 = 180

∠B = 180 - 121

So,

∠C (Exterior Angle) = ∠A + ∠B

102 = ∠A + 59

102 - 59 = ∠A

43 = ∠A

[tex]\rule[225]{225}{2}[/tex]

Hence, there is a 38.2% likelihood that the group chosen will consist of two men and two women.

A committee's primary responsibility is to aid in the smooth operation of the company. The majority of the time, the main concerns of a committee are information sharing and assisting the leadership in making decisions by providing them with the necessary knowledge.

We may employ the formula of combinations to determine the likelihood of choosing a group comprising two men plus two women from of the committee. C(7,2) = 21 ways to choose two males from a group of seven, and C(4,2) = 6 ways to choose two women from a group of four. Hence, there are 21 x 6 = 126 different ways to choose a team of two men and two women.

C(11,4) = 330 different techniques can be used to choose any four members of the committee. Thus, the following is the likelihood of choosing a team of two men and two women:

126 / 330 = 0.382 or 38.2%

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The graphs when classified are decay and growth functions

The complete solution is shown below

A graph that represents an exponential growth would increase as the input value (x) increases, while graphs of exponential decay would decrease with increment in x

This means that:

An exponential function is represented as

y = abˣ

If b > 1, then it is a growth function, otherwise it is a decay function

This means that:

For the equation y = abˣ, we have

Initial value = a

Decay rate (if b < 0) = 1 - b

Growth rate (if b > 0) = b - 1

This means that

Function (12) is unclear

13. f(x) = 11(0.4)ˣ:

Initial value = 11

Decay factor = 0.4

Decay rate = 6%

14. f(x) = (1/4)ˣ:

Initial value = 1

Decay factor = 1/4

Decay rate = 75%

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To find theta to the nearest tenth of a degree, we can use a calculator to find the inverse of the given trigonometric function. The inverse of a trigonometric function is denoted by a "-1" superscript.

For the first question, we have cos theta = 0.2442 with theta in QI. To find theta, we can use the inverse cosine function:
theta = cos^-1(0.2442) ≈ 75.7°

For the second question, we have cos theta = -0.7750 with theta in QII. To find theta, we can use the inverse cosine function:
theta = cos^-1(-0.7750) ≈ 139.2°
Since theta is in QII, we can subtract this angle from 180° to find the angle in QII:
theta = 180° - 139.2° ≈ 40.8°

For the third question, we have tan theta = 0.5860 with theta in QIII. To find theta, we can use the inverse tangent function:
theta = tan^-1(0.5860) ≈ 30.4°
Since theta is in QIII, we can add 180° to this angle to find the angle in QIII:
theta = 180° + 30.4° ≈ 210.4°

For the fourth question, we have cos theta = 0.2442 with theta in QI. This is the same as the first question, so the answer is the same:
theta = cos^-1(0.2442) ≈ 75.7°

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It will take Mrs. Reed 3 hours to catch up to Mr. Reed.

First we can start by figuring out how far Mr. Reed will have traveled when Mrs. Reed starts her journey.

Distance traveled by Mr. Reed in 3 hours at a speed of 40 mph:

When Mrs. Reed starts her journey, Mr. Reed is 120 miles ahead of her.

Now, let's determine how long it will take Mrs. Reed to catch up to Mr. Reed.

We can use the formula:

time = distance / relative speed

Where "distance" is the distance Mrs. Reed needs to travel to catch up to Mr. Reed, and "relative speed" is the speed at which Mrs. Reed is gaining on Mr. Reed, which is the difference between their speeds:

relative speed = 80 mph - 40 mph

relative speed = 40 mph

So, the time it will take for Mrs. Reed to catch up to Mr. Reed can be calculated as:

Therefore, it will take Mrs. Reed 3 hours to catch up to Mr. Reed.

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In the triangle DEF the measure of angle E is obtained as (183 - 9x)°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In the triangle DEF the value for ∠D = (4x + 1)°.

In the triangle DEF the value for ∠F = (5x - 4)°.

According to the properties of a triangle, the sum of angles of a triangle is equal to 180°.

So, the equation will be -

(4x + 1)° + (5x - 4)° + ∠E = 180°

Evaluate the expression -

(9x - 3)° + ∠E = 180°

∠E = 180° - (9x - 3)°

∠E = 180° - 9x + 3°

∠E = (183 - 9x)°

Therefore, the value for angle E is (183 - 9x)°.

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The system of equations that does not have a solution is {(x-2y=-3),(-2x+4y=6):}.

To see why, let's first look at the other two systems of equations:

{(4x+6y=12),(6x+9y=12):}

If we divide the first equation by 2, we get:

{(2x+3y=6),(6x+9y=12):}

If we then multiply the first equation by -3, we get:

{(-6x-9y=-18),(6x+9y=12):}

If we add these two equations together, we get:

{0= -6}

This is a false statement, so there is no solution for this system of equations.

Similarly, for the system of equations {(x+y=-1),(4x-3y=24):}, we can multiply the first equation by -4 and add the two equations together to get:

{-4x-4y=4, (4x-3y=24):}

{-7y=28}

This equation has a solution, so this system of equations does have a solution.

However, for the system of equations {(x-2y=-3),(-2x+4y=6):}, if we multiply the first equation by -2 and add the two equations together, we get:

{-2x+4y=6, (-2x+4y=6):}

{0=0}

This equation is always true, so there are an infinite number of solutions for this system of equations. Therefore, this system of equations does not have a unique solution.

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The points M, N, P, and Q have been plotted in the coordinate plane below.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;

Midpoint MP = [(2 + 1)/2, (-1 + 2)/2]

Midpoint MP = [3/2, 1/2]

Midpoint MP = (1.5, 0.5).

For the fourth vertex Q, we have:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(1.5, 0.5) = [(4 + x₂)/2, (0 + y₂)/2]

4 + x₂ = 2(1.5)

x₂ = -4 + 3

x₂ = -1.

0 + y₂ = 2(0.5)

y₂ = 1.

Therefore, vertex Q = (-1, 1).

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The equation of the horizontal asymptote of P isy = 22818.18.  This means that the insect population will approach a maximum value of approximately 22818 insects, no matter how many months have passed since they were introduced. The unit of measure for this value is insects per month.

a. The equation of the horizontal asymptote can be found by taking the limit of P(t) as t approaches infinity.

lim P(t) as t approaches infinity = lim (50+251)/(2+0.011t) as t approaches infinity

Since the denominator grows without bound as t approaches infinity, the limit of P(t) approaches 251/0.011 = 22818.18. Therefore, the equation of the horizontal asymptote is:

y = 22818.18

b. The horizontal asymptote tells us the maximum population that the protected area can sustain for this type of insect. In other words, as time goes on, the insect population will approach a maximum value of approximately 22818 insects. The unit of measure for the asymptote value is insects.

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The equation of the line that passes through the point (−9,−10) and is perpendicular to the given line x+6y=2y−3 is y = 4x + 26.

We first need to find the slope of the given line.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

First, let's rearrange the given equation to get it in slope-intercept form:

x + 6y = 2y - 3

4y = -x - 3

y = (-1/4)x - (3/4)

The slope of the given line is -1/4.

Since the slope of a line perpendicular to another line is the negative reciprocal of the original slope, the slope of the line we are looking for is 4.

Now we can use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1)

y - (-10) = 4(x - (-9))

y + 10 = 4x + 36

y = 4x + 26

So the equation of the line in slope-intercept form is y = 4x + 26.

Therefore, the answer is y = 4x + 26.

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Any number that has the same ratiο as 1:2 and faIIs between 0 and 6 withοut repeating can be used fοr the divisiοns οf 2 by 4 and 3 by 6.

The basic unit οf mathematics is the number. Numbers are used fοr a variety οf activities, such as measuring, cοunting, and indexing. Accοrding tο their prοperties, numbers can be cIassified intο a variety οf categοries, incIuding naturaI numbers, whοIe numbers, ratiοnaI and irratiοnaI numbers, integers, reaI numbers, cοmpIex numbers, even and οdd numbers, etc. It is pοssibIe tο determine the οutcοme number using simpIe integer arithmetic οperatiοns.

In the given questiοn, we need tο find twο sets οf three distinct numbers between 0 and 6 that have the same ratiο.

One pοssibIe sοIutiοn is:

2 divided by 4.

= 3 divided by 6

Here:

The ratiο οf the first set is 2:4 οr 1:2. When we divide 2 by 4, we get 0.5.

The ratiο οf the secοnd set is 3:6 οr 1:2. When we divide 3 by 6, we aIsο get 0.5.

Therefοre, we have:

2 divided by 4.

= 0.5

3 divided by 6.

= 0.5

Sο, we can say:

2 divided by 4

= __ divided by __

where 3 and 6 can be any numbers that have the same ratiο as 1:2.SimiIarIy,

3 divided by 6

= __ divided by __

where 3 and 6 can be any numbers that have the same ratiο as 1:2.

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The simplified answer is 16y² - 25x².

When multiplying conjugate binomials,

We use the formula (a+b)(a-b) = a²-b².

In this case, a = 4y and b = 5x. So,

We can pluggin these values into the formula and simplify:

(4y+5x)(4y-5x) = (4y)² - (5x)²

= 16y² - 25x²

Therefore, the simplified answer is 16y² - 25x². This is the final answer, and there are no further steps to simplify.

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As we see, triangle ABC is congruent to triangle BMK so, a) length of AC = 5

b) length of BM = 4.5

c) length of KM = 3

d) length of BM = 3.42 , MC = 17.58

We have a triangle ABC and KM, a segment is parallel to AC, i.e., KM || AC. First we show that triangle ABC is congruent to triangle BMK. AC and AB are transversals that intersect parallel lines. Since the two pairs of corresponding angles created by this intersection are equal, that is,

∠ BKM =∠ BAC and ∠ BMK = ∠ BCA

By Angle-Angle congruence rule, ∆ ABC is similar to triangle BMK, i.e., ∆ABC ~ ∆BMK. When two triangles are similar, the ratios of the lengths of their corresponding sides are equal, KB/AB = KM/AC --(1) or

BM/BC = KM/AC --(2)

a) AB = 10, KB = 2, KM = 1, determine AC=?

from equation (1), KB/AB = KM/AC

=> 2/10 = 1/AC

Cross multiplication

=> 2 AC = 10

=> AC = 5

b) KM= 3, AC = 6,BC = 9, determine BM= ?

from equation (2), BM/BC = KM/AC

=> BM/9 = 3/6

Cross multiplication

=> 6 BM = 27

=> BM = 9/2

=> BM = 4.5

c)BC = 25, MC = 10, AC = 5, determine KM= ?

BM = BC - MC = 25 - 10 = 15

from equation (2), BM/BC = KM/AC

=> 15/25 = KM/5

Cross multiplication

=> 25 KM = 15×5

=> KM = 75/25

=> KM = 3

d)AK = 10, KB = 4, BC = 21, determine BM=? and MC= ?

AB = AK + KB = 10 + 4 = 14

from equations (1) and (2),BK/AB = BM/BC

=> 4/14 = BM/21

Cross multiplication

=> 14 BM = 21 × 4

=> BM = 84/14 = 24/7

=> BM = 3.42

so, MC = BC - BM = 21 - 3.42 = 17.58

Hence, required value is 3.42..

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Complete question:

Given: ∆ABC, KM|| AC. See the above figure.1.

a) AB=10, KB=2, KM=1

AC-?

b) KM=3, AC=6,BC=9

BM-?

c)BC=25, MC=10, AC=5

KM-?

d)AK=10,KB=4,BC=21

BM-?,MC-?

The Andy's statement is correct because the end of the month amount is indeed 250% of his original amount.

To determine if Andy's statement is correct, we need to verify if the end of the month amount is indeed 250% of his original amount.

Let original amount of money that Andy had at beginning of month be = x ;

According to the problem, he began with $44, so x = $44.

Let amount of money that Andy had at the end of the month be = y;

According to the problem, he ended with $110, so y = $110.

Andy's statement is that the end of the month amount of $110 is 250 percent of his original amount of $44;

⇒ y = 2.5x

Substituting the values,

We get,

⇒ $110 = 2.5 × $44;

Simplifying,

We get,

⇒ $110 = $110.

Therefore, Andy's statement is correct.

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Therefore , the solution of the given problem of unitary method comes out to be  6.10 is the standard deviation.

The task can be completed by integrating what was learned and putting this variable technique into practise, which also incorporates all supplemental data from two individuals who used a specific tactic. Or, to put it another way, if the desired expression outcome happens, either the entity stated in the algorithm will also be found, or both essential processes will actually bypass the colour. For forty pens, a refundable charge of Rupees ($1.01) might be required.

Here,

Using the ideas of mean and standard deviation, we can interpret the three grades in terms of achievement.

The three categories' mean (average) is:

=> Mean = (75 + 85 + 90) / 3 = 83.33

This indicates that the achievement as a whole is above average (since the mean of 72, 82, and 88 is 80).

Which is:

=> Variance = [(75 - 83.33)² + (85 - 83.33)² + (90 - 83.33)²] / 3

=>  [67.11 + 1.36 + 44.11] / 3

=>  37.19

The variance's square root equals the standard deviation.

=> SD= √(37.19)

=> 6.10 is the standard deviation.

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Answer:

13.1y

Step-by-step explanation:

Normally in questions like this, you would be given the total area and asked to find the value of y. In this case, the area is not given, so it can be assumed the question requires you to give your answer in terms of y.

The area of a rectangle is found by multiplying the length by the width. In this case, we want to add two areas together to find the total area of the two gardens:

(3.3 * 2y) + (1.3y * 5)

We can simplify both sides of the expression:

3.3 * 2y = 6.6y

1.3y * 5 = 6.5y

Now we can add these together to find the total area, in terms of y:

6.6y + 6.5y = 13.1y

Answer:

37

Step-by-step explanation:

Approximately 272 loan applicants fall within a score of 622 and 678  assuming a bell-shaped curve.

To solve this problem, we need to use the standard normal distribution formula. First, we calculate the z-scores for the two credit score values of interest:

z-score for 622 = (622 - 650) / 14 = -2

z-score for 678 = (678 - 650) / 14 = 2

Next, we look up the probabilities for these z-scores in the standard normal distribution table or using a calculator. The probability of a z-score being between -2 and 2 is approximately 0.9544. Therefore, we can estimate that approximately 95.44% of the loan applicants fall within a score of 622 and 678.

Finally, we can calculate the number of loan applicants that fall within this range by multiplying the total number of applicants by the probability:

number of loan applicants = 285 x 0.9544 ≈ 272

Therefore, we can estimate that approximately 272 loan applicants fall within a score of 622 and 678.

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A permutation matrix is a square matrix that has exactly one entry of 1 in each row and each column, and all other entries are 0. When a permutation matrix is multiplied with another matrix, it rearranges the rows of the other matrix.

For matrix A = \begin{bmatrix}-1 & 2 & -2\\ 2 & 3 & 5\\ 1 & 2 & 2\end{bmatrix}

(a) A permutation matrix P that allows for an LU decomposition of PA is P = \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix}

When we multiply P and A, we get PA = \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}-1 & 2 & -2\\ 2 & 3 & 5\\ 1 & 2 & 2\end{bmatrix} = \begin{bmatrix}2 & 3 & 5\\ -1 & 2 & -2\\ 1 & 2 & 2\end{bmatrix}

(b) An LU decomposition of PA is L = \begin{bmatrix}1 & 0 & 0\\ -0.5 & 1 & 0\\ 0.5 & 0 & 1\end{bmatrix} and U = \begin{bmatrix}2 & 3 & 5\\ 0 & 3.5 & 4.5\\ 0 & 0 & -0.5\end{bmatrix}

So, PA = LU = \begin{bmatrix}1 & 0 & 0\\ -0.5 & 1 & 0\\ 0.5 & 0 & 1\end{bmatrix}\begin{bmatrix}2 & 3 & 5\\ 0 & 3.5 & 4.5\\ 0 & 0 & -0.5\end{bmatrix} = \begin{bmatrix}2 & 3 & 5\\ -1 & 2 & -2\\ 1 & 2 & 2\end{bmatrix}

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The coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]

The transition matrix from B to B' can be found by first finding the inverse of matrix B, then multiplying it by matrix B'. The transition matrix from B' to B can be found by first finding the inverse of matrix B', then multiplying it by matrix B. To verify that the two transition matrices are inverses of each other, we can multiply them together and see if the result is the identity matrix. Finally, to find the coordinate matrix [x]B, given the coordinate matrix [x]B', we can multiply the transition matrix from B' to B by the coordinate matrix [x]B'.

(a) Find the transition matrix from B to B'.
P−1 = B^(-1) * B' =
[(-0.04, 0.04, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(0, −1, 8), (1, 1, −8), (2, 2, −12)] =
[(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)]

(b) Find the transition matrix from B' to B.
P = B'^(-1) * B =
[(-0.33, 0.17, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(14, −2, −6), (−6, 1, 3), (12, −2, −5)] =
[(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)]

(c) Verify that the two transition matrices are inverses of each other.
PP−1 = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)] =
[(1, 0, 0), (0, 1, 0), (0, 0, 1)]

(d) Find the coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]

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Answer:

y = x+5

x+2y=16

x+2(x+5)=16

x+2x+10=16

3x+10=16

16. 3x + 10 = 16

3x+10=16

    -10  -10

3x=6

Divide 3 from both sides

x=2

y=x+5

y=2+5

y=7

17. (2,7)

Given that there was no test this week (X0 = 0), the probability that there is a test in two weeks time (X2 = 1 or X2 = 2) is given by the sum of the probabilities of the two possible states in the two-step transition probability matrix:
P(X2 = 1 or X2 = 2|X0 = 0) = P^2[0][1] + P^2[0][2] = 0.36 + 0.12 = 0.48

To compute P(X5 = 2|X3 = 1, X1 = 0), we can use the formula for conditional probability:
P(X5 = 2|X3 = 1, X1 = 0) = P(X5 = 2, X3 = 1, X1 = 0)/P(X3 = 1, X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)*P(X1 = 0)/P(X3 = 1|X1 = 0)*P(X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)/P(X3 = 1|X1 = 0)
= P(X5 = 2|X3 = 1)
= P²[1][2]
= 0.12

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The equation that represent the function is h(x) = 30x + 50 and the equation is linear.

Ann is coordinating a fashion show and needs to hire a makeup artist. The makeup artist charges 50 dollars booking fee plus an additional 30 dollars per hour .

Let's use function to represent the total cost to hire the artist for x hours.

Therefore,

h(x) = 50 + 30x

Hence, the function is linear.

Therefore, the equation that represent the situation is h(x) = 50 + 30x

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Answer:

n=10

Step-by-step explanation:

(photo linked = step-by-step)

There is no real value of n that satisfies the equation c(n,6) = c(n,4). In other words, there is no real number n such that it satisfy the given combinations.

To find the value of n that satisfies the equation c(n,6) = c(n,4), we can use the formula for combinations.

The formula for combinations, often denoted as C(n, r), calculates the number of ways to choose r items from a set of n items without regard to the order.

In this case, we have c(n, 6) and c(n, 4). The equation states that the number of ways to choose 6 items from a set of n items is equal to the number of ways to choose 4 items from the same set.

Using the formula for combinations, we can set up the equation as follows:

n! / (6!(n-6)!) = n! / (4!(n-4)!)

To solve this equation for n, we can simplify the equation by canceling out the factorials:

(n(n-1)(n-2)(n-3)(n-4)(n-5)) / (6(5)4(3)2(1)) = (n(n-1)(n-2)(n-3)) / (4(3)2(1))

By canceling out common factors and simplifying, we are left with:

(n-5) = (n-4)(n-3)

Expanding the equation, we have:

[tex]n - 5 = n^2 - 7n + 12[/tex]

Rearranging the equation and combining like terms, we get:

[tex]n^2 - 8n + 17 = 0[/tex]

At this point, we can solve the quadratic equation using factoring, the quadratic formula, or other methods. However, upon inspection, we can see that this quadratic equation does not have real solutions.

Therefore, there is no real value of n that satisfies the equation c(n,6) = c(n,4). In other words, there is no real number n such that it satisfy the given combinations.

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Answer:

Simplify both sides of the equation and combine all same-side like terms.

Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.

Divide or multiply as needed to isolate the variable.

The three basic operations used to simplify a linear system are elimination, substitution, and augmentation.

The 3 basic operations used to simplify a linear system are:
1. Swapping the order of equations: This operation is used to rearrange the equations in the system to make it easier to solve.
2. Multiplying or dividing an equation by a constant: This operation is used to make the coefficients of the variables in the equation equal to 1 or -1, which makes it easier to solve the system.
3. Adding or subtracting equations: This operation is used to eliminate one of the variables in the system, which reduces the number of equations and makes it easier to solve the system.
These operations are used to manipulate the equations in the system in order to find the values of the variables that satisfy all of the equations in the system. By using these operations, we can simplify the system and solve it more easily.

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