what is the value of x.

Answer:

2184

Step-by-step explanation:

This question involves permutations. We can solve it using the formula

[tex]\frac{n!}{(n-r)!}[/tex]

where n=14 (because we are choosing from 14 people)

and r=3 (because we are choosing 3 people)

and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)

14!/(14-3)!

= 14!/11!

= 14 x 13 x 12

= 2184

The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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Answer:

B. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are angles that are outside two lines intersected by the transversal and are located on opposite sides of the transversal. Also, they have the same degree! So, the answer is B.

Answer:

1. ΔCDE≅ΔJEH

2. ΔIHG≅ΔIHD

3. ΔIHJ≅ΔIXT

4. ΔIJT≅ΔJIH

5. ΔEFD≅ΔDKJ

6.ΔGWY≅ΔGHI

The value of line integral of the line segment from (5,4) to, (0,0) is 90.

Given that C is the line segment from (5,4) to (0,0):-

So, our first task is to calculate the line segment

After calculating the line segment, we will be able to calculate the line integral

We know that the equation of line is -

y - y1 = (y1 - y2)/ (x1 - x2) * (x - x1)

So now,

y - 0 = (4 - 0)/ (5 - 0) * (x - 0)

y = 4/5 x

5x - 4y = 0 -----------> (1)

A line integral is used to calculate the area covered by that line

c1 = ∫₀⁴ 5x dx ------> (2)

c2 = ∫₀⁵ -4y dy -----> (3)

c1 = [ 5 x²/2 ]₀⁴ = 5 * ( 4² - 0)/2 = 40

c2= [ -4 y²/2 ]₀⁵ = -4 * ( 5² - 0)/2 = 50

The value of the line integral: c1 + c2 = 40 + 50 = 90

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Answer:

15x +147

Step-by-step explanation:

Answer:

58.3

Step-by-step explanation:

divide the length value by 2.54

58.2677

Answer:

58,3 inches

Step-by-step explanation:

1 inch = 2.54 cm

[tex]148 \: cm \:*\:\frac{1\:inch}{2.54\: cm} = 58,267716535433070866141732283465\\\\148\: cm=58,3 \:inches[/tex]

Answer:

(2x + 1)^2 = 7

Step-by-step explanation:

To write the quadratic equation 4x^2 + 8x - 10 = 0 in vertex form, we need to first complete the square. To do this, we need to add and subtract the same value to the quadratic term and the linear term so that the resulting quadratic has the form (x - h)^2 = k.

In this case, we need to add and subtract the square of half of the coefficient of the linear term, which is 8/2 = 4. This gives us the equation:

4x^2 + 8x + 4 - 4 - 10 = 0

This simplifies to 4(x^2 + 2x + 1) - 14 = 0, which can be rewritten as (2x + 1)^2 - 7 = 0.

To put this in vertex form, we need to rewrite the right side of the equation as a perfect square, so we add 7 to both sides to get (2x + 1)^2 = 7.

Then, we take the square root of both sides to get 2x + 1 = ±√7. We can then solve for x to get x = -1/2 ± √7/2.

Therefore, the equation 4x^2 + 8x - 10 = 0 can be written in vertex form as (2x + 1)^2 = 7.

Answer: No, Gwen's ratio is 3:5 soup to total, and Bernard's is 1:2 soup to total

Step-by-step explanation:

Bernard donates 30 cans, 15 of which are soup.

15soup/30cans = 1soup/2cans = 1 soup to 2 total cans

Gwen donates 20 cans, 12 of which are soup.

12soup/20cans = 3soup/5cans = 3 soup to 5 total cans

an instance where a region's u.s. land surface has changed subsided due to groundwater withdrawal. The land surface in the Central Valley has subsided by as much as 30 feet in distance some areas due to unsustainable groundwater withdrawals.

The most famous case of land subsidence due to groundwater withdrawal in the United States is the Central Valley of California. The land surface in the Central Valley has subsided by as much as 30 feet distance in some areas due to unsustainable groundwater withdrawals. In addition to land subsidence, the unsustainable withdrawals have caused significant groundwater depletion, surface water contamination, and reduced agricultural productivity.

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The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.

The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.

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Answer:

a

Step-by-step explanation:

Answer:

d = 0

Step-by-step explanation:

We have the equation

7.5d = 2.5d

We divided both sides by factors and get

d = 0

Value of d is 0.

According to question

7.5d=2.5d

Lin divides each side by 2.5d

∴7.5d÷2.5d=2.5d÷2.5d

⇒3=1

which is not possible and Lin is doing wrong

Elena subtract 2.5d from each side

∴7.5d-2.5d=2.5d-2.5d

⇒5d=0

⇒d=0

So Elena is right and the value of d is 0.

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The statement would no longer be true if you did not flip the signs.

Example: 1 < x < 2 multiplied by (-1) equals -2 < x < -1, because you can't have a number that is greater than -1, and less than -2 at the same time.

The solution to the expression is (b) -3.07n - 8.2

From the question, we have the following parameters that can be used in our computation:

(7.43n − 2.2) − (6 + 10.5n)

Remove the brackets

So, we have

(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n

Evaluate the like terms

(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2

Hence, the solution is (b) -3.07n - 8.2

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The value of the given expression cos(π/2 - sin⁻¹(1/2)) will be equal to 1/2.

The fundamental six functions of trigonometry have a range of numbers as their result and a boundary input value that is the angle of the right triangle.

As per the given information in the question,

cos(π/2 - sin⁻¹(1/2))

Use the formula given below,

cos(π/2 - θ) = sin θ

From the above formula,

sin(sin⁻¹ (1/2))

= 1/2

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Answer:

Use this site, it will help you in the long run.

Answer:_18

replace _4 instead of x

-5*-4=_20

_20+2=_18

Step-by-step explanation:

Answer: the slope is [tex]\frac{4}{2}[/tex] which can be simplified to just 2.

Step-by-step explanation:

You can use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope of a line. In this case, I chose to use the coordinates (-4,0) and (-6,-4), it doesn't matter which you choose as the (x1,y1) and (x2,y2) coordinates. So, [tex]\frac{-4-0}{-6-(-4)}[/tex] becomes [tex]\frac{-4}{-2}[/tex] which is the same as [tex]\frac{4}{2}[/tex], which is equal to 2. you can repeat this with the other points given to check your answer.

The slope of the line passing through the given points is equal to 2 .

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the tangent of the angle made by the line with the x - axis. It is represented by m: m = y₂-y₁ / x₂ - x₁

Given here, are the points P (-10, -12), Q(-8, -8), R(-6, -4),S (-4, 0)

Now the slope of a line is constant for any two points that lie on a line.

therefore, slope of the line that passes through P,Q,R,S  is

m = -8-(-12) /-8-(-10)

    = 2

 or m= 0-(-4) /-4-(-6)

         = 2

clearly the slope is equal to 2 in either case that's because the line passes through all the four points.

Hence,  the slope of the line passing through the given points is equal to 2.

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The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters

First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:

tan 8 = 4.6/opposite

Solving for the opposite, we get:

opposite = 4.6/tan 8 = 5.8 meters

This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.

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Answer:

There is one unique solution, (−6, 5).

Step-by-step explanation:

2x + 4y = 8

2x + 6y = 18

2x + 4y = 8  ==> solve for 2x

2x + 4y - 4y = 8 - 4y

2x = 8 - 4y

2x + 6y = 18  ==> solve for 2x

2x + 6y - 6y = 18 - 6y

2x = 18 - 6y

8 - 4y = 18 - 6y  ==> 2x = 8 - 4y   and   2x = 18 - 6y

8 - 4y + 6y = 18 - 6y + 6y  ==> solve for y by first adding 6y on both sides to

                                                remove negative y

8 + 2y = 18  ==> simplify

8 - 8 + 2y = 18 - 8  ==> isolate y

2y = 10

y = 5

2x + 4(5) = 8  ==> substitute 5 for y in 2x + 4y = 8

2x + 20 = 8

2x - 20 + 20 = 8 - 20  ==> subtract 20 on both sides to isolate 2x

2x = -12

x = -6

x = -6, y = 5  ==> (6, 5)

Answer: There is one unique solution, (−6, 5).

After the end of the lease period the pay, the rent would increase to $3030.83 approx.

A lease is a legal agreement by which the owner of a building, a piece of land, or something such as a car allows someone else to use it for a period of time in return for money.

Given here,  a 2-year lease is - $2,657 per month plus a $200 security deposit. Now, the average increase in the rate in the U.S is 14.07%

thus, at the end of the two-year lease period, the new rent would be

= (1+14.07/100) × $2,657

= $3030.83

Hence, the new rent with a security deposit is $3030.83 + security deposit.

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The system of linear equations, y = 2x + 4 ;

2y = x + 6 has a unique solution and it is a consistent system of linear equations.

An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is

y = 2x + 4 => 2x - y + 4 = 0 --(1)

2y = x + 2 => x - 2y + 6 = 0 --(2)

Comparing the equation (1) with a₁x + b₁y + c₁=0

and equation(2) with a₂x + b₂y + c₂=0

We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2

Now, compute the ratio of coefficients of variables .

a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3

=> a1/a2 ≠ b1/b2 ,

here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.

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Complete question:

Is the system of equation is consistent and

independent consistent and dependent or inconsistent?

y = 2x + 4 , 2y = x + 6

Answer:

a is 30 degrees.

Step-by-step explanation:

The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.

[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]

A. Let x be a real number,B. Add x to both sides of the equation, then C. x - x = 0,D. Therefore, x = 0

A. Let x be a real number - This step states that we are selecting a real number for which we will prove that it is equal to 0. This step does not contain an error.

B. Subtract x from both sides of the equation - This step does not contain an error as it is the first step in the process of proving that the real number is equal to 0.

C. x - x = 0 - This step contains an error, as it doesn't provide enough information to prove that the real number is equal to 0.

D. Therefore, x = 0 - This step also contains an error, as it assumes that the proof is correct without providing any evidence.

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The probability that both coins will land on heads is 50%. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails.

This is because the result of the first coin toss does not influence the outcome of the second coin toss, meaning each toss is an independent event with a 50% chance of landing on heads.The probability that both coins will land on heads is 50%. This is because the result of the first coin toss does not influence the outcome of the second coin toss. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails. This means that the probability of both coins landing on heads is the same as the probability of either coin landing on heads, which is 50%. Therefore, the probability that both coins will land on heads is 50%.

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To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.

By using the following formula:

decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]

binary = converting binary number

i = index of the current digit in the binary number

n = total number of digits in the binary number

[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2

use the following steps to convert the binary number "10101111"

Calculate the decimal value for each digit in the binary number:

binary[0] = 1, [tex]2^{(8-0-1)}[/tex]  = [tex]2^7[/tex] = 128

binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64

binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32

binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16

binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8

binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4

binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2

binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1

Adding decimal values for each digit

Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11

= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1

= 175

Hence, the decimal number that corresponds to the binary number "10101111" is 175.

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we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so [tex]\frac{x}{100} * y = 31/2[/tex]

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Answer:

(x + 2)(x + 4)

Step-by-step explanation:

for the denominator we have (x + 2)(x + 4)(x + 4).

divide the denominator by (x + 4), you would be left with (x + 2)(x + 4).

Answer:

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): [tex]-4\leq x < 4[/tex]

Range (inequality notation): [tex]1\leq x < 4[/tex]

Step-by-step explanation:

Domain is the x-values of a function

Range is the y values of a function