Please help with these two questions!

The variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

The step for the simplification are-

Finally, on a broad note:

(2n)! - (2(ⁿC₁)(2n - 1)! - 2²(ⁿC₂)(2n - 1)! + .....2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

On further simplifying;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

Thus, the variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

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3.7261×10¹⁵ seconds  is the time it would take you to empty the lake

Given that:

Lake Eric can hold 116 cubic miles of water

One cup has a diameter of 2 and 3/4 inches and a height of 4 inches

Volume of cone cup = 1/3 πr²h

Volume of cone cup = 1/3×π×(11/8)²×4 = 7.92 cubic inches

Volume of Lake Erie = 116 cubic miles

To convert to cubic inches multiply by 2.544×10¹⁴:

Volume of Lake Erie = 116×2.544×10¹⁴ = 2.95104×10¹⁶ cubic inches

Time taken = 2.95104×10¹⁶ / 7.92 = 3.7261×10¹⁵ seconds

Therefore, it would take you 3.7261×10¹⁵ seconds to empty the lake

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The probability of the card being an ace, given that it is a non-face card will be 0.1 or 10%

There are total 52 cards.

Out of 52, 26 are red and 26 are black.

Each of the four French suits—clubs (♣), diamonds (♦), hearts (♥) and spades (♠).—has 13 ranks in a regular 52-card deck. King, Queen, and Jack are the three court cards (face cards) in each suit, and their pictures are reversed (double-headed). The ten numerical cards, or pip cards, in each suit range in value from one to 10.

Out of 52 cards, (Kings, Queen, Ace) are faced card.

And each set of cards have 4 different colour and shades.

So, total number of faced card will be = 4*3 = 12

So, total number of not a faced card = 52-12 = 40

So, the value of P (It is an ace and it is not a face card) =4/52

So, the value of P(It is not a face card)=40/50

[tex]P\left(\frac{\text { It is a ace }}{\text { It is not a face curd }}\right) =\frac{P(\text { It is an ace and it is not aface carl) }}{P(\text { It is not a face card) }} \\\\ =\frac{\frac{4}{52}}{\frac{40}{52}}\\\\=\frac{4}{40}\\\\=0.1=10\% }[/tex]

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[tex]y=x+3[/tex] for x

Flip the equation:

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

Add -3 to both sides:

[tex]x+3+-3=y+-3[/tex]

[tex]\fbox{x = y - 3}[/tex]

__________________________________________________________

[tex]x-2y=-1[/tex] for y

Add -x to both sides:

[tex]x-2y+-x=-1+-x[/tex]

[tex]-2y=-x-1[/tex]

Divide both sides by -2:

[tex]\dfrac{-2y}{-2} =\dfrac{-x-1}{-2}[/tex]

[tex]\fbox{y = $\dfrac{1}{2}x+ \dfrac{1}{2} $}[/tex]

The solutions are

a) The smallest possible value of x - y is A = -6

b) The largest possible value of 2x / y is B = 6

c) The largest possible value of x² + y² is C = 100

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as P

The value of P is

-4 ≤ x ≤ 6

Let the second inequality equation be represented as Q

The value of Q is

2 ≤ y ≤ 8

Now , the smallest value of inequality P is = -4

The largest value of inequality P is = 6

And , the smallest value of inequality Q is = 2

The largest value of inequality Q is = 8

a)

Let the smallest possible value of x - y be = A

The value of x - y is calculated as

The smallest value of P - smallest value of Q

Substituting the values in the equation , we get

A = -4 - 2

A = -6

Therefore ,  The smallest possible value of x - y is A = -6

b)

Let the largest possible value of 2x / y be = B

The value of 2x/y is calculated as

Largest value of x goes in numerator and smallest value of y goes in denominator to get the largest value of 2x/y

So , substituting the values in the equation , we get

B = ( 2 x 6 ) / 2

B = 12 / 2

B = 6

Therefore , The largest possible value of 2x / y is B = 6

c)

Let the largest possible values of x² + y² be = C

The value of x² + y²  is calculated as

The largest value of x squared + the largest value of y squared

Substituting the values in the equation , we get

C = 6² + 8²

C = 36 + 64

C = 100

Therefore , The largest possible value of x² + y² is C = 100

Hence , The solutions are

a) The smallest possible value of x - y is A = -6

b) The largest possible value of 2x / y is B = 6

c) The largest possible value of x² + y² is C = 100

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Answer: $1,504,000

Step-by-step explanation:

First, take 800,000 divided by 100% = $8000

So we know that 1% is $8000

We are missing 88%, so take 8000 times 88 = $704,000

Then we add 800,000 with 704,000 = $1,504,000

So the total sales are $1,504,000

The value of the a is 2.

What is the fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when used in conversational English.

We have,

8⁻¹ / 4⁻¹ - a⁻¹ = 1

By simplifying the given equation we get,

8⁻¹ - a⁻¹ = 1 * 4⁻¹

By further calculating the equation,

1/8 - 1/a = 1/4

4(1/8 - 1/a) = 1

4/8 - 4/a = 1

1/2 - 4/a = 1

4/a = 1/2

1/a = 4/2

a = 2/4

a = 2

Hence, the value of the a is 2.

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The area of the composite figure is 242in² as per the given information in the figure.

Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).

A crossed rectangle is a crossed (self-intersecting) quadrilateral made up of two opposing sides and the two diagonals of a rectangle[4] (therefore only two sides are parallel). It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic,  with opposite sides of equal length and equal angles that are not right angles.

Area =Area of the down rectangle+ Area of the up rectangle+2×Area of the triangle

Area= (7×24)+(4×13)+2×(1/2)×b×4

Let, 13+2x=24

Here, x=b

So, 2b=11

b=11/2

Area= 168+52+4(11/2)

Area=168+52+22

Area=242in²

Therefore, the area of the composite figure is 242in².

So, option C is correct.

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Answer:

Step-by-step explanation:

2. Subtraction property of equality

3. Simplification

4. Subtraction property of equality

5. Simplification

The measure of the third angle = 105°.

What is angles?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The sum of the angles in a triangle is :

A° + B° + C° = 180°

Where A, B and C are the three angles in a triangle.

Hence, if two of the angles are given as : 55° and 20°

The measure of the third angle will be :

Let the measure of the third angle = C

(55 + 25 + C) = 180°

180° - (55° + 20°)

180° - 75° = 105°

The measure of the third angle = 105°

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Answer:

4/5

Step-by-step explanation:

The required vertices of the triangle C'D'E' are (-8, 1), (-6, 5), and (-2, 4) respectively.

Given that,
Triangle CDE is reflected over the x-axis. What are the vertices of triangleC'D'E' is to be determined.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,

The coordinates of vertices  C, D, and E are (-8, -1), (-6, -5), and (-2, -4) respectively.

For the reflection across the x-axis is given as,

(x , y) = (x  -y)

Now,

C(-8, -1) across the x-axis C'(-8 , 1)

D(-6, -5) across the x-axis D'(-6 , 5)

E(-2, -4) across the x-axis E'(-2 , 4)

Thus the required vertices of the triangle C'D'E' are (-8, 1), (-6, 5), and (-2, 4) respectively.

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Answer:

68 cm^2

Step-by-step explanation:

A = ((a+b)/2) x h

A = ((6+11)/2) x 8

A = 68 cm^2

I hope my answer helps you.

Answer:

Area of the trapezium is 68[tex]cm^{2}[/tex]

Step-by-step explanation:

[tex]Given[/tex],

[tex]Parallel side\\[/tex] [tex]A[/tex]= 6cm

[tex]Parallel[/tex][tex]sideB=11cm[/tex]

[tex]Height = 8[/tex]

Formula to find the area of the trapezium

[tex]Area[/tex] [tex]of[/tex][tex]Trapezium[/tex]=[tex]\frac{1}{2}(a+b)h[/tex]

[tex]\frac{1}{2}[/tex][tex](6+11)8[/tex]

[tex]\frac{1}{2}[/tex] X[tex]136\\[/tex]

[tex]68[/tex]

Hence the area of the trapezium is 68

Answer:

2nd Option

Step-by-step explanation:

m=6

y=-3

so from equation

y=mx+c

y=6x-3

is the req ...... equation..

Answer: 2nd Option is the answer for this

Step-by-step explanation:

Answer:

x=36

Step-by-step explanation:

The length of a secant segment and a tangent segment drawn to a circle drawn from an external point is:

whole secant * external secant = tangent^2

(12+x)*12=24^2

144+12x=576

12x=432

x=36

Answer: 1 3/8

Step-by-step explanation:

6 - 4 5/8 = 1 3/8

Since you are missing a part to the sum, you use subtraction to find the missing part.

You will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.

What is continuous compound interest?

In theory, continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

The formula for continuously compounded interest is:

              [tex]A = P * e^{rt}[/tex]

where:

A is the ending balance (the amount you will have after 4 years)

P is the principal (the initial amount you deposited, in this case $3,000)

r is the interest rate (2.5% per year, or 0.025)

t is the time in years (4 years)

Plugging these values into the formula, we get:

            [tex]A = $3,000 * e^{(0.025 * 4)}[/tex]

Calculating this gives us an ending balance of $3,276.44.

Hence, you will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.

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Answer:

22, and -22

Step-by-step explanation:

22x22=484

-22x(-22)=484

Inequality                                                 classifications

x + 5y = −2 and x + 5y = 4                       Inconsistent

y = 3x + 4 and −2x + y = 4                       consistent and independent

3x + y = 4 and −6x − 2y = −8                   consistent and dependent

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

x + 5y = −2

x + 5y = 4  

subtracting gives

0 = -6 no solution  

A system is deemed consistent if it has at least one solution.

A consistent system is independent if it only has one solution.

-3x + y = 4

−2x + y = 4  

subtracting gives

-x = 0

x = 0

substituting x to get y

-3 * 0 + y = 4

y = 4

A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.

3x + y = 4

−6x − 2y = −8

subtracting gives

9x + 3y = 12 - none cancels out meaning infinite number of possible solutions

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The solution of the compound inequality are

-2x ≤ 4   and  10 ≥ -2x

10 < 3x - 2 OR -3x - 2 > 14

A sentence or equation having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality.

To solve the compound inequality each of them is solved individually

-2x ≤ 4   and  10 ≥ -2x

-2x ≤ 4           10 ≥ -2x

dividing by a negative sign reverses the inequality    

x ≥ -2              -5 ≤ x

plot attached

The solution of the inequality is x ≥ -2  and -5 ≤ x

10 < 3x - 2 OR -3x - 2 > 14

10 + 2 < 3x       -3x > 14 + 2

12 < 3x              -3x > 16

3 < x                 x < -5.333

3 < x                 x < -5

plot attached

The solution of the inequality is 3 < x  OR   x < -5

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After solving the quadratic equation, the value of k will be equal to 71.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given equation in the question,

4x² - 5x = -6

4x² - 5x + 6 = 0

k = b² - 4ac

⇒ (-5)² - 4(4)(6)

k = 25- 96

k = -71 or,

k = i(71)

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Montag serves as a metaphor for free thought in Fahrenheit 451. Guy doesn't fit in with society as Beatty or Mildred do.

Although the parallels are subtle, there are some similarities between the modern world and the setting of "Harrison Bergeron" in the narrative. Egality is a topic that both of them address and that has issues and effects. Another resemblance is the conflict that results from competition and attempts to stop it from happening, both of which cause issues.

The manipulative and desensitizing impact of the mass media is one political practice in American culture that the short story "Harrison Bergeron" might be seen as an oblique indictment of. overregulation of some human actions. restricting freedom of speech

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Answer:

160/3

Step-by-step explanation:

[tex]\frac{2^{2010}+2^{2008}}{2^{2005}-2^{2003}} \\ \\ =\frac{2^7 + 2^5}{2^2 - 1} \\ \\ =\frac{128+32}{4-1} \\ \\ =\frac{160}{3}[/tex]

Answer:

x=21

y=9/15 or 15/9

Step-by-step explanation

scale factor is either 15/9 or 9/15 - can't tell which way by the question

9/15x35=21

x=21

The number of players the team can bring to the tournament would be = 24 players

The softball game is the type of game that involves two teams which is made up of 9. - 10 players.

The total amount of money raised by a softball team=

$2089.50

The amount of money spent on rented bus = $1087.50

The amount left after rent deductions= 2,089.50 - 1,087.50 = 1,002

The amount budgeted for meals for each player= $41.75

The number of players that would be brought for tournament= 1,002/41.75

= 24 players.

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The area is 120 [tex]cm^{2}[/tex].

Area is the size of a two-dimensional surface, usually expressed in square units, such as square feet or square meters. It is the amount of two-dimensional space enclosed within a given set of boundaries. Area can be calculated for various shapes, including squares, rectangles, triangles, circles, and more complex shapes. Area is also a measure of the amount of space an object occupies. In mathematics, area is used to measure the size of a shape or region in a plane. It can also be used to calculate the size of a figure, such as the area of a triangle, or to measure the area of an enclosed space, such as a garden or a room.

Given:

AB = CD = 8cm

AD = BC = 12cm

EF = DH = 4cm

So, the required area is A = Area (ABCEFD) = Area (ABCD) + Area (CEFD)

Area of ABCD = Area (ABCD) = AB × BC

⇒ 12 × 8 = 96 [tex]cm^{2}[/tex]

Area of CEFD = Area (CEFD) = 0.5 (CD + EF) × HD

⇒ 0.5 × (8 + 4) × 4 = 24[tex]cm^{2}[/tex]

Now, the required area is

⇒ A = 96 [tex]cm^{2}[/tex] + 24 [tex]cm^{2}[/tex] = 120 [tex]cm^{2}[/tex]

Hence, the required area of the figure is 120 [tex]cm^{2}[/tex].

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Answer:

0

Step-by-step explanation:

          x

f(x) = ------  -  3

          7

           21

f(21) = ------  -  3

            7

f(21) = 3  -  3

f(21) = 0

I hope this helps!

The number of dark chocolate AJ sold is 75

Simultaneous equations are two or more algebraic equations that share variables e.g. m and d . They are called simultaneous equations because the equations are solved at the same time.

If the number of Milk chocolate candy is m and the number of dark chocolate candy is d, then

m+d= 200 equation 1

3m+4d= 675 equation 2

to eliminate m we multiply both equations by 3

3m+3d= 600 equation 3

3m+ 4d=675 equation 4

subtract equation 3 from 4

d = 675-600

d= 75

Therefore the number of dark chocolate candy AJ sold is 75.

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Answer:

correct answer is D) $1.94.

Step-by-step explanation:

To solve this problem, we first need to calculate the total cost of the candy bars and the sodas. The candy bars cost $0.84 each, so 3 candy bars cost 3*$0.84=$2.52. The sodas cost $1.80 each, so 2 sodas cost 2*$1.80=$3.60. The total cost of the candy bars and sodas is $2.52+$3.60=$6.12.

Since you are going to split the cost with your friend, you will pay for half, which is $6.12/2=$3.06. You pay for your half with a five dollar bill, so you will receive $5-$3.06=$1.94 in change.

I hope it helps, let me know if you have another questions.

Answer:

Step-by-step explanation:

First, we need to find the total cost of the candy bars by multiplying the number of candy bars by the price per candy bar: 3 candy bars * $0.84/candy bar = $3*0.84=2.52Next, we need to find the total cost of the sodas by multiplying the number of sodas by the price per soda: 2 sodas * $1.80/soda = $2*1.8=3.60Then, we need to add the cost of the candy bars and the sodas to find the total cost: $2.52 + $3.60 = $<<2.52+3.6=6.12>>6.12Since you are paying for half of the total cost, you need to pay half of $6.12, or $3.06.If you pay for your half with a five dollar bill, you will receive $5 - $3.06 = $5-3.06=1.94 in change. Answer: 1.94.