You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.

All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thénardier, Enjolras, Marius, Fantine, adult Cosette, adult Éponine, and Madame Thénardier. It is your job to seat these 9 actors, the 3 producers, and the director around the table.

Remember that there are 5 lead male roles and 4 lead female roles. If you must seat the male leads together, the female leads together, the 3 producers together, and the director by himself, how many different ways can you seat the 13 people around the circular table?

103,680
479,001,600
6,227,020,800
17,280

Answer:

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

Step-by-step explanation:

I assume that y - 1 is an exponent, and the equation is

[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]

[tex] 5^3 = (5^{-2})^{y - 1} [/tex]

[tex] 5^3 = 5^{-2y + 2} [/tex]

[tex] -2y + 2 = 3 [/tex]

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

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

Hello,

Step-by-step explanation:

[tex]f(x) = ln(x) {}^{4} [/tex]

[tex](ln(u)') = \frac{u'}{u} [/tex]

[tex]f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} [/tex]

[tex]f'(10) = \frac{4ln {}^{} (10) {}^{3} }{10} = \frac{12ln(x)}{x} [/tex]

[tex]f(10) = ln(10) {}^{4} [/tex]

[tex]y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)[/tex]

[tex]y = f'(a)(x - a) + f(a)[/tex]

By completing the square, we have

[tex](x+1)(x+4) = x^2 + 5x + 4 = \left(x+\dfrac52\right)^2 - \dfrac94[/tex]

[tex](x+2)(x+3) = x^2 + 5x + 6 = \left(x + \dfrac52\right)^2 - \dfrac14[/tex]

Then

[tex](x+1)(x+2)(x+3)(x+4) = \left(x+\dfrac52\right)^4 - \dfrac52 \underbrace{\left(x + \dfrac52\right)^2}_{=y} + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = y^2 - \dfrac52 y + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(y - \dfrac54\right)^2 - 1 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(\left(x + \dfrac52\right)^2 - \dfrac54\right)^2 - 1[/tex]

This product has a minimum of -1 when

[tex]\left(x + \dfrac52\right)^2 - \dfrac54 = 0[/tex]

which has two real solutions; then the minimum of the overall expression is -1 + 2019 = 2018.

Answer:

volume = 15 cm^3

Step-by-step explanation:

Volume of pyramid = 1/3  base area * height

                                = 1/3 ( 3 x 3 ) * 5 = 15 cm^3

Answer:

2y>-y+5

Step-by-step explanation:

because it has a eligible number at the right hand side

Answer:

A. four floors above the ground floor

Step-by-step explanation:

if you start at 0 which is the ground floor and go up 4, that would be +4, since, in theory, going up would be considered positive. So the answer is A.

The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

The sets are given as:

U = The set of one-digit numbers

A = {x: x is an even natural number less than or equal to 9}

One-digit numbers are numbers 0 - 9.

So, we have

U = {0, 1, 2, 3.....,9}

Natural numbers are numbers from 1.

Even natural numbers can be divided by 2 without remainder'

So, we have

A = {2, 4, 6, 8}

Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

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Answer:

Step-by-step explanation:

it is three fifths,

and it is the answer.

We have this equation:

[tex]\log(x) + \log(x + 99) = 2[/tex]

First, combine both logarithms using the multiplication property and simplify the expression.

[tex]\log[x(x + 99)] = 2[/tex]

[tex]\log[ {x}^{2} + 99x ] = 2[/tex]

Now, use the definition of logarithm to transform the equation.

[tex] {10}^{2} = {x}^{2} + 99x[/tex]

[tex] {x}^{2} + 99x - 100 = 0[/tex]

Finally, use the quadratic formula to solve the equation.

[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]

With this, we can say that the solution set is:

We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.

First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.

73 + 90 + x = 180

163 + x = 180

x = 17

So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).

17 + x = 180

x = 163

So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.

Therefore, angle r is 163 degrees. The correct answer is option C.

Hope this helps!

Answer:

d

Step-by-step explanation:

it's kinda hard to explain

Applying the distributive property, we would simplify the expression as: 5f + 16f = (5 + 16)f = 21f.

The distributive property states that, ab + ac = (b + c)a.

Using the distributive property, we have:

5f + 16f

= (5 + 16)f

= 21f

Therefore, 5f + 16f is simplified as 21f.

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la longitud del jardín del amigo de Carmen es 18 m 22 cm.

Una ecuación se forma cuando dos expresiones algebraicas se igualan usando un signo igual.

Se da que la longitud de Carme

Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.

y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.

Sea La longitud del jardín de Carmen es x m

Entonces la ecuación se convierte en

La longitud del jardín de su amigo = x + 2m 98 cm

ahora ,

x = 15m 24cm

Sustituyendo los valores en la ecuación

La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm

1m = 100cm

La longitud del jardín de su amigo = 17 m 122 cm

as 100 cm = 1m

122 cm = 1 m 22 cm

so ,

La longitud del jardín de su amigo = 18 m 22 cm.

Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.

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Answer:

0

Step-by-step explanation:

numerator are the same the difference between same number or variable will be zero

If block has length 100 yards and breadth 76 yards then we have to drive 5 times to drive one mile.

Given The length of block is 100 yards, the breadth of block is 76 yards.

We have to find number of times we need to drive one mile.

The perimeter of a rectangle= 2(length +breadth)

length is 100 yards

Breadth is 76 yards

perimeter=2(100+76)

=2*176

=352 yards.

We know that 1 mile is equal to 1760 yards.

We have to find number of times to drive 1 mile=1760/352

=5 times.

Hence we have to drive 5 times around the block which have length 100 yards and breadth 76 yards.

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Answer:

[tex]10^{0.4785+1.468x}=y[/tex]

Step-by-step explanation:

So I'm assuming when you typed "log yhat=.4785 + 1.468x", you meant to write: [tex]log(y)=0.4785+1.468x[/tex]. And generally a logarithm can be written in the form [tex]log_ba=c[/tex] which can then be rewritten as [tex]b^c=a[/tex], but since the log has no base, it's assumed to be 10. So in this case you have the equation:

[tex]log_{10}y=0.4785+1.468x[/tex], which can then be written in exponential form as:

[tex]10^{0.4785+1.468x}=y[/tex]

Using the scale ratio, the length of the dress is: 6 ft.

Given a scale for the dress pattern as, 2 inches : 1 foot, it means 2 inches of the model equals 1 foot of the actual dress.

Therefore, using the scale ratio, let x represent the length of the dress. We would have:

2/1 = 12/x

x = (12 × 1)/2

x = 6 ft.

The length of the dress is: 6 ft.

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Diego's height is 7 units

The statement is given as:

77 is the product of 7 and Diego's height

This means that:

77 = 7 * d

Divide both sides by 7

d = 11

Hence, Diego's height is 7 units

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Answer:

12

Step-by-step explanation:

LCD of 1/4 and 1/6 is the least common denominator that is divisible by 4 and 6 at the same time and is the least.

So it the same to find least common multiple of 4 and 6 that is 12.

The answer is 12.

Answer:

6  1/12 miles total

Step-by-step explanation:

3 1/4 = 13/4

2 5/6 = 17/6        to ADD fractions, you must have a common denominator

                              I will use 12   for these

13/4 = 39/12

17/6 = 34 /12

now you can add and simplify     39/12 + 34/12 = 73/12 = 6 1/12  miles

The probability that the market will go up and interest rate will go down during the period in question is 0.03.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the market will go up and interest rate will go down  = 0.08 X 0.40 = 0.03

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The area of the exposed surface is 442 square feet

A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.

Analysis:

The exposed surface is the area of the four triangles.

The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft

Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.

In conclusion, area of exposed surface is 442 square feet.

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Answer:

SI =PXRXT/100

Step-by-step explanation:

THIS WOULD HELP YOU

Answer:

 (3x + 3) (9x + 7) is the duplicate ratio of 3:5 . the value of x is 2.

Answer:

3

Step-by-step explanation:

whenever solving for x, you have to work backwards…like so:
3 squared is 9

27 divided by nine is 3

x=3

To double check the answer, substitute the value that we just found into x

(3x3)x3=27

Answer:

[tex]x=\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]3^{2x}=27[/tex]

Rewrite 27 in exponential form with base 3:

[tex]\implies 3^{2x}=3^3[/tex]

As both exponents have the same base,

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies 2x=3[/tex]

Divide both sides by 2:

[tex]\implies x=\dfrac{3}{2}[/tex]

The amount that's was attributed to the project from the start based on the percentage is $7,500,000.

From the information given, the remaining percentage will be:

= 100% - (25% + 20% + 35%)

= 100% - 80%

= 20%

Let the total amount be x.

Therefore, 20% of x = 1,500,000

0.2x = 1,500,000

x = 1500000/0.2

x = 7500000

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The attached graph represents the image of the triangles

To do this, we make use of the following coordinates

A = (1, 0)

B = (5, 0)

C = (1, 6)

The lengths of the triangle are calculated using

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(1-5)^2 + (0 -0)^2} = 4[/tex]

[tex]BC = \sqrt{(1-5)^2 + (6 -0)^2} = 7.2[/tex]

[tex]AC = \sqrt{(1-1)^2 + (6 -0)^2} = 5[/tex]

Using the scale factor of 2, we have the image of the dilation to be:

D = (2, 0)

E = (10, 0)

F = (2, 12)

The lengths of these sides are

DE = 8

EF = 14.4

DF = 10

See attachment for the image of the triangles ABC and DEF

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The end behavior of the function is as:

as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞

The end behavior of a function will describe the behavior of the graph of the function at the "ends" of the x-axis.

By determining the highest degree of the polynomial function. As the highest degree term will grow faster than the other terms as x gets very large or very small, its behavior will dominate the graph.

The graph of the function is f(x)=2∛x

the function leads to infinity so the end behavior of the function is

as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞

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Answer:

a the assumption is that after the 60% discount, the 20% will contribute to the old price, not the adjusted price

b this is incorrect because the 20% discount will be added on after the 60% discount has been used

c the 500 dollars would turn to 100 dollars

d 40

e it would be best to first apply the 60% coupon first over the 20% coupon