Question 2: Remember that there are 5 lead male roles and 4 lead female ones. If you must seat the male leads together and the female leads together, the three producers together and the director by himself, how many different ways can you seat 13 people around the circular table?

Answers

Answer 1

Answer: 103,680
----------------------------------------------

Explanation:

There are 13 people total. We can group up the male leads since they must sit together. Consider this group of five as one "person". Do the same for the female leads since they must sit together as well. The same applies to the producers.

Effectively we have these groups
* Male leads
* Female leads
* Producers
* Director

So we have 4 "people" in a sense sitting around the table giving (n-1)! = (4-1)! = 3! = 3*2*1 = 6 different ways to arrange these four groups.

Within the "male leads" group, there are 5! = 120 ways to permute the members.
Within the "female leads" group, there are 4! = 24 ways to permute the members.
Within the "producers" group, there are 3! = 6 ways to permute the members.
Within the "director" group, there's only one person so 1! = 1 way to arrange the members
So there are 120*24*6*1 = 17,280 different ways to arrange any one of the six permutations of the four groups.

Overall, there are 6*17,280 = 103,680 total permutations.

Related Questions

Which of the following is a rational number?

Answers

The rational number would be 16

Choose the best definition for the following term:substitution

Answers

the action of replacing someone or something with another person or thing

A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.

can someone help me, i am very confused, i need to find the volume of the figure put i dont know how
please help me and write steps

Answers

Ok so what you need to know about an octahedron is it's basically two square pyramids stacked on top of each other (one is upside down of course).

The formula for volume of a pyramid is Bh/3.
Base= 8*8=64
Height= 3 each
64*3/3= 64 mm^3 per pyramid.

64*2=128 mm^3 for the octahedron

Final answer: 128 mm^3

What is the end point and mid point

Answers

The endpoints are the points which represent or marks the end of a line segment or an interval. So, the endpoints would be the same points given which are ( 5/3, 1 ) and ( 0, 2). The midpoint, on the other hand, is the point that is located halfway through the line segment or the interval. It divides the segment into two parts with equal lengths. We calculate it by the formula,
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

We substitute the points given above to the formula as follows:

midpoint = ((5/3 + 0) / 2, (1 + 2) / 2)
midpoint = 5/6 , 3/2

So, the midpoint is located at point 5/6, 3/2.

Answer:

end point is (-5/3 , 3)

mid-point: (5/6, 3/2)

Step-by-step explanation:

Read the following statement: All real numbers have a reciprocal. Which of the following choices is a counterexample to the statement?

1/4
0
1
-7

Answers

0 as its reciprocal is 0.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

All real numbers have a reciprocal.

But we know that 0 has no inverse, means there is no reciprocal exists for 0.

Because,

[tex]\dfrac{1}{0}=\infty[/tex]

So, 0 is a counter example to the statement.

Hence, Second option is correct.

Quintin set a goal to do 15 push-ups each day. By how much would he exceed his goal if he did 17 push-ups in a day?

2
7
19
32

Answers

17-15 =2

he would exceed by 2 a day

How long does it take a plane, traveling at a speed of 110 m/s, to fly once around a circle whose radius is 2850 m?

Answers

V=110, s= 2×π×r (circumference of a circle)
t=s/v=110/2×π×2850

Answer:

It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]

Step-by-step explanation:

The first step in this exercise is to find the total distance that the plane will fly.

This distance is equal to the perimeter of a circle whose radius is 2850 m.

Given a circle of radius R, the perimeter ''P'' can be calculated as :

[tex]P=\pi .d=\pi .2.R[/tex]

Where ''d'' is the diameter of the circle that is equal to 2.R

The distance that the plane will fly in the exercise is :

[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]

Now, the speed is equal to distance divided by time.

[tex]speed=\frac{distance}{time}[/tex]

We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.

[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]

[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]

[tex]t=(162.792)s[/tex]

We find that the time is [tex]162.792[/tex] seconds.

Assume that a researcher randomly selects 14 newborn babies and counts the number of girlsâ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting 9 or more girls.

Answers

Probability is the mathematics of chance. In other words, it is the fraction or percentage of a certain event successfully happening. For this problem, you want to determine the probability of selecting 9, 10, 11, 12, 13 or 14 girls. The solution is as follows:

P = nCr p^r q^n-r
where
n is number of total events (n = 14)
r is the number of events that could happen (9, 10, 11, 12 ,13 and 14)
p is the probability of an event being a girl (p = 50% or 0.5)
q is the probability of either an event being a boy (q = 1-p = 0.5)
nCr is a combination formula which is n!/(r!(n-r)!)

P = [14C9* (.5)^9 * (0.5)^5]+ [14C10* (.5)^10 * (0.5)^4]+[14C11* (.5)^11 * (0.5)^3]+[14C12* (.5)^12 * (0.5)^2]+[14C13* (.5)^13 * (0.5)^1]+[14C14* (.5)^14 * (0.5)^0]

P = 0.211 or 21.1%

Final answer:

To find the probability of selecting 9 or more girls out of 14 newborn babies, sum the probabilities for selecting 9 to 14 girls from the given table.

Explanation:

To find the probability of selecting 9 or more girls out of 14 babies, we need to calculate the sum of the probabilities of selecting 9, 10, 11, 12, 13, and 14 girls. Refer to the given table that summarizes the probabilities for each value of x. Add the probabilities for these values to get the probability of selecting 9 or more girls.

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ten less than twice a number is the same as 7 times the number. find the number

Answers

The number is -2 // Math [n is equivalent to number]: 2n -10 = 7n
2n = 7n + 10
-5n = 10
-n = 2
n = -2
// Hope this helped, please give me brainliest, thanks!! //

In the triangle below, determine the measure of side a.

Answers

use trigonometry
sin 42 = a / 21

a = 21 sin 42 = 14.05

When determining the number of significant figures in a number, zeroes to the left of the decimal point are never counted.
a. True
b. False?

Answers

The number of significant figures in a number means the number of digits that actually have a meaning in the number and should be included in measurements.

Zeros are not counted in special cases, these cases are as follows:
1- When the zero is the first digit from the left followed by other digits before the decimal point
Example: 02.5 , 009.3 (zeros are not counted here)
However, in a number as 30.3, the zero is definitely counted

2- When the zero is the last digit on the right after the decimal point
Example: 23.330 , 8.90 (zeros are not counted here)

Based on this, the above mentioned statement is false.
Since zeros are counted before the decimal point when they are not the leftmost digits
counted in : 30.4
not counted in : 03.4

(1 point) solve the separable differential equation y′(x)=2y(x)+18−−−−−−−−−√, y′(x)=2y(x)+18, and find the particular solution satisfying the initial condition y(5)=9.

Answers

We write the equation in terms of dy/dx,
y'(x)=sqrt (2y(x)+18)
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9))

Separating the variables in the equation, we will have:
1/sqrt(y + 9) dy= sqrt(2) dx

Integrating both sides, we will obtain
2sqrt(y+9) = x(sqrt(2)) + c
where c is a constant and can be determined by using the boundary condition given
y(5)=9 : x = 5, y = 9
sqrt(9+9) = 5/sqrt(2) + C

C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2

Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2

sqrt(y+9) = (2x + 2) / 2sqrt(2)

Squaring both sides, we will obtain,
y + 9 = ((2x+2)^2) / 8

y = ((2x+2)^2) / 8 - 9

An activity book has 21 pages of crossword puzzles, 18 pages of cryptograms, and 12 pages of mazes. bianca randomly selects a page, completes the activity, and then randomly selects another page to complete. what is the probability that bianca first completes a maze and then completes a crossword puzzle?

Answers

21 crosswords, 18 cryptograms, 12 mazes....total of 51 activities

P(maze) : 12/51...reduces to 4/17
P(crossword) 21/50

P(both) : 4/17 * 21/50 = 84/850 = 42/425 <=

Final answer:

The probability that Bianca first completes a maze and then completes a crossword puzzle is approximately 9.8%.

Explanation:

To find the probability that Bianca first completes a maze and then completes a crossword puzzle, we need to calculate the probability of each event occurring and then multiply them together.

The total number of pages in the activity book is 21 + 18 + 12 = 51 pages.

The probability of selecting a maze page first is 12/51, and after completing the maze page, there are now 50 pages remaining in the book, 21 of which are crossword puzzles.

So, the probability of selecting a crossword puzzle page after completing a maze page is 21/50.

To find the probability of both events happening, we multiply the probabilities: (12/51) * (21/50) = 0.098 or 9.8%.

Quadrilateral abcd has side lengths of ab = 13w 5, bc = 5z 2, cd = 13w 5, and ad = 3z + 5. find the value of z for which quadrilateral abcd is a parallelogram.

Answers

Final answer:

To find 'z', utilise the properties of a parallelogram where opposite sides are equal. Setting these sides equal to each other and solving for 'z' provides the answer, 'z' = 3.5.

Explanation:

In this problem, you're given a quadrilateral ABCD for which you are supposed to find the value of 'z' when the quadrilateral is a parallelogram. In a parallelogram, the opposite sides are equal. Therefore, we can set AB = CD and BC = AD, and then solve for 'z'. From AB = CD (13w + 5 = 13w + 5), no information is required as their lengths are already equal. From BC = AD (5z - 2 = 3z + 5), solving for 'z' would give us 'z' = 7/2 or 3.5.

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A line contains points (−2,−2) and (1,4). Find the distance between the line and the point (6,−1).

Answers

In analytical geometry, derived equations are already available for finding the distance between a point and a line. The equation is

[tex]d = \frac{|Ax + By+ C|}{ \sqrt{ A^{2}+ B^{2} } } [/tex]

This is basing on the standard equation of a line in the form of:
Ax + By + C = 0, where A, B and C are coefficients.
These constants are coming from the equation of the line, while the point (x,y) is substituted to the x and y terms of the equation.

However, we must first know the equation of the line. Let us use the slope-intercept form: y = mx + b, where m is the slope which is equal to (y2-y1)/(x2-x1) while b is the y-intercept. For points (−2,−2) and (1,4), the slope is

m = (4--2)/(1--2) = 2

Then, we substitute any of those points to determine b. The answer would be the same either way. Let's use (-2,-2).
-2 = 2(-2) + b
b = 2

Thus, the equation of the line is y = 2x + 2. Rearranging into the standard form, it becomes 2x - y + 2 = 0. Therefore, A=2, B=-1 and C=2. Substituting the values to the equation by replacing x and y with coordinates of point (6,−1),

[tex]d = \frac{|2(6) + (-1)(-1)+ 2|}{ \sqrt{ 2^{2}+ (-1)^{2} } }[/tex]

d = 3√5 or 6.71 units

Two ants race across a table 61 cm long. one travels at 5.13 cm/s and the other at 3.99999 cm/s. when the first one crosses the finish line, how far behind is the second one? answer in units of cm

Answers

time = distance / speed

Ant 1 : travels at 5.13 cm/s for 61 cm
t = d / s
t = 61 / 5.13
t = 11.89 seconds

Ant 2 : travels at 3.99999 cm/s for 61 cm
t = 61 / 3.99999
t = 15.25 seconds

so Ant B is (15.25 - 11.89) = 3.36 seconds behind Ant A

What is the factorization?

-3x^3+15x^2+42x

A. 3(x+7)(x+2)
B. 3(x^2)(x+2)
C. -3x(x+7)(x-2)
D. -3x(x-7)(x+2)

Answers

First take out the GCF
-3x(x^2-5x-14)
-3x(x-7)(x+2)
-7+2=-5
-7*2=-14

Answer: D

Use basic identities to simplify the expression.
cos θ - cos θ sin2θ

Answers

cos Ф - cos Ф.sin² Ф

sin² Ф = 1 - cos² Ф
cos Ф - cos Ф( 1-cos² Ф) = cos Ф - cos Ф - cos³ Ф = cos³ Ф

cos Ф - cos Ф.sin² Ф = cos³ Ф

The solution for the expression will be cos Ф - cos Ф.sin² Ф = cos³ Ф.

What are trigonometric identities?

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

The given trigonometric expression will be solved as below,

cos Ф - cos Ф.sin² Ф

We know that, sin² Ф = 1 - cos² Ф

E = cos Ф - cos Ф( 1-cos² Ф)

E = cos Ф - cos Ф - cos³ Ф

E = cos³ Ф

Therefore, the expression is cos Ф - cos Ф.sin² Ф = cos³ Ф.

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A cylinder has a height of 2 meters and a diameter that is 5 times the measure of the height. Using 3.14 for pi, which of the following can be used to calculate the volume?

(3.14)(2m)2(10m)
(3.14)(2m)2(5m)
(3.14)(10m)2(2m)
(3.14)(5m)2(2m)

Answers

Given that diameter of cylinder is 5 times the height and height=2m, then the diameter will be:
2*5=10 m
the radius=10/2=5 m
the volume of the cylinder will be:
V=πr^2h
π=3.14
hence;
v=3.14*(5^2)*(2)
the answer is:
(3.14)(5m)^2(2m)

The answer is (3.14)(5m)^2(2m)

Hope that helps <3

The rule T1, -4 RO, 180°(x, y) is applied to rectangle KLMN. Which rectangle shows the final image??

Answers

Let me help you!

Looking at the visual, we can see five figures: KLM, 1, 2, 3, and 4.
Applying the rule T1, -4 RO, 180°(x, y) to rectangle KLMN - without even solving - just by merely observing, we can say (without a doubt) that the rectangle KLMN will most likely fall in the negative axis.

First rotation: -4 to the left.
Second rotation: -4 to the left.
Last rotation: -4 to the left making the last figure 3. <----- What we are looking for!

Therefore, the rectangle which shows the final image is figure 3 or rectangle 3.

Answer:

Figure 3.

Step-by-step explanation:

We perform the rotation first. A 180° rotation about the origin maps every point

(x, y)→(-x, -y). This means it negates both the x- and y-coordinates.

The pre-image points are:

K(3, -4); L(3, -1); M(5, -1); N(5, -4). Performing the rotation and negating the coordinates will give us:

K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).

Now we perform the translation. The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate. This maps to our new points:

K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)

These are the points of figure 3.

If Polly walks across the street to buy a cracker and the people who sell them only have one left and there's a long line out the door... will Polly get a cracker? I'm so confused :/ thanks so much for the help!

Answers

Let me break this down for you.

Polly walks across the street to buy a cracker (singular)

The sellers of the crackers only have 1 left to sell and there is a long line out the door.

Unless the owners have more frackers readily available to continue to sell, Polly will NOT get a cracker unfortunately.

Hope this helps! :)

Paul bought 9 total shirts for a total length f $72. Tee shirts cost $10 and long sleeve shirts cost $7. How many of each type shirt did he buy

Answers

x = tee shirts, y = long sleeved shirts

x + y = 9....x = 9 - y
10x + 7y = 72

10(9 - y) + 7y = 72
90 - 10y + 7y = 72
-10y + 7y = 72 - 90
-3y = - 18
y = -18/-3
y = 6 <=== 6 long sleeved shirts

x + y = 9
x + 6 = 9
x = 9 - 6
x = 3 <== 3 tee shirts

6 long sleves and 3 short

What is the solution of the equation e^xe^2x = 4? Round your answer to the nearest hundredth.

Answers

The equation is:

[e^x] [e^(2x)] = 4

1) Applying property of multiplication of powers wiith same base =>

e ^ (x + 2x) = 4

=> e ^ (3x) = 4

2) Applying logarigth properties

3x = ln(4)

=> x = ln(4) / 3 ≈ 1.38629 / 3 ≈ 0.4621

Answer: x = ln(4) / 3 ≈ 0.4621

URGENT

A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?

A.
5/143

B.

7/143

C.

28/143

D.

30/143

Answers

5/13 * 4/12 * 3/11 is our representation, which yields 5/143, A. There is no replacement therefore the amount of available total candidates and available women shrink with each position filled.

Answer:

[tex]A. \frac{5}{143}[/tex]

Step-by-step explanation:

Given,

Number of women = 5,

Number of men = 8,

Total persons = 5 + 8 = 13,

∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]

Also, the ways of selecting 3 women = [tex]^5C_3[/tex]

Hence, the probability of selecting 3 women

[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]

[tex]=\frac{^5C_3}{^{13}C_3}[/tex]

[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]

[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]

[tex]=\frac{60}{13\times 12\times 11}[/tex]

[tex]=\frac{5}{143}[/tex]

Hence, OPTION A is correct.

H-79= -83 Solve the equation ?

Answers

Ok so take -79 and add it too -83 so -83 + 79 to get your answer of H= what ever answer you get

H-78=-83
Add 78 on both sides
H=-4
Check=
-4-79=-83
-83=-83
So h=-4.

Find the degree of the monomial. 6y2w8

Answers

Degree of a monomial or polynomial is the highest exponent you can see in the expression. The two variables, y and w, both have exponent of 1. So, the degree of this monomial should be 1.

which choice is equal to the repeating decimal below? 0.6

a) 0.666
b) 6/10
c) 0.66666666

Answers

the answer is 6/10 my fren :) good luck.

Hello.

[tex]6/10 = 0.6 [/tex]

I am confused by the question though. 0.6 is not a repeating decimal. But either way, 6/10 = 0.6

Feel free to ask me more questions on my profile. I am more than happy to help. Don't forget Brainliest! :)

He scatter plot shows the number of pages scanned (y) in different number of hours (x) by a scanning machine: which function best represents the data shown in the scatter plot

Answers

do you understand how to solve or do you want me to explain

The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?
{2, 4}
{-2, -4}
{12, 14}
{-12, -14}
{0, 5}

Answers

f(x) = x+5 is the same as y = x+5

Plug in y = 7 and solve for x
y = x+5
7 = x+5
7-5 = x+5-5
2 = x
x = 2
So x = 2 is part of the domain

Now plug in y = 9 and solve for x
y = x+5
9 = x+5
9-5 = x+5-5
4 = x
x = 4
and x = 4 is also part of the domain

Therefore the domain is {2,4}

I Need Help ASAP! This is Due in 30 Minutes!

I don't Understand it at all and I need Help

Create a factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

Answers

This looks like an odd problem.

Just start with a simple expression with 7 as a factor, and then multiply it out.

For example:

7(x+1)(x+2)

Here 7 could be the GCF.

Now multiply it out:

7(x^2+3x+2) =

7x^2+21x+14

So our factorable polynomial is 7x^2+21x+14

And its two equivalent forms are:

7(x^2+3x+2)
and
7(x+1)(x+2)

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