In how many ways can 5 different novels, 4 different mathematics books, and 1 biology book be arranged on a bookshelf if: (a) The books can be arranged in any order? Your answer is: 3628800 (b) The mathematics books must be together and the novels must be together? Your answer is : 6 (c) The mathematics books must be together but the other books can be arranged in any order? Your answer is: 5040

Answers

Answer 1

Answer:

(a) 3628800 ways

(b) 17280 ways

(c) 120960 ways

Step-by-step explanation:

Given

[tex]Novels = 5[/tex]

[tex]Maths = 4[/tex]

[tex]Biology = 1[/tex]

[tex]Total = 10[/tex]

Solving (a): Arrangement with no restriction.

We simply count each book with no restriction. i.e. 10 books

So, the number of arrangement is:

[tex]Arrangement =10![/tex]

[tex]Arrangement =10*9*8*7*6*5*4*3*2*1[/tex]

[tex]Arrangement =3628800[/tex]

Solving (b): Maths book together and Novels together

First, arrange the 4 maths books as:

[tex]Maths = 4![/tex]

Next, arrange the 5 novels as:

[tex]Novels = 5![/tex]

Lastly, take the 4 maths book as [1], the 5 novels as [1] and the remaining [1] biology book.

So, we have: 3 books

Arrange 3 books, we have:

[tex]Books = 3![/tex]

Total arrangement is:

[tex]Total = 4! * 5! * 3![/tex]

[tex]Total = 4*3*2*1 * 5*4*3*2*1 * 3*2*1[/tex]

[tex]Total = 17280[/tex]

Solving (c): Maths book together

First, arrange the 4 maths books as:

[tex]Maths = 4![/tex]

Next, take the 4 maths book as [1], then the remaining 6 books (i.e. 5 novels and 1 biology)

So, we have: 7 books

Arrange 7 books, we have:

[tex]Books = 7![/tex]

Total arrangement is:

[tex]Total = 4! * 7![/tex]

[tex]Total = 4*3*2*1 * 7*6*5*4*3*2*1[/tex]

[tex]Total = 120960[/tex]


Related Questions

What is the inverse statement,"If I listen to this song, then it will get stuck in my head"?

Answers

Answer:

D. If I do not listen to this song, then it will not get stuck in my head.

Step-by-step explanation:

Answer:

"If I don't listen to this song, then it won't get stuck in my head."

A data set includes data from student evaluations of courses. The summary statistics are n​, ​, s. Use a significance level to test the claim that the population of student course evaluations has a mean equal to . Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Answers

Complete question :

A data set includes data from student evaluations of courses. The summary statistics are nequals92​, x overbarequals4.09​, sequals0.55. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Answer:

H0 : μ = 4.25

H1 : μ < 4.25

T = - 2.79

Pvalue =0.0026354

we conclude that there is enough evidence to conclude that population mean is different from 4.25 at 10%

Step-by-step explanation:

Given :

n = 92​, xbar = 4.09​, s = 0.55 ; μ = 4.25

H0 : μ = 4.25

H1 : μ < 4.25

The test statistic :

T = (xbar - μ) ÷ s / √n

T = (4.09 - 4.25) ÷ 0.55/√92

T = - 0.16 / 0.0573414

T = - 2.79

The Pvalue can be obtained from the test statistic, using the Pvalue calculator

Pvalue : (Z < - 2.79) = 0.0026354

Pvalue < α ; Hence, we reject the Null

Thus, we conclude that there is enough evidence to conclude that population mean is different from 4.25 at 10%

Answer:

Step-by-step explanation:

The null and alternative hypotheses are:

Null hypothesis: The population mean of student course evaluations is equal to 4.25.

Alternative hypothesis: The population mean of student course evaluations is not equal to 4.25.

The significance level is 0.01, so the test will be a two-tailed test.

The test statistic is calculated as:

t = (x - μ) / (s / √n) = (4.18 - 4.25) / (0.54 / √97) = -2.63

The degrees of freedom for the t-distribution is n-1 = 96. Using a t-table or a calculator, the P-value for a two-tailed test with 96 degrees of freedom and a t-value of -2.63 is approximately 0.010.

Since the P-value (0.010) is less than the significance level (0.01), we reject the null hypothesis. We have sufficient evidence to conclude that the population mean of student course evaluations is not equal to 4.25.

In other words, the data provides strong evidence to suggest that the average student course evaluation rating is significantly lower than 4.25.

If right I’ll mark brainiest need ASAP

Answers

Answer

Step-by-step explanation: Anybody who help me I will mark brainliest in give you 180 points you have to go on my page in answer all my questions

Determine the amplitude or period as requested . Amplitude of y = - 1/5 * sin x a - 1/5 1/5 b 5 d. pi/5

Answers

Answer:

The amplitude is 1/5

Step-by-step explanation:

Given

[tex]y = -\frac{1}{5}\sin(x)[/tex]

Required

Determine the amplitude

The general cosine function is:

[tex]y = A\sin(k(x + c)) +d[/tex]

Where

[tex]Amplitude = |A|[/tex]

Compare [tex]y = A\sin(k(x + c)) +d[/tex] and [tex]y = -\frac{1}{5}\sin(x)[/tex]

[tex]A = -\frac{1}{5}[/tex]

So:

[tex]Amplitude = |-\frac{1}{5}|[/tex]

[tex]Amplitude = \frac{1}{5}[/tex]

Which angle is an acute angle?
A. An angle measuring 325°
B. An angle measuring 265°
C. An angle measuring 125°
D. An angle measuring 85°

Answers

Anything less than 90 degrees or Pi/2, so that would be d.

Answer:

The answer is Option D

Step-by-step explanation:

Option D is the right answer since 85° is a acute angle. Acute angles are angles below 90°

Hope this helps!

Have a good day

im sooooooooo bord sooooo you get 100 points for ansering 1+1¥¥¥¥¥¥¥¥

Answers

Answer:

1+1=2

Step-by-step explanation:

THANKS YOU YAY HOPE IT HEOPS

Answer:

2 thanks

Step-by-step explanation:

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius ?

Answers

Step-by-step explanation:

Cone Volume = 1/3 ×( π r² h)      h = 2 × diameter  =  2 × 2 × r

Cone Volume = 1/3 ×( π r² h)      h = 2 × diameter    diameter = 2r

                                                       =  2 × (2 × r)  

                                                       = 4r

                                                         

Cone Volume = 1/3 ×( π r² 4r)

                        =  (4 π r³ / 3)

Gino wants to leave at least 20% tip on his restaurant bill of $197.40. Approximately how much tip should he add to the bill?

Answers

So exactly it would be 39.48, but do you want me to round to a specific ten?

PLEASE HELP THIS IS DUE TODAY

rearrange the parallelogram as a rectangle. Then find the area.

Answers

answer= 12. hope this helped. almost 100% sure this is right.

find the cost of fencing a rectangular field 250m long and 130m wide at rupees 30 per meter​

Answers

Answer:

length of rectangular =250m

breath =130m

perimeter of rectangular field =(130*250)

=32500m

cost of fencing a rectangular field at the rate of 30 per meter

cost of the rectangular field =32500*30  

=rupees 975000

hope it helps

{7x+4y=-8
{-8x-5y=13
Solve system of equation

Answers

Answer:

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

Step-by-step explanation:

The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).

What is the solution of the equation?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The solution of the equation means the value of the unknown or variable.

The system of the equation is given below.

7x + 4y = – 8      …1

8x + 5y = –13     …2

Multiply equation 1 by 5 and equation 2 by 4. Then subtract the equation 1 from 2, then we have

32x – 35x = –52 – (–40)

          –3x = –12

              x = 4

Substitute the value of x in equation 1, then the value of y will be

7(4) + 4y = – 8

 28 + 4y = –8

          4y = –36

            y = –9

The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).

More about the solution of the equation link is given below.

https://brainly.com/question/545403

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A company bought 7 machines. Each machine weighs 642.4 pounds. How many pounds do the 7 machines weigh altogether?

Answers

Answer:

4496.8 pounds

multiply 642.4by7

Please solve this: the area of a rectangular piece of card is 56cm square.

Answers

9514 1404 393

Answer:

  7 cm

Step-by-step explanation:

The formula for the area of a rectangle tells you the area is the product of length and width:

  A = LW

  56 = 8W

From your knowledge of multiplication tables, you know that ...

  56 = 8·7

That is, W = 7 . . . cm.

The width of the card is 7 cm.

Answer:

7 cm is the answer.

Step-by-step explanation:

#CarryOnLearning

Add.write the answer as a mixed number in the simplest form.

Answers

Answer:

5[tex]\frac{11}{12}[/tex]

Step-by-step explanation:

GCF of 4 and 6 is 12

1/6 = 2/12

3/4 = 9/12

4 + 1 = 5

2/12 + 9/12 = 11/12

5 11/12

Answer:

71/12

Step-by-step explanation:

First you want to make the denominators in the fractions the same number. To do so, we need to multiply both the numerators and the denominators. Do this until the denominators are the same.

[tex]\frac{1}{6} *\frac{4}{4} = \frac{4}{24}[/tex]

[tex]\frac{3}{4} *\frac{6}{6} = \frac{18}{24}[/tex]

Now add

[tex]4\frac{4}{24} + 1\frac{18}{24} = 5\frac{22}{24}[/tex]

After adding, you need to multiply the whole numbers by the denominator and add that number to the numerator.

[tex]5*24=120[/tex]

[tex]\frac{120}{24} +\frac{22}{24} = \frac{142}{24}[/tex]

Finally simplify

[tex]\frac{142}{24} / \frac{2}{2} = \frac{71}{12}[/tex]

Two women share 60 eggs
it the ratio 1 to 2. How many eggs does each recieves?

Answers

Answer:

One woman receive 20 eggs

And the other receive 40 Egss

Explanation:

So the ratio is 1:2 so we gonna add them to get the total so 1+2=3

To find each amount divide each by the total so 1/3 and 2/3

To find the first amount

1/3×60=20

To find the other amount you can either subtract

60-20=40

or

2/3×60=40

One woman receive 20 eggs and the other receive 40 eggs.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

So the ratio is 1:2 so we have to add them to get the total.

So 1+2=3

In order to find each amount divide each by the total.

So 1/3 and 2/3

The first amount,

1/3 × 60 = 20

The other amount,

60-20=40

or

2/3 × 60 = 40

Thus, One woman receive 20 eggs and the other receive 40 eggs.

Learn more about the unitary method;

https://brainly.com/question/23423168

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[tex]\boxed {\boxed {prove : \: 3 \: is \: greater \: than \: 5​ }} [/tex]

Answers

3 has more letters than 5. Hence 3 is greater than 5

Which of the following is equivalent to 19 L?
A. 1,900 mL
B. 0.019 mL
C. 19,000 mL
D. 0.0019

Answers

the answer is A which is 1900 ml

A,1,900 is the answer best

Yesterday, a movie theater sold 269 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all the movie theater made $494 from
popcom sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
The movie theater sold large bags of popcorn and small bags of popcorn.

Answers

Answer:

S=194, L=75 L+S=269, 4L+1S=$494

Step-by-step explanation:

what is the surface area of this design

Answers

Answer:

the correct answer is 197 in^2

the first answer 197in^2

The height meters of a mass projected vertically upwards at a time seconds s=ut-0.5gt².
Determine how long the mass will take after being projected to reach a height of 16m on the ascent.
b. on the descent when u=30m/s and g=9.8m/s​

Answers

9514 1404 393

Answer:

  t ≈ 0.590 s (ascent); 5.532 s (descent)

Step-by-step explanation:

We are interested in the values of t when s=16.

  s = 30t -4.9t²

  4.9t^2 -30t +16 = 0 . . . . . substitute 16 for s; put in standard form

The quadratic formula can be used to find the solutions:

  t = (-(-30) ±√((-30)² -4(4.9)(16)))/(2(4.9))

  t = (30 ±√586.4)/9.8 ≈ 0.59023, 5.53221 . . . . seconds after launch

a) It will take 0.590 seconds to reach 16 m height initially.

b) It will take 5.532 seconds to return to 16 m height on descent.

Santino fires a paintball 3 meters from the ground such that the initial trajectory is perfectly horizontal. Assume the paintball does not hit anything and the ground is level. When will the paintball hit the ground?

Answers

The Answer is 160m/s

Help me somebody pleaseeee

Answers

What do you need help with?

Hope you are doing well! :)

1. find the greatest mass
that can be taken on exact
number of times from 360g
504g, and 672 g​

Answers

Answer:

72g

Step-by-step explanation:

I hope it's right I figured it out by common factor

A car wash attendant counted the number of cars washed and the total amount of money earned. The company charged the same price for each car washed and earned $165 for 15 cars, $231 for 21 cars, and $275 for 25 cars. Write an equation for the relationship between the number of cars washed, n, and the number of dollars earned, m.

Answers

The answer is m(n)= 11n
If you take the different of the money from 21 cars and 25 cars, you get 44 and since 21 and 25 is only a difference of 4, you’ll divide the 44 earned by the 4 cars washed to get $11 per car and then just make sure to use the correct variables

HELP!
Which expression is equivalent to -6(-2/3+2x) ?

Answers

Answer:

-6(-2/3+2x)

=12/3+12x

=4+12x

4(1+3x)

Joe wants his overall test average to be 85%. What score would he need on his next test if the test scores he has so far are: 70%, 105%, 75%, 90%, 90%?

Answers

Answer:

He would need a score of 0.8 = 80%.

Step-by-step explanation:

Average score:

The average score is the sum of all scores divided by the number of tests.

What score would he need on his next test if the test scores he has so far are: 70%, 105%, 75%, 90%, 90%?

Combining with the next text, there will be 6, and the sum will be: 0.7 + 1.05 + 0.75 + 0.9 + 0.9 + x = 4.3 + x.

Joe wants his overall test average to be 85%.

So

[tex]\frac{4.3 + x}{6} = 0.85[/tex]

[tex]4.3 + x = 5.1[/tex]

[tex]x = 5.1 - 4.3 = 0.8[/tex]

He would need a score of 0.8 = 80%.

A bag contains 2 red, 4 blue, and 4 yellow marbles. What is the probability of pulling a red marble, putting the marble back, and then pulling a blue marble?\

Answers

Answer:

Di ko po alam sorry

Step-by-step explanation:

Di ko alam putaenamo

PLEASE ANSWER ASAP TIMED! A candle shop owner collected data on customers favorite scents as shown in the table. A customer is randomly selected. If the probabilities of a customer choosing floral and coconut as their favorite scents are the same what is the value of the missing probabilities? Inside the chart lavender 0.31 vanilla 0.18 cinnamon 0.23 floral? Coconut? The answer choices are 0.10 0.14 0.20 0.28

Answers

Answer: .14

Step-by-step explanation: 2020 edg

Answer:

.14

Step-by-step explanation:

I just took the test

Can someone please help

Answers

9514 1404 393

Answer:

  C.  39°

Step-by-step explanation:

The measure of the angle where the chords cross is the average of the measures of the subtended arcs.

  x = (AB +CD)/2 = (28° +50°)/2 = 78°/2

  x = 39°

I need the answer real fast PLZ​

Answers

Answer:

54%

Step-by-step explanation:

I did the test.

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