A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen

Answers

Answer 1

Answer:

792 ways

Step-by-step explanation:

We can solve this using the combination formular

[tex]nCr= \frac{n!}{r!(n-r)!}[/tex] where n represents the total number of objects/items, and r represents the number of items being chosen at a time.

Hence, in this case, n =  12, r = 5, which is = [tex]nCr= \frac{12!}{5!(12-5)!}[/tex] = 792.

Therefore, there are 792 ways to choose five books so that no two adjacent books are chosen.


Related Questions

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below.

The figure shows a right triangle with legs marked 40 and 9.

Answers

Answer:

41

Step-by-step explanation:

The Pythagorean Theorem:

[tex]x^2+y^2=z^2[/tex]

where x and y are two legs, and z is the hypotenuse

Plugging this in, we have

[tex]40^2 + 9^2 = 1681\\\sqrt{1681}=41[/tex]

Answer: Hypotenuse is 41

A 115​-inch is cut into two pieces. One piece is four times the length of the other. Find the lengths of the two pieces.

Answers

Answer:

Shorter piece: 23 inches

Longer piece: 92 inches.

Step-by-step explanation:

Since the longer piece is four times the length of the other, we multiply 23*4 and we get 92 inches.

(3x+5)+(2x+3)
Please show steps

Answers

Answer:

first you do the mutpiton in the first perentes then you do addition

Step-by-step explanation:

3x + (5+3) + 2x
3x + 8 + 2x

(3x+2x) + 8
5x + 8

Your answer is 5x + 8



Please help me please

Answers

Answer:

the ham is the least expensive, the roast beef is most expensive

Step-by-step explanation:

hope this helps.

I'm going to k.m.s GOODBYE WORLD

Answers

Answer:

nooooo

Step-by-step explanation:

Answer:honestly i might too at some point but if you decide not to and want to talk about what happened, let me know. i'm not a therapist and i'm not the best with words, but i do like to listen to what others have to say and learn from their lives. i hope you choose to live, but i sadly cannot stop you.

Step-by-step explanation:

Does the graph represent a function? Why or why not?
10-
-10
10
-10-
O A. No, because it fails the vertical line test.
B. No, because it fails the horizontal line test.
O C. Yes, because it passes the vertical line test.
O D. Yes, because it passes the horizontal line test.

Answers

Answer:

no because it fails the vertical line test

Yes because it passes the vertical line test

Please help ASAP! Answer the questions like 1. 2. 3 pls

Answers

Answer:

1. 3, because 30 divided by 10 is 3.

2-6, What is the recipe? By understanding the OG recipe I can multiply every number by three.

You can put the recipe in the comments and I will edit this answer. :)

~PumpkinSpice1

3 is your lucky number

For question one, You need to multiply 10 by 3. To get this you can divide 30 by 10, this gives you the number you need to multiply 10 by, in this case its 3.

The next two questions are not able to be answered because I need the amount of oil or flour to determine how much to use for 30 cupcakes.

But, if you have 1 cup of oil for 10 servings, and you want 30 servings, like before, multiply by 3.

Same for flour, it doesnt matter how much of it you need, just multiply by 3 from the amount you use for 10 servings.

If your confused on 4, 5 and 6. Just remember, 3 is the lucky number.

Please helpppp guyssssss

Answers

Answer:

the answer is B because the 30x how much they charge each hiur and the other one has a trend of 25 each hour so P charges 5 more .

What is the answer to 1/3x(15+6)?

Answers

Answer:

1/3×21

=7

Step-by-step explanation:

first step: solve the barket part

second step: Solve division or multiplication which first..Follow Rule:BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction.

The correct answer is 7

Slope is known as the run over the rise. True or False

Answers

Answer:

false. slope is calculated by rise over run

Answer:

FALSE

Step-by-step explanation:

Slope is known as the RISE OVER RUN.

Can I get brainliest? Plz!!!

Find the product of (x - 3)2.

Answers

Answer:

2x-6

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x - 3)^2 = x^2 - 3x - 3x + 9 = x^2 - 6x + 9

A ladder is 2 metres long. It leans against a wall
so the base is 86 cm from the wall.
a Write 86 cm in metres.
b How far up the wall does the ladder reach?​

Answers

Step-by-step explanation:

jsjsjskksksndkdkkdkf

WILL GIVE BRAINLIEST TO WHOEVER IS RIGHT ​

Answers

Answer:

lies  you wont give brainliest

Step-by-step explanation:

juanito has a rope 1.75 meters long. He needs to cut it into shorter ropes each 0.1 meter long​

Answers

Answer:

17.5

Step-by-step explanation:

[tex]1.75 \div 0.1 = 17.5[/tex]

Is (2, 10) a solution to this system of inequalities? y 7 X 1 y > 4x + 2​

Answers

yes it is, 700 is greater than 10.

Please help me solve this! If you could solve my other questions that haven't been solved that would be great!

Answers

Answer:

The simplest form of the complex fraction [tex]\frac{\frac{8}{9}}{8}[/tex] is  [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

In the complex fractions [tex]\frac{\frac{a}{b}}{c}[/tex] = [tex]\frac{a}{b}[/tex] ÷ c

To simplify it change ÷ to × and reciprocal c

[tex]\frac{\frac{a}{b}}{c}[/tex] = [tex]\frac{a}{b}[/tex] ÷ c = [tex]\frac{a}{b}[/tex] × [tex]\frac{1}{c}[/tex] = [tex]\frac{a}{bc}[/tex]

In the complex fractions [tex]\frac{a}{\frac{b}{c}}[/tex] = a ÷ [tex]\frac{b}{c}[/tex]

To simplify it change ÷ to × and reciprocal [tex]\frac{b}{c}[/tex]

[tex]\frac{a}{\frac{b}{c}}[/tex] = a ÷ [tex]\frac{b}{c}[/tex] = a × [tex]\frac{c}{b}[/tex] = [tex]\frac{ac}{b}[/tex]

Let us solve the question

∵ The complex fraction is [tex]\frac{\frac{8}{9}}{8}[/tex]

∵  [tex]\frac{\frac{8}{9}}{8}[/tex] = [tex]\frac{8}{9}[/tex] ÷ 8

→ Change ÷ to × and reciprocal 8

∴  [tex]\frac{8}{9}[/tex] ÷ 8 =  [tex]\frac{8}{9}[/tex] × [tex]\frac{1}{8}[/tex]

→ Cancel 8 up with 8 down

∴  [tex]\frac{8}{9}[/tex] × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{9}[/tex]

The simplest form of the complex fraction [tex]\frac{\frac{8}{9}}{8}[/tex] is  [tex]\frac{1}{9}[/tex]

Answer:

1

Step-by-step explanation:

In the fraction 8/9, 8 is the numerator and 9 is the denominator. When you ask "What is 8/9 simplified?", we assume you want to know how to simplify the numerator and denominator to their smallest values, while still keeping the same value of the fraction. We do this by first finding the greatest common factor of 8 and 9, which is 1.

An internet site sells 75 feature type cell phones. The ratio of the number of smartphones to the number of feature phones is 3:5. How many cell phones are smart phones?

Answers

There are 45 smart phones

25) (1,-5) parallel to y = - 10x - 3

Answers

Hope it helps :))
Here is the working

what is 206 divided :) 6

Answers

Answer:

if you mean 206 divided by 6 than the answer will 34.3 (rounded)

Step-by-step explanation:

I used a calculator

Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights below 125 oz is:

A. .500

B. .159

C. .341

D. .841

Answers

Answer:

125 is 1 dev above, so it's  13.5 + 2.35,so it's B. 0.159And i think the proportion of infants with birthweights between 125 oz and 140 oz is :D. 0.136


Which of the following could be the perimeters of the three squares below?
A 12ft, 16 ft and 20 ft
B 20 ft, 16 ft and 24 ft
C) 40 ft, 80 ft and 120 ft
D 16 ft, 24 ft and 28 ft

Answers

Answer:

Option (A)

Step-by-step explanation:

Option (A).

Since, perimeter of a square = 4×(side)

Perimeters of 3 squares = 12 ft, 16 ft and 20 ft

Side lengths of three squares will be = [tex]\frac{12}{4}, \frac{16}{4},\frac{20}{4}[/tex]

                                                             = 3 ft, 4 ft and 5 ft

If these sides are the measures of the sides of the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

5² = 4² + 3²

25 = 16 + 9

25 = 25

True.

Therefore, these are the sides of the given right triangle.

Option (B).

Perimeters of three squares are 20 ft, 16 ft and 24 ft.

Sides lengths of three squares = [tex]\frac{20}{4},\frac{16}{4}, \frac{24}{4}[/tex]

                                                    = 5 ft, 4 ft and 6 ft

By Pythagoras theorem,

6² = 4² + 5²

36 = 61

False.

Therefore, these sides are not of the given right triangle.

Option (C)

Perimeters of the squares = 40 ft, 80 ft and 120 ft

Side lengths of the squares = 10 ft, 20 ft and 30 ft

If these sides are the sides of the given right triangle, they will follow the Pythagoras theorem.

By Pythagoras theorem,

(30)² = (10)² + (20)²

900 = 500

False.

Option (D)

Perimeters of the given squares are 16 ft, 24 ft and 28 ft.

Side lengths of these squares will be 4 ft, 6 ft and 7 ft.

If these sides form a right triangle they will follow the Pythagoras theorem.

By Pythagoras theorem,

7² = 4² + 6²

49 = 16 + 36

49 = 52

False.

Therefore, these are not the sides of a right triangle.

Option (A) will be the answer.

help please with #3

Answers

Answer: x = 2a over b + c

Step-by-step explanation:

1. Multiply both sides by two. This cancels out 2 and turns a into 2a. It should look like 2a = bx + cx

2) Since both b and c have x’s, we turn it into (b + c)x

3. Then divide both sides by b+c to get 2a over b + c = x

Could anyone give a hand?

Answers

Answer: 73.5

first you work out the total area of this shape.

area: 105

this mean you can start working out the non-shaded area to do this you need to multiply 7cm with 6cm which is 42cm then you divide by 2 to get 21cm.

then to work ou the other non-shaded area in the left you multiply 3cm and 7cm together getting 21cm you then divide it and you get 10.5.

you then add 10.5cm and 21cm together to get 31.5cm, subtract that answer with the total area which gets the answer 73.5!

DUE IN 10 MINUTES!!!!!!!!!!!!!!!!!!!!!!!!!!

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Should be 1/4 I think

Answer:

1/4

Step-by-step explanation:

Finding the area, any help?​

Answers

Answer:

Volume: x^6

Area: 6x^4

Step-by-step explanation:

volume: length x width x height

area: 6 sides of x^4 so 6x^4

24 is the answer because you multiply areas

Which algebraic expression represents “Sarah has fives times as much homework today as yesterday”?
5 + h
5 h
h minus 5
StartFraction h Over 5 EndFraction

Answers

The answer is 5h


This is because the phrase “times” represents multiplication, therefore your answer would be 5 x h but you can represent that as just 5h.!

Answer:5h

Step-by-step explanation: i just did the quiz

ILL GIVE BRAINLIEST!!! The average of x+6, 6x+2, and 2x+7 is 4x-7. What is x?

Answers

Answer:

yStep-by-step explanation:

Combine like terms: 4 - 3m - 1 + 2m

Answers

Answer:

-m+3

Step-by-step explanation:

4 - 3m - 1 + 2m

4-1-m

-m+3

As the standard deviation of outcomes for Martin Products increases, investing in Martin Products becomes riskier because:__________a. the range of outcomes having some probability becomes widerb. an outcome at or near the expected return of 10% becomes less likelyc. although the chances of some big gains increase, the chances for some big losses also increase.d. all of the above reasonse. none of the above reasons

Answers

Answer:

c. although the chances of some big gains increase, the chances for some big losses also increase.

Step-by-step explanation:

In the Martin Products, there is a probability that the investment could either succeed or fail. The standard deviation of the outcome carried out to determine the risks involved in investing in his products helps in trying to offer the investors the clearer picture of the risks involved.

Answer:

d. all the reasons above

2. Melissa estimated that she would read 250 pages
last week. She read 290 pages. What is the
percent error of Melissa's estimate? Round to
the nearest whole percent.
I will give brainliest!!!

Answers

Answer:

Is it 11.6%?

Step-by-step explanation:

I divided 290/250

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