What are the x-intercepts ?

english has 26 different letters. how many consecutive words have to be selected in a book to have at least 5 that start with th

Valentin [98]

The words need not be English language words 142506

What is permutation and combination?

A set of elements can be divided into subsets in two different ways: combination and permutation.

The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.

If the word has 5 different letters then it is just 26-choose-5 or (26/5).

If the word has 4 different letters then it is just 26-choose-4 or (26/4)

have 4 options to choose which letter to duplicate twice.

This gives = 4*(26/4)

If the word has 3 different letters then it is just 26-choose-3 or (26/3).

you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives = 6*(26/3).

If the word has 2 different letters then it is just 26-choose-2 or (26/2).

The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is = 4*(26/2).

The word has just 1 distinct letter you have = (26/1).

we get :

N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) + (26/1)

= 142506

The words need not be English language words = 142506

Learn more about permutation and combination

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5 0

1 year ago

The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacemen

mamaluj [8]

<h2>Answer:</h2>

(a)

The probability is : 1/2

(b)

The probability is : 1/2

<h2>Step-by-step explanation:</h2>

The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.

The total combinations that are possible are:

(1,2) (1,3) (1,4) (1,5)

(2,1) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,5)

(5,1) (5,2) (5,3) (5,4)

i.e. the total outcomes are : 20

(a)

Let A denote the event that the first number is 4.

and B denote the event that the sum is: 9.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

We know that it could be calculated by using the formula:

$P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is: (4,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 9

(4,5) and (5,4) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

(b)

Let A denote the event that the first number is 3.

and B denote the event that the sum is: 8.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( since, the only outcome out of 20 outcomes is: (3,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 8

(3,5) and (5,3) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

7 0

3 years ago

What are the basics for triganometrey

zheka24 [161]

Whiteboard full of trigonometric facts that you need to know...

4 0

3 years ago

-6 + -4y + -11y + 16y = -10 I need the answer A.S.A.P

Alja [10]

Answer:

y = -4

Step-by-step explanation:

Step 1 :

Solving a Single Variable Equation :

1.1 Solve : y+4 = 0

Subtract 4 from both sides of the equation :

y = -4

One solution was found :

y = -4

Processing ends successfully

plz mark me as brainliest :)

4 0

3 years ago

Read 2 more answers

A. f(x) = l-2xl - 3 Domain: {1, 2, 3} Find the range

gizmo_the_mogwai [7]

Hello there!

We are given the function:

$\displaystyle \large{ f(x) = | - 2x| - 3} \\$

To find the range, we know that domain is the set of all x-values and also called 'input' while range is the set of all y-values and also called 'output'.

Basic Function - you add the input, you get the output. You add x-value in a function, you get y-value. You add domain, you get range.

So, we substitute x = 1,2 and 3 in the function.

x = 1

$\displaystyle \large{ f(1) = | - 2(1)| - 3} \\ \displaystyle \large{ f(1) = | - 2| - 3} \\$

Recall that any numbers in absolute value are always positive.

$\displaystyle \large{ f(1) = 2 - 3} \\ \displaystyle \large{ f(1) = - 1} \\$

x = 2

$\displaystyle \large{ f(2) = | - 2(2)| - 3} \\ \displaystyle \large{ f(2) = | - 4 | - 3} \\ \displaystyle \large{ f(2) = 4 - 3} \\ \displaystyle \large{ f(2) = 1}$

x = 3

$\displaystyle \large{ f(3) = | - 2(3)| - 3} \\ \displaystyle \large{ f(3) = | - 6| - 3} \\ \displaystyle \large{ f(3) = 6 - 3} \\ \displaystyle \large{ f(3) = 3}$

Therefore, Range: {-1,1,3}

Let me know if you have any questions!

Topic: Absolute Value Function / Modulus Function

6 0

3 years ago