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3 years ago

Small library contains 700 novels. how many ways can You check out three novels

Mathematics

1 answer:

schepotkina [342]3 years ago

8 0

The first book you select can be any one of 700.

. . . For each of those ...

The second book can be any one of the other 699.

. . . For each of those ...

The third book can be any one of the remining 698.

The total number of ways to gather three books from the shelves into your hands is (700 · 699 · 698) = 341,531,400 ways .

BUT ...

When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves. You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.

So, even though there are 341,531,400 ways to gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.

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Triangle abc is such that ab=4 and ac=8 if m is the midpoint of bc and am=3, what is the length of bc?

zavuch27 [327]

This is an interesting question. I chose to tackle it using the Law of Cosines.
AC² = AB² + BC² - 2·AB·BC·cos(B)
AM² = AB² + MB² - 2·AB·MB·cos(B)
Subtracting twice the second equation from the first, we have
AC² - 2·AM² = -AB² + BC² - 2·MB²

We know that MB = BC/2. When we substitute the given information, we have
8² - 2·3² = -4² + BC² - BC²/2
124 = BC² . . . . . . . . . . . . . . . . . . add 16, multiply by 2
2√31 = BC ≈ 11.1355

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3 years ago

What Happens to the value of the expression 100 minus X as X increases

Marta_Voda [28]

Step-by-step explanation:

if f (x) = 100 - x;

as x increases, the value of f(x) will decrease

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2 years ago

Read 2 more answers

Directions: Use a proportion to solve the problem.

spin [16.1K]

So, since she weights 6 times more on earth, say for every lb on the moon is 6lbs on earth then.

now, if 1lb on the moon is 6lbs on earth, how much is 90 earth lbs on the moon?

$\bf \begin{array}{ccll}
moon&earth\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&6\\
m&90
\end{array}\implies \cfrac{1}{m}=\cfrac{6}{90}\implies \cfrac{1\cdot 90}{6}=m$

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3 years ago

Does anyone know how to solve this?

Ivahew [28]

Answer:

Multiplay 30 by 5 Then multiply five-by-five then Multiply 20 by 5 Then take away your answer

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2 years ago

A cryptographic hash takes a message as input and produces a fixed-length string as output, called the digital fingerprint. A br

Allushta [10]

Answer:

$1.85x10^{19}$ attempts are required to find a matching pair if the digital fingerprint is 64 bits long.

$3.40*10^{38}$ attempts are required to find a matching pair if the digital fingerprint is 128 bits long.

Step-by-step explanation:

Each bit has two options. So

How many attempts are required to find a matching pair if the digital fingerprint is 64 bits long?

So for each of the 64 bits, we have the following number of options.

2 - 2 - 2 - 2 -... - 2

So, in all, there are

$T = 2^{64} = 1.85x10^{19}$

options.

So, $1.85x10^{19}$ attempts are required to find a matching pair if the digital fingerprint is 64 bits long.

128 bits long?

Using the same logic as the first question.

$T = 2^{128} = 3.40*10^{38}$

So, $3.40*10^{38}$ attempts are required to find a matching pair if the digital fingerprint is 128 bits long.

5 0

3 years ago

Small library contains 700 novels. how many ways can You check out three novels￼

Small library contains 700 novels. how many ways can You check out three novels