Find the slope of the line through the two points below.<br> (5,-1) and (0, 3)

How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.

Talja [164]

<h3>Answer:</h3>

There are 40,320 ways, in which 8 books can be arranged on a shelf.

<h3>Solution:</h3>

Here, we are to find the number of ways in which 8 books can be arranged on a shelf. The total number of books is 8 and the way of arranging books is also 8.

If one book is placed in the first place, then 7 books will be placed in front of it. If 2 books are placed in the 2nd place, then only 6 books can be placed after that book. This sequence will continue till 1 .

<u>Permutations </u><u>:</u>

A permutation is an arrangement of objects in a definite order.

➲<u> P ( n, r )= n ! / ( n - r ) !</u>

n = total number of objects

r = number of objects selected

The number of ways to arrange 8 books on a shelf will be :

➝ P ( n, r ) = n ! / ( n - r ) !

➝ P ( n, r ) = 8 ! / ( 8 - 8 ) !

➝ P ( n, r ) = 8 ! / 0 !

➝ P ( n, r ) = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 1

➝ P ( n, r ) = 40, 320

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ~ Hence, there are <u>40,320 ways</u> in which 8 books can be arranged on a shelf !

7 0

1 year ago

hillary is cycling across montana taking a 845 mile course . the first week she covered.320 miles. the second week she traveled

Blababa [14]

Answer:

175 miles

Step-by-step explanation:

Hillary has travelled

320 + 350 = 670 miles

in the first two weeks.

Therefore, Hillary starts with 670 miles and needs to add a certain number of miles "x" to get 845 in total.

670 + x = 845

And if we subtract 670 from both sides:

x = 845 - 670 = 175

175 miles

3 0

2 years ago

A brand of clay brick tiles has the dimensions 3 5 8 by 7 5 8 by 1 2 inch. These thin bricks are commonly used for floors. Estim

raketka [301]

Answer: The cost to tile the floor is $318.24.

Step-by-step explanation:

Since we have given that

Dimensions of floor is 12 by 17 foot.

So, Area of floor would be

$12\times 17\\\\=204\ sq.\ foot$

As we know that 1 foot = 12 inch

So, Area of floor would be

$204\times (12)^2\\\\=204\times 144\\\\=29376\ sq.\ foot$

Dimension of brick tiles is given by

$3\dfrac{5}{8}\ by\ 7\dfrac{5}{8}\ by\ \dfrac{1}{2}$

So, Area of brick tiles is given by

$2(lb+bh+lh)\\\\=2(\dfrac{29}{8}\times \dfrac{61}{8}+\dfrac{61}{8}\times \dfrac{1}{2}+\dfrac{29}{8}\times \dfrac{1}{2})\\\\=2(\dfrac{1769}{64}+\dfrac{61}{16}+\dfrac{29}{16})\\\\=2\times \dfrac{1769+244+116}{64}\\\\=\dfrac{2129}{32}$

So, Number of clay brick would be

$29376\div \dfrac{2129}{32}\\\\=29376\times \dfrac{32}{2129}\\\\=\dfrac{29376\times 32}{2129}\\\\=441.53\\\\\approx 442$

cost of each clay brick = $0.72

So, Total cost of flooring would be

$442\times 0.72\\\\=\$318.24$

Hence, The cost to tile the floor is $318.24.

7 0

2 years ago

Rewrite ^3 sqrt 27x-81-5 to make it easy to graph a translation. Describe the graph.

iragen [17]

First we have to rewrite this function.Instead of :^3 sqrt (...) we can write : (...)^(1/3).
f ( x ) = ( 27 x - 81 ) ^(1/3) - 5 = ( 27 * ( x - 3 ) ) ^(1/3) - 5 = = 3 * ( x - 3 )^(1/3) - 5 And this makes it easy to graph a translation.The parent function is y = x^(1/3). The zero of this function is ( 0, 0 ).
Then it will be stretched vertically by a factor of 2 and translated: 3 units right and 5 units down.

8 0

2 years ago

Identify one way to rewrite the expression using the Distributive Property. 2(9 + 3) A. (2 × 9) − (2 × 3) B. (2 × 9) + (9 × 3) C

Dmitry_Shevchenko [17]

The answer is D.

Because you want to find the rewrite way of distributive right? 2(9+3)

Therefore it’s (2x9) + (2x3)

3 0

2 years ago

Find the slope of the line through the two points below. (5,-1) and (0, 3)