The word arrange means that the order in which the books are placed is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this question:

5 books from a set of 13. So

$P_{(13,5)} = \frac{13!}{(13-5)!} = 154440$

There are 154,440 ways.

8 0

3 years ago

Find the measures of two angles, one positive and one negative that are coterminal with pi/5

lozanna [386]

To find coterminal angles for an angle, β, given in radians use the following formula:
coterminal angle = β + 2πk
where k is an integer {..., -3, -2, -1, 0, 1, 2, 3, ...}
Negative Coterminal Angle: k = -1
NCA = π/5 + 2π(-1)
= -9π/5
Positive Coterminal Angle: k = 1
PCA = π/5 + 2π(1)
= 11π/5
The following answers are just one of many possible answer... you have infinite number of choices for k.
$NCA = \frac{-9 \pi }{5}$
$PCA= \frac{11 \pi }{5}$

7 0

3 years ago

What additional information do you need to prove that ∆AMD ≅ ∆CNB by the HL Theorem?

Maurinko [17]

(H)ypotenuse (L)eg, right-triangle theorem.

based on the provided graph, we know the hypotenuses are equal, thus the tickmarks, so H is true, now the L part, we only need either of the pair of legs to be equal DM = NB or AM = CN, if either one is true, we're golden.

8 0

3 years ago