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Readme [11.4K]
2 years ago
9

DJ Davon is making a playlist for work; he is trying to decide what 12 songs to play and in what order they should be played. If

he has his choices narrowed down to 14 blues, 25 country, and 21 disco songs, and he wants to play an equal number of blues, country, and disco songs, how many different playlists are possible
Mathematics
1 answer:
Marta_Voda [28]2 years ago
5 0

Answer:

3.63 * 10^19

Step-by-step explanation:

Given that :

Number of choices to select = 12

Category available :

Blues - 14

Country - 25

Disco - 21

To select an equal number of song for each category ; then 4 songs will be selected from each :

Using combination :

(14C4 * 25C4 * 21C4)

Since the order matters for the 12 selected songs ; it thus requires 12 permutation

Thus ;

(14C4 * 25C4 * 21C4) * 12!

nCr = n! / (n-r)!r!

Using calculator;

14C4 = 1001 ;

25C4 = 12650

21C4 = 5985

12! = 479001600

Hence,

(1001 * 12650 * 5985) * 479001600

= 36301596217286400000

=3.63 * 10^19

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Crank

43\frac{3}{4} cups of cheese is needed to make 10 pizzas.

<u><em>Explanation</em></u>

For making one pizza, amount of cheese needed = 4\frac{3}{8} cups = \frac{35}{8} cups.

Now for finding the total amount of cheese needed to make 10 pizzas, we need to <em>multiply \frac{35}{8} cups by 10. </em>

So, (\frac{35}{8}*10)cups= \frac{350}{8}cups= \frac{175}{4}cups= 43\frac{3}{4} cups

Thus, 43\frac{3}{4} cups of cheese is needed to make 10 pizzas.

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3 years ago
As part of a quality-control program, 4 batteries from a box of 17 is chosen at random for testing. In how many ways can this te
belka [17]

Answer:

This test batch can be chosen in 2380 ways

Step-by-step explanation:

The order in which the batteries are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In how many ways can this test batch be chosen?

4 batteries from a set of 17. So

C_{17,4} = \frac{17!}{4!(17-4)!} = 2380

This test batch can be chosen in 2380 ways

5 0
3 years ago
I need some help with this question..
Anuta_ua [19.1K]
It is (B) I think:) hope this helps
6 0
3 years ago
The slope of the line that passes through the points (8, y) and (-4, 10) is 4.
mart [117]
Y = 4x + b
10 = -16 + b, b = 6
Y = 4x + 6
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3 0
2 years ago
Expression A Expression B Expression C (−5)(−0.4)(1.8) (-45)(-19)(-112) −1(5+17) Expression D Expression E Expression F (−5)(−0.
kramer

Answer:

Expressions A, E, and F

Step-by-step explanation:

In general, when negative integers are multiplied; if the negative integers are even, then the product would be positive. But if the negative integers are odd, then the product would be negative.

Thus,

A. (−5)(−0.4)(1.8) = (2.0)(1.8)

                           = 3.6

B. (-45)(-19)(-112) = (855)(-112)

                           = -95760

C. −1(5+17) = -1(22)

                 = -22

D. (−5)(−0.4)(1.8)(−3.25) = (2.0)(-5.85)

                                      = -11.7

E. (-49)(-34)(-12)(-12) = (1666)(144)

                                = 239904

F. −1(3.5−7) = -1(-3.5)

                  = 3.5

Thus expressions A, E and F have positive products.

4 0
3 years ago
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