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Gala2k [10]
3 years ago
8

DJ Giovanni is making a playlist for a friend; he is trying to decide what 12 songs to play and in what order they should be pla

yed. If he has his choices narrowed down to 22 country, 11 reggae, and 5 pop songs, and he wants to play an equal number of country, reggae, and pop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
Mathematics
1 answer:
Elena L [17]3 years ago
4 0

Answer:

5.78×10¹⁵

Step-by-step explanation:

The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.

The number of ways he can choose 4 country songs (ignoring the order) is ₂₂C₄ = 7315.

The number of ways he can choose 4 reggae songs (ignoring the order) is ₁₁C₄ = 330.

The number of ways he can choose 4 pop songs (ignoring the order) is ₅C₄ = 5.

The total number of combinations is 7315 × 330 × 5 = 1.21×10⁷.

Once he has his 12 songs selected, the number of ways he can arrange them is ₁₂P₁₂ = 12! = 4.79×10⁸.

So the total number of possible playlists is:

(1.21×10⁷) × (4.79×10⁸) = 5.78×10¹⁵

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vladimir1956 [14]

65 = 2(d + 1) + 5d
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3 years ago
A farmer owns pigs, chickens, and ducks. When all her animals are together, she has 30 feathered animals, and the animals all to
tatiyna

To solve this problem, let us first assign some variables. Let us say that:

x = pigs

y = chickens

z = ducks

 

From the problem statement, we can formulate the following equations:

1. y + z = 30                                         ---> only chicken and ducks have feathers

2. 4 x + 2 y + 2 z = 120                      ---> pig has 4 feet, while chicken and duck has 2 each

3. 2 x + 2 y + 2 z = 90                        ---> each animal has 2 eyes only

 

Rewriting equation 1 in terms of y:

y = 30 – z

Plugging this in equation 2:

4 x + 2 (30 – z) + 2 z = 120

4 x + 60 – 2z + 2z = 120

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4 x = 60

x = 15

 

From the given choices, only one choice has 15 pigs. Therefore the answers are:

She has 15 pigs, 12 chickens, and 18 ducks.

3 0
3 years ago
A set of cards includes 20 yellow cards, 16 green cards, and 24 blue cards. What is the probability that a blue card is chosen a
baherus [9]

Answer:

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Step-by-step explanation:

Because that is the highest amount so it is most likely youll get that one.

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3 years ago
A rectangular prism has a length of 5 meters, a width of 6 3/4 meters, and a height of 3 1/2 meters. What is the volume of the p
kirza4 [7]

Answer:

<h2>118.13 m³</h2>

Step-by-step explanation:

Given,

Length ( l ) = 5 meters

Width ( w ) = 6 \frac{3}{4} meters

Height ( h ) = 3  \frac{1}{2} meters

Now, Let's find the volume of rectangular prism :

volume \:  = l \:  \times  \: w \:  \times  \: h

plug the values

= 5 \times  \frac{27}{4}  \times  \frac{7}{2}

Calculate the product

= \frac{5 \times 27 \times 7}{4 \times 2}

=  \frac{945}{8}

= 118.13 \:  {m}^{2}

Hope this helps..

Best regards!!

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3 years ago
"what quadrant is...." PLEASE PLEASE HELP!!!! Thank you so so much!!! *will give brainliest*
sdas [7]

Given:

\tan \theta > 0 and \sec \theta.

To find:

The quadrant.

Solution:

We know that,

In I quadrant, all trigonometric ratios are positive.

In II quadrant, only \sin \theta, \text{cosec}\theta are positive and others are negative.

In III quadrant, only \cot \theta, \tan\theta are positive and others are negative.

In IV quadrant, only \cos \theta, \sec\theta are positive and others are negative.

We have,

\tan \theta > 0 and \sec \theta.

Here, \tan \theta is positive and \sec \theta is negative. So, \theta lies in the III quadrant.

Therefore, the correct option is C, i.e., III.

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