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? Express your answer in scientific notation rounding to the hundredths place.
Answers
Answer:
1.80 * 10^19
Step-by-step explanation:
If he has narrowed down his choices to 14blues, 25 country and 21 disco songs and he has to make a list of 12 songs with equal representation of each genre of song, the it means there will be 4 songs from each genre of music.
We select this 4 different songs using the combination formula for selection and multiply our results.
This means we have:
12C4 for blues,
25C4 for country
21C4 for disco.
This gives:
=12C4 * 25C4 * 21C4
= 495 * 12650 * 5985
And the order they can be played = 12!.
We then multiply the number of ways to get these songs by the order they can come in.
That is:
=495 * 12650 * 5985 * 12!
= 1.7951 * 10^19
= 1.80 * 10^19 (nearest hundredth).
Final answer:
DJ Davon can make approximately 3.57 x 10^21 different playlists, if he includes an equal number of blues, country, and disco songs. This calculation utilizes combination and permutation formulas.
Explanation:
DJ Davon wants to play an equal number of blues, country, and disco songs, which means he will play 4 songs from each genre. The number of ways to select 4 songs out of each genre is represented by the combination formula C(n,r) = n! / [r!(n-r)!].
So, for each genre, the number of ways to select 4 songs is:
Blues: C(14,4) = 1001
Country: C(25,4) = 12,650
Disco: C(21,4) = 5985.
After the songs are selected, the order of the playlist matters, so we use the permutation formula. Given 12 slots for the songs, the number of ways to order them is P(n) = n!, which for 12 is 479,001,600. The total number of different playlists is product of blues, country and disco song combinations and the permutations, which gives 3.57 x 10^21. This rounded to the hundredths place in scientific notation is 3.57 x 10^21.
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Related Questions
Please help, having some trouble!
What is the additive inverse of the complex number 9-4i?
-7/3 x = 7 solve for x
Which statements can be used to write an algebraic expression to represent the phrase? ( The product of number and eighteen )check all that apply:A. replace a number with a variable?b. product represents additionc. product represents multiplication?d. the coefficient is 18.e. the correct algebraic expression is 18t.f. 18 is a veritable.g. the correct algebraic expression is t/18.
Answers
The number of federally insured banks in the year 1990 was 12,100.
Given data:
To find the number of federally insured banks in the year 1990, you need to substitute the value of t = 1990 into the given function B(t):
B(t) = -329.4t + 13747
Since t corresponds to the year and t = 0 corresponds to 1985, we need to calculate for t = 1990 - 1985.
t = 5.
Substitute t = 5 into the function:
B(5) = -329.4 * 5 + 13747
Now, perform the calculations:
B(5) = -1647 + 13747
B(5) = 12100
Hence, there were approximately 12,100 federally insured banks in the year 1990.
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Final answer:
Using the given equation and by substituting t with 5 (for the year 1990, five years after 1985) in that equation, we find that there were 13363 federally insured banks in 1990.
Explanation:
The question is asking how many federally insured banks there were in 1990, given that the number of banks in any given year from 1985 to 2007 is given by the equation
B(t) = -329.4t + 13747
. In this equation,
t
is the year with t=0 corresponding to 1985. To find the answer, we should substitute in the appropriate value of t, which would be 5 because 1990 is five years after 1985. Thus, the equation becomes B(5) = -329.4*5 + 13747. This simplifies to 15010 - 1647, which equals
13363
. Therefore, there were 13363 federally insured banks in 1990.
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Find the measure of Z2.
Z2 = [?]°
Answers
Answer:
40 = <2
Step-by-step explanation:
<1 and <2 are corresponding angles and corresponding angles are equal when the lines are parallel
<1 = <2
40 = <2
After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1982, the hay in that country was contaminated by a radioactive
isotope (half-life 5 days). If it is safe to feed the hay to cows when 9% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
The farmers needed to wait approximately
(Round to one decimal place as needed.)
days for it to be safe to feed the hay to the cows.
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1.
(1,1)
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Enter your answer in the answer box and then click Check Answer.
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Answers
Answer:
17.5 days
Step-by-step explanation:
The half life of this element is five days.
For the first five days it will decrease to 100*0.5=50%.
For the second five days it will decrease to 50*0.5= 25%
For the third five days it will decrease to 25*0.5 = 12.25%
It means in each day in the five days it reduce 0.1 of the it's remaining amount.
12.5 - 9 = 3.5 %
0.5 of 12.5 = 6.25%
It's going to be 15 days + 2.5 days= 17.5 days
Answers
Using proportions, it is found that there are 68 blue tiles.
- This question is solved by proportions, using a rule of three.
- For every 21 red tiles used, 4 blue tiles are used, hence, out of every 25 tiles, 4 are blue. How many blue tiles are there out of 425?
The rule of three is:
4 blue - 25 total
x blue - 425 total
Applying cross multiplication:
There are 68 blue tiles.
To learn more about proportions, you can check brainly.com/question/24372153
Final answer:
To determine the number of blue tiles used in a pattern, a proportion can be set up with the ratio of red to blue tiles and the total number of tiles. By setting the unknown number of blue tiles as x and cross-multiplying, we find that there are 68 blue tiles used.
Explanation:
To solve how many blue tiles are used, we can set up a proportion based on the given pattern. For every 21 red tiles, there are 4 blue tiles. If a total of 425 tiles are used, we can express this relationship as a fraction:
Red tiles : Blue tiles = 21 : 4
Since the total number of tiles is 425, we can express the unknown number of blue tiles as x. The number of red tiles would then be 425 - x. Our proportion is:
21 / 4 = (425 - x) / x
Cross-multiplication gives us:
21x = 4(425 - x)
Solving for x gives us:
21x = 1700 - 4x
21x + 4x = 1700
25x = 1700
x = 1700 / 25
x = 68
So, there are 68 blue tiles used.
= 5x - 9, find each value
Answers
Answer:
BD = 88
BC = 27
CD = 61
Explanation:
Given that,
BD = 7x - 10
BC= 4x - 29
CD = 5x - 9
Here we assume BD is a line segment and C is a point lies between B & D.
BD = BC + CD
7x - 10 = 4x - 29 + 5x - 9
Now combine like terms
7x - 10 = 4x + 5x - 29 - 9
7x - 10 = 9x - 38
Move 7x from left hand side to right hand side
-10 = 9x - 7x - 38
-10 = 2x - 38
Add 38 both the side
-10 + 38 = 2x - 38 + 38
28 = 2x
Divide by 2 both the side
x = 14
Now put the value of x and find the length of BD, CD, BC
BD = 7x - 10 = 7*14 - 10 = 98 - 10 = 88
BC= 4x - 29 = 4*14 - 29 = 56 - 29 = 27
CD = 5x - 9 = 5*14 - 9 = 61
That's the final answer.
I hope it will help you.
The value of the expression will be:
BD = 88
BC = 27
CD = 61
How to solve the expression
Given that,
BD = 7x - 10
BC= 4x - 29
CD = 5x - 9
Here we assume BD is a line segment and C is a point lies between B & D.
BD = BC + CD
7x - 10 = 4x - 29 + 5x - 9
Now combine like terms
7x - 10 = 4x + 5x - 29 - 9
7x - 10 = 9x - 38
Move 7x from left hand side to right hand side
-10 = 9x - 7x - 38
-10 = 2x - 38
Add 38 both the side
-10 + 38 = 2x - 38 + 38
28 = 2x
Divide by 2 both the side
x = 14
Now put the value of x and find the length of BD, CD, BC
BD = 7x - 10 = 7*14 - 10 = 98 - 10 = 88
BC= 4x - 29 = 4*14 - 29 = 56 - 29 = 27
CD = 5x - 9 = 5*14 - 9 = 61
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Answers
Answer: Miguel forgot to create the title.
Step-by-step explanation:
Miguel made the histogram originally histogram to show the ages of all the participants that took part in a fundraiser.
The intervals of histogram are present on the given histogram. 1-10, 11-20, 21-30, 31-40, 41-50.
Same as the frequency for each interval. One notable omission from the histogram which is missing is the title, this implies that Miguel forgot to create the title.
Answer:
C: Miguel forgot to create the title.
Step-by-step explanation:
edg2020
(there is also no title in the picture:))