Answer:
3,770,461,100,000 different playlists are possible.
Step-by-step explanation:
To solve this question, the arrangements formula and the combinations formula are used. The arrangements formula is used considering the order of the musics being played, and the combinations formula is used to find the number of possible combinations of musics.
Arrangements of n elements:
The number of possible arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
0 pop songs
10 non-pop from a set of 8 + 4 + 4 = 16.
Arrangements of 10(order in which the musics are played). So
[tex]P(0) = 10!C_{16,10} = 10!\frac{16!}{6!10!} = \frac{16!}{6!} = 29059430400[/tex]
1 pop song:
9 non-pop from a set of 16, 1 pop from a set of 7. So
[tex]P(1) = 10!C_{16,9}C_{7,1} = 10!\frac{16!}{7!9!}\frac{7!}{1!6!} = 290594304000[/tex]
2 pop songs:
8 non-pop from a set of 16, 2 pop from a set of 7. So
[tex]P(2) = 10!C_{16,8}C_{7,2} = 10!\frac{16!}{8!8!}\frac{7!}{2!5!} = 980755776000[/tex]
3 pop songs:
7 non-pop from a set of 16, 3 pop from a set of 7. So
[tex]P(3) = 10!C_{16,7}C_{7,3} = 10!\frac{16!}{7!9!}\frac{7!}{3!4!} = 1452971500000[/tex]
4 pop songs:
6 non-pop from a set of 16, 4 pop from a set of 7. So
[tex]P(4) = 10!C_{16,6}C_{7,4} = 10!\frac{16!}{6!10!}\frac{7!}{3!4!} = 1017080100000[/tex]
How many different playlists are possible?
[tex]T = P(0) + P(1) + P(2) + P(3) + P(4) = 29059430400 + 290594304000 + 980755776000 + 1452971500000 + 1017080100000 = 3770461100000[/tex]
3,770,461,100,000 different playlists are possible.
will mark as brainliest:)
A Ferris wheel has a maximum height of 111 feet and a minimum height of 5 feet. it takes 80 seconds for the wheel to make a full rotation. it reaches maximum height for the first time at t=8. give an equation h(t) that gives the height of the rider at t seconds. how high is the rider after 23 seconds?
What is the approximate radius of a sphere with a volume of 268 cm^3?
Answer:
Step-by-step explanation:
[tex]V=\frac{4}{3}\pi r^3~=>r=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3*260cm^3}{4\pi}}=3.96 \approx4[/tex]
4-member curling team is randomly chosen from 6 grade 11 students and 8 grade 12 students. What is the probability that the team has at least 2 grade 11 students?
Answer:
0.5944 = 59.44% probability that the team has at least 2 grade 11 students
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
We have that:
6 + 8 = 14 students, which means that [tex]N = 14[/tex]
6 grade 11 students means that [tex]k = 6[/tex]
Teams of 4 members means that [tex]n = 4[/tex]
What is the probability that the team has at least 2 grade 11 students?
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,14,4,6) = \frac{C_{6,0}*C_{8,4}}{C_{14,4}} = 0.0699[/tex]
[tex]P(X = 1) = h(1,14,4,6) = \frac{C_{6,1}*C_{8,3}}{C_{14,4}} = 0.3357[/tex]
Then
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0699 + 0.3357 = 0.4056[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4056 = 0.5944[/tex]
0.5944 = 59.44% probability that the team has at least 2 grade 11 students
Can someone help me please
Answer:
Ishaan is correct because snakes with 17 1/4 inches occured most often in the dot plot. Raj is incorrect because 17 3/4 didnt occur the most often but it was the highest length of the snake. Ishaan is correct.
Step-by-step explanation:
The total cost of a truck rental, y, for x days, can be modeled by y=24x+39. What is the rate of change for this function?
Answer:
24 per day
Step-by-step explanation:
'x' = days, so since 24 is with x, the rate of change is 24
Find value a when the angle between vectors U=(2,a) and V = (-6;8) is pie/4
Answer:
Step-by-step explanation:
The formula to find the angle between 2 vectors is
[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is
u·v = (2×(-6)) + (a×8) so
u·v = -12 + 8a. Then we need the magnitudes of both u and v:
[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and
[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]
Putting all of together looks like this:
[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get
[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is
[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:
100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get
800 + 200a² = 256a² -768a + 576. Combine like terms to come up with
0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.
Therefore, the value for a is 14. I checked it...it works
Answer:
a = 14, U = (2, 14)
Step-by-step explanation:
the other answer is correct.
just to add the solution path for the quadratic equation
0 = 56a² - 768a - 224
in general, a quadratic equation usually expressed in x
0 = ax² + bx + c
has its solution as
x = (-b ± sqrt(b² - 4ac))/(2a)
for us here this looks like this then
a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =
= (768 ± sqrt(589824 + 4×56×224))/112 =
= (768 ± sqrt(589824 + 50176))/112 =
= (768 ± sqrt(640000))/112 = (768 ± 800)/112
a1 = (768 + 800)/112 = 1568/112 = 14
a2 = (768 - 800)/112 = -32/112 = -0.29
and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.
so, 14 is the solution for U.
If XU = 3y-5 and RT = 32, find the value of y
Answer:
Step-by-step explanation:shsjsjdhdbshchdhchfhchdfhehxbehchr hehfhehdhejsjwhd khasa
find the equation of the line that passes through a point A(1,-5) B(-2,-7)
Answer:what’s the answer?
Step-by-step explanation:
The area of a circle is 810 m2. What is the circumference, in meters? Express your
answer in terms of 7.
Answer:
answer for this solution is 18π
Step-by-step explanation:
area =πr²
81π = πr²
r² = 81
r = 9
circumference = 2πr
= 2π*9
=18π
its my final, please help!!!!!!!!!!
Answer:
both apply
Step-by-step explanation:
i guessed just do it
Zoya has to earn at least $300 to meet her fundraising goal. She has only 100 bracelets that she plans to sell at $5 each. Which inequality shows the number of bracelets, x, Zoya can sell to meet her goal?
Answer:
The two inequality are : x ≤ 100 and x ≥ 60
So the inequality is : 60 ≤ x≤ 100.
Step-by-step explanation:
Answer:
Hi so the answer to this equation is:
60 _< x _< 100
Step-by-step explanation:
Sorry if it looks a little complicated, another way of phrasing it would be 60 less than or equel to x less than or equel to 100. I think this is the answer because she only has 100 braclets so she cant sell more than that, hence less than or equel to 100. and i believe it is 60 because if she sells each braclet for 5 dollars and her goal is 300, 60 would allow her to reach her goal because 5 x 60 = 300. and she needs to earn at least 300 buckaroos for her fundraiser.
Im not super great with algebra but i hope this is right and that it helps you
peace✌
PLEASE HELP
A store is giving out cards labeled 1 through 10 when customers enter the store. If the
card is an even number, you get a 15% discount on your purchase that day. If the card is an odd
number greater than 6, you get a 30% discount. Otherwise, you get a 20% discount. The table
shows the results of 500 customers. What is the relative frequency for each discount? Use pencil
and paper. If the manager of the store wants approximately half of the customers to receive the
20% discount does this seem like an appropriate method? Explain.
Step-by-step explanation:
The relative frequency for a 15% discount is 52.1%.
What is a relative frequency?The relative frequency is the quotient of a particular frequency divided by the total number of frequencies.
Given:
A store is giving out cards labeled 1 through 10 when customers enter the store.
If the card is an even number, you get a 15% discount on your purchase that day.
The subgroup for even numbers = 2, 4, 6, 8, 10
The subgroup frequency = 56 + 50 + 54 + 49 + 54 = 263
The total frequency = 500
The relative frequency = 263/500 = 0.521 = 52.1%
Therefore, 52.1% is the relative frequency.
To learn more about the relative frequency;
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3,15,75,375 9th term
Answer:
1,171,875
Step-by-step explanation:
The sequence is multiplying by 5 every time. It will be 3, 15, 75, 375, 1875, 9375, 46,875, 234,375, and then 1,171,875
who is the mathematics creator ?
What is the answer please I need help
Answer:
I just did this question!! The correct answer is B. -3 must be a root of the polynomial 2x^2+9x+9
Step-by-step explanation:
A small county has two property appraisers, Tim and Julie. Does Tim appraise property differently on average than the Julie? Each appraiser looks at 20 properties and each independently determines the value of the property. (Tim - Julie)
How should we write the alternative hypothesis?
(mud is the population mean difference)
A. Ha: mud = 0.
B. Ha: mud > 0.
C. Ha: mud < 0.
D. Ha: mud does not equal zero.
Answer:
The answer is "Option D"
Step-by-step explanation:
In this question the "choice D" is wrong because [tex]H_a: \mu_d \neq 0[/tex].
Use the grouping method to factor this polynomial.
x^3 + 2x^2 + 12x +24
A. (x^2+6)(x+2)
B. (x^2 +2)(x+6)
C. (x^2 +2)(x+12)
D. (x^2 +12)(x+2)
Answer:
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Step-by-step explanation:
[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]
[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]
[tex] {x}^{2} (x+2)+12(x+2)[/tex]
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Hope it is helpful...a. We will attempt to answer the question "What is the average height of RCCC male students?" using data we collected the first week of this semester. Be sure to give explanations in context and include units when appropriate.
Describe the population of interest?
A sample of____(state the number) RCCC male students was taken. We found the sample mean____(symbol) to be Interpretation: In the sample of male RCCC students, the____"mean") height was approximately____inches.
The median is____Interpretation (use the one for mean as a guide):
The mode is____Interpretation (use the one for mean as a guide):
b. We know the measures of central tendency don't tell us the whole story, so we then investigated the measures of variation as well. We found that the heights had a range of_____with a standard deviation____(symbol) of_____(2 decimal places) and a variance_____(symbol) of (2 decimal places).
Height (inches) Note: There are 31 male heights.
1 70
2 70
3 70
4 70
5 71
6 64
7 64
8 65
9 65
10 66
11 66
12 67
13 67
14 68
15 68
16 68
17 69
18 72
19 72
20 72
21 72
22 73
23 73
24 73
25 73
26 73
27 73
28 74
29 75
30 75
31 75
32 75
70 70 70 70 71 64 64 65 65 66 66 67 67 68 68 68 69 72 72 72 72 73 73 73 73 73 73 74 75 75 75 22
The population of interest: Male RCCC students.
Sample size: 31.
The sample mean: 69.68 inches.
Median: 69 inches.
Mode: 70 inches.
Range: 11 inches.
Standard deviation: 3.32 (rounded to 2 decimal places).
Variance: 11.02 (rounded to 2 decimal places).
We have,
Mean:
To find the mean, we sum up all the heights and divide by the total number of data points (31 in this case):
Mean = (70 + 70 + 70 + ... + 75) / 31
Mean ≈ 69.68 inches
Median:
The median represents the middle value in the dataset when arranged in ascending order. Since the dataset has an odd number of values (31), the median will be the value in the middle position when ordered:
Median = 69 inches
Mode:
The mode represents the value(s) that occur most frequently in the dataset. In this case, the mode is the height that appears most often:
Mode = 70 inches
Range:
The range is calculated by subtracting the minimum value from the maximum value in the dataset:
Range = Maximum height - Minimum height
Range = 75 - 64 = 11 inches
Standard Deviation (σ):
To find the standard deviation, we can use the formula that involves finding the difference between each value and the mean, squaring those differences, averaging them, and taking the square root:
Standard Deviation (σ) ≈ 3.32 (rounded to 2 decimal places)
Variance (σ²):
The variance is the square of the standard deviation.
We can square the value of the standard deviation to find the variance:
Variance (σ²) ≈ 11.02 (rounded to 2 decimal places)
The height dataset (in inches) for the 31 male RCCC students is as follows:
1 70
2 70
3 70
4 70
5 71
6 64
7 64
8 65
9 65
10 66
11 66
12 67
13 67
14 68
15 68
16 68
17 69
18 72
19 72
20 72
21 72
22 73
23 73
24 73
25 73
26 73
27 73
28 74
29 75
30 75
31 75
32 75
Thus,
The population of interest: Male RCCC students.
Sample size: 31.
The sample mean: 69.68 inches.
Median: 69 inches.
Mode: 70 inches.
Range: 11 inches.
Standard deviation: 3.32 (rounded to 2 decimal places).
Variance: 11.02 (rounded to 2 decimal places).
Learn more about mean here:
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Chris' home basketball team has a 25% chance or 0.25 probability of winning any given basketball game. What is the probability that they don't win their first game of the season until the 8th game
Answer:
0.75
Step-by-step explanation:
Given that the probability of winning a game is 25%
Pr(they don't win) = 1 - Pr(they win)
Pr(they don't win) = 1 - 0.25
Pr(they don't win) = 0.75
Hence the probability that they won is 0.75 or 75%
Abhasra and Aliyah are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Abhasra sold 10 rolls of plain wrapping paper and 4 rolls of shiny wrapping paper for a total of $170. Aliyah sold 5 rolls of plain wrapping paper and 3 rolls of shiny wrapping paper for a total of $105. Find the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper.
Answer:
$9 and $20Step-by-step explanation:
Plain wrapping paper - pShiny wrapping paper - sEquations:
10p + 4s = 1705p + 3s = 105Double the second equation and subtract from the first one:
10p + 4s - 10p - 6s = 170 - 210-2s = - 40s = 20Find p:
10p + 4*20 = 17010p = 90p = 9wv^2 / Fg = r
Substitute the given values to find the value of the indicated letter.
r = ?
Given F = 11,000; W = 22,000; v = 164; g = 32
Which table of ordered pairs represents a proportional relationship?
Answer:
Third table
Step-by-step explanation:
For the relationship to be proportional
y/x = constant
First table y/x = 8/4 = 2 then 7/11 doesn't =2 so it is not
Second table y/x =52/5 = 5 then 49/7 doesn't =5 so it is not
Third table y/x = 3/6=1/2 then 5/10 = 1/2 then 7/14 = 1/2 it is proportional
Last table y/x = 6/3 = 2 then 11/8 doesn't =2 so it is not
A 12 sided die is rolled. Find the probability of rolling and even number
Answer:
0.5
Step-by-step explanation:
Wanted outcome / possible outcomes = 0.5 in this case.
El opuesto y el semejante de 8xy
Answer:
No entiendo
Step-by-step explanation:
The midpoint of a line segment from P1 to P2 is (-5,2). If P1 = (-1,7), what is P2?
Hope it helps you!
-miraculousfanx-
Answer:
p2 = (-9 , -3)
Step-by-step explanation:
let p2 be (a , b)
given :
p1(-1 , 7) = (x1 , y1)
p2(a , b) = (x2 , y2)
using midpoint formula:
midpoint = (x1 + x2/2 , y1 + y2/2)
(-5 , 2) = (-1 + a/2 , 7 + b/2)
Now , compare corresponding elements
-5 = -1 + a/2
-5*2 = -1 + a
-10 = -1 + a
-10 + 1 = a
-9 = a
2 = 7 + b/2
2*2 = 7 + b
4 = 7 + b
4 - 7 = b
-3 = b
therefore p2 = (-9 , -3)
Help need answers !!!!!!!!
Answer:
3/5
Step-by-step explanation:
Cosine = base/ hypotenuse = 6/10 = 3/5
PLEASE HELP ME GUYS :((((((( c r y
triangle area ?
Answer:
1
Step-by-step explanation:
the answer is in the image above
1.) If x varies directly as y and x = 35 when y = 7. What is the value of y when x = 25?
Answer:
y = 5
Step-by-step explanation:
[tex]x \ \alpha \ y[/tex]
[tex]=> x = k \times y\\=> 35 = k \times 7\\=> k = 5[/tex]
[tex]x = k \times y[/tex]
[tex]=>25 = 5 \times y\\ =>5 = y[/tex]
Answer:
y = 5
Step-by-step explanation:
x = 35, y = 7
x = ?y
35 = ?7
? = 5
x = 25, y = ?
x = ?y
25 = 5y
y = 5
ANSWER ASAP!! The graph of f(t)=4•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer:
the value of a rare coin in the beginning of the first year,
t = 0, so f(0) = 4• 2^0 = 4•1 = 4 (y-intercept)
Answer:
the y-intercept is at t=0, so in the model no time has past yet. it's the initial value of the coin
Find the solution(s) for x in the equation below.
x^2 - 25 = 0
A. x = -5
В. no solutions
C. x = 5
D. x = 5; x = -5
Answer:
D. x = 5; x = -5
Step-by-step explanation:
x^2 - 25 = 0
Add 25 to each side
x^2 - 25+25 = 0+25
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = ±5
